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Fabrication, Characterization and Modeling of Single-Walled Carbon Nanotube Films for Device Applications

Material Information

Title:
Fabrication, Characterization and Modeling of Single-Walled Carbon Nanotube Films for Device Applications
Creator:
Behnam, Ashkan
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (159 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Ural, Ant
Committee Members:
Bosman, Gijs
Guo, Jing
Ziegler, Kirk
Graduation Date:
8/7/2010

Subjects

Subjects / Keywords:
Carbon nanotubes ( jstor )
Electric current ( jstor )
Electric potential ( jstor )
Electrical resistivity ( jstor )
Electrodes ( jstor )
Nanotubes ( jstor )
Narrative devices ( jstor )
Noise temperature ( jstor )
Simulations ( jstor )
Temperature dependence ( jstor )
Electrical and Computer Engineering -- Dissertations, Academic -- UF
alignment, carbon, computational, density, distribution, film, four, junction, length, ms, msm, nanotubes, network, noise, percolation, photodetector, resistivity, scaling, thickness, width
Genre:
Electronic Thesis or Dissertation
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
Electrical and Computer Engineering thesis, Ph.D.

Notes

Abstract:
The main goal of this dissertation was to study electrical properties of single-walled carbon nanotube (CNT) films as new conductive and transparent materials. First, the ability to efficiently pattern CNT films with good selectivity and directionality down to sub-micron lateral dimensions by photolithography or e-beam lithography and oxygen plasma etching was demonstrated and the effect of etch parameters on the nanotube film etch rate and selectivity was studied. Then by fabricating standard four-point-probe structures using this technique, it was demonstrated that the resistivity of the films increases over three orders of magnitude as their width and thickness shrink close to the percolation threshold. A Monte Carlo simulation platform was then developed to model percolating conduction in CNT films, which could fit the experimental results and confirm the strong scaling of resistivity with various nanotube and device parameters. These experimental and computational capabilities were then used to study the 1/f noise behavior in CNT films. The results from the computational calculations were in good agreement with previous experiments. It was shown that the 1/f noise amplitude depends strongly on both device dimensions and on the film resistivity. The variation of resistivity and 1/f noise as a function of temperature was then studied experimentally and it was concluded that at very low temperatures 3D variable range hopping was the dominant mechanism for both. At 40 K and above, however, the fluctuation induced tunneling model explained the resistivity behavior and the fluctuations within or at the surface of the SiO2 substrate underneath the CNT film were the probable dominant source of the noise in this regime. Finally, metal-semiconductor-metal photodetectors were fabricated based on CNT film-Gallium Arsenide(GaAs) and CNT film-Silicon(Si) Schottky contacts to show the application of CNT film in optoelectronic devices. The Schottky barrier heights of CNT film contacts on GaAs and Si were extracted by measuring the dark I-V characteristics in the thermionic emission regime. The extracted barrier heights corresponded to a CNT film workfunction of about ~ 4.6 eV, which was in excellent agreement with previously reported values. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2010.
Local:
Adviser: Ural, Ant.
Statement of Responsibility:
by Ashkan Behnam.

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Applicable rights reserved.
Embargo Date:
10/9/2010
Resource Identifier:
004979649 ( ALEPH )
769020138 ( OCLC )
Classification:
LD1780 2010 ( lcc )

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etch rates of 2.37, 4.59, 4.58, and 6.65 nm/s were observed for CNT film, S1813, LOR3B, and

PMMA, respectively, as listed in the first column of Table 2-1. The error bar on these etch rates

is approximately + 10%. The CNT film etch rate is similar in magnitude to the -4 nm/s observed

in recent work using another ICP system [92]. For CNT films of tens of nm thickness, such as

those used in this work, the 2.37 nm/s etch rate of the initial recipe provides both reasonably

short etch times and a good control of the etch uniformity. The selectivity S of the etch between

the nanotube film and the resist mask is defined by

S = rSWNT : RESIST (2-1)

where rswN is the etch rate of the CNT film and rREsIS is the etch rate of the particular

resist used as the mask. Using this definition, selectivity values of 1:1.94, 1:1.93, and 1:2.81 are

obtained for S1813, LOR3B, and PMMA masking layers, respectively.

Carbon nanotubes are much harder to etch compared to photoresists since they are

chemically resistant and structurally stable [98]. As a result, the etch rate of the CNT film is

slower than that of resists in an 02 plasma, and the selectivity values are less than unity. Since

the resists are used as the etch mask, they need to be thick enough to withstand the nanotube film

etch. The minimum resist thickness required for a given CNT etch process is determined by the

selectivity S of the etch process. Typical S1813 only and LOR3B/S1813 dual layer resist

thicknesses used for photolithography are larger than 1 [tm; as a result, based on the selectivity

values given above, hundreds ofnm thick CNT films can easily be patterned by

photolithography. More importantly, since the PMMA etch rate is not significantly higher than

the nanotube film etch rate, typical PMMA thicknesses necessary for e-beam lithography (100-

300 nm) can be used to pattern thin CNT films (i.e. less than 100 nm) down to very small (<100









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FWranging from 200 to 400 |tm. In this case, both FL and n (which depends linearly on FW)

vary, resulting in a strong change in the amount of dark current, in agreement with the trend

observed in Fig. 5-12(d). These results show that the dark current in CNT film-GaAs MSM

devices scales rationally with device geometry.

After the dark current, I characterize the photoresponse of the CNT film-GaAs MSM

photodetectors using an optical bench equipped with a 633 nm Beam Scan HeNe laser (6.5 mW

power, -830 jtm spot size) at room temperature and compare it with the Cr/Pd metal control

samples. Figure 5-13 shows both the dark and the photo I-Vcurves for the CNT film and Cr/Pd

metal control MSM devices of identical dimensions (W= S = 30 |tm and FL = FW= 300 [tm).

Due to the low resistivity of the CNT film, the CNT film finger electrodes do not limit the

photocurrent even under illumination at high voltage bias. For example, for the device in Fig. 5-

13, the series resistance due to the CNT film electrode fingers is more than two orders of

magnitude smaller than the measured MSM device resistance at 10 V and under laser

illumination.

It can be seen in Fig. 5-13 that the dark current of the CNT film-GaAs MSM device is

significantly lower than that of the Cr/Pd control device, while the photocurrents are comparable

particularly at high applied bias voltages. This results in a significantly improved normalized

photocurrent-to-dark current ratio (NPDR [161]) for the CNT film MSM device relative to that

of the control device while achieving a comparable responsivity (defined as the photocurrent

generated per unit incident optical power). Responsivity and NPDR values extracted for the

CNT film-GaAs MSM photodetector in Fig. 5-13 are 0.161 A/W and 3.62x 106 mW1 at V= 10

V, respectively. The lower dark current of the CNT film device is most likely the result of the

smaller effective contact area between the mesh of nanotubes making up the porous CNT film










R= Ih [AIW (5-10)
P hv 1.24

where 2 is the wavelength of the light source in micrometers. Ideally, R should increase

linearly with the wavelength for a fixed value of r. In reality r is dependent on the absorption

coefficient a, which also depends on the incident wavelength. Figure 5-5 compares the

responsivity for an ideal and a real photodetector. In this schematic, we see two cut-off

frequencies: Ac (short) which is due to the absorption of the incident optical energy very close to

the surface because of the large absorption coefficient in most semiconductors, and Ac (long) due

to the inefficiency of the incident light (its energy being smaller than the bandgap of the

semiconductor) to generate electron hole pairs.

In addition, the responsivity of a photodetector depends on its effective absorption area.

For a regular MSM photodetector, incident light is mostly reflected over the area covered by the

metal electrode fingers. Consequently, the effective absorption area under illumination is

reduced. If a transparent material is used as the metal electrode, it can be expected that the

effective area and therefore responsivity will be increased. As CNT film is transparent, the use of

CNT film as the transparent electrode in MSM photodetectors is promising.

Fabrication and Characterization of MSM Photodetectors

GaAs-based MSM photodetectors with CNT film electrodes were fabricated on nominally

undoped (- 2.1 x 108 Qcm) (100) GaAs substrates. After the GaAs substrate was cleaned by

solvents, a -100 nm thick silicon nitride (SiN) isolation layer was deposited on the substrate

using plasma enhanced chemical vapor deposition (PECVD) (Fig. 5-6(a)). Subsequently, active

area windows of various dimensions were opened in the SiN film using plasma etching. This

was followed by the deposition of 40 nm thick CNT film, using the vacuum-filtration method

explained in chapter 2 (Fig. 5-6(b)). The deposited CNT film had a resistivity of about 10-4









The resistance of the tube-tube junctions depends on whether the junction is

metallic/semiconducting (MS), semiconducting/semiconducting (SS), or metallic/metallic (MM)

[29]. Based on the 2:1 ratio between the semiconducting and metallic nanotubes in the film,

about 44% of the junctions are expected to be SS, 44% MS, and 11% MM, which is in perfect

agreement with the percentages observed in the simulations. In this chapter, I modeled each

different type of tube-tube junction by a different contact resistance, instead of a single

"effective" contact resistance as done in chapter 4. In particular, based on previous experimental

studies [123,131,177], R
Rss, and RMS are the contact resistances for MM, SS, and MS junctions, respectively.

For computing the l/f noise in the CNT film, I have used a model which takes into account

the noise contributions from both the nanotubes themselves and the tube-tube junctions in the

film. Assuming independent noise sources (i.e. uncorrelated fluctuations), current noise spectral

density in the film, Si, can be written as [178],


S, = (6-2)
R R i r
n

where in is the current, s, is the current noise spectral density, and rn is the resistance of the tube

or junction associated with the nth individual noise source, and R is total resistance of the CNT

film. Replacing sn in Eq. (6-2) by its equivalent based on Eq. (6-1), S, can be written as

1 i4r A
S, (6-3)
Rf i2 r
n

where An is the noise amplitude for the nth individual noise source. Finally, an equivalent

noise amplitude Aeq can be defined for the total CNT film by normalizing Eq. (6-3), and using









Nanotubes are generated at random angles 0 with respect to the horizontal axis, where 0 is

limited to the range 0m 0a < 0 < 0m + 0o and 180 + 0 0, < 0 < 180 + 0+ + 0o. The first angle,

0a, is defined as the "Nanotube Alignment Angle", which is a measure of the degree of nanotube

alignment in the film. When 0a = 900, the nanotubes are completely randomly distributed,

whereas when 0a = 0, they are completely aligned in a specific direction. The second angle, 0m,

which I call the "Measurement Direction Angle", is the orientation of the nanotube alignment

direction with respect to the resistivity measurement direction (i.e. the channel direction between

the source and drain electrodes, which in my case is always chosen as the horizontal axis).

When m = 0, resistivity is measured parallel to the alignment direction, while when m = 900, it

is measured perpendicular to the alignment direction. As an example, Fig. 4-6 shows a 2D

nanotube film generated using my simulation code between the source and drain electrodes with

0a = 27 and m = 450, where the definition of the two angles are illustrated in the inset.

Figure 4-7 shows normalized resistivity versus width for three different nanotube

alignment angles, namely a = 180, 36, and 900 (at m = 00). It is evident from Fig. 4-7 that

normalized resistivity, Wc, and a all change as the nanotubes become more aligned (i.e. 0O

becomes smaller). The value of pmn initially decreases as 0a goes from 900 to 360 because

aligned nanotubes help to form conduction paths with fewer junctions and shorter lengths

between the source and drain electrodes. Surprisingly, however, resistivity starts to increase

when the degree of alignment in the film is increased even further (i.e. when 0a= 18). In that

case, each nanotube forms too few junctions with its neighbors, because nanotubes mostly lie

parallel to each other. Therefore, many existing conduction paths are eliminated and resistivity is

increased.









various device dimensions (as in Fig. 5-6), such as FW, FL, W, and S. Figure 5-7(b) shows the

AFM image of the area between two CNT film electrode fingers.

Let us first study the dark current of the fabricated MSM photodetectors. Figures 5-8(a)

and (b) show the I-Vand C-V characteristics (measured using a Keithley 4200 Semiconductor

Characterization System and an HP 4294A Impedance Analyzer), respectively, at room

temperature for a CNT film-Si MSM device with W= S = 50 |tm and FL = FW= 300 tm. Other

devices with different dimensions have resulted in similar characteristics. The data in Fig. 5-8

clearly exhibit the characteristic I-Vand C-V curves of two back-to-back Schottky diodes [149],

demonstrating that the CNT film forms a S. irliiy contact on Si. Moreover, the symmetry of the

I-V and C-V curves indicates that the two Schottky diodes are identical, confirming that the CNT

film acts as a uniform electronic material.

The concave increase of the current and the appearance of a transition point at small

voltages displayed in Fig. 5-8(a) are not expected for an ideal MSM device [149]. As previous

studies on the current transport in metal-insulator-semiconductor-insulator-metal (MISIM)

structures suggest, the existence of a thin layer of oxide between the CNT film and Si would

result in an I-Vcurve with a shape similar to that in Fig. 5-8(a) [153]. Since the CNT film is

porous, it is likely that native oxide forms at the CNT film-Si interface, resulting in the observed

features in the I-V curves. Since any native oxide that forms would be very thin, thermionic

emission theory can still be used to analyze the transport across the CNT film-Si junction, as

discussed below. Also, as I have shown above, in an MSM structure, at high applied voltage, the

reverse biased contact limits the current and results in current saturation. Fig. 5-8(a), however,

shows that the current does not saturate at high voltages, but rather increases monotonically with

applied voltage. This could result from Schottky barrier lowering due to charge accumulation at









FABRICATION, CHARACTERIZATION AND MODELING OF SINGLE-WALLED
CARBON NANOTUBE FILMS FOR DEVICE APPLICATIONS





















By

ASHKAN BEHNAM


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2010









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CHARACTERIZATION AND MODELING OF SINGLE-WALLED CARBON NANOTUBE
FILMS FOR DEVICE APPLICATIONS

By

Ashkan Behnam

August 2010

Chair: Ant Ural
Major: Electrical and Computer Engineering

The main goal of this dissertation was to study electrical properties of single-walled carbon

nanotube (CNT) films as new conductive and transparent materials. First, the ability to

efficiently pattern CNT films with good selectivity and directionality down to submicron lateral

dimensions by photolithography or e-beam lithography and oxygen plasma etching was

demonstrated and the effect of etch parameters on the nanotube film etch rate and selectivity was

studied. Then by fabricating standard four-point-probe structures using this technique, it was

demonstrated that the resistivity of the films increases over three orders of magnitude as their

width and thickness shrink close to the percolation threshold. A Monte Carlo simulation platform

was then developed to model percolating conduction in CNT films, which could fit the

experimental results and confirm the strong scaling of resistivity with various nanotube and

device parameters. These experimental and computational capabilities were then used to study

the l/f noise behavior in CNT films. The results from the computational calculations were in

good agreement with previous experiments. It was shown that the l/f noise amplitude depends

strongly on both device dimensions and on the film resistivity. The variation of resistivity and

l/fnoise as a function of temperature was then studied experimentally and it was concluded that

at very low temperatures 3D variable range hopping was the dominant mechanism for both. At









of nanotubes/elements in the network places increasing weight on the longest elements, shifting

the correlation to higher power means.

The results presented above show that, despite their relative simplicity, the models I have

used can capture the essential physics of the experimentally observed resistivity scaling in

single-walled nanotube films, and they can provide valuable physical insights into the effects of

various nanotube and device parameters on the geometry-dependent resi stivity scali ng i n these

films Furthermore, these results are not limited to carbon nanotubes, but are applicable to a

broader range of problems involving percolating transport in networks, composites, or films

made up of one-dimensional conductors, such as nanowires and nanorods.









Table 5-1. Device dimensions and extracted barrier heights for 8 n-type and 5 p-type Si-based
MSM structures. The average extracted barrier heights are 0.51 0.04 forp-type
devices and 0.45 0.03 for n-type devices.

Substrate Type FO and FW ([tm) W([tm) S (min) Extracted Barrier Height (eV)

N-type 300 5 5 0.451
N-type 300 5 20 0.454
N-type 300 5 30 0.464
N-type 400 5 10 0.454
N-type 400 5 20 0.460
N-type 400 10 10 0.428
N-type 400 15 15 0.446
N-type 400 20 20 0.417
P-type 300 5 10 0.504
P-type 300 5 15 0.545
P-type 300 5 20 0.472
P-type 300 5 30 0.521
P-type 300 5 50 0.522









The simulation data can be fit by a lognormal distribution given by

A ln(x/xo)2
y I-( exp- x ) with standard deviation o- 0.4. This distribution also depends on
xoaV27e 202

the other device parameters and becomes wider (i.e. becomes larger) as the device dimensions

decrease (i.e. as we approach the percolation threshold). For example, it is evident from Fig. 6-

3(b) that there is a large scatter in the noise amplitude simulation data for the 3-layer film even

after averaging 500 simulation results for each datapoint. This scatter is absent in the data for the

8-layer thick film. In experimental noise measurements, in addition to this "intrinsic" scatter due

to percolation, there are also experimental errors due to factors such as CNT film

inhomogeneities and presence of defects and impurities. As a result, the observed variation of an

order of magnitude in the experimental noise data can be expected.

As mentioned before, it can be seen in both Figs. 6-4(a) and (b) that the simulation data

starts to increase from the dashed line fits for small values of L. This increase is a result of the

change in the resistivity p of the CNT film. As the device length (L) approaches the length of

individual nanotubes (lcNT), the statistical distribution ofnanotubes in the film can result in short

conduction paths consisting of only a few nanotubes connecting source to drain, decreasing the

total resistivity of the film [99,175] The simulation plot of resistivity versus device length

shown in the inset of Fig. 6-3(a) for the simulation dataset in the main panel of Fig. 6-3(a)

illustrates this point. As can be seen, while resistivity decrease with decreasing device length is

quite significant for L < 8 |tm, its variation is less than 10% for L > 8 |tm, and the resistivity

almost saturates for L > 10 |tm. For very small device lengths, the decrease in resistivity

increases the amount of current in the device for a fixed applied bias (in addition to the increase

due to the length shrinkage), which in turn increases the total 1/f device noise at a rate faster than









The inset of Fig. 4-7 also shows that, at small alignment angles near the percolation

threshold, resistivity exhibits an inverse power law dependence on Oa given by

p Oc 0 (4-4)

where K = 2.9 is the critical exponent for nanotube alignment extracted from the slope of

the log-log plot. This strong scaling with 0a is due to the fact that as the nanotubes align parallel

to each other, many conduction paths are eliminated, which increases the resistivity significantly.

These results are in agreement with recent experimental work on the effect of nanotube

alignment on percolation conductivity in carbon nanotube/polymer composites [110].

Up to this point, I have kept 0m = 0, i.e. the direction of the channel has always been same

as the direction of alignment. For the rest of the simulations in this chapter, I use a device length

ofL = 7 |tm, device width of W= 2 |tm, nanotube density per layer ofn = 2 |tm-2, nanotube

length of ICNT = 2 |tm, and t = 15 nm and I let both the 0, and 0m vary. Figure 4-8(a) shows the

plot of normalized resistivity versus nanotube alignment angle for three different measurement

direction angles (0m = 0, 45, and 900). For 0m = 0, the resistivity slowly decreases as 60 is

reduced, reaches a minimum value at ~- 450, and then increases again with a significant slope

close to the percolation threshold, similar to the curve in the inset of Fig. 4-7.

The above results are due to the fact that in my simulations, the device length L is always

larger than nanotube length IcNT; as a result, a single nanotube can never connect source to drain.

In this case, as we have seen above, strong alignment increases the resistivity. However, if the

nanotube length was longer than the device length (i.e. IlNT > L) [58], source and drain could be

connected by single nanotubes, and strong alignment of nanotubes would reduce the resistivity.

Furthermore, in contrast to well-defined values of 60 in my simulations, a few completely

misaligned nanotubes that bridge perfectly aligned tubes can exist in experimentally aligned









To investigate the effect of chamber pressure on the etch rate, I decreased the chamber

pressure from 45 mTorr to 10 mTorr, keeping all the other etch parameters constant as in the

initial recipe. Table 2-1 shows that the nanotube film and resist etch rates increase by a factor

between 1.7 and 3.5 compared to those of the initial recipe. A lower chamber pressure results in

a more directed etch, higher ion energy, and increased etch rates due to fewer gas-phase

collisions. A faster etch rate could be useful in applications where the CNT film thickness is

large. Furthermore, by taking the ratio of the etch rates listed in Table 2-1, selectivity values of

1:0.95, 1:1.21, and 1:1.59 are obtained for S1813, LOR3B, and PMMA masking layers,

respectively. These selectivity values are higher than those of the initial recipe. This is likely

due to an increase in the physical etch component, which etches the nanotube film and resists at

similar rates. In addition, increasing the chamber pressure from 45 mTorr to 100 mTorr

(maximum pressure achievable in my system) was found not to change the etch rates of the

nanotube film and resists significantly, showing that the etch rate has already saturated at 45

mTorr pressure.

Furthermore, I have investigated the effect of substrate cooling on the etch rates of the

CNT film and resists. Increasing the helium flow rate (which actively cools the substrate) from

10 sccm to 40 sccm, keeping all other etch parameters constant as in the initial recipe, did not

change the etch rates of the CNT film and resists compared to those of the initial recipe.

The optimum etch conditions depend on the nanotube film thickness that needs to be

etched. Based on my results, for thick films, etching at low pressures would be the best option.

On the other hand, for thin films, where the etch rate and uniformity needs to be better

controlled, etching at low substrate bias power would be the best choice. For intermediate

thicknesses, the initial recipe would work the best. Furthermore, my experiments indicate that









It is clear from the inset in Fig. 3-3 that the resistivity starts to increase for widths smaller

than 20 atm. To study the effect of width scaling in greater detail, I used e-beam lithography to

fabricate devices with submicron widths, as shown in Fig. 3-3. For W< 1 tm, up to a factor of 2

variation in resistivity was observed for identical devices. This variation is much larger than the

20% scatter observed for W> 2 atm. As the device dimensions are scaled, statistical variations in

nanotubes making up the film start to become more observable, and the electrical properties of

the film become less uniform. It is clear from Fig. 3-3 that the resistivity increases about two

orders of magnitude when the width goes from 20 Crm down to 200 nm.

My resistivity vs. width data can be fit by an inverse power law of the form p oc W-" with

the critical exponent a = 1.43 for the 35 nm thick sample and a = 1.53 for the 15 nm thick

sample. The nanotube film consists of many parallel conducting paths, each path being made up

of multiple nanotubes in series. Since the in-plane orientation of individual nanotubes in the film

is random, conduction paths are not perfectly aligned with direction of current flow (device

length L). As a result, reducing the device width Weliminates not only those conducting paths

that lie entirely in the etched area, but also those that partially lie in that area. Consequently,

reducing Wincreases the resistance at a rate faster than 1/W Furthermore, the observed inverse

power law dependence on width is similar to the dependence on thickness. This is not surprising

since reducing the width also causes the film to approach the percolation threshold by decreasing

the density of conducting paths in the film, and should exhibit an inverse power law behavior

[112]. However, because the film is preferentially aligned parallel to the substrate surface, the

length scales associated with width and thickness scaling are very different. Strong scaling with

width is observed starting below 2 atm, whereas strong scaling with thickness is not observable











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Figure 5-4. Calculated current density versus applied bias for a symmetric GaAs MSM structure
with ND = 1014 cm-3 and S = 20 pm at T= 3000K, with (a) Bn = 0.82 eV and /p =
0.60 eV, (b) B, = 0.60 eV and Op = 0.82 eV and (c) Bn = /Bp = 0.71 eV (courtesy of
Leila Noriega [166]).


Wavelength, A


Figure 5-5. Responsivity for an ideal (dotted line) and a real (solid line) photodetector.









exponents are r= 4.9 and 2.9 for L = 2 and 7 |tm, respectively. Similar to the previous case, for

shorter devices, many conduction paths that have been formed between source and drain are

removed as the measurement angle increases. Therefore, resistivity increases faster for shorter

device lengths, and the critical exponent increases.

Effect of Length Distribution

Before leaving this chapter, I study the effect of length distribution on the resistivity

scaling trends. This investigation is motivated by the fact that in real networks and films, the

length of the nanotubes or bundles is not a constant, but exhibits a distribution with a form that

depends on the film's preparation method [105]. In order to show that the effect of length

distribution on the resistivity depends on the resistance of the tube-tube junctions, I compare my

results for CNT film with those for a film in which the resistance of the elements is significantly

larger the resistance of the junctions between elements (element-dominated film). I also take a

look at the effect of alignment on the length distribution dependence of the resistivity. Then, I

explain the physical origins of the results using geometrical arguments.

In my simulations, length distribution on the elements is imposed when placing elements

randomly in the layers with a length IcNT (in this case conforming to a length distribution

'(lcvr)). An example of such a film is shown in Fig. 4- 12(a). Also, like before, for aligned

networks, 0 is limited to the range 0, < 0 < 0 and 180 0, < 0 < 180 + 0O, as shown in Fig.

4-12(b). I employ the lognormal distribution which is given by

1 (n (7 ) )
S(lc ) = -exp )- )2 Fig. 4-12(c) shows sample lognormal distributions
T cNT ^ 2 ep 2C_2

with different o and / values, where o-and /u are the standard deviation and the mean,

respectively.









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explained previously, it is not enough to compensate for the increase in resistivity due to the

decrease in ICNT.

In the third case, the product of density and the square of the nanotube length (i.e n-. lcT)

is kept constant. In this case, resistivity remains almost constant, which indicates that the

resistivity increase due to reduced IcNT is balanced by the resistivity decrease due to higher n. As

a result, the resistivity dependence on IcNT and n near the percolation threshold can be fit by an


inverse power law of the form p oc (n lcNr ) where yl/f- 2. In general, the value of the ratio

yl/f depends on other device and nanotube parameters, such as L, W, and Rrato. However, for

large L, large W, and a high Rratio, such as the third curve plotted in Fig. 4-5(b), yl/f equals

approximately 2. In fact, if we divide the value of y= 5.6 extracted from the first curve in Fig. 4-

5(b) by the value of/ = 2.5 extracted from the inset in Fig. 4-4(b), we get -2.2, which is very

close to 2. Furthermore, this value of yl/f physically makes sense because increasing the

nanotube length increases the number of nanotubes in a 2D area element proportional to the

square of the length, whereas increasing the density increases this number only linearly. It has

been previously shown that the nanotube density at the percolation threshold is proportional to

I,2 in an isotropic 2D network [64].

Effect of Nanotube Alignment

As I mentioned above, there has been a great deal of recent research interest in aligning

single-walled carbon nanotubes, either individually or in a thin film network or composite

[58,110,117,118,139,140]. Therefore, as the final parameter, I study the effect of alignment (i.e.

in-plane angular orientation) of nanotubes in the film and the direction of the device with respect

to the alignment direction on the resistivity and its scaling with various device parameters.









APPENDIX: ELECTRIC AND MAGNETIC FIELD DEPENDENCE OF THE CNT FILM
RESISTIVITY IN THE VRH REGIME

In the VRH regime, resistivity of my CNT films depicts strong electric and magnetic field

dependence. The inset in Fig. A-i shows I V characteristics at three different temperatures for

device DI (refer to chapter 6). While the nonlinearity in the I Vcurve at 1.2 K is considerable,

at 10 K it is almost non-existent. To better present the effect of electric field (E), the main panel

of Fig. A-i depicts differential device resistance (R) versus E for temperatures similar to the ones

in the inset. As can be seen, the magnitude of nonlinearity decreases and the electric field

required for the onset of nonlinearity (E,) increases as the temperature increases. The resistance

at 10 K is almost constant in the whole range of electric field, indicating Ohmic behavior above

this temperature. Also shown in Fig. A-i is the R T dependence for DI (refer to Fig. 6-8 in

chapter 6) that is shifted to fit the other three curves in the high electric-field region. In VRH

regime, the temperature and electric field dependence of the resistance are correlated by

[194,195]:

R 3
R(kBT,O) = R(0, qEa) (A-l)
2 8

where q is the electron charge and a is the localization radius, estimated from the fit to be

-800 nm. This large value suggests that the conductance of the nanotubes is quite high even at

low temperatures and the long length of tubes results in the observed localization radius. This

estimation is confirmed by considering the relationship between E, and T which follows

qE,a/lkT = 0.2 [194,195].

Fig. A-2 shows magnetoresistance (MR) data for D1 at three different temperatures. As

can be seen, while at higher temperatures, MR is negative and decreases with magnetic field (B),

at very low temperatures it reaches a negative minimum and then starts to increase and finally









individual nanotube (A, = 10 10 R /1) based on the experimental results for single tube devices

[179] results in a total noise significantly smaller than the experimental values observed for the

CNT film. This reduction is expected in my simulations, as the noise amplitudes A, of the tube-

tube junctions are significantly larger than those of the nanotubes themselves due to the larger

resistance associated with the junctions. Secondly, A x L scaling with resistivity now exhibits a

power-law decrease, which is in sharp contrast to the power-law increase observed in the main

panel of Fig. 6-4 for the simulations that fit the experimental data shown in Fig. 6-3.

Furthermore, power-law increase of l/f noise with resistivity is commonly observed for CNT

films and other systems when a particular parameter is changed to modify the resistivity close to

the percolation threshold [169,172,183,184]. I will later show that my simulations exhibit a

similar power-law increase of l/f noise with resistivity, when the CNT film thickness is the

parameter that causes the change in resistivity and 1/f noise, in agreement with experimental data

[172]. Taken together, the above results strongly suggest that tube-tube junctions, and not the

nanotubes themselves, dominate the overall CNT film /lf noise. This finding is in analogy to

previous experimental and theoretical results [113,175], which show that the resistivity of the

CNT film is also dominated by tube-tube junction resistance, and not the nanotube resistance. As

long as the electronic mean free path is larger than about 100 nm, the nanotube noise remains

negligible compared to the junction noise.

Effect of Device Width

Noise scaling trends with other device parameters also confirm the above results. In

particular, I next study the effect of device width. The resistivity scaling with device width close

to the percolation threshold has been experimentally observed to be significantly more

pronounced than that with device length [113,175]. This point is also evident in the simulation










500



i 00





1o
N 10

0z


6 10
Nanotube Alignment Angle ()


0


Measurement Direction Angle (0)


Figure 4-8. Effect of nanotube alignment angle and measurement direction angle on resistivity:
(a) Log-log plot of normalized resistivity versus nanotube alignment angle for three
measurement direction angles ranging from 0 to 900. Device length L = 7 ptm, device
width W= 2 ptm, ICNT= 2 ptm, n = 2 tm-2, and t = 15 nm. The inset shows the
percolation probability versus nanotube alignment angle 0, for the same set of 0m. (b)
Log-log plot of normalized resistivity versus measurement direction angle for six
nanotube alignment angles ranging from 18 to 900. The values of the measurement
direction critical exponents r extracted from the slope of the p vs. 0m curves near the
percolation threshold (i.e. at large O8) are r= 2.9, 2.9, 2.7, 1.85, 0.65, and 0 for 0=
180, 270, 360, 450, 72, and 900, respectively. The inset shows Oh"Mx vs. 0a.


4.. 45 ra-
= T -90 1- 0o
a T Nanotube
V Alicgnmenl
\ Angle (,)


m m

M*0
- 111
Ug









10 U
10 4


1ol
10-1
S109
010-
10



0


7 8 9 10


Figure 5-13. Measured dark and photocurrent versus applied voltage for GaAs-based MSM
photodetectors with CNT film and Cr/Pd metal electrodes, as labeled in the figure.
For both devices, W= S = 30 |tm and FL = FW= 300 |tm. The dark current of the
CNT film MSM device is significantly lower than that of the Cr/Pd control device,
while the photocurrents are comparable, particularly at high applied bias voltages.


10 3

10"'
10


10-'1
10.11


S Photo Current


Dark Current
i- ..

^"o ,----""1
CNT Film
-- Ti/Au Control


I 1 2 3 4
Voltage (V)


Figure 5-14. Measured dark and photocurrent applied voltage for Si-based MSM photodetectors
with CNT film and Ti/Au metal electrodes, as labeled in the figure. For both devices,
W= 5 tm, S = 15 tm, and FL = FW= 300 tm and Si isp-type.


1 2 3 4 5 6
Voltage (V)


Photo Current

/ t
4-0*
/'

CNT Film
/ Cr/Pd Control

Dark Current

--'
-. i _~i .i i i i.i i i


-


I









the other hand, for voltages greater than VRT, the neutral region reduces to zero and the hole

current increases exponentially, according to Eq. (5-6). Consequently, the total current density is

now dominated by the hole current density Jp. Above the flat-band voltage, Jp increases slowly

according to the second term in Eq. (5-8).

In Fig. 5-4(b), on the other hand, the barrier height for holes was taken to be larger than

that for electrons, i.e., Bn = 0.60 V and Bp = 0.82 V. In this case, the hole current density is

always smaller than the electron current density. As a result, the total current density is given

simply by Eq. (5-2), which slowly increases until breakdown conditions are reached.

Finally, in Fig. 5-4(c), the barrier height of electrons was set equal to that of the holes, i.e.,

B,=n p = Eg/2 = 0.71 V. In this case, the total current density for voltages larger than the

flatband voltage (i.e., Va > VFB) is smaller than that in the previous two cases. Since the dark

current is a function of the competition between electron injection at contact 1 and hole injection

at contact 2, the lowest dark current is achieved when the electron Schottky barrier height 4Bn is

approximately equal to half the bandgap of the semiconductor material, which is 0.71 eV for

GaAs, which is expected to be the case theoretically, as well as experimentally [151].

The photocurrent or optical response of a photodetector is usually characterized by either

quantum efficiency or the responsivity. Quantum efficiency is defined as the number of electron-

hole pairs collected to produce the photocurrent Iph divided by the number of incident photons,

i.e.,

'ph /q
= Iph (5-9)
P P /hv'

where P,nc is the incident optical power and v is the frequency of the incident light source. The

responsivity of a photodetector is defined as the photocurrent generated per incident power:









nm) lateral features. In short, although the etch selectivity between the CNT film and PMMA is

less than unity (S = 0.36), it is still large enough to allow for e-beam patterning of CNT films.

Aspect ratio dependent etching has been observed in some etch processes, such as silicon

trench etching, resulting in a lower etch rate for smaller width trenches [96]. Using the approach

described in the preceding paragraph, I systematically studied the effect of the line width on the

nanotube film etch rate for widths ranging from 50 |tm all the way down to 100 nm. The spacing

between the etched lines was set equal to the width of the lines in all cases. The etch rate was

found to be almost constant at 2.37+0.3 nm/s, independent of the line width etched. This is most

likely due to the fact that all of my samples have a CNT film thickness t < 100 nm. The aspect

ratio AR of the nanotube film etched, defined as t/w, where w is the width of the line etched,

always satisfies AR < 1 for all the samples. In other words, the plasma density is high enough

and the aspect ratio is small enough so that reactant species are able to make it to the bottom of

the etched lines even for the smallest (100 nm) linewidths.

I also systematically studied the effect of changing various ICP etch parameters on the etch

rates of the CNT film and different resists, as listed in Table 2-1, using the procedure described

previously. To investigate the effect of the substrate bias power on the etch rate, I decreased the

substrate power from 100 W to 15 W, keeping all the other etch parameters constant as in the

initial recipe. Table 2-1 shows that the nanotube film and resist etch rates are decreased by about

a factor of 10 compared to those of the initial recipe. By reducing the substrate bias, the ion

energy is reduced resulting in a substantially slower etch rate. A slow etch rate could be useful

in applications where the CNT film thickness is very small and the etch rate and uniformity

needs to be precisely controlled.









two effects reverse in dominance. In order to combine the contribution of these effects into one

quantity, a natural choice is to multiply these effects together; interestingly, the result is a

formulation proportional to 13. Although it seems possible to generalize this to (13) (and


therefore K3) ) for a length distribution, the literature suggests there is no obvious correlation

for systems with even slight anisotropy, such as alignment [142,145]. Regardless, increasing

alignment can be seen to increase the relative weight of longer elements to the overall

conduction, hence driving the resistivity scaling toward higher power mean lengths.

To summarize, my study of the CNT film in this chapter using Monte Carlo simulations

illustrates clearly that near the percolation threshold, the resistivity of the nanotube film exhibits

an inverse power law dependence on all of the discussed parameters. In other words, regardless

of how we approach the percolation threshold, we observe an inverse power law behavior, which

is a distinct signature of percolating conduction. However, the strength of resistivity scaling for

each parameter, represented by the corresponding critical exponent, is different. This strength

depends on how strongly a particular parameter changes the number or characteristics of

available conduction paths in the film. Furthermore, these parameters are not completely

independent. For example, as I have demonstrated explicitly, the strength of resistivity scaling

with device width depends on nanotube density, length, and alignment. I have also studied the

effect of nanotube length distribution on the resistivity-length scaling for CNT films and films

with elements that are significantly more resistive compared to the element-element junctions. I

have observed that network resistivity correlates well with RMS length for CNT films and with

average length for element-dominated networks. In the latter case, percolation effects drive the

correlation towards RMS length for short average lengths. Furthermore, in each case, alignment









parameters such as finger width, finger spacing, and device active area. I also compare the dark

and photocurrent of the CNT film-based MSM photodetectors with standard metal-based MSMs.

My results not only provide insight into the fundamental properties of the CNT film-GaAs and

CNT film-Si junctions, but also successfully demonstrate the integration of CNT films as

Schottky electrodes in conventional semiconductor optoelectronic devices.

Characteristics of MSM Photodetectors

MSM photodetectors consist of two back-to-back Schottky diodes, formed from a

semiconducting material and two metallic contacts, as can be seen in Fig. 5-1 [149,150]. As for

the fabrication, usually semiconductor material is used as the substrate and metallic contacts are

patterned on the surface of the semiconductor. Although the structure is usually symmetric,

asymmetric structures can be fabricated by patterning two metallic contacts with different

surface areas. For such a structure, when a bias is applied between the metallic contacts, one of

the diodes operates in the forward bias, while the other diode operates in the reverse bias and its

depletion region extends into the semiconductor. If the bias is high enough, all the surface of the

semiconductor becomes depleted. In that case, if a light source shines on the surface, electron-

hole pairs that are generated in the substrate can be collected efficiently by the contacts.

In order to optimize the operation of such a device, there are several device parameters that

need to be designed carefully. First, the substrate is usually chosen with a light level of doping,

so that depletion region can extend easily in the substrate by applying a small amount of voltage.

Similarly, the distance between the contacts should be designed carefully. Usually, contact pads

are designed as interdigitated fingers, which results in an increase in the effective area that the

contacts cover (see Fig. 5-1). Quality of the Schottky contacts is also of critical importance;

device performance can be degraded due to the low quality of the interface, which lowers the

amount of current and affects the transient response of the device.









LIST OF TABLES


Table page

2-1 Etch rates of the CNT film and three different resists (S1813, LOR3B, and PMMA)
under different plasm a etch conditions....................................................... ............... 33

3-1 Average nanotube film resistivity values measured using standard four point probe
stru ctures..... .............................. ...................................... .. ........ ...... 4 1

5-1 Device dimensions and extracted barrier heights for 8 n-type and 5 p-type Si-based
M S M stru ctu res.. .................................................................................................................. 10 5










0 I II I I mll I I 11 1 11 FmFi

1o-o r R 10'2 (a)

1001 I t -------------1
a"" a





1016
10- a


10 101 102 l0 101
L (frm)


s t. I (b)
< io--7' "/..

f te to ... ..








nL


Figure 6-1. Effect of device length and film thickness on experimentally measured noise: (a)
Log-log plot of A/R versus L taken from [169]. The dashed line represents A/R = 10-11
Q-1 and the solid line is a least-squares power-law fit to the experimental data. (b)
Log-lin plot of A as a function of the number of deposited layers, nL, taken from
[172]. The inset shows variation of A as a function of the conductivity with a line
fitted to the experimental data.
fitted to the experimental data.









the effect of film doping and dedoping on its workfunction. The inset of Fig. 5-1 (b) shows log I

vs. 1/Tfor one p-type Si and one n-type Si MSM device in the temperature range 150-3400K.

Once again, the saturation of the current at temperatures below 2400K suggests that tunneling,

which depends weakly on temperature, becomes the dominant current transport mechanism

across the CNT film-Si junction at lower temperatures [158].

Next, I study the effect of the device geometry on the dark I-Vcharacteristics at room

temperature (294 K). Figure 5-12(a) shows the dark I-V curves for GaAs-based devices with

identical W, FL, and FW, but with S ranging from 10 to 20 |tm. Increasing the spacing in these

devices (with the same area) decreases the number of finger pairs n, which is given by n = FWI

2(W+ S). This decrease in turn reduces the amount of dark current in the device, in agreement

with the trend observed in Fig. 5-12(a). Figure 5-12(b) shows the dark I-Vcurves for devices

with identical FL and FW, but with W= S ranging from 15 to 30 |tm. The dark current is found

to monotonically decrease with an increase in W. It has been observed that in MSM detectors,

beyond a certain finger width, the dark current becomes roughly independent of the width W, and

is proportional to the product of FL and n [160]. This is due to current crowding at the edges of

the electrodes as illustrated explicitly in Fig. 5-12(c), which shows a MEDICI simulation of the

cross-sectional current density distribution in the GaAs substrate between two electrode fingers

(W= S = 20 [tm) at V = 3 V bias using the value of the barrier height obtained previously. It is

evident from this simulation that current crowding occurs at the electrode edges, which results in

the effective device area to be weakly dependent on the width of the electrode. Therefore, since

FL and FWare constant and W= S for all the devices shown in Fig. 5-12(b), n, thus the dark

current should be inversely proportional to W, in agreement with the observed trend in the figure.

Finally, Fig. 5-12(d) shows the dark I-Vcurves for devices with identical Wand S, but with FL =









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If the diodes are ideal and identical, the transport is due to the thermionic injection of

electrons/holes over the barriers or their tunneling through them. Drift/diffusion mechanisms are

also responsible for the transport of the minority carriers through the semiconductor. At room

temperature, tunneling is important only when the barrier is thin or if the contacts are very close

to each other. Thin barriers are a result of highly doped substrates or high electric fields. For

low-doped substrates and moderate voltage values, tunneling should be negligible at room

temperature. However, at lower temperatures, electrons/holes do not have enough energy to

surpass the barrier. In that case, tunneling might become significant.

In this section, I am going to employ thermionic emission theory to derive the current

equations at various applied voltages (Va) for an MSM photodetector with a donor concentration

(equal to ND) under dark conditions. Figure 5-2 illustrates a simple schematic and band diagram

of the symmetric device under study at equilibrium. As defined in the figure, S is the spacing

between the metal contacts, and On and Bp represent the electron and hole barrier heights,

respectively, and Vb, denotes the built-in potential. The depletion layer width, Wat each contact

is given by:


W= (5-1)
W qN

where q is the electron charge and es is the semiconductor permittivity.

When a small positive voltage (smaller than the reach-through voltage VRT to be defined

below) is applied to contact 2 with respect to contact 1, contact 1 is reverse-biased, whereas

contact 2 is forward-biased. The quantity qVi is the difference between the Fermi level (EF) of

contact 1 and EF of the semiconductor, and the quantity qV2 is the difference between the EF of









by the tube-tube contact resistance. Increasing the nanotube density decreases the film resistivity

strongly, and results in a higher critical exponent a for width scaling and lower critical width

Wc. Increasing the nanotube length also reduces the film resistivity, but increases both a and

Wc. In addition, the lowest resistivity occurs for a partially aligned rather than perfectly aligned

nanotube film. Increasing the degree of alignment reduces both a and Wc. Furthermore, when

the nanotubes are strongly aligned, the film resistivity becomes highly dependent on the

measurement direction. Consequently, I studied the effects of nanotube length, nanotube density

per layer, and device length on the scaling of CNT film resistivity with nanotube alignment and

measurement direction. I found that longer nanotubes, denser films, and shorter device lengths

all decrease the alignment critical exponent and the alignment angle at which minimum

resistivity occurs, and increase the measurement direction critical exponent. However, the

amount of increase or decrease is different for each parameter.

I systematically explained these observations, which are in agreement with previous

experimental work, by simple physical and geometrical arguments. All these results confirm that,

near the percolation threshold, the resistivity of the nanotube film exhibits an inverse power law

dependence on all of these parameters, which is a distinct signature of percolating conduction.

However, the strength of resistivity scaling for each parameter, represented by the corresponding

critical exponent, is different.

I also studied the effect of length distribution (instead of a fixed length) on the resistivity

scaling with CNT length and have compared the results for CNT films with films in which the

resistance of the elements is significantly larger than their junctions (unlike CNT films). I

observed that network resistivity correlates well with RMS length for CNT films and with

average length for element-dominated films. In the latter case, percolation effects drive the









Simulation Results

I first analyze the effects of device parameters such as device dimensions and nanotube

alignment angle on l/f noise scaling computationally to connect and explain previous

experimental results on CNT films from various groups.

Effect of Device Length

Figure 6-3(a) shows the log-log plot of the noise amplitude normalized to resistance (AIR)

versus device length (L) for a single-layer nanotube network, where filled circles denote

experimental data points from Snow et al. [169] and open circles denote my simulation results.

The device and nanotube parameters used in the simulations were device width W= 2 |tm,

nanotube length IcNT = 2 |tm, and nanotube density per layer n = 5 tm-2, which is within the

range of densities reported for thin networks of nanotubes above the percolation limit [64].

Since 2D nanotube networks were used in the experimental work [169], only a single 2D

nanotube layer was used to model the experimental data. The simulation results are in excellent

agreement with the experimental data, clearly indicating that AIR is a strong function of device

length. The dashed line in Fig. 6-3(a) is the power-law fit to the experimental data, yielding

A / R oc La with a critical exponent a= -1.3, in agreement with the simulation data for 8 < L <

20 |tm. The deviation of the simulation data from this fit for L < 8 |tm will be discussed in detail

later. This deviation could hardly be noticed in the experiments due to the large scatter in the

experimental data points. Simulations here are performed only for L > 2 |tm, because below L =

2 |tm, individual nanotubes could connect the source and drain electrodes directly (since IcNT = 2

[tm), diminishing the effects of percolation. Furthermore, simulations were limited to L < 20

|tm, since the time it takes to run the simulations becomes prohibitively long for longer devices.

The decrease in the noise amplitude with device length is consistent with Hooge's classical









The T dependence of A at temperatures above the VRH regime can provide further

information about the energy distribution of the fluctuators. More specifically, Dutta and

colleagues have suggested that for an inhomogeneous system with random fluctuations, if the

energy distribution is broad compared to kT, the relationship between D(q/), density of fluctuation

states, and A can be written in the form [189]

A(T)
D(q) oc (6-8)
T

Where r = -kTln(2rfr,), and to is a characteristic "attempt time" with a value inverse of

phonon frequency. For most materials, 10-14< 0 < 10-11 s [190], but the value of q is not very

sensitive to the absolute value of ro.

The main panel of Fig. 6-9 shows D(rq) versus r for Dl and D2, based on Eq. (6-8) with to

= 10-13 s. This value of o is chosen to provide the best fit ofEq. (6-9) to the /values extracted

experimentally, as explained below. The similarity in the dependence of A on temperature for

the two devices results in a similarity in the dependence of D on q. As can be seen, both curves

show broad peaks in the range 0.3 to 0.6 eV. These peaks are broad enough to satisfy the

assumptions made in writing Eq. (6-8) and they are responsible for most of the noise at high

temperatures [189]. As mentioned before, similar peaks have also been observed for individual

semiconducting tubes [176]. Based on the energy range of the peaks, sources of noise such as

electronic excitations within the tubes or structural fluctuation of the defects within the CNT

lattice have been ruled out [176]. For CNT films, due to the presence of the tube-tube junctions,

the picture is even more complicated. However, a possible source of the noise could be

fluctuation within or at the surface of the SiO2 substrate underneath the nanotubes [176]. In fact,

it has been shown that removing the oxide underneath the tubes can improve (reduce) their noise

amplitude up to an order of magnitude [191,192]. Therefore, similar to the individual









correlation towards RMS length for short average lengths. Furthermore, in each case, alignment

of nanotubes/elements in the network places increasing weight on the longest elements, shifting

the correlation to higher power means. These results emphasize the importance of taking the

nanoelement length distribution into account when using these films in potential device

applications.

In chapter 5, I fabricated and characterized MSM photodetectors based on CNT film-GaAs

and CNT film-Si Schottky contacts. After reviewing the fundamentals of the MSM

photodetectors, I extracted the Schottky barrier height of CNT film contacts on GaAs and Si by

measuring the dark I-V characteristics as a function of temperature. The results showed that at

temperatures above 240-260 K, thermionic emission of electrons with a barrier height of-

0.54 eV for GaAs junctions and barrier heights of 4Bn = 0.45 eV and Bp = 0.51 eV for n-type

andp-type Si junctions was the dominant transport mechanism, whereas at lower temperatures

tunneling began to dominate, suggested by the weak dependence of current on temperature.

Assuming an ideal M-S diode, these barrier heights correspond to a CNT film workfunction of

about 4.6 eV, which is in excellent agreement with previously reported values. Furthermore, I

observed that dark currents of the MSM devices scale rationally with device geometry, such as

the device active area, finger width, and finger spacing. Finally, I observed that in the case of

GaAs devices, while the photocurrent of the CNT film MSM devices is similar to that of the

metal controls (resulting in a comparable responsivity), their significantly lower dark current

results in a much higher photocurrent-to-dark current ratio relative to the control devices. Si-

based devices also exhibit a higher photocurrent-to-dark current ratio at high applied voltages

relative to metal control devices.









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alignment direction. For example, for m = 0, the transition from P = 1 to 0 starts when Oa

becomes smaller than 100, whereas for m = 900, it starts when 0a gets lower than 40.

To illustrate the effect of the measurement direction angle from a different perspective,

Fig. 4-8(b) shows the plot of normalized resistivity versus Om for six different values of 0a

ranging from 18 to 900. It is evident from Fig. 4-8(b) that when the nanotubes are randomly

distributed (i.e. 0a = 900), resistivity is almost independent of Om. In contrast, even for slightly

aligned tubes (such as 0a = 72), resistivity starts to increase with increasing 0m, and for well-

aligned nanotubes (such as = 18), this increase becomes very strong. Furthermore, the

resistivity exhibits an inverse power law dependence on Om as the film approaches the

percolation threshold at large measurement direction angles, given by

p oc (90 m )-, (4-5)

where ris the measurement direction critical exponent. The value of r extracted from the

slope of the log-log plots in Fig. 4-8(b) increases from 0.65 to 2.9 when 0a goes from 72 to 180,

which is a manifestation of the stronger dependence of resistivity on Om as the nanotubes in the

film become more aligned.

As a measure of the sensitivity of film resistivity to the measurement direction angle, I

define 0"'x as the maximum Om above which the resistivity of an aligned film becomes larger

than that of a completely random film (within + 5% error). In other words, 0" is a measure of

the degree of misalignment in the measurement direction that can be tolerated before the aligned

film becomes more resistive than a random film. By this definition, 0" is only meaningful for

alignment angles at which the resistivity (when Om = 0) is lower than that of a completely

random film, which is around 0, = 22 in my case, as seen from Fig. 4-8(a). The plot of 0"B vs.









In this chapter, I study the geometry-dependent resistivity scaling in CNT films using

Monte Carlo simulations by randomly generating nanotubes on stacked 2D rectangular planes. I

first demonstrate that these simulations can model and fit the recent experimental results on the

scaling of nanotube film resistivity with device width. Then, I systematically study the effect of

four parameters, namely tube-tube contact resistance to nanotube resistance ratio, nanotube

density, nanotube length (including the effect of length distribution) and nanotube alignment on

the CNT film resistivity and its scaling with device width. I then explain these simulation results

by simple physical and geometrical arguments.

Modeling Approach

Simulation of the electrical properties of the nanotube film was performed by randomly

generating the nanotubes using a Monte Carlo process. In particular, each nanotube in the film is

modeled as a "stick" with fixed length ICNT. The position of one end of the nanotube and its

direction on a two-dimensional (2D) plane are generated randomly. This process is repeated

until the desired value for the nanotube density n in the 2D layer is achieved. Additional 2D

layers are generated using the same approach to form a three-dimensional (3D) nanotube film.

An example of a 2D nanotube layer produced by this method is shown in Fig. 4-1(a). For profile

comparison, Fig. 4-1(b) shows an experimental AFM image of a nanotube film that I have etched

into a series of lines with width and spacing of 500 nm using the approach mentioned in chapter

2.

After the 2D nanotube layer is generated, the locations of the junctions between pairs of

nanotubes (which I call internal nodes) and between the nanotubes and source/drain electrodes

(which I call boundary nodes) are determined by the simulation code. I explained in chapter 2

that the nanotubes in the film have random in plane orientations but are mostly ordered to lie in

stacked planes. As a result, in the 3D film created by stacking several 2D nanotube layers, it is









Despite all these outstanding properties, controlling the diameter, chirality, location, and

direction of individual nanotubes has proven to be very challenging [50]. The control over some

of these parameters is necessary for successful commercialization of the applications that depend

on the superb properties of individual nanotubes. Up to date, the efforts to improve the

fabrication process of carbon nanotubes include the use of 1) electric field to control the

direction of nanotubes during CVD growth [51,52] (not very flexible and only suitable for small

scale fabrication), 2) PECVD [53] (e.g. microwave plasma, very successful, but only for vertical

alignment), 3) self-assembly techniques using DNA's, molecules and polar materials for

alignment and positioning [54-56] (good results, sometimes incompatible with current device

fabrication technology), 4) gas flow techniques [57] (local, non-uniform, small scale) and 5)

special substrates such as quartz [58] (not very suitable for device fabrication). Other less

developed and more difficult approaches use magnetic field, multi-layers of catalyst particles and

surface topography to achieve positioning and alignment. But still, lack of reproducibility,

reliability, and manufacturability of nanoelectronic devices based on individual CNTs remains

the showstopper in carbon nanotube research. In this thesis, I am going to focus on a carbon

nanotube-based material that does not have these limitations.

Single-Walled Carbon Nanotube (CNT) Films

A single-walled carbon nanotube (CNT) film is a three-dimensional film of tens of

nanometers thickness, consisting of an interwoven mesh of single-walled nanotubes, as shown in

the inset of Fig. 1-3 [59]. The CNT film exhibits uniform physical/electronic properties

independent of the diameter, chirality, location, and direction of individual tubes making up the

film [50] due to ensemble averaging [60-64]. As a result, it is highly manufacturable compared

to individual nanotubes. Furthermore, the CNT film is simultaneously conductive (resistivity

~10-4 Qcm) and optically transparent over the visible and near-infrared portions of the spectrum









weak p dependence on T, lightly doped or undoped thin CNT films depicted strong localization

behavior with close to zero conductance values at very low temperatures [101,108].

Although the CNT films in my study are not intentionally doped, nitric acid, which is used

for purifying the nanotubes, unintentionally dopes the CNT films to some extent. However, as I

have previously shown in chapter 3, nanotubes are subsequently de-doped during the processing

steps associated with the four-point-probe structure patterning, resulting in weakly doped films.

The resistivity shown in Fig. 6-7 for device Dl, therefore, depicts insulating behavior due to

strong localization of carriers at low temperatures, which can be explained by variable range

hopping (VRH). The temperature dependence ofp in the VRH regime can be written as

p(T) = p0 exp[(T0 /T)7], (6-5)

where po is a constant, To is the characteristic temperature which is proportional to the

energy separation between the available states, andp = 1/ (d+1) for Mott VRH [185], where dis

the dimensionality of the hopping conduction.

As is shown in the right inset of Fig. 6-7,p can be extracted from a plot of reduced

activation energy W, defined as

d ln(p(T))
W(T) = d (6-6)
dlnT

versus T Thep value (equal to the slope of the fit in this plot) I have extracted is 0.29,

which is very close to the theoretical value of 0.25 expected for 3D VRH [i.e. d = 3 in Eq. (6-5)].

The slight deviation from 0.25 could be related to the strong localization of carriers that cause a

transition form Mott VRH to coulomb gap (CG) VRH (For CG VRH, the exponentp should

have a value close to 0.5) [108]. More analysis of the CNT film resistivity dependence on

electric and magnetic field in the VRH regime is presented in the appendix.



































To my beloved parents










(a) -- +
V




Drain


Eu


20 (b)
15
10

O

10
I IrI


M -3 -2 -1 0 1 2 3
Voltage (V)

q (d)

Source qV qV


IqJ t p qohr,: Small
(G) Small Large Drain
Drain Source

Figure 5-10. Characterization of asymmetric GaAs-based MSM structures: (a) The schematic
and (b) measured dark current versus applied voltage for a CNT film-GaAs MSM
device without the interdigitated fingers between the electrode pads, but with
asymmetric CNT film contact areas. The source contact area is 16x104 |jm2 and the
drain contact area is 4x104 |jm2. The voltage is applied to the smaller drain contact
and the larger source contact is grounded, as shown in (a). The band diagrams
illustrating electron thermionic emission over the Schottky barrier for (c) positive and
(d) negative voltage bias.


































2010 Ashkan Behnam









In this chapter, first I use Monte Carlo simulations to study l/f noise scaling in CNT films

as a function of device parameters and film resistivity. My study focuses on the noise behavior in

CNT films at low frequencies, where the shot noise and Johnson-Nyquist noise are negligible

and 1/f noise is the only dominant noise source. I consider noise sources due to both tube-tube

junctions and nanotubes themselves. By comparing the simulation results with my own and

previous experimental data [169,172], I determine which noise source is the dominant one. I also

systematically study the effect of device length, device width, and film thickness, and nanotube

degree of alignment on the /lf noise scaling in CNT films. Furthermore, I study the temperature

dependence of l/f noise in CNT films by fabricating four-point-probe structures and measuring

their resistivity and noise amplitude as a function of temperature and frequency. I analyze the

resistivity data to determine the mechanisms that are responsible for electronic transport in CNT

films at various temperature ranges. I then interpret my noise data in association with the

resistivity results, considering different transport mechanisms that might be responsible for both.

Computational Modeling Approach

The procedure for simulating resistivity is similar to the one explained in chapter 4. One

difference is that each nanotube is assigned randomly to be either metallic or semiconducting

with the ratio of the semiconducting to metallic nanotubes set to 2:1, as typically observed

experimentally [25]. An example of a 2D nanotube layer produced by this method is shown in

Fig. 6-2(b), where semiconducting and metallic nanotubes are labeled by different colors and the

generated network can also be compared to an AFM image ofa nanotube film, which is shown in

1
Fig. 6-2(a). Like before, the resistance of an individual nanotube is calculated by R, = R -,


where / is the length of the nanotube, A is the mean free path (assumed to be 1 |tm in my

simulations), and R0 = h/4e2 is the theoretical contact resistance at the ballistic limit (-6.5 kQ).









Since the concept of RMS length, by weighing the length distribution by l/ is equivalent

to averaging of areas swept out by an element of length IcNT, the resistivity correlates with RMS

length for a junction-dominated film (like the CNT film). For a film with fixed element length,

the RMS length is equal to the average length, and as a result, the effect of one length metric is

indistinguishable from the other (refer to Fig. 4-5(b)).

For an element-dominated film, however, the situation is quite different. Figure 4-13(c)

shows normalized resistivity versus RMS length for a element-dominated film having the same

dimensions as in Fig. 4-13(a) for four different ca- p relationships. The four series separate,

suggesting that, in contrast to the CNT film case, the film resistivity is not an explicit function of

RMS length for element-dominated film. Fig. 4-13(d), on the other hand, shows normalized

resistivity versus average length for four different a p/ relationships. It is evident that for large

average lengths, all four length distributions show convergence to a singular point for each

average length. This suggests a good correlation between resistivity and average length for

element-dominated films. In this case, the film resistivity is independent of the number of

junctions, but depends on the length and number of conducting paths between the source and

drain electrodes, which correlate with average length.

However, it is evident from Fig. 4-13(d) that as the average length decreases, the four data

series increasingly diverge. Furthermore, Fig. 4-13(c) shows a corresponding convergence in the

resistivity versus RMS length plots for small lengths. These observations can be better

understood by plotting the percolation probability versus average length and RMS length, as

shown in Figs. 4-14(a) and (b), respectively. Percolation probability is a geometrical quantity

which is independent of whether a film is junction- or element-dominated. It is clear from Figs.

4-14 that when the percolation probability drops below 1, it shows a better correlation with RMS










60
6 L 7.0 [m 100
L4.O0m Z,
10090
L=2.Oim .5-10
E o


-5 10
SMeasurement
Sna Direction Angle (f)
EEu

1 V .


4 10 90
Nanotube Alignment Angle o)


Figure 4-11. Effect of device length on resistivity scaling with nanotube alignment angle: Main
panel is a log-log plot of normalized resistivity versus nanotube alignment angle for
three device lengths ranging from L = 2 to 7 Itm, when Om= 00. The inset depicts log-
log plot of normalized resistivity versus measurement direction angle for two device
lengths (L = 2 and 7 Lm) when 0,= 18'.








0 1 2 3 4
Length (Ilmn) a) (b)










s sesgt h rcng (d)









probabilistic self-area swept out by a particular element (shaded).
probabilistic self-area swept out by a particular element (shaded).









Figure 4-13(a) shows normalized resistivity versus average nanotube length given by


(lc ) = exp + / for an unaligned CNT film for four different c- / relationships


represented by the four data series. The standard error bars are not larger than the size of the

symbols for all figures. The strong scaling of the resistivity observed in this figure is similar to

the data shown in Fig. 4-5(b) for a fixed density. However, the resistivities for different length

distributions at a fixed average length are distinctly separate, suggesting that, contrary to what

one might initially expect [105], the network resistivity is not an explicit function of average

nanotube length in this case.

As a result of the monotonic decreasing nature of resistivity in Fig. 4-13(a), and noting that

the widest element length distributions produce the least resistivity, I plot in Fig. 4-13(b) the

resistivity versus RMS (second power mean) element length, given by


(/cNr) N= IlcNr2 NT,)dlCT = exp( + c2), for four different o-- 1/ relationships. Because


the RMS value of any distribution is always greater than or equal to its mean, the effect of Fig. 4-

13(b) is to shift the data series corresponding to wider distributions in Fig. 4-13(a) to the right so

that they coincide with each other. This shows that the RMS length, and not average length, is

the relevant length parameter determining network resistivity.

Figure 4-12(d) rationalizes the result of Fig. 4-13(b) by illustrating that within each

network layer, each nanotube sweeps out a circular probabilistic "self-area" that is the

superposition of all orientations it may take once anchored to a point. This self-area represents

all possible points of contact with other nanotubes, and as a result, the larger this area, the more

junctions that this nanotube can make, and the lower the resistivity of the CNT film.









LOR3B lift-off resist can be removed by standard developer solutions, with the dissolution rate

determined primarily by the prebake temperature. To protect the CNT film from potential

contamination due to the S1813 resist, for the second process, a dual layer resist structure

consisting of a 1.3 |tm thick S1813 layer on top of a 250 nm thick LOR3B layer was used.

Finally, for the third process, a dual layer resist process consisting of a 1.3 |tm thick Shipley

S1813 layer on top of a 250 nm thick PMMA layer (950K, 4% in anisole) was used. Since the

S1813 resist is not in direct contact with the nanotubes in the second and third processes, no

residue is left on the nanotube film during fabrication. However, PMMA cannot be exposed by

the 365 nm light source available in the Karl Suss MA-6 contact mask aligner that was used for

photolithography. As a result, for the third process, the S1813 layer was first exposed by the

mask aligner and developed. Subsequently, the PMMA layer was patterned by 02 plasma

etching with the S1813 layer acting as the mask. In all three resist processes, Shipley Microposit

MF319 was used as the developer. The particular resist process used was found to affect the

resistivity of the CNT film, as presented in detail later. For e-beam lithography, a single layer of

PMMA (950K, 2 or 4% in anisole depending on the feature size patterned and PMMA thickness

desired) was used as the masking layer, and a Raith 150 e-beam writer was used for exposure.

After exposure and development, the nanotube film not protected by the resist mask was

etched using an 02 chemistry in a Unaxis Shuttlelock ICP-RIE system. The schematic of the

ICP etcher is shown in Fig. 2-1. The ICP-RIE system decouples plasma density (controlled by

the ICP power supply) and ion energy (controlled by the substrate power supply). As a result,

compared to conventional diode RIE systems, very high plasma densities (>1011 ions cm-3) can

be achieved at lower pressures, resulting in more anisotropic etch profiles and significantly

higher etch rates [96,97]. Etching in ICP systems has a large physical component combined with









Fabrication and Characterization of MSM Photodetectors ...................................................... 87

6 /f NOISE SCALING AND TEMPERATURE DEPENDENT TRANSPORT IN
CARBON N AN OTUBE FILM S .................................................... ............................. 108

Introdu action ................ .... .......................... ................ ............... 108
Computational Modeling Approach...................................... 110
E xperim ental Procedure............................................................... ......................................... 113
Sim u nation R esu lts .................. .................................................................................................. 1 15
Effect of D vice Length ............................ .......................... ............................. 115
Effect of D evice W idth .......................... .. .............................. 120
Effect of Device Thickness and Tube Alignment Angle............................................. 122
E x p erim ental R esu lts ............................................................................... ........................... 12 4

7 CONCLUSIONS AND FUTURE WORKS ..................................................................... 139

S u m m ary o f R e su lts .................................................................................................................. 13 9
F u tu re W o rk s ........................ .................................................................................................... 14 3

APPENDIX: ELECTRIC AND MAGNETIC FIELD DEPENDENCE OF THE CNT FILM
RESISTIVITY IN THE VRH REGIME ................................ 145

L IST O F R E FE R E N C E S ............... .............................................................................................. 148

B IO G R A PH IC A L SK E T C H ........................................................................................................... 159









selectivity, over conventional parallel plate RIE plasma systems, making it possible to pattern

lateral features as small as 100 nm in nanotube films. Furthermore, I showed that a wide range

of nanotube film etch rates can be obtained using an ICP-RIE system by changing the substrate

bias power and chamber pressure.

Chapter 3 was dedicated to characterization of the CNT film resistivity. By fabricating

standard four-point-probe structures using the patterning capability developed in chapter 2, we

demonstrated that the resistivity of the films is independent of device length, while increasing

over three orders of magnitude compared to the bulk films, as their width and thickness shrink.

In particular, resistivity of CNT films started to increase with decreasing device width below 20

|tm, exhibiting an inverse power law dependence on width in the sub-micron range. These

results suggested that the resistivity scaling is an important effect that requires consideration

when fabricating small devices. I also showed that different resist processes result in different

CNT film resistivity values due to partial de-doping of the acid purified nanotubes during

lithography. In addition, the resistivity of nanotube films increased between two to three orders

of magnitude after partial etching by the 02 plasma, indicating that the remaining film is

significantly damaged during the etch.

I used a Monte Carlo simulation platform in chapter 4 to model percolating conduction in

single-walled carbon nanotube films. I exhibited that this simple model can fit the experimental

results on resistivity scaling as a function of device width. In addition, I demonstrated that

geometry-dependent resistivity scaling in single-walled carbon nanotube films depends strongly

on nanotube and device parameters. In particular, I studied the effect of four parameters, namely

resistance ratio, nanotube density, length, and alignment on resistivity and its scaling with device

width. Stronger width scaling is observed when the transport in the nanotube film is dominated









10-3


S ......... 1
E 10- 1 10 ,
Thickness (Layers) ....... ..




0.02 0.1
Resistivity L..-crn
0.02 0.1 0.5
Resistivity (-cm)

I
.... ... (b )
1043


10 ..... ..... 01 '
< 4 10 90 .. PP
Alignment Angle (0) L

Sim
10 Fit

0.01 0.1 1 3
Resistivity (0-cm)

Figure 6-6. Effect of device thickness on noise: (a) Log-log plot of computed A x t versus
resistivity. The change in resistivity is a result of change in the t. The extracted
critical exponent in this case is 1.8. The left inset shows log-log plot of resistivity
versus device thickness for the same device. The right inset shows log-log plot ofA x
t versus resistivity for the same device, but without any noise sources at the tube-tube
junctions. The extracted critical exponent is -0.8 in this case. (b) Log-log plot of
computed A versus resistivity. The change in resistivity is a result of change in the
nanotube alignment angle 0a. It is evident that CNT films with the same resistivity
values can have two different noise amplitudes, depending on their alignment angles.
A power-law fit to the data points (dashed line) with noise amplitudes A higher than
7x 107 yields a critical exponent of 1.3. The inset shows the log-log plot of resistivity
versus alignment angle for the same device, in which the resistivity minimum at about
450 is evident.






















Figure 2-3. CNT film patterning results studied by SEM: (a) SEM image showing concentric
nanotube film rings having widths of about 50 nm patterned by my fabrication
method. The textured area is the nanotube film and the smooth area is the exposed
SiO2 substrate where the film is completely etched. (b) SEM image of"GATORS"
patterned on nanotube film by e-beam lithography and ICP-RIE etching. The widths
of the text characters are on the order of 200-300 nm and the CNT film thickness is
20 nm. The scale bars are 100 nm and 2 |tm in parts (a) and (b), respectively.


(b)







,01 2

Distance (pm)


Figure 2-4. Nanoscale CNT film patterning results studied by AFM: (a) AFM image of a series
of nanotube film lines having equal widths (and spacings) of -200 nm half-way
etched in a 75 nm thick CNT film by e-beam lithography and ICP-RIE etching, as
described in the text. Unlike the lines shown in the AFM image of Fig. 2-2(c), the
lines in this AFM image have not been etched all the way down to the substrate, as
evident from the texture of the remaining film mesh visible in the etched areas. The
scale bar is 200 nm. (b) Cross-sectional height data for the AFM image of part (a),
showing an average etch depth of about 19 nm for this particular sample. The etch
rate can be calculated by dividing this etch depth by the total etch time.









ACKNOWLEDGMENTS

First and foremost, I express my gratitude to my supervisor, Prof. Ant Ural for his support

and guidance throughout my Ph.D. research. He allowed me to become engaged in various

projects while allocating a significant portion of his time for discussing research topics. I have

always appreciated his stability and patience. I also thank Prof Gijs Bosman for all the time and

energy he spent on teaching me various noise concepts and advising me on various subjects. I am

very gratitude for his compassion and openness. I thank Profs. Jing Guo and Jerry Fossum for

their support and the discussions we had and also Prof Kirk Ziegler for acting as one of my

thesis committee members. I thank Profs. Andrew Rinzler and Amlan Biswas and Dr.

Zhuangchun Wu for providing us with raw materials and assisting us with measurements. I thank

Profs. David Arnold, Toshi Nishida, Peter Zory and Scott Thompson for offering interesting

courses.

I thank my colleagues and friends Yongho Choi, Jason Johnson and Jeremy Hicks for all

the time we spent together whether on research or on other subjects. I also thank Yanbin An,

Nischal Arkali Radhakrishna, Karthik Nishwanatan, Leila Noriega, Carlos Torres, Keith Knauer,

Alan Teran, Moon Hee Khang, Aditti Sharma and Ryan Moreau from the nanotech group, Dr.

Shahed Reza from the noise lab, Srivatsan Parthasarathy and Andrew Koehler from Swamp

center, Siddharth Chouksey from SOI group and the rest of my kind and helpful ECE colleagues

and friends. I express my gratitude to Alvin Ogden at NRF for all the help and advice throughout

the years and also appreciate the help from Ivan Kravchenko and Bill Lewis from NRF, Kerry

Siebein from MAIC and Magie Puma Landers from Microfabritech.

I thank all of my friends and roommates in Gainesville over the last few years for their

support and companionship. These are the names that come to my mind, chronologically sorted:

Farzad Fani Pakdel, Masoumeh Rajabi, Alejandro Para, Reza Mahjourian, Hsiu Shan Liu, Sanam




























0,05-
0.3


1000


100




10


1

Width (pm)


n=2I I "
n=411,cNTprm-
(b) n = 2 pm


CNT
n 1n = /'CNT pm


U





1 2 3 4
-.




3 1 2 3 4


Nanotube Length (pm)


Figure 4-5. Effect of nanotube length on resistivity: (a) Log-log plot of normalized resistivity
versus device width for three nanotube lengths ICNT ranging from 1.5 to 4 pm, labeled
by different symbols. Simulation parameters are the same as in Fig. 4-2(a) except for
L = 4 tm. The values of the critical exponent a extracted from the slope of the p vs.
Wcurves near the percolation threshold are 1.0, 1.55, and 2.05 for INT = 1.5, 2, and 4
pm, respectively. (b) Log-log plot of normalized resistivity versus nanotube length
for three different n-blNT relationships. Simulation parameters are the same as in Fig.
4-2(a), except L = 3 atm.


(a) rr
IC 2 nm

S.... CMT 4 pm
M86%M
S4


S'<.


A^
A
AL









LIST OF FIGURES


Figure page

1-1 Scanning Electron Microscope (SEM) images of 1.5 mm long single-walled carbon
n a n o tu b e s ............... ................................................................................................................. 19

1-2 Room-temperature electrical properties of a high-performance carbon nanotube field
effect transistor. ............................................................................... 19

1-3 Transmittance spectra for two CNT films .................. ......................................... 20

1-4 V various applications of CN T film s .................................. ............................................... 21

2-1 The schem atic of the ICP-RIE system ........................................... ........................... 31

2-2 CNT film patterning results studied by AFM............................................. ...............31

2-3 CNT film patterning results studied by SEM:............................... .................... 32

2-4 Nanoscale CNT film patterning results studied by AFM ................................................. 32

3-1 Optical microscope image of a four point probe structure............................................... 40

3-2 Effect of device length and film thickness on resistivity.....................................................40

3-3 E effect of device w idth on resistivity .................................................................. .... ............... 4 1

4-1 Comparison of the texture of computationally and experimentally generated CNT
n e tw o rk s ................... ............................................................ ................ 6 9

4-2 Computational analysis of the effect of device length and width on normalized
re si stiv ity ........................................................................................ ................. 7 0

4-3 Effect of resistance ratio on resistivity ........................................... ......................... 71

4-4 Effect of nanotube density on resistivity and percolation probability .............................72

4-5 Effect of nanotube length on resistivity ..................................................... .............. 73

4-6 A 2D nanotube network generated using a Monte Carlo process .................................... 74

4-7 Effect of nanotube alignment angle on resistivity scaling with device width ..................74

4-8 Effect of nanotube alignment angle and measurement direction angle on resistivity .......75

4-9 Effect of nanotube length on resistivity scaling with nanotube alignment angle and
m easurem ent direction angle ......... ................. ........................................... ............... 76









and 0B are the electron and hole Schottky barrier heights, respectively, and A(,n and A Bare

the Schottky barrier height lowering for electrons and holes, respectively. If ,Bn << Bp or

,B >> p,, only one of the terms in Eq. (5-11) dominates. On the other hand, if 0,, and Op are

comparable, both terms must be included. Furthermore, since both MS contacts are identical,

,Bn + Bp = E,, where Eg is the bandgap of GaAs or Si. As a result, if ,, or p << Eg/2 only

the electron or the hole term, respectively, dominates the total current. In such a case where only

one type of carrier dominates Eq. (5-11), the corresponding Schottky barrier height can be

obtained from the slope of the Richardson plot of log I/T2 versus 1/T. The Richardson plot of the

current-temperature data in the temperature range 280 to 340 K for the MSM device in Fig. 5-

9(a) at V= 3 V, together with the corresponding data for two other devices, which have the same

active area but different width and spacing, are shown in Fig. 5-9(b). From the slope of these

plots, Schottky barrier heights of ~B= 0.53, 0.54, and 0.54 eV are extracted for devices with W=

S = 15, 20, and 30 |tm, respectively. The similarity in the barrier height values extracted for

these devices confirms that the CNT film-GaAs interface is uniform from device to device and

does not depend on contact geometry. Extracted barrier heights represent an "effective" value

resulting from an ensemble averaging of barriers formed between the GaAs substrate and

metallic/semiconducting nanotubes in the CNT film with various chirality, diameter, and doping

levels. Since the Richardson plots exhibit a straight line and the extracted barrier height value of

-0.54 eV is much smaller than half the GaAs bandgap of Eg 1.42 eV, either holes or electrons,

but not both, must be the dominant carriers responsible for the current transport in the MSM

devices. However, based on this temperature-dependent I-Vdata alone, the type of carrier

cannot be determined.









TABLE OF CONTENTS

page

A C K N O W L ED G M EN T S......... ..................... ............................................................................. 4

L IST O F T A B L E S ... .. .................... ..... ..................................................................... .............. ....... 8

L IST O F F IG U R E S ................................................................. 9

A B S T R A C T .................................................................................................... ...... 12

CHAPTER

1 SINGLE-WALLED CARBON NANOTUBE NETWORKS AND FILMS .......................... 14

In tro d u ctio n ................................................................................................................................. 14
Single-Walled Carbon Nanotube (CNT) Films..................................... 15
Organization ........................................ ..................... 17

2 FABRICATION AND PATTERNING OF CNT FILMS ................................................. 22

In tro d u ctio n ............... ................................................................................................................. 2 2
Fabrication and Patterning Process .................................................................... ....... 23
Effect of Various Process Parameters on the Results ............................................................26

3 EXPERIMENTAL STUDY OF RESISTIVITY SCALING IN CNT FILMS ....................... 34

In tro d u ctio n ....................... ....................................................................................................... 3 4
Resistivity Scaling with Device Dimensions ........................................ 35
Resistivity Dependence on Process Parameters ...... ...............................................38

4 COMPUTATIONAL STUDY OF RESISTIVITY SCALING IN CNT FILMS ................... 42

In tro d u ctio n ................................................................................................................................. 4 2
M o d elin g A p p ro a ch .................................................................................................................... 4 3
R results and D iscu ssion ...................................................... 45
Effect of Resistance Ratio ........... ............................. 49
Effect of Nanotube Density ........................................ 50
Effect of Nanotube Length ................ ................................ 51
Effect of N anotube A lignm ent ...................................... .............................. 53
Effect of Length Distribution .......... .............................62

5 METAL-SEMICONDUCTING-METAL PHOTODETECTORS BASED ON CNT
FILM-GAAS AND CNT FILM-SI SCHOTTKY CONTACTS.............. ...............81

In tro du ctio n ................ ............ ........ .................................................................................... 8 1
Characteristics of M SM Photodetectors .................................. .............. .............. 82









40 K and above, however, the fluctuation induced tunneling model explained the resistivity

behavior and the fluctuations within or at the surface of the SiO2 substrate underneath the CNT

film were the probable dominant source of the noise in this regime. Finally, metal-

semiconductor-metal photodetectors were fabricated based on CNT film-Gallium Arsenide

(GaAs) and CNT film-Silicon(Si) Schottky contacts to show the application of CNT film in

optoelectronic devices. The Schottky barrier heights of CNT film contacts on GaAs and Si were

extracted by measuring the dark I-V characteristics in the thermionic emission regime. The

extracted barrier heights corresponded to a CNT film workfunction of about 4.6 eV, which was

in excellent agreement with previously reported values.









CHAPTER 1
SINGLE-WALLED CARBON NANOTUBE NETWORKS AND FILMS

Introduction

Single-walled carbon nanotubes (CNTs) have attracted significant research attention in the

last decade because of their remarkable physical and electronic properties, including their high

mobility, current density, mechanical strength, high surface-to-volume and length-to-diameter

aspect ratios [1-13]. In addition, small and medium scale growth/fabrication of nanotubes is

readily available with approaches such as arc-discharge, laser ablation and chemical vapor

deposition (CVD) being the more common ones (Fig. 1-1 [14]). These favorable properties have

encouraged several groups to try to incorporate nanotubes in various device structures to

improve their performance. For example, because of the existence of semiconducting nanotubes

that show short range ballistic transport characteristics even at room temperature, several groups

have utilized them as the channel material for nano-scale transistors [11,12,15-29]. An example

of a field effect transistor successfully fabricated is shown in Fig. 1-2 [28]. In these structures,

the bandgap and doping density of the channel are controlled by the diameter/chirality of the

tube and the environment that it is exposed to. Metallic nanotubes also have applications of their

own, such as interconnects [30-35]. In general, electronic properties of nanotubes (such as their

Fermi level) vary in response to their environment due to their small diameter, exposed atoms

and large surface to volume ratio. Therefore, they are very suitable for gas and molecule sensing

applications [36-41]. Their mutual electrical and mechanical properties have also encouraged

their use in applications such as nano-composites and Atomic Force Microscopy (AFM) tips [42-

47]. Other nanotube applications include Field Emission Displays (FED) [48,49] and single-

electron transistors [13].









analysis of the noise spectrum at low frequencies, no features other than 1/f behavior were

detected over the range of measured temperatures (except for slight fluctuations in the exponent

/f as Tvaries, as shown in the inset of Fig. 6-9). Due to the high resistance of D2 at low

temperatures, I was able to perform noise measurements only down to 77 K for this device. The

temperature dependence of A in Fig. 6-8 follows the same pattern for both Dl and D2 for T> 77

K. However, there is roughly four orders of magnitude difference in the absolute value of A in

these samples, which will be discussed later when I consider the effect of device dimensions on

noise. At high temperatures close to 300 K, A is a weak function of T, however, as Tdecreases

down to 77 K, A starts to decrease for both Dl and D2. The value of A for Dl reaches a

minimum at around 40 K and then starts to increase significantly at lower temperatures. This

trend is strikingly different from the one that has been recently observed for individual

semiconducting nanotubes [176], where A continuously decreases as Tgoes down to 4 K. Due to

the insulating behavior of the CNT film at low temperatures (A and p both increase significantly

when Tdecreases), the noise behavior might be determined by two separate mechanisms at high

and low temperatures. For Dl at T<< 40 K, A exhibits a power law dependence on Tin the form

A oc T-" with v = 1.53. It has been suggested that for Mott VRH systems in which A increases as

T decreases, a power law-based relationship with an exponent close to 1.5 exists between A and

T [188]. The exponent v extracted from my data is very close to this value. Another interesting

feature is the position of the noise minimum in the A vs. T curve for Dl, which is 40 K. This

temperature is very close to the To value in the VRH model extracted from thep vs. Tdata.

These observations imply that VRH theory applies to the temperature dependence of both

resistivity and noise in my CNT films at low temperatures (T<< 40 K).









57. H. J. Xin and A. T. Woolley, Nano Lett. 4, 1481 (2004).

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66. S. A. Bashar, Ph.D. thesis, University of London, 1998.

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In order to determine the type of carrier responsible for the current transport, I have also

fabricated GaAs-based MSM structures with asymmetric CNT film contact areas, without the

interdigitated fingers between the electrode pads, as illustrated in Fig. 5-10(a). Figure 5-10(b)

shows the dark I-V characteristics for one of these structures with a source contact area of

16 x104 lm2 and a drain contact area of 4 x 104 [tm2. The voltage is applied to the smaller drain

contact and the larger source contact is grounded, as shown in Fig. 5-10(a). The band diagrams

corresponding to positive and negative voltage bias are shown in Figs. 5-10(c) and (d),

respectively. At positive voltage bias, when electrons are injected over the large contact and

holes over the small contact, the current is large, and at negative voltage bias, when electrons are

injected over the small contact and holes over the large contact, the current is small. This proves

that electrons dominate the current transport in these devices.

As a result, my dark current characterization of the CNT film-GaAs MSM devices implies

that thermionic emission of electrons over a Schottky barrier of height ,,n 0.54 eV is the

dominant transport mechanism at temperatures above 260 K. Assuming an ideal MS junction

where the Fermi level is not pinned, this extracted barrier height corresponds to a CNT film

workfunction of M = 4.6 eV, which is in excellent agreement with the range of previously

reported workfunction values [156,157].

The inset in the Richardson plot of Fig. 5-9(b) shows current versus 1/T for the device with

W= S = 20 |tm in a wider temperature window (from 150 K to 340 K) at V= 3 V. As it can be

seen, the current starts to saturate at temperatures lower than -260 K, which suggests that

tunneling, which depends weakly on temperature, begins to dominate the transport across the

CNT film-GaAs junction at lower temperatures [158,159].













u




1-3
10-1
r't"


10
Temperature (K)


100


Figure 6-7. Effect of temperature on resistivity: Main panel is a log-log plot ofp versus Tfor
device Dl. Black squares are experimental datapoints, while red and blue lines are
fits to the experimental results based on the VRH and FIT models, respectively. The
right inset is a log-log plot of reduced activation energy (W) versus Tfor the same
device. The red line in this inset is a power-law fit to the data with an exponent -0.29.


101'2


10 100
Temperature (K)


101






10-6


Figure 6-8. Effect of temperature on noise: Main panel is a log-log plot of A versus T for devices
Dl (lefty-axis) and D2 (right y-axis). Due to the high resistance of D2 at low
temperatures, noise measurements could be performed only down to 77 K for this
device. A power-law fit to the three leftmost Dl datapoints yields an exponent of
1.53. The black lines are drawn as a guide for the eye. The inset is a log-log plot of
current spectral density (Si) versusffor a device in Set 1 with L = 1000 ptm and W=
50 ptm (open circles), demonstrating the l/f type behavior at low frequencies and
saturation of the noise at high frequencies. The black line in this inset is a fit to the
low frequency regime with a slope f of 0.99.


Exp D1
- VRH Fit
SFIT Fit


SExp D
Fit
10 100
Ternperature(K)


~_




































Figure 4-1. Comparison of the texture of computationally and experimentally generated CNT
networks: (a) A 2D random nanotube network generated using a Monte Carlo process
for a device with device length L = 4 |tm, device width W= 4 [tm, ICNT = 2 |tm and n
=4 |tm-2. (b) AFM image of a nanotube film etched into a series of lines with width
and spacing of 500 nm by e-beam lithography and reactive ion etching (chapter 2).










qN 2 2qN -
VRT qND S2 -_S 2qN -b,
2e-s _s


(5-5)


When the applied voltage exceeds VRT, the hole current in Eq. (5-3) reduces to


-q \ qv2
Jp =A*T2ekB vbe -e 1
P


(5-6)


and the total dark current is given by the sum of Eqs. (5-2) and (5-6). As the applied voltage is

increased even further, the electric field at the edge of the contact 2 becomes zero and the energy

band at contact 2 becomes flat as shown in Fig. 5-3(b). This is known as the flat-band condition

with the corresponding flat-band voltage, VFB given by


F qN S.
28,


(5-7)


For V > VFB, the expression for the electron current density is still given by Eq. (5-2).


However, the hole current reduces to J = AT2 exp(- ), where OB is the effective hole
kT

barrier height under the applied electric field. As a result, the total dark current can be written as


JDark =n p =A TkB +AT2e kB (5-8)

Based on equations (5-2) to (5-8), total amount of dark current density, as well as its

electron and hole components can be calculated, as is shown in Fig. 5-4 for a symmetric GaAs

MSM structure with ND = 1014 cm-3 and S = 20 [im at T= 3000K. Other parameters used in this

calculation are mo = 9.11 x10-31 Kg, me = 0.067mo, m = 0.45mo, Lp = 0.01 cm and D = 100

cm2/sec. In Fig. 5-4(a), where B, = 0.82 V and Bp = 0.60 V, respectively. In this case, the

electron current density is much larger than the hole current density for voltages less than the

reach-through voltage. As a result, the J, term in Eq. (5-4) dominates the current behavior. On












---- t= 35nm
-.---. t=15nm

UI


10












10'


^11o
E 9

lo 9

a .
3

0


* *L=300pm
SL=450mum
L=7500um
1. L-9a.0 m


10 20 30 40
Wkith (upm)


..


Y
*



S 1
m


1 1 Width (pm) 10


Figure 3-3. Effect of device width on resistivity: Main panel is a log-log plot of resistivity versus
width for structures with t = 15 and 35 nm and L = 7, 50, and 200 |tm. For W< 2 1tm,
the data can be fit byp a W-153 for t= 15 nm andp a W-143 for t = 35 nm, as shown
on the plot by different style dashed lines. The inset shows pversus Won a linear
scale for Win the range 5-50 jtm. The film thickness is 55 nm. The line connecting
the average of the data points at a given width provides a guide to the eye.




Table 3-1. Average nanotube film resistivity values measured using standard four point probe
structures for nanotube films patterned by S1813 only, PMMA/S1813, and
LOR3B/S1813 resist processes.
S1813 PMMA/S1813 LOR3B/S1813
Resist Process
Only Dual Layer Dual Layer
Resistivity (10-4 Ocm) 5.2 6.3 6.9


*"
T.






L=200m U
L= 50pm
L=7[pm
i .









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that observed for larger device lengths, as implied by Eq. (6-4). This increase in l/f noise causes

the critical exponent ac to increase for small values of L as evidenced by the deviation from the

dashed power-law fits in Figs. 6-4(a) and (b).

The effect of the change in resistivity at small L (due to percolation) on the noise

amplitude A can be illustrated further by re-plotting the data in Fig. 6-3(b) for the CNT film with

t = 16 nm asA x L versus resistivity, as shown in Fig. 6-4. We have seen above that the

simulation data for the t = 16 nm curve in Fig. 6-3(b) exhibits approximately A IR L which

indicates thatA x L is a constant if pis constant. As a result, by plotting A x L versus pin Fig.

6-4, any explicit dependence of A on L is eliminated, except for an implicit dependence through

resistivity, since p = p(L) as seen in the inset of Fig. 6-3(a).

The simulation data in Fig. 6-4 can be fit by a power-law relationship given by A x L oc pP

with an extracted critical exponent of/7= 0.4. Since the resistivity is almost constant for many

of the data points, they fall on top of or close to each other in Fig. 6-4; however, the scaling trend

can still be observed. This observed power law behavior is in agreement with previous results

observed for percolation systems [172,183,184] and is a direct manifestation of percolation

affecting the 1/f noise in the CNT film.

Up to this point, based on the relative noise amplitudes chosen to fit the experimental

data, it is assumed that the tube-tube junctions dominate the l/f noise in the CNT film. In

contrast, the inset in Fig. 6-4 shows the log-log plot of A x L versus resistivity, when nanotubes

are assumed to be the only sources of l/f noise in the film (tube-tube junction noise amplitudes

are set to zero, i.e. a = 0). There are two striking differences between the results in the main

panel and the inset in Fig. 6-4. First, the noise amplitude A has dropped more than 3 orders of

magnitude when I exclude the junction noise. In other words, the noise amplitude chosen for an









4-10 Effect of nanotube density on resistivity scaling with nanotube alignment angle and
m easurem ent direction angle ...................................................................... ..................... 77

4-11 Effect of device length on resistivity scaling with nanotube alignment angle ...................78

4-12 Generated CNT networks consisted of nanotubes with a length distribution ....................78

4-13 Effect of nanotube length distribution on resistivity ......................................................79

4-14 Effect of nanotube length distribution on percolation probability .................................. 80

4-15 Effect of nanotube length distribution on resistivity scaling with alignment angle........... 80

5-1 Schem atics of M SM structure .......................................... ... ...................... ............... 98

5-2 Physical representation of M SM structure ................................................ ................. 98

5-3 Band diagrams of the symmetric MSM structure .............................98

5-4 Calculated current density versus applied bias for a symmetric GaAs MSM structure.... 99

5-5 Responsivity for an ideal (dotted line) and a real (solid line) photodetector-................... 99

5-6 Fabrication of GaAs-based MSM photodetectors.................................. 100

5-7 Fabrication of Si-based M SM photodetectors.................................................................. 101

5-8 Si-based M SM dark characteristics............................................... .......................... 101

5-9 Temperature-dependence of the GaAs-based MSM dark current............................... 102

5-10 Characterization of asymmetric GaAs-based MSM structures............................... 103

5-11 Temperature-dependence of the Si-based MSM dark current......................... 104

5-12 Dependence of MSM current on device and finger dimensions................................ 106

5-13 Measured dark and photocurrent versus applied voltage for GaAs-based MSM
ph oto detectors ................................................... ........... ....... 10 7

5-14 Measured dark and photocurrent applied voltage for Si-based MSM photodetectors..... 107

6-1 Effect of device length and film thickness on experimentally measured noise ............. 131

6-2 Experimental and computational analysis of noise.......................................................132

6-3 E effect of device length on noise .............................................................................. .. 133

6-4 Effect of resistivity change due to device length on noise ................................................ 134









60000


50000 "- 0-3 -4 ,
1.2K 10K
0 o ExpD1 0.
S40000 >-0.3
-0-6 /
S30000 -40-20 0 20 40
Current (p)
20000

10000 -- --. .

0.05 0.5 5 50
Electric Field (V/cm)

Figure A-i. Effect of electric field on resistance at very low temperatures: Main panel is a
linear-log plot of the R versus E for Dl at 3 different temperatures. Open circles are R
versus T experimental datapoints (also shown in Fig. 6-8 in chapter 6) plotted on the
same panel and scaled to fit the R versus E results. The inset shows I V
characteristics of device Dl for the 3 temperatures at which the main panel curves are
shown.


1 2 3 4 5
Magnetic Field (T)


6 7 8


Figure A-2. Effect of magnetic field on resistance at very low temperatures. Main panel is a
linear-linear plot of magnetoresistance (AR R) versus B for device Dl at 3 different
temperatures.


10-


5





-5J


-10
0
-5-









113. A. Behnam, L. Noriega, Y. Choi, Z. C. Wu, A. G. Rinzler, and A. Ural, Appl. Phys. Lett.
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6x 10.


4x10'


E

-2 O
<


2x1056


0,02


0,03 0,04
Resistivity (n-cm)


0,05


Figure 6-4. Effect of resistivity change due to device length on noise: Main panel is a log-log
plot of computed A x L versus resistivity for the device shown in Fig. 6-3 (b) with t =
16 nm. The change in resistivity is a result of the change in device length. The
extracted critical exponent of the dashed line fit is 0.4. The inset shows log-log plot
ofA x L versus resistivity for the same device as in the main panel, but without any
noise sources at the tube-tube junctions. The extracted critical exponent is -2.9 in this
case.


1 *' Sim
10 -Fit


0,025 0.04
Res~itis'it/ (-Cicm)

.,ru
- p
Esols






















Figure 1-1. Scanning Electron Microscope (SEM) images of 1.5 mm long single-walled carbon
nanotubes grown using a CVD approach [14].


10-1






10-8


a

-6o


1-10

-15

-20


VW1 Y)


Figure 1-2. Room-temperature electrical properties of a high-performance carbon nanotube field
effect transistor with diameter of 3.5 nm and channel length of 3.5 |tm (taken from
[28]): (a) Transfer characteristics under three different drain-source voltages (b)
Output characteristics under 8 different gate-source voltages from -0.5 V to -7.5 V in
steps of-0.5 V.











500



100


Width (pm)


Figure 4-3. Effect of resistance ratio on resistivity: Main panel is a log-log plot of normalized
resistivity versus device width for Rato ranging from 10-2 to 104, labeled by different
symbols. The values of the critical exponent a extracted from the slopes of the pvs.
Wcurves near the percolation threshold (i.e. at small W) are 0.5, 0.8, 1.55, and 1.95
for Rrato = 10-2, 1, 102, and 104, respectively. The inset shows the critical exponent a
as a function of the resistance ratio. The symbols are the simulation results and the
solid line represents a sigmoidal fit showing a smooth transition between a z 0.5 and
a 2.


Lf



i


* Bush ~er~


10. o 10o- 10
Resistance Ratio

* Rr = 10-2
S ratio
Rr = 1
ratio
R = 102

R o 104





W.-s-










I I F I (a)









I



O


0- -----i--'-'-


RMS Length (jm)


Figure 4-14. Effect ofnanotube length distribution on percolation probability: Percolation
probability versus log (a) average and (b) RMS length for the resistivity data in Fig.
4-13. Only two plots are shown since percolation probability is a geometrical
quantity which is independent of whether a film is junction- or element-dominated.


10 .
RMS =1.8m


1021% A A=u12
V10 A = 0= /








lei

10
6 10
Align ment Angle


100 6 10
Alignment Angle


Figure 4-15. Effect ofnanotube length distribution on resistivity scaling with alignment angle:
Log-log plot of normalized resistivity versus alignment angle for (a) CNT (junction-
dominated) film with fixed RMS length = 1.8 |tm and (b) element-dominated film
with fixed average length = 1.8 jtm for four different c / relationships, as labeled by
different symbols. Both plots show a progressive divergence of the data for highly-
aligned networks.


(b)


A







A p=a/12
r



|= C8T





I I I r









the length of individual nanotubes making up the film. Figure 4-5(a) shows normalized

resistivity versus device width for three different nanotube lengths ranging from ICNT = 1.5 to 4

|tm, for a device with L = 4 |tm. It is evident from this figure that as IcNT increases, the critical

width Wc moves to higher widths and the critical exponent increases. For tube-tube junction

resistance limited transport (i.e. high Rro), when ICNT is longer, conduction paths have a wider

width distribution. Therefore, as Wis decreased, conduction paths start to get disconnected at

higher values of Wc. Furthermore, due to the increased number of paths per width removed from

the film because of the higher nanotube length, critical exponent also increases for films with

longer ICNT once the width decreases below Wc.

I have also studied resistivity scaling as a function of nanotube length for three different

length-density relationships, as shown in Fig. 4-5(b). In the first case, where the density is kept

constant (at a value of 2 [tm-2), the resistivity increases sharply as ICNT decreases. Nanotubes with

shorter lengths have a lower chance to make junctions and form a continuous path between

source and drain, which results in a higher resistivity. Below a critical nanotube length, this

strong resistivity scaling with IcNT can be fit by an inverse power law of the form p oc lC ,

where y = 5.6 is the critical exponent for nanotube length scaling extracted from the simulation

data.

In the second case, the resistivity versus nanotube length is plotted when the density-

nanotube length product is kept constant. Physically, this corresponds to the case when the net

weight of the nanotubes vacuum-filtered to form the film is kept constant while the nanotubes

are cut into smaller lengths. Figure 4-5(b) shows that the resistivity still increases with

decreasing nanotube length in this case, but with a critical exponent of 2.5, which is less than the

previous case. Although the increase in nanotube density in this case decreases the resistivity as









until below 50 nm. The width begins to affect resistivity for values on the order of the nanotube

length in the film, as expected.

Resistivity Dependence on Process Parameters

As I mentioned above, the values of resistivity I observed in the experiments for a device

with large dimensions is higher than the values reported for a similar film [61]. One of the

sources for the increase in the resistivity can be the fabrication process itself. In order to

characterize the effect of the process chemistry on the resistivity of the patterned nanotube films,

I have fabricated standard four-point-probe structures with the three types of resist processes

mentioned in chapter 2. The structures are fabricated with 50 |tm width and 750 |tm length. My

experiments showed that identical resistivity values are extracted regardless of whether the

electrical probes are placed on the Cr/Pd metal contacts or directly on the nanotube film pads,

since the effects of contact resistance are eliminated in a four point probe measurement. The

resistivity values to be reported in this section were obtained from four point probe structures

which did not have the metal contacts. This enables us to compare the effects of the three types

of resist processes on the resistivity of nanotube films directly, without introducing any

contamination due to the second lithography process used for metal contact patterning.

I observed before that the resistivity of patterned nanotube films increases significantly

compared to bulk films as their width and thickness shrink, particularly for devices having

submicron dimensions. Therefore, for this experiment, I designed structures with large length (L

= 500 and 1000 [tm), large width (W= 10, 20, 30, 50 and 100 [tm), and large thickness (t = 75

nm) to avoid geometrical effects on the resistivity of patterned nanotube films. In other words,

the resistivity values measured using these large structures are the minimum resistivity values














V2lta e I Vlg(
( c _'" 4 -FL =F m '
..40 S=20m W = --- -W= S= 30m



CC-
n 20 -- --

X (a) ,_-. (-b)
0 ..----- ---,- Q *-,-,---.-----_
0 1 2 3 0 1 2 3
Voltage (V) Voltage (V)

(c) 40 FL = FW = 40m (d)
-- FL = FW= 310pm

film0 MM ,c 3--- FL=FW =200pm ,


o 20 40 60 F -
X Gm) 10
O '"----------------
O 1 2 3
Voltage (V)

Figure 5-12. Dependence of MSM current on device and finger dimensions: (a) Dark current
versus applied voltage at room temperature (294 K) for CNT film-GaAs MSM
devices with W= 5 jtm and FL = FW= 400 |tm, but with spacing S ranging from 10
to 20 |tm, as labeled in the figure. (b) Dark current versus applied voltage for CNT
film-GaAs MSM devices with FL = FW= 300 |tm, but with W= S ranging from 15 to
30 jtm, as labeled in the figure. (c) MEDICI simulation of the cross-sectional current
density distribution in the GaAs substrate between two CNT film electrode fingers (W
= S = 20 jtm) at V= 3 V bias calculated using the value of the barrier height extracted
from the measurements. Darker colors correspond to higher current density. (d) Dark
current versus applied voltage for CNT film-GaAs MSM devices with W= 5 jtm and
S = 15 atm, but with FL = FWranging from 200 to 400 atm, as labeled in the figure.


M-
-- --S-lOp1m ""
-.1Si, = lr r


- -W== S=115v.









where Ro is the theoretical contact resistance at the ballistic limit (-6.5 kQ) and 2 is the

mean free path, assumed to be 1 itm in my simulations based on previous experimental results

[133-137].

Writing Kirchoff s Current Law (KCL) at each internal node for a mesh with n internal

nodes, I get a set ofn equations with n unknowns, where the n unknowns are the voltages Vn at

each node. The voltages applied to the source/drain electrodes set up the necessary boundary

conditions. Once the voltage at each node is solved, the total current in the film is calculated by

a summation over the currents flowing into the drain boundary nodes. Finally, the resistance,

and as a result, the resistivity p of the nanotube film in the linear regime is calculated by dividing

the voltage drop between the source and drain electrodes by the total current in the film.

For each data point presented in this section, 200 or more independent nanotube film

configurations were randomly generated and their results were averaged in order to remove

statistical variations in the data calculated from different realizations of the nanotube film. In

addition, the percolation probability P, defined as the probability that the nanotube film is

conducting (i.e. the probability of finding at least one conducting path between the source and

drain electrodes) is also calculated to complement the resistivity data.

Results and Discussion

Fig. 4-2(a) shows the normalized resistivity of the CNT film as a function of device width

W The symbols are the experimental data points presented in Fig. 3-3 for a nanotube film with

device length L = 7, 50, and 200 |tm, and average thickness t = 15 nm. The solid line represents

the theoretical fit to the experimental data using my simulations. In Fig. 4-2(a), both the

theoretical and experimental resistivity values have been normalized by dividing the absolute

value of resistivity at each data point by its value at large W, where the resistivity saturates at a









CHAPTER 6
1/F NOISE SCALING AND TEMPERATURE DEPENDENT TRANSPORT IN CARBON
NANOTUBE FILMS

Introduction

For some of the applications suggested for CNT films and networks, such as chemical and

optoelectronic sensors, intrinsic signal to noise ratio is undoubtedly one of the most important

device figures of merit that determine the detection limit of the device [89,167]. It has been

shown that for both single nanotubes (regardless of their intrinsic parameters like diameter and

chirality) and CNT films, l/f noise level can be quite high compared to other conventional

materials [168,169]. As a result, determining the magnitude of the 1/f noise, its sources, and its

scaling with various CNT film parameters is crucial not only for understanding the fundamental

physics of percolation transport, but also for assessing the potential of CNT films for

applications where the device noise is an important figure of merit [170].

One of the first reports on l/f noise in single-walled carbon nanotube networks and mats

[168] observed that the noise obeys the empirical equation,

S, A
S A(6-1)
P' fP

where Sr is the current noise spectral density, I is the current bias, fis the frequency, f3is a

constant close to 1, and A is the noise amplitude, which is a measure of the 1/f noise level

[168,171]. Furthermore, the noise amplitude A was reported to be proportional to the device

resistance R, namely A = 10- R Later studies showed that dependence of A on device

parameters, such as device length and resistivity, is more complicated than that [169,172]. For

example, in CNT networks, the dependence of A on device length L was reported to be

R
A = 9 x 10 -R (Fig. 6-1(a)) over a wide range of L; hence the noise amplitude dependence on
= 1 1









empirical law [182], where the l/fnoise amplitude A varies inversely with the number of charge

carriers N in the device, i.e. A oc 1/N [169]. However, since the resistance of the CNT film

L
device is given by R = p where p is the resistivity, and N scales with the device volume, i.e.
Wt

N oc LWt, AIR is expected to scale as AIR oc L2. Previously, it was suggested that the deviation

from this ideal result is due to nonuniformity of the CNT network [169]. My results, on the other

hand, suggest that the observed exponent is probably due to the effect of other device parameters

on the l/f noise amplitude.

To illustrate this point further, Fig. 6-3(b) shows how the film thickness t affects the

scaling of AIR with L. The simulation parameters are the same as in Fig. 6-3(a), except that n =

1.25 tm-2 (which falls within the range of experimentally reported values for thin nanotube

networks [64]) and the number of layers is more than one, which determines the thickness of the

simulated CNT film. Two curves are illustrated, one for a film consisting of 8 layers (t 16 nm,

assuming each nanotube layer is 2 nm "thick") and the other for a film consisting of 3 layers (t ~

6 nm) shown by open circles and squares, respectively. The extracted critical exponents from

the power-law fits to the simulation data for L > 6 jtm, shown as dashed lines in Fig. 6-3(b), are

a= -1.9 and a= -0.8 for the 8 and 3 layer CNT film, respectively. As its thickness is reduced,

the 3D CNT film becomes like a 2D network and approaches the percolation threshold [62,113],

and the critical exponent a decreases significantly. Furthermore, the magnitude of the critical

exponent extracted for the 3-layer CNT film is smaller than that for the 1-layer 2D network

simulated in Fig. 6-3(a) due to the significantly lower density per layer, n, which is another

parameter that affects the critical exponent a. The noise amplitude A, also exhibits an inverse

power law dependence on n, decreasing with increasing n. For comparison with the simulation









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and the GaAs substrate, considering that the reported values of the Schottky barrier height for as-

deposited Cr layers on GaAs are typically higher than the barrier height that I have extracted for

the CNT film contact on GaAs [162-164]. Since the morphology of the CNT film and its

interface with a substrate are very different than those of a planar spatially homogeneous metal

thin film having the same workfunction, more controlled fundamental measurements of the

interface properties of CNT film-GaAs junctions are necessary in order to better elucidate the

link between the structural and electronic properties of the CNT film-GaAs metal-semiconductor

junctions.

Figure 5-13 also shows that photocurrents of the control device and particularly the CNT

film do not saturate, but increase with applied voltage. This dependence on voltage is much

more pronounced than that of the dark current. In an MSM structure, the depletion region depth

inside the semiconductor increases with higher applied voltages, which enables the collection of

more photogenerated electron-hole pairs. However, the depletion region depth of the nominally

undoped GaAs substrates used in this work (1.59 cm at 3 V) is significantly larger than the

absorption length of GaAs at k = 633 nm wavelength (5.9x 105 cm). As a result, the depletion

depth increase cannot account for the increased current in this case. An alternative explanation is

that an increase in bias induces an increase in current by Schottky barrier lowering due to charge

accumulation at the CNT film-GaAs interface states and image force lowering at the edges of the

electrodes, similar to the dark current case [154]. The electric field and current density are

highest at the edges of the electrodes, as illustrated in the MEDICI simulation of Fig. 5-12(c),

and as a result, the majority of the photogenerated carriers are collected there, amplifying the

effect of image-force lowering at these edges.













10-5



10i


U


(a)

I


*
A\
N'\


-A


Width (pim)
S ,

m Sim
- Fit


0.5 1
Width (pm)


Fi






10 -
< 1Q

,z

10-6 J


0.025


0.1
Resislivily (f-cm)


Figure 6-5. Effect of device width on noise: (a) Log-log plot of computed A versus Wfor a
device with L = 5 jtm, t = 16 nm and other parameters same as in Fig. 6-3(b). There
are two separate scaling regimes. The extracted exponent of the dashed line fit for
large widths (where resistivity is constant) is -1.1. The extracted exponent of the
dashed line fit for small widths is -5.6. The inset shows log-log plot of resistivity
versus device width for the same device as in the main panel. (b) Log-log plot of
computed A x Wversus resistivity. The change in resistivity is a result of change in
device width. The extracted critical exponent in this case is 1.7. The inset shows log-
log plot of A versus resistivity for the same device.


t EO.1
s-


-









A, = ar, was assumed; in other words, the noise amplitude A, of an individual tube-tube

junction scales linearly with the junction resistance rn. In all of my simulations, a proportionality

constant of a = 10-10 was used independent of other device and nanotube parameters, determined

from a fit to experimental data. It has been experimentally observed that the l/f noise of a

junction between a single ID nanotube and a 3D metal source/drain contact could be quite

significant, although it does not have to necessarily scale with the contact resistance [181].

Further experimental work is necessary for a detailed understanding of the /lf noise at the

junction of two individual nanotubes.

Each data point in the following figures represents the average of 500 independent

simulations in order to remove the statistical variations in the simulation data calculated from

different realizations of the CNT film. Device and nanotube parameters such as film thickness t,

nanotube length ICNT, and nanotube density per layer n were chosen to match the experimental

values. In addition to matching the l/f noise data, simulations using these parameters, together

with the chosen junction and nanotube resistances result in similar CNT film resistivity values to

those measured in experiments [175].

Experimental Procedure

For experimental noise measurements, CNT film-based four point probe structures were

produced using the same vacuum filtration process that is described in chapters 2 and 3. Film

thicknesses of-15 nm and 75 nm that are above the percolation threshold were used for noise

measurements. The contact areas on each structure were connected to the sample holder using

conductive silver-based epoxy glue and gold wires. Then the samples were measured at room

temperature or were inserted into the low temperature setup which uses a Janis variable

temperature insert to achieve a temperature range from 300 K down to 1.2 K. By using four-










10-20,


10-21 -1/fFit





10 1000
L Frequency (Hz)

Figure 6-2. Experimental and computational analysis of noise: (a) AFM image of a nanotube
film with an approximate thickness of t = 15 nm where nanotubes are randomly
distributed. (b) A 2D nanotube network generated using Monte Carlo simulations for
a device with length L = 4 |tm, width W= 4 |tm, nanotube length IcrNT = 2 |tm, and
nanotube density per layer n = 10 |tm-2. Semiconducting and metallic nanotubes are
shown in cyan and blue color, respectively. The inset illustrates the alignment angle
0a, explained more in chapter 4. (c) Log-log plot of current spectral density (Si)
versusffor a device in Set 1 withL = 1000 |tm and W= 50 |tm (open circles),
demonstrating the l/f type behavior at low frequencies and saturation of the noise at
high frequencies. The black line in this inset is a fit to the low frequency regime with
a slope f of 0.99.


0S. n .-
o xFm


1










n rn = I2R and V = IR, where I and Vare the total current and voltage in the CNT film,
n

respectively:

S f 1(6-4)
Aeq 1'2 2 2Z irA (6-4)
S1 n

In Eq. (6-4), all the parameters are known except for the noise amplitudes An for individual

noise sources. For individual single-walled carbon nanotubes, it was initially suggested that the

noise amplitude scales with nanotube resistance, in other words A, oc Rc,, [168]. Later studies

revealed that the nanotube l/f noise amplitude follows an inverse relationship with the number of

carriers N, and hence with the nanotube length ICNT, i.e. A, oc 1//INT [179]. Based on these


experimental results, I have used A, = 10 10 Ro //Tr for the l/f noise amplitude of individual

nanotubes in this work, where ICNT is expressed in microns and Ro = 6.5 kM. The chosen

coefficient of 10-10Ro results in a noise amplitude close to that observed experimentally for

individual single-walled carbon nanotubes [179].

Unlike individual nanotubes, determining An for tube-tube junctions based on the available

experimental literature is rather difficult. Although the noise in nanotube-based field effect

transistors has been studied [179], there is hardly any experimental data on the noise amplitude

ofnanotube-nanotube junctions. However, as I will present in the next sections, the CNT film

noise amplitude observed experimentally and its scaling with device parameters can be fit by my

simulations only ifI assume that the total CNT film noise is dominated by the tube-tube

junctions in the film. The presence of defects or structural deformations [180] at the tube-tube

junctions can be speculated as the specific source of this noise, although further experimental

studies need to be undertaken to answer this question in depth. In this work, a relationship









The etch profiles in Figs. 2-2(b) and 2-2(d) are not sufficient to determine how sharp the

actual etch profile is, since the radius of curvature and the sidewall angle of the AFM tip could

decrease the sharpness of the observed transition profile. Figs. 2-3(a) and (b) show SEM images,

respectively, of concentric nanotube film rings and letters printed in nanotube film using e-beam

lithography and ICP etching. The width of the text characters are on the order of 200-300 nm

and the CNT film thickness is 20 nm, demonstrating that the nanotube film can indeed be

patterned into nanometer size structures of arbitrary shape by this fabrication method.

Effect of Various Process Parameters on the Results

In order to characterize quantitatively the CNT film and resist etch rates using the initial

ICP-RIE etch recipe given previously, a series of lines with equal width and spacing were

partially etched in 50-100 nm thick nanotube films, such that some nanotube film still remained

in the etched areas. Figure 2-4(a) shows an AFM image of such a series of lines with -200 nm

width and spacing partially etched in a 75 nm thick CNT film. Unlike the lines in Fig. 2-2(c), the

lines in Fig. 2-4(a) have not been etched all the way down to the substrate, as evident from the

texture of the remaining film visible in the etched areas. By measuring the height difference

between the partially etched and not-etched film lines using cross-sectional AFM analysis, the

average etch depth, and as a result, the etch rate can be calculated. For example, Fig. 2-4(b)

shows the cross-sectional AFM profile for the lines shown in Fig. 2-4(a), giving an average etch

depth of about 19 nm for this particular sample. Dividing this depth by the etch time of 8 s, a

nanotube film etch rate of-2.4 nm/s is obtained.

The S1813, LOR3B, and PMMA etch rates were determined by measuring the initial and

final resist thicknesses using a Nanometrics Nanospec spectrometer, and dividing by the etch

time. Using the initial recipe (i.e. 300 W ICP power, 100 W substrate bias power, 45 mTorr

chamber pressure, 20 sccm 02 flow rate, and 10 seem helium flow rate for substrate cooling),









0a). Unlike external device dimensions L, W, and t, the alignment angle 0a changes device

resistance R and noise magnitude A only implicitly by changing p and the nature of the

conduction paths. As a result, A is not normalized in this figure. Interestingly, it is evident from

Fig. 6-6(b) that CNT films with the same resistivity values can have two different noise

amplitudes, depending on their alignment angles. As the alignment angle decreases from 90,

the resistivity becomes smaller, but A remains approximately constant. However, below 06'"

[about 450 in the inset of Fig. 6-6(b)], the noise amplitude starts to increase strongly with

resistivity. A power-law fit to the noise data with an amplitude higher than 7x10-, i.e. A oc p',

yields a critical exponent of r= 1.3. It can be inferred from the trend in Fig. 6-6(b) that other

parameters being constant, partial alignment of nanotubes at the minimum resistivity angle, 06'"

, gives the lowest resistivity-lowest noise configuration; hence in order to optimize a device

design, it is better to have the nanotubes partially aligned in the film rather than perfectly

aligned.

Experimental Results

In order to understand the noise mechanisms in CNT films better, I have analyzed the

resistance and l/f noise trends in these films as a function of temperature. Figure 6-7 shows the

log-log plot of resistivity (p) versus temperature (T) for one of the devices in Set 1 with L = 1500

|tm and W= 50 |tm (This device will be called Dl from now on). It is clear that increases over

one order of magnitude as Tdecreases from 300 to 1.2 K. For CNT films, the temperature

dependence ofp depends strongly on parameters such as the doping of the film, the density and

structure of the nanotubes (e.g. diameter and length), and device dimensions [101,108]. For

example, while highly doped thick CNT films were found to show metallic behavior with very









To compliment the resistivity data, the inset of Fig. 4-10(a) shows the percolation

probability P versus nanotube alignment angle for the same set of densities, illustrating that the

percolation threshold for alignment angle is also a function of density. For example, for n = 1

tm-2, the transition from P = 1 to 0 starts when Oa becomes smaller than -300, whereas for n = 3

-2
[tm-2, it starts when Oa gets lower than -5.

Fig. 4-10(b) shows the plot of normalized resistivity versus measurement direction angle

for four nanotube densities at O = 18. The extracted measurement direction critical exponent

values are r= 1.4, 2.45, 2.9, and 3.0 for n = 1, 1.5, 2, and 3 |tm-2, respectively. This change of

with density is also less pronounced than that with nanotube length. The inset of Fig. 4-10(b)

shows the percolation probability P versus measurement direction angle for the same set of

densities, illustrating that the percolation threshold for measurement direction angle is also a


-2
strong function of density. For example, for n = 1 |tm-2, the transition from P = 1 to 0 starts when

0m becomes larger than -7, whereas for n = 3 |tm-2, it starts when 0m gets higher than -50.

Finally, Fig. 4-11 shows the plot of normalized resistivity versus nanotube alignment angle

for three device lengths L ranging from 2 to 7 |tm when Om = 0. From this figure, I extract O0'"

- 35, 45, and 45 and Kc= 0.9, 2.2, and 2.9 for L = 2, 4, and 7 |tm, respectively. When the

device length is shorter, the source and drain are connected by conduction paths consisting of

only a few nanotubes in series. However, as the device length is increased, more nanotubes are

necessary to form a conduction path, which is less likely to happen when the nanotubes become

strongly aligned. Therefore, ais higher for longer device lengths compared to shorter ones.

Similarly, 06'" shifts to higher values for longer devices. The inset also depicts normalized

resistivity versus measurement direction angle for two device lengths when O = 18. The critical









the substrate bias power can be used to control the nanotube film etch rate without significantly

changing the selectivity. Therefore, one can lower the chamber pressure to achieve the best

selectivity and then adjust the substrate bias power to achieve the optimum etch rate based on the

film thickness.

To compare the etch rates of CNT film and the three resists in an ICP-RIE system to those

in a conventional parallel plate RIE system, I have also etched the CNT film and resists using a

Plasma Sciences RIE 200W etcher, in which there is only one RF power source of 13.56 MHz

frequency, and as a result, the plasma density and the ion energy are no longer decoupled. Using

an RF power of 20 W, 02 flow rate of 12.5 sccm, and a chamber pressure of 140 mTorr, I have

observed that the etch rates of both the CNT film and resists are substantially lower in this

system, as listed in the last column of Table 2-1. The etch rate of the CNT film in the

conventional RIE system was 0.05 nm/s, which is about 5 times slower than that in the ICP-RIE

system even with a low substrate bias power of 15 W (See Table 2-1). This is due to a lower

plasma density in the conventional RIE system. Furthermore, for the conventional RIE system,

the etch selectivity between the CNT film and the resist mask has decreased to 1:2.8, 1:3.8, and

1:11 for S1813, LOR3B, and PMMA, respectively. This is due to a reduction in the physical

etching component using the conventional RIE system. These results demonstrate that the use of

an ICP etcher provides significant advantages, such as faster etch rates and better selectivity,

over conventional parallel plate plasma systems in order to be able to pattern submicron features

in nanotube films.

In the following chapters, I use the techniques developed in this chapter and pattern CNT

films for characterization and device applications.









Finally, in chapter 6, I first used Monte Carlo simulations and noise modeling to

systematically study the 1/f noise in CNT films. I demonstrated that my computational model can

fit previous experimental results on the scaling of l/f noise amplitude in CNT films. My results

show that the l/f noise amplitude depends strongly on device dimensions and on the film

resistivity, following a power-law relationship with resistivity near the percolation threshold after

properly removing the effect of device dimensions. Furthermore, the noise-resistivity and noise-

device dimension critical exponents extracted from the power-law fits are not universal

invariants, but rather depend both on the parameter that causes the change in resistivity and

noise, and the values of the other device parameters. In addition, the simulation fit to the

experimental data strongly suggests that tube-tube junctions, and not the nanotubes themselves,

dominate the overall CNT film 1/f noise.

I then studied experimentally the variation of resistivity and l/f noise as a function of

temperature and concluded that at very low temperatures (< 40 K) 3D variable range hopping is

the dominant mechanism for both resistivity and 1/f noise. At temperatures above 40 K,

however, the fluctuation induced tunneling model explains the resistivity behavior. The noise

amplitude exhibited a minimum at around 40 K and then started to increase with increasing

temperature. In the high temperature regime, the density of fluctuators as a function of energy,

extracted from the temperature dependence of noise amplitude, depicted a peak at around 0.3-0.6

eV. The fluctuations within or at the surface of the SiO2 substrate underneath the CNT film

could be the source of this peak and therefore the dominant source of the noise at high

temperatures.

Future Works

The work presented in earlier chapters open up the possibility to further study various

aspects of CNT film properties. First, the model developed for the CNT film in chapter 4 can be









semiconducting nanotube case, a significant portion of the noise observed at room temperature in

CNT films can also be related to the fluctuation of trapped charges in the oxide.

Based on Dutta et al. [189], there should also be a relationship between the frequency

scaling exponent /f and the dependence of A on temperature in the form [189]


lc I lnA 11 (6-9)
Iln(2zfz'o) aIn T "

In order to check the accuracy of Eq. (6-8) for CNT films, the inset in Fig. 6-9 compares

the values of f as a function of Tthat are extracted from the experimental results and calculated

from Eq. (6-9). The agreement between the two sets is very good for T> 40 K (above the VRH

regime) and so the relationship between the energy distribution of fluctuations and the

temperature scaling of the noise amplitude stated in Eq. (6-8) is correctly established.

As mentioned before, the value of A at room temperature is about 4 orders of magnitude

larger for device D2 compared to Dl (see Fig. 6-8). This difference is due to two reasons: First,

the dimensions ofD2 (L = 50 |tm and W= 0.4 [tm) are significantly smaller compared to those of

Dl (L = 1500 |tm and W= 50 [tm). As I have shown above for CNT films, A is almost inversely

proportional to the total number of carriers (N) and hence inversely proportional to both L and W

in the region that film resistivity is constant (i.e. well above the percolation threshold) [169,193].

As a result, the large difference between the dimensions of the two devices can partially explain

the difference in their A values. As a reminder, Fig. 6-10(a) shows the strong dependence of the

noise amplitude normalized to resistance (AIR) at room temperature versus device length (L) for

four devices in Set 1. Also shown in this figure are my Monte Carlo simulation results,

described in detail previously. This figure is similar to the one that is shown in Fig. 6-3(b). The









noise-resistivity critical exponent is not a universal invariant, rather it depends on the parameter

that is causing the change in the 1/f noise.

Effect of Device Thickness and Tube Alignment Angle

As we have seen in Fig. 6-3(b), CNT film thickness has a strong effect on the noise scaling

with device length. Several studies have shown that film thickness t also has a strong effect on

the CNT film resistivity, especially for extremely thin films [62,113]. Recently, Soliveres et al.

have experimentally studied the dependence of the 1/f noise amplitude on film thickness [172].

Next, I investigate this dependence by my simulations.

The left inset of Fig. 6-6(a) shows log-log plot of resistivity versus number of layers (i.e.

thickness) where resistivity is almost constant for films with 10 layers or more, while strong

inverse power law dependence of resistivity on thickness exists for thin films near the

percolation threshold. As a result, like device width, film thickness can be expected to have a

strong impact on noise, as shown by the experimental results of Soliveres et al. [172]. The main

panel of Fig. 6-6(a) shows the log-log plot of the noise amplitude normalized by thickness A x t

versus resistivity computed for the same CNT film device as in the inset. Similar to the width

case, the normalized amplitude A x t is used because A varies with thickness linearly in the

regime when resistivity is constant. The simulation data can be fit by A x t c p", where the

extracted critical exponent is v= 1.8. These results can be compared to the experimental data of

Soliveres et al. [172]. Although they report a critical exponent for A, not A x t, renormalization

of their data gives v= 1.1. The disagreement in the simulation (1.8) and experimental (1.1)

critical exponents reported is most likely due to differences between other device/nanotube

parameters, such as density per layer, and the film properties such as the purity and homogeneity

of the deposited CNT film.









CHAPTER 7
CONCLUSIONS AND FUTURE WORKS

Summary of Results

The main scope of this work was to study CNT film electrical properties using both

experimental and simulation approaches and to further evaluate its potential as a transparent

conductive electrode for applications such as optoelectronics and flexible electronics.

In chapter 2, I developed the nanolithographic patterning capability that would open up

significant opportunities for fabricating and integrating single-walled nanotube films into a wide

range of electronic and optoelectronic devices. I demonstrated the ability to efficiently pattern

CNT films with good selectivity and directionality down to submicron lateral dimensions by

photolithography or e-beam lithography and 02 plasma etching using an ICP-RIE system. I

systematically studied the effect of ICP-RIE etch parameters on the nanotube film etch rate and

etch selectivity. Decreasing the substrate power from 100 W to 15 W, decreased the nanotube

film and resist etch rates by about a factor of 10. Decreasing the chamber pressure from 45

mTorr to 10 mTorr increased the nanotube film and resist etch rates by a factor between 1.7 and

3.5. It also increased the etch selectivity between the nanotube film and the resist masks. On the

other hand, increasing the chamber pressure from 45 mTorr to 100 mTorr did not change the etch

rates of the nanotube film and resists significantly. Similarly, increasing the helium flow rate

(which actively cools the substrate) from 10 sccm to 40 sccm did not produce a significant

change on the etch rates of the CNT film and the three resists. Furthermore, the CNT film etch

rate was found to be independent of the line width etched for linewidths ranging from 50 |tm

down to 100 nm. In addition, by comparing the etch rates of CNT film and the three resists in an

ICP-RIE system to those in a conventional parallel plate RIE system, I demonstrated that using

an ICP-RIE system provides significant advantages, such as faster etch rates and better etch









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100





S10
0

z

1


(a) n 1. Opm-
n- 1.5 jm- 2
Sn = 2. Opm'
A n 3- pm


1



0 *

1 10
*, Nanotube Alignment
.. Angle ()


T o41
S, -
V V
Ai n
A A AAA.&1


10
Nanolube Alignment Angle (o)


10
Measurement Direction Angle ()


Figure 4-10. Effect ofnanotube density on resistivity scaling with nanotube alignment angle and
measurement direction angle: (a) Log-log plot of normalized resistivity versus
nanotube alignment angle for four nanotube densities per layer ranging from 1 to 3
pm-2 when O,= 0. O0,"' values are located at ~ 500, 450, 45, and 400 and K = 2.8,
-2
3.0, 2.9, and 2.9 for n = 1, 1.5, 2, and 3 m-2 respectively. The inset shows the
percolation probability versus nanotube alignment angle 0a for the same set ofn. (b)
Log-log plot of normalized resistivity versus measurement direction angle for four
-2
nanotube densities per layer ranging from 1 to 3 tm-2 when 0 = 18. The inset shows
the percolation probability versus 0m for the same set ofn.


100(b)
(b)









nanotube length distribution on the resistivity. I find that, for junction resistance-dominated

random networks, such as CNT films, the resistivity correlates with root mean square (RMS)

element length and not the average length. In chapter 5, I demonstrate the Schottky behavior of

CNT film contacts on GaAs and Silicon by fabricating and characterizing Metal-Semiconductor-

Metal photodetectors with CNT film electrodes. I determine the mechanisms responsible for the

transport and extract the Schottky barrier height of CNT film contacts on GaAs and Si by

measuring the dark I-Vcharacteristics as a function of temperature. Furthermore, I characterize

the effect of device geometry on the dark current and compare the dark and photocurrent of the

CNT film-based photodetectors with standard metal-based ones. In chapter 6, I study both

theoretically and experimentally the low frequency l/f noise in CNT films and its scaling with

device dimensions, as well as with temperature. On the computational front, I consider noise

sources due to both tube-tube junctions and nanotubes themselves. By comparing the simulation

results with my own and previous experimental data, I determine which noise source is the

dominant one. I also systematically study the effect of device length, device width, and film

thickness, and nanotube degree of alignment on the l/f noise scaling in CNT films. I study the

temperature dependence of l/f noise in CNT films experimentally by fabricating four-point-

probe structures and measuring their resistivity and noise amplitude as a function of temperature

and frequency. I analyze the resistivity data to determine the mechanisms that are responsible for

electronic transport in CNT films in various temperature regimes. I then interpret my noise data

in accordance with the resistivity results, considering different transport mechanisms that might

be responsible for both. Finally, in chapter 7 I summarize my findings and future possibilities.




Full Text

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1 FABRICATION, CHARACTERIZATION AND MODELING OF SINGLE -WALLED CARBON NANOTUBE FILMS FOR DEVICE APPLICATIONS By ASHKAN BEHNAM A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Ashkan Behnam

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3 To my beloved parents

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4 ACKNOWLEDGMENTS First and foremost, I express my gratitude to my supervisor, Prof Ant Ural for his support and guidance throughout my Ph.D. research. He allowed me to become engaged in various projects while allocating a significant portion of his time for dis cussing research topics I have always appreciated his stab ility and patience. I also thank Prof. Gijs Bosman for all the time and energy he spent on teaching me various noise concepts and advising me on various subjects. I am very gratitude for his compassion and opennes s. I thank Prof s Jing Guo and Jerry Fossum for their support and the discussions we had and also Prof. Kirk Ziegler for acting as one of my thesis committee members. I thank Profs. Andrew Rinzler and Amlan Biswas and Dr. Zhuangchun Wu for providing us with raw material s and assisting us with measu rements. I thank Profs. David Arnold, Toshi Nishida, Peter Zory and Scott Thompson for offering interest ing courses. I thank my colleagues and friends Yongho Choi, Jason Johnson and Jeremy Hicks for all the time we spent together whether on research or on other subjects. I also thank Yanbin An, Nischal Arkali Radhakrishna Karthik Nishwanatan Leila Noriega, Carlos Torres, Keith Knauer, Alan T e ran, Moon Hee K ha ng, Aditti Sharma and Ryan Moreau from the nanotech group, Dr. Shahed Reza from the noise lab, Srivatsan Parthasarathy and Andrew Koehler from Swamp center, Siddharth Chouksey from SOI group and the rest of my kind and helpful ECE colleagues and friends. I express my gratitude to Alvin Ogden at NRF for all the help an d advice throughout the years and also appreciate the help from Ivan Kravchenko and Bill Lewis from NRF, Kerry Siebein from MA IC and Magie Puma Landers from Microfabritech I thank all of my friends and roommates in Gainesville over the last few years for their support and companionship. Thes e are the names that come to my mind chronologically sorted : Farzad Fani Pakdel, Masoumeh Rajabi, Alej andro P ara Reza Mahjourian, Hsiu Shan Liu, Sanam

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5 Dolatshahi, Babak Mahmoudi, Ayyoub Mehdizadeh, Danial Sabri Dasht i, Behnam Behdani, Moojan Daneshmand, Zahra Nasrollahi, Saeed Moghaddam, Romina Mozaffarian, Azam Feiz, Sahar Mirshamsi, and Negin Jahanmiri I also acknowledge the efforts of Debra Anderson, Maud Frazer and the rest of people at international center for providing a friendly environment for international students I also thank all of my professors, colleagues and friends back in Iran and in US who have continuously supported me all this time and wish them the best in their lives. My deep est gratitude goes to my family my parents Parviz and Soudabeh and my sister Niloofar for their endless love compassion and support without which I would not be able to follow my research in peace. My appreciation for the effect they had on my life goes beyond any wo rds.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 8 LIST OF FIGURES .............................................................................................................................. 9 ABSTRACT ........................................................................................................................................ 12 CHAPTER 1 SINGLE -WALLED CARBON NANOTUBE NETWORKS AND FILMS .......................... 14 Introduction ................................................................................................................................. 14 Single -W alled Carbon Nanotube (CNT) Films ......................................................................... 15 Organization ................................................................................................................................ 17 2 FABRICATION AND PATTERNING OF CNT FILMS ........................................................ 22 Introduction ................................................................................................................................. 22 Fabrication and Patterning Process ............................................................................................ 23 Effect of Various Process Parameters on the Results ............................................................... 26 3 EXPERIMENTAL STUDY OF RESISTIVITY SCALING IN CNT FILMS ....................... 34 Introduction ................................................................................................................................. 34 Resistivity Scaling with Device Dimensions ............................................................................ 35 Resistivity Dependence on Process Parameters ........................................................................ 38 4 COMPUTATIONAL STUDY OF RESISTIVITY SCALING IN CNT FILMS ................... 42 Introduction ................................................................................................................................. 42 Modeling Approach .................................................................................................................... 43 Results and Discussion ............................................................................................................... 45 Effect of Resistance Ratio ................................................................................................ 49 Effect of Nanotube Density .............................................................................................. 50 Effect of Nanotube Length ............................................................................................... 51 Effect of Nanotube Alignment ......................................................................................... 53 Effect of Length Distribution ........................................................................................... 62 5 METAL SEMICONDUCTING -METAL PHOTODETECTORS BASED ON CNT FILM GAAS AND CNT FILM -SI SCHOTTKY CONTACTS .............................................. 81 Introduction ................................................................................................................................. 81 Characteristics of MSM Photodetectors .................................................................................... 82

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7 Fabrication and Characterization of MSM Photodetectors ...................................................... 87 6 1/f NOISE SCALING AND TEMPERATURE DEPENDENT TRANSPORT IN CARBON NANOTUBE FILMS ............................................................................................. 108 Introduction ............................................................................................................................... 108 Computational Mode ling Approach ......................................................................................... 110 Experimental Procedure ............................................................................................................ 113 Simulation Results .................................................................................................................... 115 Effect of De vice Length .................................................................................................. 115 Effect of Device Width ................................................................................................... 120 Effect of Device Thickness and Tube Alignment Angle .............................................. 122 Experimental Results ................................................................................................................ 124 7 CONCLUSI ONS AND FUTURE WORKS ........................................................................... 139 Summary of Results .................................................................................................................. 139 Future Works ............................................................................................................................. 143 APPENDIX : ELECTRIC AND MAGNETIC FIELD DEPENDENCE OF THE CNT FILM RESISTIVITY IN THE VRH REGIME ................................................................................. 145 LIST OF REFERENCES ................................................................................................................. 148 BIOGRAPHICAL SKETCH ........................................................................................................... 159

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8 LIST OF TABLES Table page 2 1 Etch rates of the CNT film and three different resists (S1813, LOR3B, and PMMA) under different plasma etch conditions ................................................................................. 33 3 1 Average nanotube film resistivity values measured using standard four point probe structures ................................................................................................................................. 41 5 1 Device dimensions and extracted barrier heights for 8 n -type and 5 p-type Si -based MSM structures.. .................................................................................................................. 105

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9 LIST OF FIGURES Figure page 1 1 Scanning Electron Microscope (SEM) images of 1.5 mm long single -walled carbon nanotubes ................................................................................................................................ 19 1 2 Room -temperature electrical properties of a high performance carbon nanotube field effect transistor. ...................................................................................................................... 19 1 3 Transmittance spectra for two CNT films ............................................................................ 20 1 4 Various applications of CNT films ....................................................................................... 21 2 1 The schematic of the ICP RIE system .................................................................................. 31 2 2 CNT film patterning results studied by AFM ....................................................................... 31 2 3 CNT film patterning results studied by SEM: ...................................................................... 32 2 4 Nanoscale CNT film patterning results studied by AFM .................................................... 32 3 1 Optical microscope image of a four point probe struc ture .................................................. 4 0 3 2 Effect of device length and film thickness on resistivity ..................................................... 40 3 3 Effect of device width on resistivity ..................................................................................... 41 4 1 Comparison of the texture of computationally and experimentally generated CNT networks .................................................................................................................................. 69 4 2 Computational analysis of the effect of device length and width on normalized resistiv ity ................................................................................................................................. 70 4 3 Effect of resistance ratio on resistivity .................................................................................. 71 4 4 Effect of nanotube density on resistivity and percolation probability ................................ 72 4 5 Effect of nanotube length on resistivity ................................................................................ 73 4 6 A 2D nanotube network generated using a Monte Carlo process ....................................... 74 4 7 Effect of nanotube alignment angle on resistivity scaling with device width .................... 74 4 8 Effect of nanotube alignment angle and measurement direction angle on resistivity ....... 75 4 9 Effect of nanotube length on resistivity scaling with nanotube alignment angle and measurement direction angle ................................................................................................. 76

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10 4 10 Effect of nanotube density on resistivity scaling with nanotube alignment angle and measurement direction angle ................................................................................................. 77 4 11 Effect of device length on resistivity scaling with nanotube alignment angle ................... 78 4 12 Generated CNT networks consisted of nanotubes with a length distribution .................... 78 4 13 Effect of nanotube length distribution on resistivity ............................................................ 79 4 14 Effect of nanotube length distribution on percolation probability ...................................... 80 4 15 Effect of nanotube length distribution on resistivi ty scaling with alignment angle ........... 80 5 1 Schematics of MSM structure ............................................................................................... 98 5 2 Physical representation of MSM structure ........................................................................... 98 5 3 Band diagrams of the symmetric MSM structure ................................................................ 98 5 4 Calculated current density versus applied bias for a symmetric GaAs MSM structure .... 99 5 5 Responsivity for an ideal (dotted line) an d a real (solid line) photodetector .................... 99 5 6 Fabrication of GaAs -based MSM photodetectors .............................................................. 100 5 7 Fabrication of Si -based MSM photodetectors .................................................................... 101 5 8 Si -based MSM dark characteristics ..................................................................................... 101 5 9 Temperature -dependence of the GaAs -based MSM dark current ..................................... 102 5 10 Characterization of asymm etric GaAs -based MSM structures ......................................... 103 5 11 Temperature -dependence of the Si -based MSM dark current ........................................... 104 5 12 Dependence of MSM current on device and finger dimensions ....................................... 106 5 13 Measured dark and photocurrent versus applied voltage for GaAs -based MSM photodetectors ....................................................................................................................... 107 5 14 Measured dark and photocurrent applied voltage for Si -based MSM photodetectors ..... 107 6 1 Effect of device length and film thickness on experimentally measured noise ............... 131 6 2 Experimental and computational analysis of noise ............................................................ 132 6 3 Effect of device length on noise .......................................................................................... 133 6 4 Effect of resistivity change due to device length on noise ................................................ 134

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11 6 5 Effect of device width on noise ........................................................................................... 135 6 6 Effe ct of device thickness on noise ..................................................................................... 136 6 7 Effect of temperature on resistivity ..................................................................................... 137 6 8 Effect of temperature on noise ............................................................................................ 137 6 9 Dependence of density of states on energy ........................................................................ 138 6 10 Experimental observation of the effect of device length and width on noise .................. 138 A 1 Effect of electric field on resistance at very low temperatures ......................................... 147 A 2 Effect of magnetic field on resistance at very low temperatures ...................................... 147

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12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CHARACTERIZATION AND MODELING OF SINGLE -WALLED CARBON NANOTUBE FILMS FOR DEVICE APPLICATIONS By A shkan Behnam Aug ust 2010 Chair: Ant Ural Major: Electrical and Comp uter Engineering The main goal of this dissertation was to study electrical properties of single -walled carbon nanotube (CNT) films as new conductive and transparent materials. F irst the a bility to efficiently pattern C NT films with good selectivity and directionality down to submicron lateral dimensions by photolithography or e beam lithography and oxygen plasma etching was demonstrated and the effect of etch parameters on the nanotube film etch rate and selectivity was studied Then by fabricating standard four -point -probe structures using this technique it was demonstrated that the resistivity of the films increases over three orders of magnitude as their width and thickness shrink close to the percolation threshold. A Monte Carlo simulation platform was then developed to model percolating conduction in CNT films, which could fit the experimental results and confirm the strong scaling of resistivity with various nanotube and device parameters These experimental and c omputational capabilities were then used to study the 1/ f noise behavior in CNT films T he results from the computational calculations were in good agreement with previous experiments It was shown that the 1/ f noise amplitude depends strongly on both device dimensions and on the film resistivity. The variation of resistivity and 1/ f noise as a function of temperature was then studied experimentally and it was concluded that at very low temperatures 3D variable range hopping was the dominant mechanism for both. At

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13 40 K and above however, the fluctuation induced tunneling model expl ain ed the resistivity behavior and t he fluctuations within or at the surface of the SiO2 substrate underneath the CNT film were the probable dominant source of the noise in this regime Finally, metal semiconductor -metal photodetectors were fabricated based on CNT film Ga llium A r s enide (GaAs) and CNT film -Si licon(Si) Schottky contacts to show the applica tion of CNT film in optoelectronic devi c es T he Schottky barrier height s of CNT film contacts on GaAs and Si were extracted by measuring the dark I -V characteristics in the thermionic emission regime The extracted barrier height s correspond ed to a CNT film workfunction of about ~ 4.6 eV, which was in excellent agreement with previously reported values.

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14 CHAPTER 1 SINGLE -WALLED CARBON NANOTUBE NETWORKS AND FILMS Introduction Single -walled carbon nanotubes ( CNT s) have attracted significant research attention in the last decade because of their remarkable physical and electronic properties including their high mobility current density, me chanical strength, high surface -to -volume and length to -diameter aspect ratio s [1 13] In addition, small and medium scale growth/fabrication of nanotubes is readily available with approaches such as arc -discharge, laser ablation and chemical vapor deposition (CVD) being the more common ones (Fig. 1 1 [14] ). These favorable properties have encourag ed several groups to try to incorporate nanotubes in various device structures to improve their performance. For example, because of the existence of semiconducting nanotubes that show short range ballistic transport characteristics even at room temperatur e several groups have utilize d them as the channel material for nano -scale transistors [11,12,1529] An example of a field effect transistor successfully fabricated is shown in Fig. 1 2 [28] In these structures, the bandgap and doping density of the channel are controlled by the diame ter/chirality of the tube and the environment that it is exposed to. Metallic nanotubes also have applications of their own, such as interconnect s [30 35] In general, electronic properti es of nanotubes (such as their Fermi level) vary in response to th eir environment due to their small diameter, exposed atoms and large surface to volume ratio. Therefore, they are very suitable for gas and molecule sensing applications [36 41] Their mutual electrical and mechanical properties have also encouraged their use in applications such as nano -composites and Atomic Force Microscopy (AFM) tips [42 47] O th er nanotube applications include Field Emission Displays (FED) [48,49] and single electron transistors [13]

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15 Despite all these outstanding properties, controlling the diameter, chirality, location, and direction of individual nanotubes has proven to be very challenging [50] The control over some of these parameters is necessary for successful commercialization of the applications that depend on the superb properties of individual nanotubes. Up to date, the efforts to improve the fabrication process of carbon nanotubes include the use of 1) electric field to control the direction of nanotubes during CVD growth [51,52] (not very flexible and only suitable for small scale fabrication ) 2) PECVD [53] (e.g. microwave plasma, very successful but only for vertical al ignment), 3) self assembly techniques using DNAs, molecules and polar materials for alignment and positioning [54 56] (good results, sometimes incompatible with current device fabrication technology) 4) gas flow techniques [57] (local, non uniform, small scale) a nd 5) special substrates such as quartz [58] (not very suitable for device fabrication) Other less develo ped and more difficult approaches use magnetic field, multilayers of catalyst particles and surface topography to achieve positioning and alignment But still lack of reproducibility, reliability, and manufacturability of nanoelectronic devices based on individual CNTs remains the showstopper in carbon nanotube research. In this thesis I am going to focus on a carbon nanotube -based material that does not have these limitations. Single Walled Carbon N anotube (CNT) F ilm s A single -walled carbon nanotube (CNT) film is a three -dimensional film of tens of nanometers thickness, consisting of an interwoven mesh of single -walled nanotubes, as shown in the inset of Fig. 1 3 [59] The CNT film exhibits uniform physical/electronic properties independent of the diameter, chirality, location, and directio n of individual tubes making up the film [50] due to ensemble averaging [60 64] As a result, it is highly manufacturable c ompared to individual nanotubes Furthermore, the CNT film is simultaneously conductive (resistivity ~104 cm) and optically transparent over the visible and near -infrared portions of the spectrum

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16 [61,63,65] For example, it has been demonstrated that an as prepared nanotube film of 50 nm thic kness has a transmittance greater than 70% over the visible part of the spectrum, and this transmittance increases to more than 90% in the near IR, as shown in Fig. 1 -3 [61] The resistivity and transmittance of CNT films in the visible and infrared range are comparable to transparent, conductive oxides, such as indium tin oxide (ITO), which are commonly used as electrodes in optoelectronic device applications [61,66,67] ITO, however, is brittle, and repeated be nding of ITO layers lead to cracking and delamination [68] CNT films, in contrast, combine strength and flexibility, and exhibit extreme durability during bending [69] These outstanding properties establish CNT films as a new class of optically transparent, electrically conducting, and mechanic ally flexible electrodes that can be easily integrated with conventional semiconductors for use in photovoltaic and optoelectronic devices. Several promising device applications of CNT films have recently been demonstrated, such as ohmic contacts in organic and GaN light -emitting diodes (LEDs) [70 73] organic solar cells [74 77] and electrochromic devices [78] thin film transistors [79 82] flexible microelectronics [69,8385] and MEMS and chemical sensors [59,8692] Two of these applications are shown in Fig. 1 -4. I am interested not only in developing practical methods to incorporate CNT films in various device structures, but also in study ing the electronic and optical properties of CNT films as well as the ir interface with common semiconductors such as Si licon (Si) and Gallium Arsenide ( GaAs ). The interest is partially due to the complex structure of t he CNT film: As a percolation system composed of nanotubes with nano-scale diameters and micron -scale lengths, CNT film properties should depend strongly on the interaction between nanotubes, their or ganization within the film and the dimensions of the film relative to those of nanotubes. A better physical understanding of geometrydependent percolating transport in single -walled

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17 carbon nanotube films is essential for characterizing and evaluating thei r performance in potential electronic and optoelectronic device applications. Organization This thesis is organized as follows. In chapter 2, I show successful patterning of CNT films down to 100 nm lateral dimensions by photolithography or e -beam lithogra phy and subsequent O2 plasma etching using an inductively coupled plasma reactive ion etching system I systematically study the effect of ICP RIE etch parameters, such as substrate bias power, chamber pressure, and substrate cooling on the nanotube film etch rate and etch selectivity and demonstrate the advantages of ICP RIE system over conventional parallel plate RIE plasma systems. I also characterize the effect of the line width etched on the nanotube film etch rate for widths ranging from 50 m down to 100 nm I study the transport characteristics of the films patterned into four point probe structures (with down to 200 nm lateral dimensions ) as a function of their dimensions in chapter 3. I depict that the resistivity of the films is independent of device length, while increasing over three orders of magnitude compared to the bulk films, as their width and thickness shrink Furthermore, I investigate the effect of different resist processes on the resistivi ty of patterned C NT films, and the effect of ICP reactive ion etching on the resistivity of partially etched films. Chapter 4 is devoted to my investigation of geometry -dependent resistivity scaling in CNT films as a function of nanotube and device paramet ers using Monte Carlo si mulations. I first demonstrate that these simulations can model and fit the experimental results on the scaling of the film resistivity with device width. Then I systematically study the effect of four parameters, namely tube tube contact resistance to nanotube resistance ratio, nanotube density, nanotube length, and nanotube alignment on the film resistivity an d its scaling with device width providing explanation for the trends observed. I also study the effect of the

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18 nanotube length distribution on the resistivity I find that, for junction resistance -dominated random networks, such as CNT films, the resistivity correlates with root mean square (RMS) element leng th and not the average length. In chapter 5, I demonstrate the Schot tky behavior of CNT film contacts on GaAs and Silicon by fabricating and characterizing Metal -Semiconductor Metal photodetectors with CNT film electrodes. I determine the mechanisms responsible for the transport and extract the Schottky barrier height of CNT film contacts on GaAs and Si by measuring the dark I -V characteristics as a function of temperature. Furthermore, I characterize the effect of devi ce geometry on the dark current and compare the dark and photocurrent of the CNT film based photodetectors with standard me tal -based ones. In chapter 6 I study both theoretically and experimentally the low frequency 1/ f noise in CNT films and its scaling with device dimensions, as well as with temperature. On the computational front, I consider noise source s due to both tube tube junctions and nanotubes themselves. By comparing the simulation results with my own and previous experimental data, I determine which noise source is the dominant one. I also systematically study the effect of d evice length, device width, and film thickness, and nanotube degree of alignment on the 1/ f noise scaling in CNT films. I study the temperature dependence of 1/ f noise in CNT films experimentally by fabricating four point probe structures and measuring their resistivity and noise amplitude as a function of temperature and frequency. I analyze the resistivity data to determine the mechanisms that are responsible for electronic transport in CNT films in various temperature regime s. I then interpret my noise data in accordance with the resistivity results, considering different transport mechanisms that might be responsible for both. Finally, in chapter 7 I summar ize my findings and future possibilitie s.

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19 Figure 1 1 Scanning Electron Microscope (SEM) images of 1.5 mm long single -walled carbon nanotubes grown using a CVD approach [14] Figure 1 2 Room -temperature electrical properties of a high -performance carbon nanotube field effect transistor with diameter of 3.5 nm and channel length of 3.5 m (taken from [28] ): (a) Transfer characteristics under three different drain -source voltages (b) Output characteristics under 8 different gate -source v oltages from 0.5 V to 7.5 V in steps of 0.5 V.

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20 Figure 1 3 Transmittance spectra for two CNT films of thickness 50 nm (on quartz) and 240 nm (free -standing) [61] The curves with greater transmittance (upper left) are for the 50 nm film. Gray curves denote the charge -transfer, hole -doped films and black curves denote those films after dedoping. The inset shows an AFM image of a CNT film of 25 nm thickness [59]

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21 Figure 1 4 Various applications of CNT films: (a) SEM image of an opto-mechanical actuator composed of bi -layer beams of CNT film(CNF) and SU8 [92] Inset shows a 3 3 3 actuator array. (b) SEM image of the squared region in (a) showing the bilayer cross section of the actuator. The inset shows the profile of the CNT film patterned. (c) The displacement of the CNT film/SU8 actuator as a function of the laser intensity. (d) Optical microscope image of an array of CNT film TFTs on plastic [93] Inset shows an SEM image of channel. (e) Transfer char acteristics of the CNT film TFT. Channel length and channel width are 100 and 250 m, respectively, and drain -source voltage is 0.5 V. Inset shows the output characteristics when gate -source is ranging from 100 to 0 V with steps of 10 V. (f) Device mobi lities versus channel length on plastic (squares) and on the SiO2 /Si CVD growth substrate (circles). Inset shows the on/off ratio versus channel length. A 100 nm thick layer of SiO2 formed the gate dielectric in the latter case, while a 1.7 m thick layer of epoxy formed the gate dielectric in the former case.

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22 CHAPTER 2 FABRICATION AND PATT ERNING OF CNT FILMS Introduction Any potential device application utilizing CNT films requires the capability to efficiently pattern them. Nanotube networks have been patterned recently by a variety of techniques including the use of a CO2 snow jet [64] transfer printing [60,94] and O2 plasma etching [79] in the micron regime. In addition, more recently, nanotube films with various thicknesses have b een patterned into micron size features using photolithography and inductively coupled plasma (ICP) reactive ion etching (RIE) [92] Although line widths down to about 1.5 m have been success fully patterned using this method, patterning of submicron features in CNT films has not been demonstrated. Moreover, the effect of ICP RIE etch parameters on the CNT film etch rate and etch selectivity has not been systematically characterized. In this chapter I use photolithography or e -beam lithography, and subsequent O2 plasma etching in an ICP RIE system to pattern nanotube films down to submicron lateral dimensions. I experimentally show that features with linewidths less than 100 nm can be succes sfully patterned using this technique with good selectivity and directionality. In addition, I systematically study the effect of ICP RIE etch parameters, such as the substrate bias power and chamber pressure, on the CNT film etch rate and etch selectivit y. I also compare O2 plasma etching of CNT films in an ICP RIE system to that in a conventional parallel plate RIE system. I find that using an ICP -RIE system significantly increases the CNT film etch rate and improves the etch selectivity between the CN T film and polymethyl methacrylate (PMMA) compared to a conventional RIE system, making it possible to pattern CNT films down to ~100 nm lateral dimensions by e beam lithography.

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23 Fabrication and P atterning P rocess CNT films were deposited by a vacuum filtration method as described in detail in a few publications [59,61,70] In summary, a dilute suspension of purified CNT s was vacuum -filtered onto a filtration membrane. The nanotubes used in the film were grown by dual pulsed laser vaporization. The nanotubes deposit as a thin film on the membrane with the thickness of the film controlled by the concentration of nanotubes in the suspension and the volume of the suspension filtered. During the film formation, the first nanotubes to land on the flat membrane surface are forced to lie parallel to the surface. Subsequently deposited nanotubes take on the same planar orientations. The result is a film morphology where the nanotubes have random in plane orientations bu t are preferentially aligned parallel to the surface of the substrate. After the filtration step, the film can be transferred onto a desired substrate by placing the film side against the substrate, applying pressure, and drying the film. To complete the p rocess, the filtration membrane is dissolved in a solvent, leaving only the nanotube film adhered to the substrate. Since the growth process produces nanotubes with a wide length distribution and most nanotubes in the film are entangled it is difficult to precise ly determine the length of the nanotubes used in the film. However, b ased on further AFM measurements, it is estimated that most nanotubes in the film have lengths in the range 1 10 m. Following the deposition step, the CNT film was patterned either by photolithography or e beam lithography. For photolithography, three different types of resist processes were used as the mask. The first process used a 1. 3 m thick layer of Shipley Microposit S1813 photoresist. It was found by extensive AFM imaging that when the S1813 resist is deposited directly on top of individual nanotubes, it leaves a residue [95] On the other h and, it was observed that Microchem LOR3B lift off resist and PMMA do not contaminate the nanotubes [95] The

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24 LOR3B lift -off resi st can be removed by standard developer solutions, with the dissolution rate determined primarily by the pre bake temperature. To protect the CNT film from potential contamination due to the S1813 resist, for the second process, a dual layer resist structure consisting of a 1.3 m thick S1813 layer on top of a 250 nm thick LOR3B layer was used. Finally, for the third process, a dual layer resist process consisting of a 1.3 m thick Shipley S1813 layer on top of a 250 nm thick PMMA layer (950K 4% in a nisol e) was used. Since the S1813 resist is not in direct contact with the nanotubes in the second and third processes, no residue is left on the nanotube film during fabrication. However, PMMA cannot be exposed by the 365 nm light source available in the Kar l Suss MA 6 contact mask aligner that was used for photolithography. As a result, for the third process, the S1813 layer was first exposed by the mask aligner and developed. Subsequently, the PMMA layer was patterned by O2 plasma etching with the S1813 l ayer acting as the mask. In all three resist processes, Shipley Microposit MF319 was used as the developer. The particular resist process used was found to affect the resistivity of the CNT film, as presented in detail later For e -beam lithography, a si ngle layer of PMMA ( 950K 2 or 4 % in a nisole depending on the feature size patterned and PMMA thickness desired) was used as the masking layer, and a Raith 150 e -beam writer was used for exposure. After exposure and development, the nanotube film not protected by the resist mask was etched using an O2 chemistry in a Unaxis Shuttlelock ICP RIE system. The schematic of the ICP etcher is shown in F ig 2 1. The ICP RIE system decouples plasma density (controlled by the ICP power supply) and ion en erg y (controlled by the substrate power supply) As a result, compared to conventional diode RIE system s, very high plasma densities (>1011 ions cm3) can be achieved at lower pressures resulting in more anisotropic etch profiles and significantly higher et ch rates [96,97] Etching in ICP systems has a large physical component combined with

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25 a smaller chemical component. O2 plasma is commonly used for removing organic materials such as photoresist and has also been used to etch carbon nanotubes [79,92] The reaction between oxygen and organic materials produces volatile species such as CO and CO2, which are pumped out during the etch process [96] The etch parameters for my initial CNT etch recipe were 300 W power on the 2 MHz ICP RF supply, 100 W power on the 13.56 MHz substrate RF supply 45 mTorr chamber pressure, and a 20 sccm O2 flow rate. In addition, a helium flow rate of 10 sccm was used to cool down the substrate. In the next section, I discuss how changing various etch parameters affects the etch rates of the CNT film and resists. After the ICP -RIE etch, the resist mask layers were stripped in acetone when S1813 or PMMA were used as the mask, and in Microchem Nanoremover PG when LOR3B was included in the mask since LOR 3B does not dissolve in acetone. Resulting CNT film etch profiles were characterized by a Digital Instruments Nanoscope III AFM. Figure 2 2(a) shows the AFM image of a ~3 m line etched in a ~20 nm thick nanotube film using the LOR3B/S1813 dual resist photolithography process (i.e. the second process) and the initial ICP etch recipe given previously. The cross -sectional height profile for the same AFM image is plotted in Fig. 2 2(b), showing clearly the transition between the fil m and the etched regions. Similar etch profiles were ob tained using the other two resist processes described previously. Figure 2 2 (c) shows an AFM image of a series of lines with nanotube film width and spacing of about 5 00 nm patterned by e -beam lithog raphy and ICP etching of a CNT film of about 20 nm thickness. The cross -sectional height profile for the same AFM image is plotted in Fig. 2 2(d), showing a clear transition between the film and the etched regions even at these submicron lateral dimension s

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26 The etch profiles in Figs. 2 2 (b) and 2 2 (d) are not sufficient to determine how sharp the actual etch profile is, since the radius of curvature and the sidewall angle of the AFM tip could decrease the sharpness of the observed transition profile. Figs. 2 3(a) and (b) show SEM images, respectively, of concentric nanotube film rings and letters printed in nanotube film using e -beam lithography and ICP etching The width of the text characters are on the order of 200300 nm and the CNT film thickness is 20 nm, demonstrating that the nanotube film can indeed be patterned into nanometer size structures of arbitrary sha pe by this fabrication method. Effect of V arious P rocess P arameters on the R esults In order to characterize quantitative ly the CNT film and resist etch rate s using the initial ICP RIE etch recipe given previously, a series of lines with equal width and spacing were partially etched in 5 0 100 nm thick nanotube film s, such that some nanotube film still remained in the etched areas. Figure 2 4(a) shows an AFM image of such a series of lines with ~200 nm width and spacing partially etched in a 75 nm thick CNT film. Unlike the lines in Fig. 2 2 (c), the lines in Fig. 2 4(a) have not been etched all the way down to the substrate, as evident from the texture of the remaining film visible in the etched areas. By measuring the height difference between the partially etched and not -etched film lines using cross -sectional AFM analysis, the average etch depth, and as a result, the etch rate can be calculated. For example, Fig. 2 4(b) shows the cross-sectional AFM profile for the lines shown in Fig. 2 4(a), giving an average etch depth of about 19 nm for this particular sample. Dividing this depth by the etch time of 8 s a nanotube fi lm etch rate of ~2.4 nm/s is obtained. The S1813, LOR3B, and PMMA etch rates were determined by measuring the initial and final resist thickness es using a Nanometrics Nanospec spectrometer and dividing by the etch time. Using the initial recipe (i.e. 3 00 W ICP power, 100 W substrate bias power, 45 mTorr chamber pressure, 20 sccm O2 flow rate, and 10 sccm helium flow rate for substrate cooling),

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27 etch rates of 2.37, 4.59, 4.58, and 6.65 nm/s were observed for CNT film, S1813, LOR3B, and PMMA, respectively as listed in the first column of Table 2 1 The error bar on these etch rates is approximately % 10 The CNT film etch rate is similar in magnitude to the ~4 nm/s observed in recent work using another ICP system [92] For CNT films of tens of nm thickness, such as those used in this work, the 2.37 nm/s etch rate of the initial recipe provides both reasonably short etch times and a good control of the etch uniformity. The s electivity S of the etch between the nanotube film and the resist mask is defined by RESIST SWNTr r S : (2 1) where SWNTr is the etch rate of the CNT film and RESISTr is the etch rate of the par ticular resist used as the mask. Using this definition, selectivity values of 1:1.94, 1:1.93, and 1:2.81 are obtained for S1813, LOR3B, and PMMA masking layers, respectively. Carbon nanotubes are much harder to etch compare d to photoresists since they are chemically resistant and structurally stable [98] As a result, the etch rate of the CNT film is slower than that of resists in an O2 plasma and the selectivity values are less than unity. Since the resists are used as the etch mask, they need to be thick enough to w ithstand the nanotube film etch. The min imum resist thickness required for a given CNT etch process is determined by the selectivity S of the etch process Typical S1813 only and LOR3B/S1813 dual layer resist thicknesses used for photolithography are larger than 1 m; as a result, based on the selectivity values given above, hundreds of nm thick CNT films can easily be patterned by photolithography. More importantly, since the PMMA etch rate is not significantly higher than the nanotube film etch rate, typical PMMA thicknesses necessary for e -beam lithography (100300 nm) can be used to pattern thin CNT films ( i.e. less than 100 nm) down to very small (<100

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28 nm) lateral features. In short, although the etch selectivity between the CNT film and PMMA is less than unity ( S = 0.36), it is still large enough to allow for e -beam patterning of CNT films. Aspect ratio dependent etching has been observed in some e tch processes, such as silicon trench etching, resulting in a lower etch rate for smaller width trenches [96] Using the approach described in the preceding paragraph I systematically studied the effect of the line width on the nanotube film etch rate for widths ranging from 50 m all the way down to 100 nm The spacing between the etched lines was set equal to the width of the lines in all cases. T he etch rate was found to be almost constant at 2.37 0.3 nm/s, independent of the line width etched. This is most likely due to the fact that all o f my samples have a CNT film thickness t < 100 nm. The aspect ratio AR of the nanotube film etched, defined as t / w, where w is the width of the line etched always satisfies 1 AR for all the samples. In other words, the plasma density is high enough and the aspect ratio is small enough so that reactant species are able to make it to the bottom of the etched lines even for the smallest (100 nm) linewidths. I also systematically studied the effect of c hanging various ICP etch parameters on the etch rates of the CNT film and different resists, as listed in Table 2 1 using the procedure described previously. To investigate the effect of the substrate bias power on the etch rate, I decreased the substrat e power from 100 W to 15 W, keeping all the other etch parameters constant as in the initial recipe Table 2 1 shows that the nanotube film and resist etch rates are decreased by about a factor of 10 compared to those of the initial recipe. By reducing t he substrate bias, the ion energy is reduced resulting in a substantially slower etch rate. A slow etch rate could be useful in applications where the CNT film thickness is very small and the etch rate and uniformity needs to be precisely controlled.

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29 To i nvestigate the effect of chamber pressure on the etch rate, I decreased the chamber pressure from 45 mTorr to 10 mTorr, keeping all the other etch parameters constant as in the initial recipe Table 2 1 shows that the nanotube film and resist etch rates increase by a factor between 1.7 and 3.5 compared to those of the initial recipe. A lower chamber pressure results in a more directed etch, higher ion energy, and increased etch rates due to fewer gas -phase collisions. A faster etch rate could be useful in applications where the CNT film thickness is large. Furthermore, by taking the ratio of the etch rates listed in Table 2 1 selectivity values of 1:0.95, 1:1.21, and 1:1.59 are obtained for S1813, LOR 3B, and PMMA masking layers, respectively. These selectivity values are higher than those of the initial recipe. This is likely due to an increase in the physical etch component, which etches the nanotube film and resist s at similar rates. In addition, increasing the chamber pressure from 45 mTorr to 100 mTorr (maximum pressure achievable in my system) was found not to change the etch rates of the nanotube film and resists significantly, showing that the etch rate has already saturated at 45 mTorr pressu re Furthermore, I have investigated the effect of substrate cooling on the etch rates of the CNT film and resists. Increasing the helium flow rate (which actively cools the substrate) from 10 sccm to 40 sccm, keeping all other etch parameters constant as in the initial recipe, did not change the etch rates of the CNT film and resists compared to those of the initial recipe The optimum etch conditions depend on the nanotube film thickness that needs to be etched. Based on my results, for thick films, etc hing at low pressures would be the best option. On the other hand, for thin films, where the etch rate and uniformity needs to be better controlled, etching at low substrate bias power would be the best choice. For intermediate thicknesses, the initial r ecipe would work the best. Furthermore, my experiments indicate that

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30 the substrate bias power can be used to control the nanotube film etch rate without significantly changing the selectivity. Therefore, one can lower the chamber pressure to achieve the best selectivity and then adjust the substrate bias power to achieve the optimum etch rate based on the film thickness. To compare the etch rates of CNT film and the three resists in an ICP RIE system to those in a conventional parallel plate RIE system I have also etched the CNT film and resists using a Plasma Sciences RIE 200W etcher, in which there is only one RF power source of 13.56 MHz frequency, and as a result, the plasma density and the ion energy are no longer decoupled. Using an RF power of 20 W O2 flow rate of 12.5 sccm, and a chamber pressure of 140 mTorr, I have observed that the etch rates of both the CNT film and resists are substantially lower in this system, as listed in the last column of Table 2 1 T he etch rate of the CNT film in the conventional RIE system was 0.05 nm/s, which is about 5 times slower than that in the ICP -RIE system even with a low substrate bias power of 15 W (See Table 2 1 ). This is due to a lower plasma density in the conventional RIE system. F urthermore, for the conventional RIE system, the etch selectivity between the CNT film and the resist mask has decreased to 1:2.8, 1:3.8, and 1:11 for S1813, LOR3B, and PMMA, respectively. This is due to a reduction in the physical etching component using the conventional R IE system. These results demonstrate that the use of an ICP etcher provides significant advantages such as faster etch rates and better selectivity over conventional parallel plate plasma systems in order to be able to pattern submicron features in nanotube films. In the following chapters, I use the techniques developed in this chapter and pattern CNT films for characterization and device applications.

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31 Figure 2 1 The schematic of the ICP RIE system showing the separate ICP and substrate power supplies. Figure 2 2 CNT film patterning results studied by AFM: (a) Top view AFM image of a ~3 m line etched in a ~20 nm thick CNT film using the LOR3B/S1813 dual layer resist photolithography process and the initial ICP etch recipe described in the text. The SiO2 substrate is exposed in the center area, where the film is completely removed. The CNT mesh making up the nanotube film is clearly visible at the left and right of the AFM image. The scale bar is 1 m (b) Cross -sectional height data for th e AFM image of part (a). (c) AFM image of a series of nanotube film lines having equal widths and spacings of ~500 nm, patterned on SiO2 by e -beam lithography and ICP RIE etching, as described in the text. The film thickness is ~ 20 nm and the scale bar i s 1 m. (d) Cross -sectional height data for the AFM image of part (c).

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32 Figure 2 3 CNT film patterning results studied by SEM: (a) SEM image showing concentric nanotube film rings having widths of about 50 nm patterned by my fabrication method. The textured area is the nanotube film and the smooth area is the exposed SiO2 substrate where the film is completely etched. (b) SEM image of GATORS patterned on nanotube film by e -beam lithography and ICP RIE etching The widths of the text characters are on the order of 200300 nm and the CNT film thickness is 20 nm. The scale bars are 100 nm and 2 m in parts (a) and (b), respectively. Figure 2 4 Nanoscale CNT film patterning results studied by AFM: (a) AFM image of a series of nanotube film lines ha ving equal widths (and spacings) of ~200 nm half way etched in a 75 nm thick CNT film by e beam lithography and ICP -RIE etching, as described in the text. Unlike th e lines shown in the AFM image of Fig. 2 2(c), the lines in this AFM image have not been et ched all the way down to the substrate, as evident from the texture of the remaining film mesh visible in the etched areas The scale bar is 200 nm. (b) Cross -sectional height data for the AFM image of part (a), showing an average etch depth of about 19 nm for this particular sample. The etch rate can be calculated by dividing this etch depth by the total etch time.

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33 Table 2 1 Etch rates of the CNT film and three different resists (S1813, LOR3B, and PMMA) under different plasma etch conditions using t he Unaxis Shuttlelock ICP -RIE system and the Plasma Sciences RIE 200W system. The initial ICP RIE recipe in column I corresponds to an ICP power of 300 W, substrate bias power of 100 W, chamber pressure of 45 mTorr, and O2 flow rate of 20 sccm. In additi on, a Helium flow rate of 10 sccm was used to cool down the substrate. The headings of the other columns indicate the parameters changed compared to the initial recipe, with all the other parameters kept constant. The parallel plate RIE system etch param eters were RF power of 20 W, O2 flow rate of 12.5 sccm, and a chamber pressure of 140 mTorr. Material ICP RIE System Etch Rates (nm/s) Parallel Plate RIE System Etch Rate (nm/s) Initial recipe Low Substrate Bias Power (1 5 W ) Low Chamber Pressure (10 mTorr) CNT film 2. 37 0.23 8.28 0.05 S1813 4.59 0.39 7.85 0. 14 LOR 3B 4.58 0. 44 10.0 0.19 PMMA 6.65 0.63 13.2 0. 55

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34 CHAPTER 3 EXPERIMENTAL STUDY O F RESISTIVITY SCALING IN CNT FILMS Introduction The first step to validate the usefulness of CNT networks and films for potential electronics and optoelectronics applications is to understand their electrical properties as a function of various geometrical, compositional and environmental parameters. These parameters include (but are not limit ed to) film dimensions (length, width and thickness), quality of individual nanotubes (CNT length, diameter and chirality) and the junctions between the tubes, nanotube density and alignment within the film, temperatur e stress, electrical and magnetic fie ld and finally pressure and type of gases that the film is exposed to. Specifically, i t is expected that due to the percolative nature of conduction in the film, its electrical properties would show a strong depende nce on some of these parameters such as the film dimensions. A f ew groups have studied the transport properties of thin 2D nanotube networks and thic k 3D CNT films [61,62,64,84,99110] with a few reports focusing on the CNT film resistivity dependence on device geometry [64,84,99] However, how electrical properties of nanotube films scale as a function of device geometry, particularly device width, at submicron dimens ions remains unexplore d. In this chapter I use th e aforementioned patterning capability to fabricate standard four point probe structures for experimentally studying the dependence of CNT film resistivity on its dimensions and the resist process used for its etching At room temperature and ambient air pressures, m easured resistivity values for lithographically patterned nanotube films are found to be independent of device length, while increasing over three orders of magnitude compared to bulk films, as the width and the thickness of the films shrink.

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35 Resistivity S caling with Device D imensions CNT film fabrication steps were same as the ones explained in chapter 2 [61] The substrate used here was (100) silicon with a 500 nm layer of thermally grown SiO2 on top. Following deposition, the CNT film was patterned by photolithography or e -beam lithography, and subsequently etched using the ICP RIE setup [111] Structures with lengths L = 10 to 1000 m, and widths W = 2 to 100 m have been fabricated on samples with film thickness t = 3 5, 55, and 75 nm by photolithography, and structures with L = 7, 50, and 200 m and W = 200 nm to 20m were fabricated on samples with t = 15 and 35 nm by e -beam lithography. For all samples, the average thickness of the nanotube film, as measured by AFM, randomly sampled at numerous locations over a substrate area of more than 4 cm2, was found to be within 5 nm. Figure 3 1 shows an optical microscope image of a typical four -point probe structure that was fabricated. Chromium/Palladium metal contacts, which are labeled 1 4 in Fig. 3 1 were patterned on the nanotube film pads by e -beam evaporation and subsequent lift off. A fter fabrication, I electrically characterized the four point probe structures at room temperature and in ambient atmosphere. The resistivity of each structure was obtained from the usual formula, ) Wt / L ( R where R is the resistance extracte d from the slope of the measured I -V curves, which exhibited linear behavior in all cases. The effects of contact resistance are eliminated with the use of a four point probe measurement Figure 3 2 plots the resistivity versus length L for 4 -point probe structures with different widths and thicknesses fabricated by photolithography. The data shows that, for a given width and thickness, the resistivity does not change significantly over a length span of two orders of magnitude. Each of the data points in F ig. 3 2 represents an average of 6 devices having the same geometry. The device -to -device variation in the resistivity for devices of identical

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36 dimensions was found to be less than 20% for the data presented in Fig. 3 2, which is also in agreement with pre vious experim ental and theoretical work for a device above the percolation threshold [64, 99] Although the resistivity is constant for devices with L larger than about 10 m, as is shown in Fig. 3 2, for devices with smaller lengths (where the nanotube length is comparable to device length) resistivity starts to decrease as L shrinks [64,99] I will explain this observation in the following chapter. Next, I study the effect of film thickness on resistivity. A s can be seen in the inset of Fig. 3 2, resistivity dependence on thickness is very weak above approximately 50 nm. Independent experimental results by another group also show that the resistivity saturates above a thickness of 50 nm [62] On the other hand, resistivity increases significantly as the devices get thinner. This behavior is also in agreement with previous work, in which an inverse power law scaling of the form ) t t (c was observed, where tc is the critical thickness at the percolation threshold, and is the critical exponent [62] Using tc = 3 nm from Ref. [62] and fitting this equation to my experimental data shown in the inset of Fig. 3 2, I obtain = 2.3. Reducing the thickness causes the film to approach the percola tion threshold by decreasing the density of nanotubes. Standard percolation theory predicts an inverse power law behavior for the nanotube density dependence of resistivity near the percolation threshold with = 1.94 for an ideal 3D system, which is close to my fitted value [112] The inset of Fig. 3 3 shows the resistivity as a function of device width for a 55 nm thic k film for W = 5 to 50 m patterned by photolithography. It is clear that for wide devices (>20m), the resistivity saturates at a constant value of 6.7104 This value is greater than previously reported for similar CNT films [61] which will be explained later in this chapter

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37 It is clear from the inset in Fig. 3 3 that the resistivity starts to increase for widths smaller than 20 m. To s tudy the effect of width scaling in greater detail, I used e -beam lithography to fabricate devices with submicron widths, as shown in Fig. 3 3. For W < 1 m, up to a factor of 2 variation in resistivity was observed for identical devices. This variation i s much larger than the 20% scatter observed for W > 2 m. As the device dimensions are scaled, statistical variations in nanotubes making up the film start to become more observable, and the electrical properties of the film become less uniform. It is cle ar from Fig. 3 3 that the resistivity increases about two orders of magnitude when the width goes from 20 m down to 200 nm. My resistivity vs. width data can be fit by an inverse power law of the form W with the critical exponent = 1.43 for the 35 nm thick sample and = 1.53 for the 15 nm thick sample. The nanotube film consists of many parallel conducting paths, each path being made up of multiple nanotubes in series. Since the in-plane orientation of individual nanotubes in the film is random, conduction paths are not perfectly aligned with direction of current flow (device length L ). As a result, reducing the device width W eliminates not only those conducting paths that lie entirely in the etched area, but also those that parti ally lie in that area. Consequently, reducing W increases the resistance at a rate faster than 1/ W Furthermore, the observed inverse power law dependence on width is similar to the dependence on thickness. This is not surprising since reducing the width also causes the film to approach the percolation threshold by decreasing the density of conducting paths in the film, and should exhibit an inverse power law behavior [112] However, because the film is preferentially aligned parallel to the substrate surface, the length scales associated with width and thickness scaling are very different. Strong scaling with width is obs erved starting below 2 m, whereas strong scaling with thickness is not observable

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38 until below 50 nm The width begins to affect resistivity for values on the order of the nanotube length in the film, as expected. Resistivity Dependence on Process P arameters As I mentioned above, the values of resistivity I observed in the experiments for a device with large dimensions is higher than the values reported for a similar film [61] One of the sources for the increase in the resistivity can be the fabrication process itself. In order to characterize the effect of the process chemistry on the resistivity of the patterned nanotube films, I have fabricated standard four -point probe structures with the three types of resist processes mentioned in chapter 2. The structures are fabricated with 50 m width and 750 m length. My experiments show ed that identical resistivity values are extracted regardless of whether the electrical probes are placed on the Cr/Pd metal contacts or directly on the nanotube film pads, since the effects of contact resistance are eliminated in a four point probe measurement The resistivity values to be reported in th is section were obtained from four point probe structures which did not have the metal contacts. This enables us to compare the effects of the three types of resist processes on the resistivity of nanotube films directly, without introducing any contamina tion due to the second lithography process used for metal contact patterning. I observed before that the resistivity of patterned nanotube films increase s significantly compared to bulk films as their width and thickness shrink, particularly for devices ha ving submicron dimensions. Therefore, for this experiment, I designed structures with large length ( L = 500 and 1000 m), large width ( W = 10, 20, 30, 50 and 100 m), and large thickness ( t = 75 nm) to avoid geometrical effects on the resistivity of patter ned nanotube films. In other words, the resistivity values measured using these large structures are the minimum resistivity values

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39 representative of those of bulk CNT films [113] After fabrication, the devices were measured at room temperature and in ambient atmosphere. Table 3 1 lists the average resistivity values measured using four point probe structures patterned by the three different resist processes, showing that the LOR3B/S1813 dual layer resist process results in the highest resistivity, followed by the PMMA/S1813 proces s, with the S1813 only process giving the lowest resistivity. Furthermore, for all three resist processes, the resistivity values are higher than those measured for the as -prepared nanotube film, which is about 1.5104 cm [61] It is known that nitric acid, which is used for purifying CNT s, dopes them and hence decreases the film resistivity during nanotube film preparation [61] The increase in resistivity after lithography is likely due to the partial de -doping of the acid purified nanotubes during the processing steps associated w ith the patterning. The results in Table 3 1 suggest that the level of de -doping depends on the resist chemistry, yielding different resistivity values for different resist processes. The fabricated four point probe structures were also used to investig ate the effect of ICP reactive ion etching (that I used for etching the film) on the resistivity of partially etched nanotube films. Nanotube film devices with an initial thickness of 100 nm were etched by the initial recipe for 10 seconds (so that the fi lm becomes about ~ 24 nm thinner) and the resistivity of the film before and after etching was compared. An AFM image of a CNT film part ially etched in shown in Fig. 2 4. Regardless of the size and location of the devices, their resistivity increased betw een two to three orders of magnitude, showing that the remaining film has been significantly damaged by the O2 plasma during etching. Since the nanotube film is porous, reactant species can penetrate into the film and damage the nanotubes deeper in the fi lm.

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40 Nanotubes that have been damaged can no longer contribute to electrical conduction, and therefore the film resisti vity increases significantly. Figure 3 1 Optical microscope image of a four point probe structure I have fabricated with length L = 200 m, width W = 2 m, and thickness t = 75 nm. Cr/Pd metal contacts, labeled 1 4, are visible as bright squares on top of the nanotube film pads and the scale bar is 100 m. Figure 3 2 Effect of device length and film thickness on resistivity: Mai n panel is a l oglog plot of resistivity versus length for 4 point probe structures with different widths W and thicknesses t Each symbol shows a different combination of W and t values, as labeled in the figure. The lines are fits to the data. The ins et shows the resistivity versus thickness for devices with L = 200 m and different W values as labeled. The dashed line is an inverse power law fit with a critical exponent = 2.3.

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41 Figure 3 3 Effect of device width on resistivity: Main panel is a l og -log plot of resistivity versus width for structures with t = 15 and 35 nm and L = 7, 50, and 200 m. For W < 2 m, the data can be fit by W 1.53 for t = 15 nm and W 1.43 for t = 35 nm, as shown on the plot by different style dashed lines The inset shows versus W on a linear scale for W in the range 5 50 m. The film thickness is 55 nm. The line connecting the average of the data points at a given width provides a guide to the eye Table 3 1 Average nanotube film resistivity value s measured using standard four point probe structures for nanotube films patterned by S1813 only PMMA/S1813, and LOR3B/S1813 resist processes Resist Process S1813 Only PMMA/S1813 Dual Layer LOR3B/S1813 Dual Layer Resistivity (104 cm) 5.2 6.3 6.9

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42 CHAPTER 4 COMPUTATIONAL STUDY OF RESISTIVITY SCALING IN CNT FILMS Introduction In the previous chapter, I observed the strong dependence of CNT film resistivity on its geometrical parameters close to percolation threshold Other groups have also experimentally studied the effect of nanotube length [105] density [64] and alignment [110] on the resistivity of thin networks and thick films of nanotubes. I n order to investigate the physical and geometrical origin s of these experimental findings more systematically, simulation and modeling techniques have to be employed. Although there have been s everal experimental reports on CNT films and networks, relatively little work has been done on their modeling and simulation [82,99,114119] In a previous numerical simulation work, resistivity scaling with device length has been studied for different nanotube densities [99] In another work, the effect of nanotube alignment on the percolation probability of nanotube/polymer composites has been calculated by 2D Monte Carlo simulations [110] Also, there have been a few works on the optimization of CN T film parameters such as nanotube alignment and the fraction of metallic to semiconducting nanotubes for improving device characteristics in thin film transistors [117,119] As an example well aligned dense networks of nanotubes have been grown on quartz wafers and used as the channel material in thin film transistors [58,118] T he performance of these transistors was studied using a numerical stick percolation based model [118] There have been a few other theoretical studies on the conductivity of networks and composites made up of conducting sticks, but with an emphasis on investigating the effect of stick alignment on the percolation th reshold [120122] However, a systematic study of the effects of various nanotube and device parameters on the CNT film resistivity has not been reported previously.

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43 In this chapter I study the geometry -dependent resistivity scaling in CNT films using Monte Carlo simulation s by randomly generating nanotubes on stacked 2D rectangular planes I first demonstrate that these simulations can mode l and fit the recent experimental results on the scaling of nanotube film resistivity with device width. Then, I systematically study the effect of four parameters, namely tube tube contact resistance to nanotube resistance ratio, nanotube density nanotube length (including the effect of length distribution ) and nanotube alignment on the CNT film resistivity and its scaling with device width. I then explain these simulation results by simple physical and geometrical arguments. Modeling A pproach Si mulation of the electrical properties of the nanotube film was performed by rand omly generating the nanotubes using a Monte Carlo process In particular, each nanotube in the film is modeled as a stick with fixed length lC NT. T he position of one end of the nanotube and its direction on a two dimensional ( 2D ) plane are generated randomly. This process is repeated until the desired value for the nanotube density n in th e 2D layer is achieved Additional 2D layers are generated using the same approach to form a three -dimensional (3D) nanotube film An example of a 2D nanotube layer produced by this method is shown in Fig. 4 1(a). For profile comparison, Fig. 4 1(b) shows an experimental AFM image of a nanotube film that I have etched into a series of lines with width and spacing of 500 nm using the approach mentioned in chapter 2. After the 2D nanotube layer is generated, the locations of the junctions between pair s of nanotubes (which I call internal nodes) and between the nanotubes and source/drain electrodes (which I call boundary nodes) are determined by the simulation code I explained in chapter 2 that the nanotubes in the film have random in plane orientations but are mostly ordered to lie in stacked planes. As a result, in the 3D film created by stacking several 2D nanotube layers, it is

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44 assumed that only nanotubes in nearest neighbor 2D layers form junctions and the locations of these junctions are also determined by the simulation code Therefore the effective integrated density of a 3D film consisting of l layers of density n per layer is always less than n l since only nanotubes in nearest neighbor 2D layers are electrically connected. In general, the relationship between n and the effective integra ted density depends on other device and nanotube parameters, and cannot be expressed in a simple analytic form. The value of the contact resistance at each tubetube junction depends on whether the junction is metallic /semiconducting (MS) semiconducting /s emiconducting (SS), or metallic /metallic (MM) and also on other properties of the junction, such as the diameter of the tubes and their atomic structure at the junction [123132] In particular, it has been shown that MS junctions have a significantly larger contact resistance than MM or SS junctions due to the fact that they form Schottky barriers [123] In m y simulations in this chapter each tube -tube junction is modeled by an effective contact resistance RJCT regardless of the type of junction, following the simplified approach of Ref. [99] After the location s of the junctions are determined, coordinates of the neighbors of each internal node, which are defined as other nodes that are in direct electrical contact with that node, are located. By this definition, a node must be connected by nanotube segments to all of its neighbors. T he resistance between two neighboring nodes can easily be determined by calculating the length of the nanotube segment connecting them. The resistance of a singlewalled carbon nanotube segment RCNT as a function of its length l is calculated using the ex pression l R RCNT 0 (4 1)

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45 w here R0 is the theoretical contact resistance at the ballistic limit ( ~ ) and is the mean free path, assumed to be 1 m in my simulations based on previous experimental results [133137] Writing Kirchoffs Current Law (KCL) at each internal node for a mesh with n internal nod es, I get a set of n equations with n unknowns, where the n unknowns are the voltages Vn at each node. The voltages applied to the source/drain electrodes set up the necessary boundary conditions. Once the voltage at each node is solved the total curren t in the film is calculated by a summation over the currents flowing into the drain boundary nodes. Finally, the resistance, and as a result, the resistivity of the nanotube film in the linear regime is calculated by dividing the voltage drop between th e source and drain electrodes by the total current in the film. For each data point presented in this section 200 or more independent nanotube film configurations were randomly generated and their results were averaged in order to remove statistical variations in the data calculated from different realizations of the nanotube film. In addition, the percolation probability P defined as the probability that the nanotube film is conducting ( i.e. the probability of finding at least one conducting path b etween the source and drain electrodes ) is also calculated to complement the resistivity data Results and D iscussion Fig. 4 2(a) shows the normalized resistivity of the CNT film as a function of device wi dth W The symbols are the experimental data points presented in Fig. 3 3 for a nanotube film with device length L = 7, 50, and 200 m, and average thickness t = 15 nm The solid line represents the theoretical fit to the experimental data using my simulation s In Fig. 4 2(a), b oth the theoretical and experimental resistivity values have been normalized by dividing the absolute value of resistivity at each data point by its value at large W where the resistivity saturates at a

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46 constant minimum valu e min. The same normalization procedure is used for a ll figures in this chapter When several resistivity curves are shown in a single figure, all curves are normalized by the min of only one of them, preserving the ir relative resistivity magnitudes. In my simulations, I have used a device length of L = 7 m as explained in detail below, and nanotube length of lCNT = 2 m since the average nanotube length in the nanotube films used in my experimental work is estimated to be around 2 m based on AFM images within the range mentioned in chapter 2 In addition, I have estimated the average thickness ( i.e. vertical height ) of a single nanotube layer in the nanotube film to be ~ 3 nm which is about twice the a verage diame ter of the CNTs making up the film This estimation takes into account the ext ra volume that interwoven nanotubes occupy. As a result, five stacked 2D nanotube layers were used to model the experimental film thickness of t = 15 nm. With those nanotube and device values fixed, two fitting parameters were used to match the experimental data: (1) N anotube density n per nanotube layer and (2) Resistance ratio ( Rr atio), which I define as the ratio of the tube tube junction contact resistance RJCT to the theoretical contact resistance at the ballistic limit R0: 0R R RJCT ratio (4 2) By this definition, Rratio >> 1 implies tube tube junction resistance limited transport, whereas Rratio << 1 implies nanotube resistance limited transport in the film. As I mentioned in the previous chapter and is shown in Fig. 4 2(a), below the critical width ( WC) of about 2 m, resistivity starts to increase and near the percolation threshold its scaling can be characterized by an inverse power law of the form W w ith as the critical exponent for width scaling. As I will show in detail later, changing th e r esistance ratio affects only the

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47 critical exponent wh ereas changing the nanotube density changes both the critical exponent and the critical width As a result, to fit the experimental data of Fig. 4 2(a), first, the nanotube density was varied to match the critical width WC, and then the resistance ratio was varied to match the critical exponent The best fit shown by the solid line in Fig. 4 -2 (a) was obtained with n = 2 m2 per nanotube layer and Rratio = 100. T he extracted density value is consistent with the density of nanotubes estimated from AFM images of the nanotube films used in the experimental work The error bar on the nanotube density n extracted using the fitting procedure is 15 % The extracted value for the r esistance ratio can also be compared to estimates from previous work. In particular, i t has been sh own by several experiments that tube -tube junction resistance is larger than the resistance of the nanotubes themselves by a factor of around 3070 for SS and MM junctions, and by a factor of at least an order of magnitude higher than that for MS junctions [123] Since MS junctions are more resistive, they do not contribute to conduction as much as SS and MM junctions do. As a result, Rratio defined in Eq. (2) is expected to be higher than but close to the range 30 70 obse rved for SS and MM junctions The value of Rratio = 100 I have extracted using the fitting procedure is consistent with these observations The experimentally observed value of could still be matched by the simulation even when Rratio was changed by 50 % putting a bound on the sensitivity of the fit to the value of Rratio. It is clear from Fig. 4 2(a) that the simulation results agree well with the experimental data However, the decrease in resistivity for widths above 2 m observed experimentally ( although not as strong as below W < 2 m ) is not captured by the simulations. This di screpancy can be explained by the presence of some nanotubes much longer than 2 m in the experimental nanotube films, whereas in the simulations all nanotubes were assumed to have a fixed length lCNT = 2 m As I will show explicitly later, when lCNT incr eases, WC moves to higher widths.

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48 As a result, the decrease in resistivity observed experimentally is consistent with the existence of some mu ch longer nanotubes in the film. Furthermore, experiments on thicker films have shown that, even in the presence of some longer nanotubes, the resistivity eventually saturates for device widths above 20 m, as is al so clear in the inset of Fig. 3 3 It can also be seen from the experimental data in Fig. 4 2(a) that for longer devices, the inverse power law behavior seems to hold up to a wider device width. This can be explained by the fact that for longer devices, there is a higher probability that som e conduction paths are eliminated sooner as the device width shrinks resulting in a larger critical width WC. However, the number of experimental data points is too few for a conclusive fit for each separate length, and the simulation time becomes prohib itively long for device lengths above approximately 10 microns Due to these limitations, I have chosen to use the smallest length device ( L = 7 m) for my simulations, and fit all the experimental data points with a single inverse power law curve. Altho ugh this is an approximation, it can still capture the essential physics of the experimentally observed resistivity scaling in single -walled nanotube films. Fig ure 4 2(b) illustrates normalized resistivity versus device length L for three different nanotub e densities calculated using my simulation code for a device with W = 2 m. All other simulation parameters are the same as th ose in Fig. 4 2(a). Unless otherwise mentioned, the same device and nanotube parameters will be used i n the remain der of this chapter It is evident from Fig. 4 2(b) that the resistivity starts to decrease from its maximum constant value when the device length L becomes smaller, in agreement with previous experimental and theoretical results [64,99] At large L each conduction path consist s of many nanotubes in series and the total length and the number of junc tions of each conduction path vary linearly with the device length. As a result, the total film resistance also varies linearly with L and the film behaves like

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49 a homogeneous material with a constant resistivity. On the other hand, when L becomes compara ble to the nanotube length, the statistical distribution of nanotubes in the film can result in short conduction paths consisting of only a few nanotubes connecting source to drain, decreasing the total resistance of the film Fig. 4 2(b) shows that the effect of L on resistivity is more pronounced when the nanotube density is lower. This is because if the nanotube density is low the number of conduction paths between source and drain decrease s drastically as the device length increa ses which increases the resistivity more strongly. This effect has also been observed in previous th eoretical and experimental work [64,99] In addition to matching the experimental data, as is presented in Fig. 4 2 I have also used numerical simulation s to systematically stud y the effect s of four parameters, namely r esistance ratio n anotube density, nanotube length and its distribution and nanotube alignment on the CNT film resistivity and its scaling with device width. Effect of Resistance R atio Fig 4 3 shows the normalized resistivity versus device width for Rratio ranging from 102 to 104. It is evident from Fig. 4 3 that increasing Rratio increases the critical exponent but does not have a significant effect on the critical width WC, since WC is only determined by nanotube density and geometrical parameters In particular, increases from 0.52 to 1.95 when Rratio changes from 102 to 104. When Rratio is very low, nanotubes form low resistance contacts with each other, and the film resistivity depends m ainly on the total length of the conduction paths. On the other hand, when Rratio is very high, film resistivity mainly depends on the number of contacts in the conduction path s. When the device width is reduced, the number of tube -tube junctions in the remaining conduction paths increases significantly due to the random angular distribution of the remaining nanotube segments, whereas the lengths of the remaining

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50 conduction paths do not increase that strongly As a result, increasing Rratio results in a large r value of the critical exponent To illustrate this point further, the inset of Fig 4 3 depicts as a function of Rratio. In the nanotube resistancelimited transport r egime, is constant at a value of about 0.5. It starts to increase as the resistance ratio increases above 1 and finally saturat es at a valu e of around 2 in the junction resistancelimited transport regime Since also depe nds on several other parameters, such as nanotube density, lengt h, and alignment t he lowest and highest values obtained from the inset of Fig. 4 3 do not give the absolute limits on However, the inset does show that other parameters being constant, the critical exponent exhibits a minimum and a maximum at the two limiting cases of the resistance ratio Effect of N anotube D ensity Figure 4 4(a) shows the norm alized resistivity versus device width for different nanotube densities ranging from 1 to 3 m2. It is evident from this figure that as the density increases, three events take place: First, the resistivity of the film decreases. Adding m ore nanotubes to the film increase s the number of conducting paths and decrease s the average path length between source and drain, and as a result, decrease s the resistivity Secondly, the critical width WC shifts to lower widths. At higher densities, there are more con ductio n paths which have narrower width distribution s As a result, for dense films, width scaling effects become visible only at smaller widths which results in a smaller value of WC. Finally, the critical exponent increases This is due to the increa sed number of paths per width (relative to the total number of paths ) removed from the film because of the higher nanotube density. In other words, for a film with higher nanotube density, resistivity starts to increase at a smaller WC, but the rate of power law increase is much faster

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51 Figure 4 4( b ) depi cts these trends from a different point of view by plotting the percolation probability P defined earlier, versus wid th for different densities ranging from 1 to 3 m2. For all densities, the probability of having a conduction path goes from 1 at large widths to zero at very small widths. However, as the width decreases the percolation probability transition profile from 1 to zero is quite different for different densities. At higher densities, th e transition starts at smaller widths, which indicates a smaller WC, but the transition slope is steeper which indicates a high er value of F or a general 3D percolation problem, it has been shown that near the percolation threshold, the resistivity exh ibits an inverse power law dependence on density given by ) (Cn n (4 3 ) where nC is the critical density at the percolation threshold and is the critical exponent for density [138] I have also studied this dependence as shown in the inset of Fig. 4 4( b ), where normalized resistivity versus density is plotted for a device with L = 4 m and W = 4 m It is evident from this inset that the resistivity as a function of density obeys Eq. (4 3 ) near the percolation threshold with a critical exponent = 2.5 extracted from the simulation data. When more nanotubes are added to the film, the number of conducting paths increases and the average path length between source and drai n decreases both of which reduce the film resistivity Furthermore, t he rate of change of resistivity decreases at high density values, sin ce adding more nanotubes to an already dense film is less likely to introduce a significant number of new conduction paths or reduce the length and the number of junctions in existing paths. Effect of N anotube Length It is clear from Fig s 4 2 (a) and (b) that the device geometry -dependent resistivity scaling behavior in nanotube films is observed when the device length or width becomes comparable to

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52 the length of individual nanotubes making up the film Fig ure 4 5(a) shows normalized resistivity versus de vice width for three different nanotube lengths ranging from lCNT = 1.5 to 4 m for a device with L = 4 m It is evident from this figure that a s lCNT increases, the critical width WC moves to higher widths and the critical exponent increases. For tube -tube junction resistance limited transport (i.e. high Rratio), when lCNT is longer, conduction paths have a wider width distribution. Therefore, as W is decreased conduction paths start to get disconnected at higher values of WC. Furthermore, due to the increased number of paths per width removed from the film because of the higher nanotube length, critical exponent also increases for films with longer lCNT once the width decreases below WC. I have also studied resistivity scaling as a function o f nanotube length f or three different length -density relationships as shown in Fig. 4 5(b). In the first c ase where the density is kept constant (at a value of 2 m2) the resistivity increases sharply as lCNT decreases. Nanotubes with shorter lengths have a lower chance t o make junctions and f orm a continuous path between source and drain, which results in a higher resistivity Below a critical nanotube length t his strong resistivity scaling with lCNT can be fit by an inverse power law of the form CNTl where = 5.6 is the critical exponent for nanotube length scaling extracted from the simulation data. In the second case the resistivity versus nanotube length is plotted when the density nanotube length product is kept constant Physically, this corresponds to the case when the net weight of the nanotubes vacuum -filtered to form the film is kept constant while the nanotubes are cut into smaller lengths. Figure 4 5(b) shows that the resistivity still increases with decreasing na notube length in this case but with a critical exponent of 2.5 which is less than the previous case. Although t he increase in nanotube de n sity in this case decreases the resistivity as

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53 explained previously, it is not enough to compensate for the increase in resistivity due to the decrease in lCNT. In the third case t he product of density and the square of the nanotube length (i.e 2 CNTl n ) is kept constant I n this case, resistivity remains almost constant, which indicates that the resistivity increase due to reduced lCNT is balanced by the resistivity decrease due to higher n As a result, t h e resistivity dependence on lCNT and n near the percolation threshold can be fit by a n in verse power law of the form ) (CNTl n where / ~ 2 In general, t he value of the ratio / depends on other device and nanotube parameters, such as L W and Rratio. However, for large L large W and a high Rratio, such as the third curve plotted in Fig. 4 5(b), / equals approximately 2. In fact, if we divide the value of = 5.6 extracted from the first curve in Fig. 4 5(b) by the value of = 2.5 ext racted from the inset in Fig. 4 4(b), we get ~2.2, which is very close to 2. Furthermore, t his value of / physically makes sense because increasing the nanotube length increases the number of nanotubes in a 2D area element proportional to the square of the length, whereas increasing the density increases this number only linearly It has been previously shown that the nanotube density at the percolation threshold is proportional to 2 CNTl in an isotropic 2D network [64] Effect of Nanotube A lignment As I mentioned above, t here has been a great deal of recent research interest in aligning single -walled carbon nanotubes, either individually or in a thin film network or composite [58,110,117,118,139,140] Therefore, as the final parameter I study the effect of alignment (i.e. in -plane angular orientation) of nanotubes in the film and the direction of the device with respect to the alignment direction on the resistivity and its sca ling w ith various device parameters.

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54 Nanotubes are generated at random angles with respect to the horizontal axis, where is limited to the range a m a m and a m a m 180 180 The first angle, a, is defined as the Nanotube Alignment Angle, which is a measure of the degree of nanotube alignment in the film. When a = 90o, the nanotubes are completely randomly distributed, whereas when a = 0o, they are completely aligned in a specific direction. The second angle, m, which I call the Mea surement Direction Angle, is the orientation of the nanotube alignment direction with respect to the resistivity measurement direction (i.e. the channel direction between the source and drain electrodes, which in my case is always chosen a s the horizontal axis). When m = 0o, resistivity is measured parallel to the alignment direction while when m = 90o, it is measured perpendicular to the alignment direction As an example, Fig. 4 6 shows a 2D nanotube film generated using my simulation code between the source and drain electrodes with a = 27o and m = 45o, where the definition of the two angles are illustrated in the inset Figure 4 7 shows n ormalized resistivity versus width for three different nanotube alignment angles namely a = 18o, 36o, and 90 (at m = 0 ). It is evident from Fig. 4 7 that normalized resistivity WC, and all change as the nanotubes become more aligned (i.e. a becomes smaller) The value of min initially decreases as a goes from 90o to 36o because aligned nanotubes help to form conduction paths with fewer junctions and shorter lengths between the source and drain electrodes. Surprisingly however resistivity starts to increase when the degree of alignment in the film is increased even further (i.e. when a = 18o). In that case, each nanotube forms too few junctions with its neighbors, because nanotubes mostly lie parallel to each other. Therefore, many existing conduction paths are eliminated and resistivity is increased.

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55 Furthermore it can be seen from Fig. 4 7 that as the nanotube alignment angle a decreases both WC and decrease This is because a s the nanotubes become more aligned, the width distribution s of conduction pat hs in the film become narrower. As a result, width scaling becomes visible only at smaller widths, which decreas es WC, and relatively fewer conduction paths per width are removed, which decreas es In short, a lthough min first decreases then increases as a decreases WC and decrease monotonically with decreasing a. The inset in Fig. 4 7 illustrates the effect of alignment on width scaling from a different point of view. Normalized resistivity versus nanotube alignment angle a is plotted in this figure for W = 2 m and m = 0 It is evident from this inset that the resistivity slowly decreases as a is reduced, and reaches a minimum value at a ~ 4 5o, which I define as Min a the nanotube alignment angle at which minimum resistivity occurs. As a is reduced even further resistivity starts to increase. The reason for this behavior is the same as that discussed for min in Fig. 4 7 In other words, the resistivity minimum occurs for a partially aligned, rather than perfectly aligned nanotube film. As the nanotubes become even further aligned, the number of conduction paths begins to decrease significantly. For example, in the case of almost perfect alignment, each nanotube forms only very few junctions with its neighbors, since it lie s almost parallel to them As a result of this competition between the decrease in the number of junctions and lengths of the conduction paths (which decreases the resistivity) and the decrease in the num ber of conduction paths (which increases the resistivity), the resistivity minimum occurs for a partially aligned, rather than a perfectly aligned nanotube film. T he location of this resistivity minimum can depend on other device and nanotube parameters, and therefore, should be calculated for each device condition separately.

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56 The inset of Fig. 4 7 also shows that, at small alignment angles near the percolation threshold, resistivity exhibits an inverse power law dependence on a given by a ( 4 4 ) where = 2.9 is the critical exponent for nanotube alignment extracted from the slope of the loglog plot. This strong scaling with a is due to the fact that as the nano tubes align parallel to each other, many conduction paths are eliminated, which increases the resistivity significantly. These results are in agreement with recent experimental work on the effect of nanotube alignment on percolation conductivity in carbon nanotube/polymer composites [110] Up to this point, I have kept m = 0o, i.e. the direction of the channel has always been same as the direction of alignment. For the rest of the simulations in this chapter, I use a device length of L = 7 m, device width of W = 2 m, nanotube density per layer of n = 2 m2, nanotube length of lCNT = 2 m, and t = 15 nm and I let both the a and m vary. Figure 4 8 (a) shows the plot of normalized resistivity versus nanotube alignment angle for three different measurement direction angles (m = 0o, 45o, and 90o). F or m = 0o, the resistivity slowly decreases as a is reduced, reaches a minimum value at a ~ 45o, and then increases again with a significant slope close to the percolation threshold, similar to the curve in the inset of Fig. 4 -7. The above results are due to th e fact that i n my simulations the device length L is always larger than nanotube length lCNT; as a result, a single nanotube can never connect source to drain. In this case, as we have seen above, strong alignment increases the resistivity. However, if the nanotube length was longer than the device length (i.e lCNT > L ) [58] source and drain c ould be connected by single nanotubes, and strong alignment of nanotubes would reduce the resistivity. Furthermore, in contrast to well -defined values of a in my simulations, a few completely misaligned nanotubes that bridge perfectly aligned tubes can exist in experimentally aligned

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57 nanotube films and networks, reducing the resistivity significantly by introducing additional conduction paths [118] The effect of the measurement direction angle m on the resistivity scaling with nanotube alignment is also depicted in Fig. 4 8(a). When a = 90o, nanotubes have completely random orientation and the value of resistivity is independent of the measurement direction angle m. As a result, the curves for m = 0, 45, and 90o intersect as shown in Fig. 4 8(a). In contrast to the case when m = 0o, for m = 45o and 90o, as a decreases the resistivity increases continuously without exhibiting any minimum. In these latter two cases, since the measurement direction is not parallel to the alignment direction, the number of junctions and lengths of the conduction paths between the source and drain do not decrease significantly with more alignment. As a result, the reduction in the number of conduction paths dominates the resistivity change, and the resistivity continuously increases. For all three m values in Fig. 4 8(a), the resistivity exhibits an inverse power law dependence on a (equation 4 4) as the film approaches the percolation threshold at small al ignment angles with the exponents = 2.9, 3.6, and 3.9 for m = 0o, 45o, and 90o, respectively. The alignment critical exponent increases for large m values since the reduction in the number of conduction paths begins to d ominate the resistivity change as m increases. To compliment the resistivity data the inset of Fig. 4 8(a) shows the percolation probability P defined above, versus nanotube alignment angle for the same set of m. For measurement directions that are not parallel to the nanotube alignment direction, the percolation threshold (i.e. the transition point where the percolation probability drops from one to zero) occurs at higher values of a. This is due to the fact that it becomes more difficult to form a conduction path for strongly aligned films if the measurement direction is very different from the

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58 alignment direction. For example, for m = 0o, the transition from P = 1 to 0 starts when a becomes smaller than 10o, whereas for m = 90o, it starts when a gets lower than 40o. To illustrate the effect of the measurement direction angle from a different perspective, Fig. 4 8 (b) shows the plot of n ormalized resistivity versus m for six different values of a ranging from 18o to 90o. It is evident from Fig. 4 8 (b) that when the nanotubes are randomly distributed (i.e. a = 90o), resistivity is almost independent of m. In contrast, even for slightly aligned tubes (such as a = 72o), resistivity starts to increase with increasing m, and for well aligned nanotubes (such as a = 18o), this increase becomes very strong. Furthermore, the resistivity exhibits an inverse power law dependence on m as the film approaches the percolation threshold at large measurement direction angles, give n by ) (m90 (4 5 ) where is the measurement direction critical exponent. The value of extracted from the slope of the log -log plots in Fig. 4 8 (b) increases from 0.65 to 2.9 when a goes from 72o to 18o, which is a manifestation of the stronger dependence of resistivity on m as the nanotubes in the film become more aligned. As a measure of the sensitivity of film resistivity to the measurement direction angle, I define Max m as the maximum m above which the resistivity of an aligned film becomes larger than that of a completely random film ( with in % 5 error) In other words, Max m is a measure of the degree of misalignment in the measurement direction that can be tolerated before the aligned film becomes more resistive than a random film. By this definition, Max m is only meaningful for alignment angles at which the resistivity ( when m = 0o) is lower than that of a completely random film, which is around a = 22o in my case, as seen from Fig. 4 8 (a). The plot of Max m vs.

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59 a is shown in the inset of Fig. 4 8 (b). We can see that Max m increases as the film becomes less aligned. This demonstrates once again that for well aligned nanotubes, the film resistivity becomes very sensitive to the measurement direction. The location of the resistivity minimum and the value s of and are not universal, but depend strongly on other devi ce and nanotube parameters. As a result, I now study the effect of three parameters, namely nanotube length, nanotube density per layer, and device length on the scaling of resistivity as a function of a and m, as I have done above for the effects of these three parameters on the absolute value of resistivity. Figure 4 9 (a) shows the plot of n ormalized resistivity versus nanotube alignment angle for three values of lCNT when m = 0o. As the nanotube length i s increased from lCNT = 1.5 to 3.0 m, Min a decreases from 55o to 30o, and the critical exponent decreases from 2.9 to 1.6. Longer nanotubes form more junctions with each other, and therefore, even when they are strongly aligned the number of conducting paths is not reduced as strongly as in the case of shorter nanotubes In other words, increasing the alignment does not eliminate as many conduction paths for longer tubes as it does for shorter ones. This shifts both Min a and to lower values as lCNT increases. The inset of Fig. 4 9(a) shows Min a versus nanotube length. It is evident that as the nanotubes get shorter, the rate of change of Min a increases A film consisting of shorter nanotubes is closer to the percolation threshold, and therefore, even a slight increase in alignment can remove a significant number of additional conduction paths from the film As a result, for very short nanotubes, Min a approaches 90o. Fig. 4 9(b) shows the plot of normalized resistivity versus measurement direction angle for three values of lCNT when a = 18o. I have used a = 18o for the resistivity vs. measurement

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60 direction angle plots in Figs. 4 9 to 4 11, since the effect of m on resistivity is most pronounced for well alig n ed nanotubes, as seen in Fig. 4 8 (b ). A lower a value was not chosen since for lower nanotube alignment angles, the nanotube film falls below the percolation threshold even at small values o f m. A higher a value was not chosen, because at higher a, the effect of the measurement direction on resistivity is not as pronounced as at a = 18o, and therefore the effects of device and nanotube parameters illustrated in Figs. 4 9 to 4 11 would not be as evident. The measurement direction critical exponent extracted fro mFig. 4 9(b) shows an increase with increasing nanotube length ( = 1.7, 2.9, and 3.75 for lCNT = 1.5, 2, and 3 m, respectively). This is the opposite of the trend observed for in Fig. 4 9(a). Since initially the number of conduction paths is more for films with longer nanotubes, misaligning the measurement direction reduces the number of paths ( and hence incre ases the resistivity ) more rapidly than that for films with shorter nanotubes This results in a larger. Fig. 4 10(a) shows the plot of normalized resistivity versus nanotube alignment angle for four nanotube densities n ranging from 1 to 3 m2 when m = 0o. Compared to the case of nanotube length, Min a and do not change as signific antly when the nanotube density changes. This can be explained by the fact that increasing the nanotube length increases the number of nanotubes in a 2D area element proportional to the square of the length, whereas increasing the density increases this number only linearly as demonstrated above This results in a larger change in both Min a and as a function of the length of the nanotu bes compared to that of their density.

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61 To compliment the resistivity data, the inset of Fig. 4 10(a) shows the percolation probability P versus nanotube alignment angle for the same set of densities, illustrating that the percolation threshold for alignm ent angle is also a function of density. For example for n = 1 m2, the transition from P = 1 to 0 starts when a becomes smaller than ~ 30o, whereas for n = 3 m2, it starts when a gets lower than ~ 5o. Fig. 4 10(b) shows the plot of normalized resistivity versus measurement direction angle for four nanotube densities at a = 18o. The extracted measurement direction critical exponent values are = 1.4, 2.45, 2.9, and 3.0 for n = 1, 1.5, 2, and 3 m2, respectively. This change of with density is also less pronounced than that with nanotube length. The inset of Fig. 4 10(b) shows the percolation probability P versus measurement direction angle for the same set of densities, illustrating that the percolation threshold for measuremen t direction angle is also a strong function of density. For example, for n = 1 m2, the transition from P = 1 to 0 starts when m becomes larger than ~7o, whereas for n = 3 m2, it starts when m gets higher than ~5 0o. Finally, Fig. 4 11 shows the plot of normalized resistivity versus nanotube alignment angle for three device lengths L ranging from 2 to 7 m when m = 0o. From this figure, I extract Min a ~ 35o, 45o, and 45o and = 0.9, 2.2, and 2.9 for L = 2, 4, and 7 m, respectively. When the device length is shorter, the source and drain are connected by conduction paths consisting of only a few nanotubes in series. However, as the device length is increased, more nanotubes are necessary to form a conduction path, which is less likely to happen when the nanotubes become strongly aligned Therefore, is higher for longer device lengths compared to shorter ones. Similarly, Min a shifts to higher values for longer devices. The inset also depicts n orma lized resistivity versus measurement direction angle for two device lengths when a = 18o. The critical

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62 exponents are = 4.9 and 2.9 for L = 2 and 7 m, respectively. Similar to the previous case, for shorter devices, many conduction paths that have bee n formed between source and drain are removed as the measurement angle increases. Therefore, resistivity increases faster for shorter device length s, and the critical exponent increases. Effect of Length D istribution Before leaving this chapter, I study the effect of length distribution on the resistivity scaling trends This investigation is motivated by the fact that i n real networks and films the length of the nanotubes or bundles is not a constant, but exhibit s a distribution with a form that depend s o n the films preparation method [105] In order to show that the effect of length distribution on the resistivity depends on the resistance of the tube tube junctions, I compare my results for CNT film with th ose for a film in which the resistance of the elements is significantly larger the resistance of the junctions between elements (element -dominated film) I also take a look at the effect of alignment on the length distribution dependence of the resistivity. Then, I expla in the physical origins of the results using geometrical arguments. In my simulations, length distribution on the elements is imposed when placing element s randomly in the layer s with a length lCNT (in this case conforming to a length distribution ) (CNTl ). An example of such a film is shown in Fig. 4 12(a) Also, like before, f or aligned networks, is limited to the range a a and a a 180 180 as shown in Fig. 4 12(b) I employ the lognormal distribution which is given by 2 22 ) ) (ln( exp 2 1 ) ( CNT CNT CNTl l l Fig. 4 12(c) shows sample lognormal distributions with different and values, where and are the standard deviation and the mean, respectively.

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63 Figure 4 13(a) shows normalized resistivity versus average nanotube length given by 2 exp2 CNTl for an unaligned CNT film for four different relationships represented by the four data series. The standard error bars are not larger than the size of th e symbols for all figures. The strong scaling of the resistivity observed in this figure is simi lar to the data shown in Fig. 4 5(b) for a fixed density. However, the resistivities for different length distributions at a fixed average length are distinctl y separate, suggesting that, contrary to what one might initially expect [105] the network resistivity is not an explicit function of average nanotube length in this case. As a result of the monotonic decreasi ng nature of resistivity in Fig. 4 13(a), and noting that the widest element length distributions produce the least resistivity, I plot in Fig. 4 13(b) the resistivity versus RMS (second power mean) element length, given by 2 2 2exp ) ( CNT CNT CNT CNTdl l l l for four different relationships. Because the RMS value of any distribution is always greater than or equal to its mean, the effect of Fig. 4 13(b) is to shift the data series corresponding to wider distributions in Fig. 4 13(a) to the right so th at they coincide with each other. This shows that the RMS length, and not average length, is the relevant length parameter determining network resistivity. Figure 4 12(d) r a tionalizes the result of Fig. 4 13(b) by illustrating that within each network lay er, each nanotube sweeps out a circular probabilistic self area that is the superposition of all orientations it may take once anchored to a point. This self area represents all possible points of contact with other nanotubes and as a result, the large r this area, the more junctions that this nanotube can make, and the lower the resistivity of the CNT film

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64 Since the concept of RMS length, by weighing the length distribution by 2 CNTl is equivalent to averaging of areas swept out by a n element of length lCNT, the resistivity correlates with RMS length for a junction -dominated film ( l ike the CNT film) For a film with fixed element length, the RMS length is equal to the average length, and as a result, the effect of one length metric is indistinguishable from the other (refer to Fig. 4 5(b)) For an element -dominated film however, the situation is quite different. Figure 4 13(c) shows normalized resistivity versus RMS length for a element -dominated film having the same dimensions as in Fig. 4 13(a) for four different relationships. The four series separate, suggesting that, in contrast to the CNT film case, the film resistivity is not an explicit function of RMS length for element -d ominated film Fig. 4 13(d), on the other hand, shows normalized resistivity versus average length for four different relationships. It is evident that for large average lengths, all four length distributions show convergence to a singular point for each average length. T his suggests a good correlation between resistivity and average length for element -dominated films. In this case, the film resistivity is independent of the number of junctions, but depends on the length and number of conducting paths between the source a nd drain electrodes, which correlate with average length. However, it is evident from Fig. 4 13(d) that as the average length decreases, the four data series increasingly diverge. Furthermore, Fig. 4 13(c) shows a corresponding convergence in the resistiv ity versus RMS length plots for small lengths. These observations can be better understood by plotting the percolation probability versus average length and RMS length, as shown in Figs. 4 14(a) and (b), respectively. Percolation probability is a geometri cal quantity which is independent of whether a film is junction or element -dominated. It is clear from Figs. 4 14 that when the percolation probability drops below 1, it shows a better correlation with RMS

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65 length compared to average length. Physically, this is due to the fact that a conducting path may only extend to another element at a junction, which is proportional to the circular probabilistic self area swept out by each element, as previously shown in Fig. 4 12(d) and discussed in previous work [141,142] Since percolation probability correlates with RMS length, which is itself a formulation of average self area, percolation effects are seen to drive the resistivity scaling toward RMS length for short element lengths, as observed in Figs. 4 13(c) and (d) At this point, it is worth discussing the applicability of the concept of excluded area introduced by Balberg et al [142] in determining the percolation threshold [143] for a 2D network of elements with a length distribution. A logical extension of the excluded area idea for a system of widthless sticks with a length distibution ) l (CNT gives the averag e excluded area A as j i CNTl A sin2 where i and j are the angles two interacting sticks labeled by i and j make with the horizontal axis, respectively (See Fig. 1 in Ref. [142] ). This result, wh ich is proportional to average length, contradicts the simulation results in Figs. 4 14 and other Monte Carlo simulations reported in the literature. As also discussed by Balberg et al [142] the proper ave raging of the excluded area suggested by my Monte Carlo simulations is j i CNTl A sin2 which is proportional to RMS length. This implies that the concept of self area associated with a n element illustrated in Fig. 4 12(d) explains the simulation re sults near the percolation threshold better when there is a length distribution, although its geometrical meaning is not as transparent as that of excluded area. Finally, I have also studied the effect of alignment of elements in the film on the resistivity for different length distributions. Figure 4 15(a) shows normalized resistivity as a function of alignment angle a for the CNT film where each data series has a fixed RMS of 1.8 m, but a

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66 different relationship. As reported above for the case of fixed element length (see Fig. 4 8) the curves are not monotonic, but rather they reach a minimum at some intermediate a that is neither perfectly aligned nor unaligned for all cases of and As the alignment angle decreases and imposes tighter constraints on the orientations of the elements, the RMS correlation observed for junctiondominated films vanishes. A similar result is observed for the average length correlation of element -dominated film s in Fig. 4 15(b), where each data series has a fixed average length of 1.8 m, but a different relationship. Similar to the explanation of Fig. 4 13(b), since wider length distributions exhibit a smaller resistivity in Figs. 4 15, and m m CNT n n CNTl l fo r n > m for a particular length distribution, these results indicate that the correlation for aligned film s shifts towards higher power mean lengths, namely towards the third power mean 3 3 CNTl for both resistive regimes. Indeed, the increasing divergence of the plots with alignment represents an increasing reliance on longer elements to carry charge from source to drain. In an attempt to explain this result, first let us consider a network with fixed element length lCNT [121,142,144] For aligned elements (i.e. small a ), I compute the average longitudinal (source -drain direction) displacement of a n element for all given by a a CNT CNTl d la a ) sin( ) cos( 2 where 1) 4 (a is the uniform angular distribution Physically, this quantity measures how much a particular conducting element aids in ferrying charge from source to drain, which we see increases with decreasing a This effect competes with the corresponding shrinking probabilistic contact self area which rationalizes the region of minimum resistivity observed in Fig. 4 15 for slight network anisotropy as the region where the

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67 two effects rever se in dominance. In order to combine the contribution of these effects into one quantity, a natural choice is to multiply these effects together; interestingly, the result is a formulation proportional to 3l Although it seems possibl e to generalize this to 3l (and therefore 3 3l) for a length distribution, the literature suggests there is no obvious correlation for systems with even slight anisotropy, such as alignment [142,145] Regardless, increasing alignment can be seen to increase the relative weight of longer elements to the overall conduction, hence driving the resistiv ity scaling toward higher power mean lengths. To summarize, my study of the CNT film in this chapter using Monte Carlo simulations illustrate s clearly that near the percolation threshold, the resistivity of the nanotube film exhibits an inverse power law dependence on all of the discussed parameters. In other words, regardless of how we approach the percolation threshold, we observe an inverse power law behavior, which is a distinct signature of percolating conduction. However, the strength of resistivity scaling for each parameter, represented by the corresponding critical exponent, is different. This strength depends on how strongly a particular parameter changes the number or characteristics of available conduction paths in the film. Furthermore, these parameters are not completely independent. For example, as I have demonstrated explicitly, the strength of resistivity scaling with device width depends on nanotube density, length, and alignment. I have also studied the effect of nanotube length distribu tion on the resistivity length scaling for CNT films and films with elements that are significantly more resistive compared to the element -el ement junctions. I have observed that network resistivity correlates well with RMS length for CNT films and with average length for element -dominated networks. In the latter case, percolation effects drive the correlation towards RMS length for short average lengths. Furthermore, in each case, alignment

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68 of nanotubes/ elements in the network places increasing weight on the longest elements, shifting the cor relation to higher power means. The results presented above show that, despite their relativ e simplicity, the models I have used can capture the essential physics of the experimentally observed resistivity scaling in single -walled nanotube films, and they can provide valuable physical insights into the effects of various nanotube and device parameters on the geometry -dependent resistivity scaling in these films. Furthermore, these re sults are not limited to carbon nanotubes, but are applicable to a broader range of problems involving percolating transport in networks, composites, or films made up of one -dimensional conductors, s uch as nanowires and nanorods.

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69 Figure 4 1 Comparison of the texture of computationally and experimentally generated CNT networks: (a) A 2D random nanotube network generated using a Monte Carlo process for a device with device length L = 4 m, device width W = 4 m, lCNT = 2 m and n = 4 m2. (b) AFM image of a nanotube film etched into a series of lines with width and spacing of 500 nm by e -beam lithography and reactive ion etching (chapter 2).

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70 Figure 4 2 Computational analysis of the effect of device length and width on normalized resistivity : (a) Log log plot of normalized nanotube film resistivity versus device width The individual data points are the experimental results from chapter 3, Figure 3 3, for a nanotube film with device length L = 7, 50, or 200 m (labeled by different symbols) and average thickness t = 15 nm The solid line represents my simulation best fit to the experimental data with Rratio = 100 and n = 2 m2. The other simulation parameters are L = 7 m, lCNT = 2 m, and t = 15 nm. (b) Log -log plot of normalized resistivity versus device length L for three different nanotube densities n as labeled by different symbols in the plot, calculated using my simulation code for a device with W = 2 m

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71 Figure 4 3 Effect of resista nce ratio on resistivity: Main panel is a l oglog plot of normalized resistivity versus device width for Rratio ranging from 102 to 104, labeled by different symbols The values of the critical exponent extracted from the slopes of the vs. W curve s near the percolation threshold (i.e. at small W ) are 0.5, 0.8, 1.55 and 1.95 for Rratio = 102, 1, 102, and 104, respectively. The inset shows the critical exponent as a function of the resistance ratio The symbols are the simulation results and the solid line represents a sigmoidal fit showing a smooth transition between

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72 Figure 4 4 Effect of nanotube density on resistivity and percolation probability: (a) Log -log plot of n ormaliz ed resistivity versus device width for four nanotube densities n ranging from 1 to 3 m2, labeled by different symbols. The values of the critical exponent extracted from the slope of the vs. W curve s near the percolation threshold are 1.1, 1.35, 1.55, and 2.2 for n = 1, 1.5, 2, and 3 m2, respectively. (b ) Percolation probability P versus device wid th for n ranging from 1 to 3 m2. The inset shows the log log plot of normalized resistivity versus nanotube density plotted for a device with L = 4 m, W = 4 m

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73 Figure 4 5 Effect of nanotube length on resistivity: (a) Log -log plot of n ormalized resistivity versus device width for three nanotube lengths lCNT ranging from 1.5 to 4 m, labeled by different symbols. Simulation parameters are the same as in Fig. 4 2(a) except for L = 4 m The values of the critical exponent extracted from the slope of the vs. W curve s near the percolation threshold are 1.0, 1.55, and 2.05 for lCNT = 1.5, 2, and 4 m, respectively. (b) Log -log plot of n ormalized resistivity versus nanotube length for three different n lCNT relationships Simulation parameters are the same as in Fig. 4 2(a), except L = 3 m.

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74 Figure 4 6 A 2D nanotube network generated using a Monte Carlo process for a device with device length L = 4 m, device width W = 4 m, lCNT = 2 m, n = 2 m2, and t = 15 nm. In this case, the nanotube alignment angle a = 27o and the measurement direction angle m = 45o, where the definition of the two angles are illustrated in the inset. Figure 4 7 Effect of nanotube alignment angle on resistivity scaling with device width: Main panel is a l oglog plot of n ormalized resistivity versus device width at three nanotube alignment angles a ranging from 18o ( partially aligned ) to 90o ( completely random ). The values of the critical exponent extracted from the slope of the vs. W curve s near the percolation threshold are 0.7, 1.35, and 1.55 for a = 18o, 36o, and 90o, respectively. The ins et shows the loglog plot of n ormalized resistivity versus nanotube alignment angle a for a device with W = 2 m.

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75 Figure 4 8 Effect of nanotube alignment angle and measurement direction angle on resistivity: (a) Log log plot of normalized resistivity versus nanotube alignment angle for three measurement direction angles ranging from 0o to 90o. Device length L = 7 m, device width W = 2 m, lCNT = 2 m, n = 2 m2, and t = 15 nm. The inset shows the percolation probability versus nanotube alignment angle a for the same set of m. (b) Log log plot of normalized resistivity versus measurement direction angle for six nanotube alignment angles ranging from 18o to 90o. The values of the measurement direction critical exponents extracted from the slope of the vs. m curves near the percolation threshold (i.e. at large m) are = 2.9 2.9, 2.7, 1.85, 0.65, and 0 for a = 18o, 27o, 36o, 45o, 72o, and 90o, respectively. The inset shows m Max vs. a.

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76 Figure 4 9 Effect of nanotube length on resistivity scaling with nanotube alignment angle and measurement direction angle: (a) Log log plot of normalized resistivity versus nanotube alignment angle for three nanotube lengths ranging from 1.5 to 3 m when m = 0o. Re sistivity minima are located at a min ~ 55o, 45o, and 30o and alignment critical exponent values are = 2.9 2.9, and 1.6 for lCNT = 1.5, 2, and 3 m, respectively. The inset depicts a min versus nanotube length. (b) Loglog plot of normalized resistivity versus measurement direction angle for three nanotube lengths ranging from 1.5 to 3 m when a = 18o.

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77 Figure 4 10. Effect of nanotube density on resistivity scaling with nanotube alignment angle and measurement direction angle: (a) Log log plot of normalized resistivity versus nanotube alignment angle for four nanotube densities per layer ranging from 1 to 3 m2 when m = 0o. a min values are located at ~ 50o, 45o, 45o, and 40o and = 2.8, 3.0, 2.9, and 2.9 for n = 1, 1.5, 2, and 3 m2, respectively. The inset shows the percolation probability versus nanotube alignment angle a for the same set of n (b) Log log plot of normalized resistivity versus measurement direction angle for four nanotube densities per laye r ranging from 1 to 3 m2 when a = 18o. The inset shows the percolation probability versus m for the same set of n

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78 Figure 4 11. Effect of device length on resistivity scaling with nanotube alignment angle: Main panel is a l oglog plot of normalized resistivity versus nanotube alignment angle for three device lengths ranging from L = 2 to 7 m, when m = 0o. The inset depicts loglog plot of normalized resistivity versus measurement direction angle for two device lengths ( L = 2 and 7 m) when a = 18o. Figure 4 12. Generated CNT networks consisted of nanotubes with a length distribution: (a) A random 2D network in which nanotubes are generated with various lengths following a lognormal length distribution. (b) Illustration of the definition of the alignment angle a (Same definition as in Fig. 4 6) (c) Various lognormal length distributions with the solid and long-dashed curves sharing the same average length and solid and short dashed curves sharing the same RMS length. (d) Illustration of the circular probabilistic self area swept out by a particular element (shaded).

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79 Figure 4 1 3 Effect of nanotube length distribution on resistivity: (a) Log log plot of normalized resistivity of a CNT film versus (a) average element length and (b) RMS length for four different relationships (labeled by different symbols). The network has a thickness of five -layers with device length L = 15 m, device width W = 15 m, and density per layer n = 1.2 m2. Log log plot of normalized resistivity of a n element dominated network versus (c) RMS length and (d) average length using the same device parameters as in parts (a) and (b).

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80 Figure 4 14. Effect of nanotube length distribution on percolation probabilit y: Percolation probability versus log (a) average and (b) RMS length for the resistivity data in Fig. 4 13. Only two plots are shown since percolation probability is a geometrical quantity which is independent of whether a film is junctionor element dom inated. Figure 4 15. Effect of nanotube length distribution on resistivity scaling with alignment angle: Log log plot of normalized resistivity versus alignment angle for (a) CNT (junction dominated) film with fixed RMS length = 1.8 m a nd (b) element -dominated film with fixed average length = 1.8 m for four different relationships, as labeled by different symbols. Both plots show a progressive divergence of the data for highly aligned networks.

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81 CHAPTER 5 METAL SEMICO NDUCTING -METAL P HOTODETECTORS BASED ON CNT FILM GAAS AND CNT FILM -SI SCHOTTKY CONTACTS Introduction As I mentioned in chapter 1, CNT film is a conductive and transparent material [61 63,65] maki ng it promising as a contact layer for optoelectronic and photovoltaic devices, such as light emitting diodes (LEDs) [70 73] organic solar cells [74 77] and electrochromic devices [78] Recently, CNT films have been used as ohmic contacts on GaN [70] and organic materials [72 77] in LEDs and solar cells Also, the contact between a single nanotube and highly d oped GaAs substrate is studied before [146] Furthermore, a previous study on the transport between vertical nanotubes and Si substrate has shown that the transport mechanism was a combination of tunneling and thermionic emission [147,148] Nevertheless optoelectronic devices where the CNT film is used as a uniform Schottky contact material have not been previously demonstrated. In this chapter I demonstrate the Schottky behavior of CNT film contacts on GaAs and Si by fabri cating and characterizing Metal Semiconductor -Metal (MSM) photodetectors with CNT film electrodes First, we look at DC electr ical characteristics (i.e. dark and photocurrent) of MSM photodetectors, their potential applications and the use of highly transparent and conductive electrode s for performance improvement Then I explain the fabrication process of MSM structures with interdigitated CNT film finger electrodes. By studying the temperature dependence of the dark current of the fabricated MSM devices I find the mechanisms responsible for transport in these devices and extract the Schottky barrier height of the CNT film on GaAs and Si In order to determine the type of carrier responsible for the current transport, I also fabricate MSM str uctures with asymmetric CNT film contact areas, without the interdigitated fingers between the electrode pads. Furthermore, I characterize the effect of device geometry on the dark current, and find that dark current scales rationally with geometrical

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82 par ameters such as finger width, finger spacing, and device active area. I also compare the dark and photocurrent of the CNT film -based MSM photodetectors with standard metal -based MSMs. My results not only provide insight into the fundamental p roperties of the CNT film GaAs and CNT film Si junctions but also successfully demonstrate the integration of CNT films as Schottky electrodes in conventional semiconductor optoelectronic devices. Characteristics of MSM P hotodetector s MSM photodetectors c onsist of two back to -back Schottky diodes formed from a semiconducting material and two metallic contacts, as can be seen in Fig. 5 -1 [149,150] As for the fabrication, usual ly semiconductor material is used as the substrate and metallic contacts are patterned on the surface of the semiconductor. Although the structure is usually symmetric, asymmetric structures can be fabricated by patterning two metallic contacts with differ ent surface areas. For such a structure, w hen a bias is applied between the metallic contacts, one of the diodes operates in the forward bias, while the other diode operates in the reverse bias and its depletion region extends into the semiconductor. If the bias is high enough, all the surface of the semiconductor becomes depleted. In that case, if a light source shines on the surface, electronhole pairs that are generated in t he substrate can be collected efficiently by the contacts. In order to optimize the operation of such a device there are several device parameters that need to be designed carefully. First, the substrate is usually chosen with a light level of doping, so that depletion region can extend easily in the substrate by applying a small am ount of voltage. Similarly, the distance between the contacts should be designed carefully. Usually, contact pads are designed as interdigitated fingers, which results in an increase in the effective area that the contacts cover (see Fig. 5 1) Quality of the Schottky contacts is also of critical importance; device performance can be degraded due to the low quality of the interface, which lowers the amount of current and affects the transient response of the device.

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83 If the diodes are ideal an d identical, the transport is due to the thermionic injection of electrons/holes over the barrier s or their tunneling through the m Drift/diffusion mechanisms are also responsible for the transport of the minority carriers through the semiconductor. At room temperature, tunneling is important only when the barrier is thin or if the contacts are very close to each other. Thin barriers are a result of highly doped substrates or high electric fields. For low -doped substrates and moderate voltage values, tunnel ing should be negligible at room temperature. However, at lower temperatures, electrons/holes do not have enough energy to surpass the barrier. In that case, tunneling might become significant. In this section, I am going to employ t hermionic emission the ory to derive the current equations at various applied voltage s ( Va) for an MSM photodetec tor with a donor concentration (equal to ND) under dark conditions. Figure 5 2 illustrate s a simple schematic and band diagram of the symmetric device under study at equilibrium As defined in the figure, S is the spacing between the metal contacts, and Bn and Bp represent the electron and hole barrier heights, respectively and Vbi denotes the built in potential. The depletion layer width W at each contact is given by : D bi SqN V W2 (5 1) w here q is the electron charge and S is the semiconductor permittivity. When a small positive voltage (smaller than the reach -through voltage VRT to be defined below ) is applied to contact 2 with respect to contact 1, contact 1 is reverse biased, whereas contact 2 is forward biased. The quantity qV1 is the difference between the Fermi level (EF) of contact 1 and EF of the semiconductor, and the quantity qV2 is the dif ference between the EF of

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84 the semiconductor and EF of contact 2. Please note that 2 1V V Va There is an electron current Jn due to the thermionic emission of electrons from contact 1, given by ) exp( 1 ) exp(1 2 *T k qV T k q T A JB B Bn n n (5 2 ) wh ere *nA is the effective Richardson constant for electrons, T is absolute temperature, kB is the Boltzmanns constant, and Bn is the effective electron barrier height under the applied electric field. There is also a hole current Jp due to the thermionic emission of holes from contact 2 and then their diffusion through the substrate given by 1 / cosh 1 / tanh2 11 2 2 1 2 T k p V T k q p T k qV p p no p pB qV bi Bp B Be L W W e T A e L L W W p qD J (5 3) where Dp is the hole diffusion coefficient, pno is the equilibrium hole density, Lp is the diffusion length, pA the effective Richardson constant for holes, Bp is the hole barrier height and W2-W1 is the distance that the holes diffuse. The value of the total dark current density (JDark) is the sum of the electron current density and the hole current density: p n DarkJ J J (5 4) As the applied voltage increases, the sum of the depletion widths also increases. The voltage at which the two depletion widths touch each other is defined as the reach though voltage VRT. This condition is illustrated in Fig. 5 3 (a) where the device is fully depleted. The expression for the reach -through voltage VRT can be found by setting the sum of the depletion widths equal to the spacing between the two metal electrodes S :

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85 bi S D S D RTV qN S S qN V 2 22 (5 5) When the applied voltage exceeds VRT, the hole current in Eq. ( 5 3) reduces to 122 T k V T k q p pB qV bi Bp Be e T A J (5 6) and the total dark current is given by the sum of Eqs. ( 5 2 ) and ( 5 6) As the applied voltage is increased even further, the electric field at the edge of the contact 2 becomes zero and the energy band at contact 2 becomes flat as shown in Fig. 5 3 (b ). This is known as the flat -band condition with the corresponding flat -band voltage VFB given by 22 S qN VS D FB (5 7 ) For Va > VFB, the expression for the electron current density is still given by Eq. (5 2 ). However, the hole current reduces to ) exp(* 2 *T k q T A JB Bp p p where Bp is the effective hole barrier height under the applied electric field. As a result, the total dark current can be written as *2 2 *Bp B Bn BT k q p T k q n p n Darke T A e T A J J J (5 8 ) Based on equations (5 2) to (5 8 ), total amount of dark current density, as well as its electron and hole components can be calculated, as is shown in Fig. 5 4 for a symmetric GaAs MSM structure with ND = 1014 cm3 and S = 20 m at T = 300oK Other parameters used in this calculation are mo = 9.11 1031 Kg, me = 0.067mo, mp = 0.45mo, Lp = 0.01 cm and Dp = 100 cm2/sec In Fig. 5 4 (a), where Bn = 0.82 V and Bp = 0.60 V, respectively. In this case, the electron current density is much larger than the hole current density for voltages less than the reach through voltage. As a result, the Jn term in Eq. ( 5 4) dominates the current behavior. On

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86 the other hand, for voltages greater than VRT, the neutral region reduces to zero and the hole current increases exponentially, according to Eq. ( 5 6). Consequently, the total current density is now dominated by the hole current density Jp. Above the flat -band voltage Jp in creases slowly according to the second term in Eq. ( 5 8 ). In Fig. 5 4 (b), on the other hand, the barrier height for holes was taken to be larger than that for electrons, i.e. Bn = 0.60 V and Bp = 0.82 V. In this case, the hole current density is always smaller than the electron current density. As a result, the total current density is given simply by Eq. ( 5 2), which slowly increases until breakdown conditions are reached. Finally, in Fig. 5 4 (c), the barrier height of electrons was set equal to that of the holes, i.e. Bn = Bp = Eg/2 = 0.71 V. In this case, the total current density for voltages larger than the flatband voltage (i.e. Va > VFB) is smaller than that in the previous two cases. Since the dark current is a function of the competition between electron injection at contact 1 and hole injection at contact 2, the lowest dark current is achieved when the electron Schottky barrier height Bn is approximately equal to half the bandgap o f the semiconductor material, which is 0.71 eV for GaAs which is expected to be the case theoretically, as well as experimentally [151] The photocurrent or optical response of a photodetector is usually characterized by either quantum efficiency or the responsivity Q uantum efficiency is defined as the number of electronhole pairs collected to produce the photocurrent Iph divided by the number of incident photons, i.e., h P q I inc ph/ / (5 9 ) where Pinc responsivity of a photodetector is defined as the photocurrent generated per incident power:

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87 W A m h q P I Rinc ph/ 24 1 ) ( (5 1 0 ) where is the wavelength of the light so urce in micrometers. Ideally, R should increase linearly with the wavelength for a fixed value of In reality is dependent on the absorption coefficient which also depends on the incident wavelength. Figure 5 5 compares the responsivity for an ideal and a real photodetector. In this schematic, we see two cut -off frequencies: c (short) which is due to the absorption of the incident optical energy very close to th e surface because of the large absorption coefficient in most semiconductors, and c (lon g) due to the inefficiency of the incident light (its energy being smaller than the bandgap of the semiconductor) to generate electron hole pairs. In addition, the responsivity of a photodetector depends on its effective absorption area For a regular MSM photodetector, incident l ight is mostly reflected over the area covered by the metal electrode fingers. Consequently, the effective absorption area under illuminati on is reduced. If a transparent material is used as the metal electrode, it can be expected that the effective area and therefore responsivity will be increased. As CNT film is transparent, the use of CNT film as the transparent electrode in MSM photodetectors is promising Fabrication and C haracterization of MSM P hotodetector s GaAs -based MSM photodetectors with CNT film electrodes were fabricated on nominally undoped (~ 810 1 2 cm) (100) GaAs substrates. After the GaAs substrate was cleaned by solvents, a ~100 nm thick silicon nitride (SiN) isolation layer was deposi ted on the substrate using plasma enhanced chemical vapor deposition (PECVD) ( Fig. 5 6(a)). Subsequently, active area windows of various dimensions were opened in the SiN film using plasma etching. This was followed by the deposition of ~40 nm thick CNT film, using the vacuum -filtration method explained in chapter 2 (F ig. 5 6(b)). The deposited CNT film had a resistivity of about 104

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88 .cm The CNT film was then patterned into interdigitated finger electrodes based on the recipe mentioned in chapter 2 (Fig. 5 6(c)) Finally, for ease of electrical probing, a Chromium/Palladium (7 nm/43 nm) metal stack was patterned on the nanotube film contact pads using photolithography, e beam evapor ation, and subsequent lift -off (Fig. 5 -6(d)). The CNT film contact p ads end up on top of the SiN isolation, which eliminates parasitic leakage paths, and therefore reduces the dark current [152] Figure 5 6 (e) shows the optical microscope image of a finis hed MSM photodetector and Fig. 5 6 (f) shows the AFM image of the area between two CNT film electrode fingers. In order to study the effect of device geometry on the dark current, MSM devices with different active area width FW finger length FL finger width W and finger spacing S were fabricated. These dimensions are labeled in Fig. 5 6 (e). Finger widths smaller than 5 m were not used, since I showed by 4 point -probe measurements and Monte Carlo simulations in chapters 3 and 4 that the CNT film resistivity increases strongly at smaller widths because the film approaches the percolation threshold. In order to compare the CNT film -based MSM photodetectors wi th the standard metal based MSMs, a control sample with e beam evaporated Cr/Pd (7/43 nm) metal electrodes instead of the CNT film was also fabricated. Si -based MSM structures with CNT film electrodes were fabricated using the same approach. They were fabricated on lightly doped (1014 1015 cm3) n and p type Si substrates. After the growth of a 4 00 nm thick thermal oxide, a ctive area windows of various d imensions were etched in the oxide using HF This was followed by the deposition of a ~ 50 nm thick CNT film The CNT film was then patterned into interdigitated finger electrodes by photolithography and inductively coupled plasma (ICP) etching, and for electrical probing, a Chromium/Palladium metal stack was patterned on the CNT film contact pads using e beam evaporation Figure 5 7 (a ) shows an optica l microscope image of a finished Si -based MSM device, illustrating the

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89 various device dimensions (as in Fig. 5 6) such as FW FL W and S Figure 5 7 (b ) shows the AFM image of the area between two CNT film electrode fingers. Let us first study the dark current of the fabricated MSM photodetectors. Figures 5 8(a) and (b) show the I -V and C -V cha racteristics (measured using a Keithley 4200 Semiconductor Characterization System and an HP 4294A Impedance Analyzer) respectively, at room temperature for a CNT film -Si MSM device with W = S = 50 m and FL = FW = 300 m O ther devices with different dimensions have resulted in similar characteristics The data in Fig. 5 8 clearly exhibit the characteristic I -V and C -V curves of two back to -back Schottky diodes [149], demonstrating that the CNT film forms a Schottky contact on Si. More o ver, the symmetry of the I-V and C -V curves indicates that the two Schottky diodes are identical, confirming that the CNT film acts as a uniform electronic material. The concave increase of the current and the appearance of a transition point at small voltages displayed in Fig. 5 8 (a) are not expected for an ideal MSM device [149] As previous studies on the current transport in metal -insulator -semiconductor -insulator -metal (MISIM) structures suggest, the existence of a thin layer of oxide between the CNT film and Si would result in an IV curve with a shape similar to that in Fig. 5 8 (a) [153] Since the CNT film is porous it is likely that native oxide forms at the CNT film Si interface, resulting in the observed features in the I -V curves Since any native oxide that forms would be very thin, thermionic emission theory can still be used to analyze the transport across the CNT film -Si junction, as discussed below. Also, as I have shown above, in an MSM structure, at high applied voltage, t he reverse biased contact limits the current and results in current saturation. Fig. 5 8 (a), however, shows that the current does not saturate at high voltages, but rather increases monotonically with applied voltage. This could result from Schottky barr ier lowering due to charge accumulation at

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90 surface states and due to the strong electric field at the edges of the electrodes [154] or individual nanotubes. The inset in Fig. 5 9 (a) shows the dark IV characteristics for a CNT film -GaAs MSM device with W = S = 15 m and FL = FW = 300 m at room temperature (294 K) in linear scale. The data clearly exhibit the characteristic I -V curves of two back to -back Schottky diodes making up the MSM photodetector (similar to Si -based devices), demonstrating that the CNT film makes a Schottky cont act to GaAs. The main panel in Fig. 5 9 (a) shows the dark (i.e. no illumination) log I -V characteristics for the same device measured at 6 different temperatures between 230 and 340 K using a Lakeshore Cryotronics TTP4 low temperature probe station. During these measurements, the substrate was under vacuum and electrically floating. Fig. 5 9 (a) shows that after the first steep rise, the current does not completely saturate at high voltages, but slowly increases with increasing voltage. Like the Si case, t his slow increase in the current at higher voltages can be explained by Schottky barrier lowering due to charge accumulation at surface states, and image force lowering at the edges of the electrodes where there is a strong electric field, as previously reported for MSM photodetectors [154,155] The Schottky barrier height of the CNT film -GaAs or CNT film -Si junction can be extracted from the temperature -dependent I -V measurements. At high bias voltages (i.e. voltages larger than the flat -band voltage), the total dark current in an MSM device based on thermionic emission theory is given by equation ( 5 8), repeated here for convenience: T k q T k q p T k q T k q nB Bp B Bp B Bn B Bne e T AA e e T AA I/ / 2 / / 2 (5 11) where A is the effective area, nA and pA are the effective Richardson constants for electrons and holes, respectively, T is the absolute temperature, q is the electronic charge, Bn

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91 and Bpare the electron and hole Schottky barrier heights, respectively, and Bn and Bp are the Schottky barrier height lowerings for electrons and holes, respectively. If Bp Bn or Bp Bn only one of the terms in Eq. ( 5 11) dominates On the other hand, if Bn and Bpare comparable, both terms must be included. Furtherm ore, since both M S contacts are identical, g Bp BnE where Eg is the bandgap of GaAs or Si As a result, if /2 or g Bp BnE only the electron or the hole term, respectively, dominates the total current. I n such a case where only one type of carrier dominates Eq. ( 5 11), the corresponding Schottky barrier height can be obtained from the slope of the Richardson plot of log I/T2 versus 1/T The Richardson plot of the current -temperature data in the temperature range 280 to 340 K for the MSM device in Fig. 5 9 (a) at V = 3 V, together with the corresponding data for two other devices, which have the sam e active area but different width and spacing, are shown in Fig. 5 9 (b). From the slope of these plots, Schottky barrier heights of B = 0.53, 0.54, and 0.54 eV are extracted for devices with W = S = 15, 20, and 30 m, respectively. The similarity in the barrier height values extracted for these devices confirms that the CNT film GaAs interface is uniform from device to device and does not depend on contact geometry. Extracted barrier heights represent an effective value resulting f rom an ensemble averaging of barriers formed between the GaAs substrate and metallic/semiconducting nanotubes in the CNT film with various chirality, diameter, and doping levels. Since the Richardson plots exhibit a straight line and the extracted barrier height value of ~0.54 eV is much smaller than half the GaAs bandgap of Eg ~1.42 eV, either holes or electrons, but not both, must be the dominant carriers responsible for the current transport in the MSM devices. However, based on this temperature -depend ent I -V data alone, the type of carrier cannot be determined.

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92 In order to determine the type of carrier responsible for the current transport, I have also fabricated GaAs-based MSM structures with asymmetric CNT film contact areas, without the interdigit ated fingers between the electrode pads, as illustrated in Fig. 5 10(a). Figure 5 10(b) shows the dark I -V characteristics for one of these structures with a source contact area of 410 16 m2 and a drain contact area of 410 4 m2. The voltage is applied to the smaller drain contact and the larger source contact is grounded, as shown in Fig. 5 10(a). The band diagrams corresponding to positive and negative voltage bias are shown in Figs. 5 10(c) and (d), respectively. At po sitive voltage bias, when electrons are injected over the large contact and holes over the small contact, the current is large, and at negative voltage bias, when electrons are injected over the small contact and holes over the large contact, the current i s small. This proves that electrons dominate the current transport in these devices. As a result, my dark current characterization of the CNT film GaAs MSM devices implies that thermionic emission of electrons over a Schottky barrier of height 54 0.Bn eV is the dominant transport mechanism at temperatures above 260 K. Assuming an ideal M S junction where the Fermi level is not pinned, this extracted barrier height corresponds to a CNT film workfunction of 6 4.M eV, which is in excellent agreement with the range of previously reported workfunction values [156,157] The inset in the Richardson plot of Fig. 5 9 (b) shows current versus 1/T for the device with W = S = 20 m in a wider temperature window (from 150 K to 340 K) at V = 3 V. As it can be seen, the current starts to saturate at temperatures lower than ~260 K, which suggests that tunneling, which depends weakly on temperature, begins to domina te the transport across the CNT film GaAs junction at lower temperatures [158,159]

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93 Similar approach was followed to extract the Schottky barrier height between the CNT film and Si, i.e. the IV characteristics of several MSM devices as a function of temperature was measured. Figure 5 11(a) shows the log I -V curves of a CNT film p type Si MSM device at t emperatures between 150 and 340K. The Schottky barrier height of the CNT film -Si junction have been extracted from the slope of the Richardson plot of log I/T2 versus 1/T at a fixed voltage Figure 5 11(b) depicts the Richardson plots for two n type Si and two p type Si MSM devices with CNT film electrodes in the temperature range 260 to 340K at 3 V voltage bias. From the slopes of Richardson plots for eight n type Si and five p type Si MSM structures, an electron barrier height of 03. 0 45 0 Bn eV and a hole barrier height of 04 0 51 0 Bp eV were extracted, respectively, showing that thermionic emission dominates the current transport in this temperature range. Table 5 1 shows the details of the extracted barrier height values and device dimensions for all of n type and p type devices, indicating that the variation in extracted values is quite small for various device dimensions. Furthermore, the type s of carrier s responsible for conduction in n and p -type Si devices were confirmed as el ectrons and holes, respectively from the asymmetric device measurements Under the assumption that the Fermi level is not pinned, the workfunction of the CNT f ilm was determined to be 03 0 50 4 .M eV and 04 066 4 .M eV from the n type and p type Si MSM device measurements, respectively (Again, in good agreement with the previous ly reported carbon nanotube workfunction values). It is worth noting that the barrier height and workfunction values reported here include the effect of Schottky barrier lowering since they have been extracted at high bias. F urthermore, t he dedoping of the film during the fabrication process [113] most likely reduces the extracted workfunction value. As a result, measurements on isolated M -S junctions in a controlled environment are necessary for a more accurate determination of the zero -bias barrier heights and

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94 the effect of film doping and dedoping on its workfunction. The inset of Fig. 511(b) shows log I vs. 1/ T for one p -type Si and one n type Si MSM device in the temperature range 150340 K. Once again, t he saturation of the current at temperatures below 240 K suggests that tunneling, which depends weakly on temperature, becomes the dominant current transport mechanism across the CNT film -Si junc tion at lower temperatures [158] Next, I study the effect of the device geometry on the dark IV characteristics at room temperature (294 K). Figure 5 12(a) shows the dark I -V curves for GaAs-based devices with identical W FL and FW but with S ranging from 10 to 20 m. Increasing the spacing in these devices (with the same area) decreases the number of finger pairs n which is given by n = FW / 2( W + S ). This decrease in turn reduces the amount of dark current in the device, in agreement with the trend observed in F i g. 5 12(a). Figure 5 12(b) shows the dark I -V curves for devices with identical FL and FW but with W = S ranging from 15 to 30 m. The dark current is found to monotonically decrease with an increase in W. It has been observed that in MSM detectors, be yond a certain finger width, the dark current becomes roughly independent of the width W and is proportional to the product of FL and n [160] This is due to current crowding at the edges of the electrodes as illustrated explicitly in Fig. 5 12(c), which shows a MEDICI simulation of the cross -sectional current density distribution in the GaAs substrate between two electrode fingers ( W = S = 20 m) at V = 3 V bias using the value of the barrier height obtained previously. It is evident from this simulation that current crowding occurs at the electrode edges, which results in the effective device area to be weakly dependent on the width of the electrode. Therefore, since FL and FW are constant and W = S for all the devices shown in Fig. 5 12(b), n thus the dark current should be inversely proportional to W in agreement with the observed trend in the figure. Finally, Fig. 5 12(d) shows the dark I -V curves for devices with identical W and S but with FL =

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95 FW ranging from 200 to 400 m. In this ca se both FL and n (which depends linearly on FW ) vary, resulting in a strong change in the amount of dark current, in agreement w ith the trend observed in Fig. 5 12(d). These results show that the dark current in CNT film GaAs MSM devices scales rationall y with device geometry. After the dark current, I characterize the photoresponse of the CNT film GaAs MSM photodetectors using an optical bench equipped with a 633 nm Beam Scan HeNe laser (6.5 mW power, ~830 m spot size) at room temperature and compare it with the Cr/Pd metal control samples. Figure 5 13 shows both the dark and the photo I -V curves for the CNT film and Cr/Pd metal control MSM devices of identical dimensions ( W = S = 30 m and FL = FW = 300 m). Due to th e low resistivity of the CNT film, the CNT film finger electrodes do not limit the photocurrent even under illumination at high voltage bias. For example, for the device in Fig. 5 13, the series resistance due to the CNT film electrode fingers is more than two orders of magnitude smaller than the measured MSM device resistance at 10 V and under laser illumination It can be seen in Fig. 5 1 3 that the dark current of the CNT film GaAs MSM device is significantly lower than that of the Cr/Pd control device, while the photocurrents are comparable particularly at high applied bias voltages. This results in a significantly improved normalized photocurrent -to -dark current ratio (N PD R [161] ) for the CNT film MSM device relative to that of the c ontrol device while achieving a comparable responsivity (defined as the photocurrent generated per unit incident optical power ). Responsivity and NPDR values extracted for the CNT film GaAs MSM photodetector in Fig. 5 1 3 are 0.161 A/W and 3.62106 mW1 at V = 10 V respectively. The lower dark current of the CNT film device is most likely the result of the smaller effective contact area between the mesh of nanotubes making up the porous CNT film

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96 and the GaAs substrate, considering that the reported values of the Schottky barrier height for as deposited Cr layers on GaAs are typically higher than the barrier height that I have extracted for the CNT film contact on GaAs [162 164] Since the morphology of the CNT film and its interface with a substrate are very different than those of a planar spatially homogeneous metal thin film having the same workfunction, more controlled fundamental measurements of the interface properties of CNT film GaAs junctions are necessary in order to better elucidate the link between the structural and electronic properties of the CNT film GaAs metal -semiconductor junctions. Figure 5 13 also shows that photocurrents of the control device and particularly the CNT film do not saturate, but increase with applied voltage. This dependence on voltage is much more pronounced than that of the dark current. In an MSM structure, the depletion region depth inside the semiconductor increases with hi gher applied voltages, which enables the collection of more photogenerated electron-hole pairs. However, the depletion region depth of the nominally undoped GaAs substrates used in this work (1.59 cm at 3 V) is significantly larger than the absorption leng th of GaAs at = 633 nm wavelength ( 5.9 05 cm). As a result, the depletion depth increase cannot account for the increased current in this case. An alternative explanation is that an increase in bias induces an increase in current by Schottky barrier lowering due to charge accumulation at the CNT film GaAs interface states and image force lowering at the edges of the electrodes similar to the dark current case [154] The electric field and current density are highest at the edges of the electrodes, as illustrated in the MEDICI simulation of Fig. 5 12(c), and as a result, the majority of the photogenerated carriers are collected there, amplifying the effect of image -force lowering at these edges.

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97 I also characterized the photoresponse of the CNT film -Si MSM structures and compare d it with the photoresponse of metal control samples. For Si -based metal control samples e -beam evaporated Ti /Au (30/70 nm) metal electrodes were deposited instead of CNT film electrodes. Figure 5 14 shows the dark and photo I -V curves f or the CNT film and Ti/Au control p -type Si MSM devices with identical dimensions Both th e dark and photocurrent of the CNT film MSM device is seen to be lower compared to the Ti/Au control. As the Schottky barrier height Bp between Ti and Si is not smaller than that between the CNT film and Si ( I have extracted slightly hi gher Bp values for the control samples compared to those for the CNT film samples [165] ), th e lower dark current of the CNT film device is most likely the result of the sm aller effective contact area between the mesh of nanotubes making up the porous CNT film and the Si substrate It is also evident from Fig. 5 14 that at high voltages, the photocurrent of the CNT film MSM device approaches to that of the Ti/Au control, re sulting in a comparable responsivity and a higher photocurrent -to -dark current ra tio Responsivity and NPDR values extracted for the CNT film Si MSM device at V = 5 V are 0.133 A/W and 1.71104 mW1, respectively. The stronger increase in the photocurrent of the CNT film MSM device compared to the Ti/Au control is most likely because of more defects at the CNT film -Si interface, which result in stronger Schottky barrier lowering [154]

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98 Figure 5 1 Schematics of MSM structure: ( a) top view of an MSM structure with interdigitatedfinger design ( b) cross -section al view of the same device along the AA line in part (a) (courtesy of Leila Noriega [166] ). Figure 5 2 Physical r epresentation of MSM structure: (a) device schematic in its simplest form (spacing between metal conta cts S) (b) band diagram under equilibrium for an N type semiconductor. Barrier heights and built in voltages are defined for both contacts [150] Figure 5 3 Band diagrams of the symmetric MSM structure, showing the (a) reach -through and (b) flat band conditions [150]

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99 Figure 5 4 Calculated current density versus applied bias for a symmetric GaAs MSM structure with ND = 1014 cm3 and S = 20 m at T = 300oK, with (a) Bn = 0.82 eV and Bp = 0.60 eV, (b) Bn = 0.60 eV and Bp = 0.82 eV and (c) Bn = Bp = 0.71 eV (courtesy of Leila Noriega [166] ). Figure 5 5 R esponsivity for an ideal (dotted line) and a real (solid line) photodetector. Responsivity, RWavelength,

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100 Figure 5 6 Fabrication of GaAs -based MSM photodetectors: (a) (d) Schematic of the process flow for GaAsbased MSM photodetectors with CNT film electrodes along the dashed line AB shown in part (e): (a) SiN isolation layer deposited on a GaAs substrate, (b) CNT film prepared by vacuum -filtration deposited on the substrate after opening the active windows in the SiN layer, (c) CNT film patterned into interdigitated electrode fingers by photolithography and ICP etching, and (d) Cr/Pd metal contacts patterned on the nanotube film contact pads using photolithography, e beam evaporation, and subsequent lift -of f. (e) Optical microscope image of the finished MSM photodetector, showing the various device dimensions. (f) AFM image showing the area between two CNT film electrode fingers of the MSM device of part (e).

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101 Figure 5 7 Fabrication of Si -based MS M photodetectors: (a) Top view optical microscope image of a CNT film Si MSM structure, showing the definition of various device dimensions. ( b ) AFM image showing the area between two CNT film electrode fingers of the MSM structure. Figure 5 8 Si bas ed MSM dark characteristics: (a) Current -voltage and (b) Capacitance -voltage characteristics measured at room temperature for a CNT film n type Si MSM structure with FL = FW = 300 m and W = S = 50 m.

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102 Figure 5 9 T em perature -dependence of the GaAs-based MSM dark current: (a) Dark current versus applied voltage measured at 6 differen t temperatures between 230 and 340 K for a CNT film GaAs MSM device with W = S = 15 m and FL = FW = 300 m. The inset shows the dark IV characteristics of this d evice at room temperature (294 K) in linear scale. (b) The Richardson plot of log I/T2 versus 1/T at V = 3 V voltage bias in the temperature range 280 to 340 K for three CNT film -GaAs MSM devices of identical active area ( FL = FW = 300 m), but differen t finger width W and spacing S as labeled in the figure. The dashed lines are linear best -fits to the experimental data, from the slope of which Schottky barrier heights of B = 0.53, 0.54, and 0.54 eV are extracted for devices with W = S = 15, 20, and 30 m, respectively. The inset shows log current versus 1/T for the MSM device with W = S = 20 m in a wider temperature window (from 150 to 340 K) at V = 3 V bias.

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103 Figure 5 10. Characterization of asymmetric GaAs -based MSM structur es: (a) The schematic and (b) measured dark current versus applied voltage for a CNT film GaAs MSM device without the interdigitated fingers between the electrode pads, but with asymmetric CNT film contact areas. The source contact area is 16 104 m2 and the drain contact area is 4 104 m2. The voltage is applied to the smaller drain contact and the larger source contact is grounded, as shown in (a). The band diagrams illustrating electron thermionic emission over the Schottky barrier for (c) positiv e and (d) negative voltage bias.

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104 Figure 5 11. Temperature dependence of the Si -based MSM dark current: (a) Log current versus applied voltage measured at nine different temperatures between 150 and 340K for a CNT film p type Si MSM device with W = 5 m, S = 10 m, and FL = FW = 300 m. (b) The Richardson plot of log I/T2 versus 1/T at V = 3 V bias in the temperature range 260 to 340K for four CNT film -Si MSM devices of identical active area ( FL = FW = 300 m) and finger width ( W = 5 m), but different finger spacing S and different Si doping type. F rom the slope of the linear fits Schottky barrier heights of Bn = 0.45 and 0.46 eV and B p = 0.50 and 0.52 eV are extracted for S = 20 and 30 m n type and for S = 10 and 30 m p type Si de vices, respectively. The inset shows log current versus 1/T for the n type and p type Si MSM structures with S = 30 m in a wider temperature window (from 150 to 340K) at V = 3 V bias.

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105 Table 5 1 Device dimensions and extracted barrier heights for 8 n type and 5 p type Si based MSM structures. The average extracted barrier heights are 0.51 0.04 for p -type devices and 0.45 0.03 for n type devices. Substrate Type FO and FW ( m) W ( m) S ( m) Ext racted Barrier Height (eV) N type 300 5 5 0.451 N type 300 5 20 0.454 N type 300 5 30 0.464 N type 400 5 10 0.454 N type 400 5 20 0.460 N type 400 10 10 0.428 N type 400 15 15 0.446 N type 400 20 20 0.417 P type 300 5 10 0.504 P type 300 5 15 0.545 P type 300 5 20 0.472 P type 300 5 30 0.521 P type 300 5 50 0.522

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106 Figure 5 1 2 Dependence of MSM current on device and finger dimensions: (a) Dark current versus applied voltage at room temperature (294 K) for CNT film GaAs MSM devices with W = 5 m and FL = FW = 400 m, but with spacing S ranging from 10 to 20 m, as labeled in the figure. (b) Dark current versus applied voltage for CNT film GaAs MSM devices with FL = FW = 300 m, but with W = S ranging from 15 to 30 m, as labeled in the figure. (c) MEDICI simulation of the cross -sectional current density distribution in the GaAs substrate between two CNT film electrode fingers ( W = S = 20 m) at V = 3 V bias calculated using the value of the barrier he ight extracted from the measurements. Darker colors correspond to higher current density. (d) Dark current versus applied voltage for CNT film GaAs MSM devices with W = 5 m and S = 15 m, but with FL = FW ranging from 200 to 400 m, as labeled in the figu re.

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107 Figure 5 1 3 Measured dark and photocurrent versus applied voltage for GaAs-based MSM photodetectors with CNT film and Cr/Pd metal electrodes, as labeled in the figure. For both devices, W = S = 30 m and FL = FW = 300 m. The dark current of the CNT film MSM device is significantly lower than that of the Cr/Pd control device, while the photocurrents are comparable, particularly at high applied bias voltages. Figure 5 14. Measured dark and photocurrent applied voltage for Si based MSM photodete ctors with CNT film and Ti/Au metal electrodes, as labeled in the figure. For both devices, W = 5 m, S = 15 m, and FL = FW = 300 m and Si is p type.

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108 CHAPTER 6 1/F NOISE SCALING AND TEMPERATURE DEPEND ENT TRANSPORT IN CAR BON NANOTUBE FILMS Introduction For some of the applications suggested for CNT films and networks, such as chemical and optoelectronic sensors, intrinsic signal to noise ratio is undoubtedly one of the most important device figures of merit that determine the detection limi t of the device [89,167] It has been shown that for both single nanotubes (regardless of their intrinsic parameters like diameter and chirality) and CNT films, 1/f noise level can be quite high compared to other conventional materials [168,169] As a result, determining the magnitude of the 1/ f noise, its sources, and its scaling with various CNT film parameters is crucial not on ly for understanding the fundamental physics of percolation transport, but also for assessing the potential of CNT films for applications where the device noise is an important figure of merit [170] One of the first reports on 1/ f noise in single -walled carbon nanotube networks and mats [168] observed that the noise obeys the empirical equation, f A I SI2 (6 1) where SI is the current noise spectral density, I is the current bias, f is the frequency, is a constant close to 1, and A is the noise amplitude, which is a measure of the 1/ f noise level [168,171] Furthermore, the noise amplitude A was reported to be proportional to the device resistance R namely R A1110 Later studies showed that dependence of A on device parameters, such as device length and resistivity, is more complicated than that [169,172] For example, in CNT networks, the dependence of A on device length L was reported to be 3 1 1110 9 L R A (Fig. 6 1 (a)) over a wide range of L ; hence the noise amplitude dependence on

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109 L is 3 0 L A instead of L A implied from a direct proportionality to resistance [169] The same work also reported a power law relationship between noise amplitude and resistivity, i.e. 6 1 A (instead of a linear relationship A predicted from a direct prop ortionality to resistance) when the application of a gate bias caused the change in resistivity of the CNT network. In a more recent study, 3 1 A was reported (Fig. 6 1 (b)) when the number of deposited CNT film layers nL (i.e. CNT film thickness) caused the change in the CNT film resistivity [172,173] In order to investigate the physical and geometrical origins of these experimental findings more systematically, simulation and modeling techniques need t o be employed. Although there has been recent modeling and simulation work on the electrical and thermal conductivity of CNT networks and films [99,116,174,175] a computational study of 1/ f noise in CNT films has not been reported previously. Furthermore, a systematic study of the sources of noise and the effects of various device and nanotube parameters on the percolation scaling of 1/ f noise in CNT films remains unexplored. More infor mation about the nature of the noise sources and their energy distribution in CNT films can be obtained by investigating the temperature dependence of 1/ f noise. For individual semiconducting nanotubes, a recent study has shown a peak at around 0.4 0.5 eV of the density of states as a function of energy extracted from the temperature dependent noise data (explained later), which has been related to the traps at the interface between the nanotube and the oxide substrate [176] However, the temperature dependence of 1/ f noise in CNT films remains unexplored. Such a study for weakly doped CNT films can be expected to show more interesting results due to the localization effects that result in insulating behavior at low temperatures [108]

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110 In this chapter, first I use Monte Carlo simulations to study 1/ f noise scaling in CNT films as a function of device parameters and film resistivity. My study focus es on the noise behavior in CNT films at low frequencies where the shot noise and JohnsonNyquist noise are negligible and 1/ f noise is the only dominant noise source. I consider noise sources due to both tube tube junctions and nanotubes themselves. By comparing the simulation results with my own and previous experimental data [169,172] I determine which noise source is the dominant one. I also systematically study the effect of d evice length, device width, and film thickness, and nanotube degree of alignment on the 1/ f noise scaling in CNT films. Furthermore I study t he temperature dependence of 1/ f noise in CNT films by fabricating four -point -probe structures and measuring their resistivity and noise amplitude as a function of temperature and frequency. I analyze the resistivity data to determine the mechanisms that a re responsible for electronic transport in CNT films at various temperature ranges. I then interpret my noise data in associatio n with the resistivity results, considering different transport mechanisms that might be responsible for both. Computational Mo deling A pproach The procedure for simulating resistivity is similar to the one explained in chapter 4 One difference is that each nanotube is assigned randomly to be either metallic or semiconducting with the ratio of the semiconducting to metallic nanotubes set to 2:1, as typically observed experimentally [25] An example of a 2D nanotube layer produced by this method is shown in Fig. 6 2 (b), where semiconducting and metallic nanotubes are labeled by different colors and the ge nerated networ k can a lso be compared to an AFM image of a nanotube film, which is shown in Fig. 6 2 (a). Like before the resistance of an individual nanotube is calculated by l R RCNT 0 where l is the length of the nanotube, is the mean free path (assumed to be 1 m in my simulations), and 2 04 / e h R

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111 The resistance of the tube -tube junctions depends on whether the junction is metallic/semiconducting (MS), semiconducting/semiconducting (SS), or metallic/metallic (MM) [29]. Based on the 2:1 ratio between the semiconducting and metallic nanotubes in the film, about 44% of the junctions are expected to be S S, 44% MS, and 11% MM, which is in perfect agreement w ith the percentages observed in the simulations. In this chapter I modeled each different type of tube -tube junction by a different contact resistance, instead of a single effective contact resistance as done in chapter 4 In particular, based on previous experimental studies [123,131,177] RMM = 25 R0, RSS = 75 R0, and RMS = 1000R0 were assumed, where RMM, RSS, and RMS are the contact resistances for MM, SS, and MS junctions, respectively. For computing the 1/ f noise in the CNT film, I have used a model which takes into account the noise contributions from both the nanotubes themselves and the tube -tube junctions in the film. Assuming independent noise sources (i.e. uncorrelated fluctuations), current noise spectral density in the film, SI, can be written as [178] n n n n n n n Ir i r s i R S2 2 21 ( 6 2) where in is the current, sn is the current noise spectral density, and rn is the resistance of the tube or junction associated with the n th individual noise source, and R is tot al resistance of the CNT film. Replacing sn in Eq. ( 6 2) by its equivalent based on Eq. (6 1 ), SI can be written as n n n n n n n Ir i A r i Rf S2 2 41 ( 6 3) where An is the noise amplitude for the n th individual noise source. Finally, an equivalent noise amplitude Aeq can be defined for the total CNT film by normalizing Eq. ( 6 3), and using

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112 R I r i2 n n 2 n and IR V where I and V are the total current and voltag e in the CNT film, respectively: n n 2 n 4 n 2 2 2 I eqA r i I V 1 I f S A (6 4) In Eq. ( 6 4), all the parameters are known except for the noise amplitudes An for individual noise sources. For individual single -walled carbon nanotubes, it was initially suggested that the noise amplitude scales with nanotube resistance, in other words CNT nR A [168] Later studies revealed that the nanotube 1/ f noise amplitude follows an inverse relationship with the number of carriers N and hence with the nanotube length lCNT, i.e. CNT nl A / 1 [179] Based on these experimental results, I have used CNT nl R A / 100 10 for the 1/ f noise amplitude of individual nanotubes in this work, where lCNT is expressed in microns and R0 = 6.5 k The chosen coefficient of 1010R0 results in a noise amplitude close to that observed experimentally for individual single -walled carbon nanotubes [179] Unlike individual nanotubes, determining An for tube tube junctions based on the available experimental literature is rather difficult. Although the noise in nanotube -based field effect transistors has been studied [179] there is hardly any experimental data on the noise amplitude of nanotube -nanotube junctions. However, as I will present in the next section s the CNT film noise amplitude observed experimentally and i ts scaling with device parameters can be fit by my simulations only if I assume that the total CNT film noise is dominated by the tube-tube junctions in the film. The presence of defects or structural deformations [180] at the tube tube junctions can be speculated as the s pecific source of this noise, although further experimental studies need to be undertaken to answer this question in depth. In this work, a relationship

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113 n nar A was assumed; in other words, the noise amplitude An of an individual tube tube junction scales linearly with the junction resistance rn. In all of my simulations, a proportionality constant of a = 1010 was used independent of other device and nanotube parameters, determined from a fit to experimental data. It has been experimental ly observed that the 1/ f noise of a junction between a single 1D nanotube and a 3D metal source/drain contact could be quite significant, although it does not have to necessarily scale with the contact resistance [181] Further experim ental work is necessary for a detailed understanding of the 1/ f noise at the junction of two individual nanotubes. Each data point in the following figures represents the average of 500 independent simulations in order to remove the statistical variations in the simulation data calculated from different realizations of the CNT film. Device and nanotube parameters such as film thickness t nanotube le ngth lCNT, and nanotube density per layer n were chosen to match the experimental values. In addition to matching the 1/ f noise data, simulations using these parameters, together with the chosen junction and nanotube resistances result in similar CNT film resistivity values to those measured in experiments [175] Experimental P rocedure For experimental noise measurements, CNT film -based four point probe structures were produced using the same vacuum filtration process that is described in chapters 2 and 3. Film thicknesses of ~ 15 nm and 75 nm that are above the percolation threshold were used for noise measurements T he contact areas on each structure were connected to the sample holder using conductive silver based epoxy glue and gold wires. Then the sam ple s were measured at room temperature or were inserted into the low temperature setup which uses a Janis variable temperature insert to achieve a temperature range from 300 K down to 1.2 K. By using four -

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114 point probe structures, the contribution of contac ts to both resistance and noise are eliminated. For noise measurements, the voltage fluctuations were magnified via an ultra low noise amplifier (BrookDeal, 60 dB gain) and the noise voltage spectral density SV was measured using an HP 3582A spectrum analyzer. The effects of amplifier and resistance thermal noise sources were subtracted from the measured spectrum by repeating the measurement for a low noise resistor with the same resistance value as that of the CNT film device. T hree sets of CNT film devices have been prepared for experimental measurements : The first set (Set 1) includes devices with large dimensions well above the percolation threshold (with dimensions L = 1500 m and W = 50 m, L = 1000 m and W = 25 m, L = 1000 m and W = 50 m, and L = 50 m and W = 5 m). The second set (Set 2) includes devices with narrow widths approaching the percolation threshold ( L = 50 m and W ranging from 0.3 to 2 m). As mentioned in chapter 3, the resistivity of C NT films increases significantly for W < 2 m, since the film gets closer to the percolation threshold. Devices in both of these two sets have thicknesses of 75 nm. The third set (Set 3) includes devices with ~15 nm thickness, 50 m and 1000 m device length, and device widths ranging from 2 to 50 m An example of the noise current spectral density measured at room temperature for a device in Set 1 under 75 A current bias is shown in the Fig. 6 2 (c) At this current level, 1/ f noise is domina nt at low frequencies ~ f < 100 Hz, obeying Eq. (6 1) with = 0.99, whereas at higher frequencies Nyquist thermal noise, which has a constant current noise spectral density given by SI = 4kT/R where R is the CNT film resistance, becomes the dominant noise source.

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115 Simulation R esults I first analyze the effects of device parameters such as device dimensions and nanotube alignment angle on 1/ f noise scaling computationally to connect and explain previous experimental results on CNT films from various groups. Effect of Device L ength Figure 6 3 (a) shows the log -log plot of the noise amplitude normalized to resistance ( A / R ) versus device length ( L ) for a single -layer nanotube network, where filled circles d enote experimental data points from Snow et al [169] and open cir cles denote my simulation results. The device and nanotube parameters used in the simulations were device width W = 2 m, nanotube length lCNT = 2 m, and nanotube density per layer n = 5 m2, which is within the range of densities reported for thin networks of nanotubes above the percolation limit [64] Since 2D nanotube networks were used in the experimental work [169] only a single 2D nanotube layer was used to model the experimental data. The simulation results are in excellent agreement with the experimental data, clearly in dicating that A / R is a strong function of device le ngth. The dashed line in Fig. 6 3 (a) is the power law fit to the experimental data, yielding L R A / with a critical exponent = 1.3, in agreement with the simulation data for 8 < L < 20 m The deviation of the simulation data from this fit for L < 8 m will be discussed in detail later. This deviation could hardly be noticed in the experiments due to the large scatter in the experimental data points. Simulations here are performed only for L > 2 m, because below L = 2 m, individual nanotubes could connect the source and drain electrodes directly (since lCNT = 2 m), diminishing the effects of percolation. Furthermore, simulations were limited to L < 20 m, since the time it takes to run the simulations becomes prohibitively long for longer devices. The decrease in the noise amplitude with device length is consistent with Hooges classical

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116 empirical law [182] where the 1/ f noise amplitude A varies inversely with the number of cha rge carriers N in the device, i.e. N A / 1 [169] However, since the resistance of the CNT film device is given by Wt L R where is the resistivity, and N scales with the device volume, i.e. LWt N A / R is expected to scale as 2/ L R A Previously, it was suggested that the deviation from this ideal result is due to nonuniformity of the CNT network [169] My results, on the other hand, suggest that the observed exponent is probably due to the effect of other device parameters on the 1/ f noise amplitude. To illustrate this point further, Fig. 6 3 (b) shows how the film thickness t affects the scaling of A / R with L The simulation parameters are the sam e as in Fig. 6 3 (a), except that n = 1.25 m2 (which falls within the range of experimentally reported values for thin nanotube networks [64] ) and the number of layers is more than one, which determines the thickness of the simulated CNT film. Two curves are illustrated, one for a film consisting of 8 layers ( t ~ 16 nm, assuming each nanotube layer is 2 nm thick) and the other for a film consisting of 3 layers ( t ~ 6 nm) shown by open circles and squares, respectively. The extracted critical exponents from the power -law fits to the simulation data for L > 6 m, shown as dashed lines in Fig. 6 3 (b), are = 1.9 and = 0.8 for the 8 and 3 layer CNT film, respectively. A s its thickness is reduced, the 3D CNT film becomes like a 2D network and approaches the percolation threshold [62,113] and the critical exponent decreases significantly. Furthermore, the magnitude of the critical exponent extracted for the 3 layer CNT film is smaller than that for the 1 layer 2D network simulated in Fig. 6 3 (a) due to the significantly lower density pe r layer, n which is another parameter that affects the critical exponent The noise amplitude A also exhibits an inverse power law dependence on n decreasing with increasing n For comparison wi th the simulation

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117 data, my experimental measurements of t he 1/ f noise amplitude in the third set (Set 3) CNT film devices are also shown in Fig. 6 3 (b) as filled circles (I will come back to my experimental results later in this chapter) As can be seen, the simulation results for the t = 16 nm CNT film are in e xcellent agreement with the experimental data, and both exhibit a critical exponent which is very close to the ideal case of = 2. In other words, as we get further away from the percolation threshold by changing other device and nanotube parameters, su ch as increasing the thickness or nanotube density, A / R dependence on L approaches 1/ L2. In this case, extrapolation of the simulation data to large values of length ( L > 20 m) is therefore valid, as the CNT film characteristics are similar to a uniform material for large device lengths. The deviation from this slope observed in the experiments [169] and my simulation data is a clear signature of percolation transport in the CNT film. Furthermore, these results clearly show that the critical exponent for the device length dependence of A / R is not a universal invarian t; rather it depends strongly on other device and nanotube parameters, such as the CNT film thickness and nanotube density. These results illustrate the complex interdependencies that exist for the scaling of the 1/ f noise in CNT films arising from percol ation transport. Another important point is that there is a significant amount of scatter (about an order of magnitude) in the experimental noise amplitude data from both Snow et al. [169] and my own measurements as shown in Figs. 6 4 (a) and (b). One of the reasons for this scatter is the percolative nature of the tran sport in the CNT film. In other words, different physical distribution of nanotubes in the film for devices with the same L can cause the resistivity and noise amplitude to vary significantly. The extent of this scatter is illustrated in the inset of Fig 6 4 (b) for the t = 16 nm CNT film simulation data. Here, distribution of the noise amplitude A for 500 different realizations of the CNT film generated randomly is shown for the device length of L = 2 m.

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118 The simulation data can be fit by a lognormal distr ibution given by 2 2 0 02 ln exp 2 ) (x/x x A y y with standard deviation the other device parameters and becomes wider (i.e. decrease (i.e. as we approach the percolation threshold). For example, it is evident from Fig. 6 3 (b) that there is a large scatter in the noise amplitude simulation data for the 3 layer film even after averaging 500 simulation results for each datapoint. This scatter is absent in the data for the 8 layer thick film. In experimental noise measurements, in addition to this intrinsic scatter due to percolation, there are also experimental errors due to factors such as CNT film inhomogeneities and presence of defects and impurities. As a result, the observed variation of an order of magnitude in the experimental noise data can be expected. As mentioned before, it can be seen in both Figs. 6 4 (a) and (b) that the simulation data starts to increase from the dashed line fits for small values of L This increase is a result of the change in the resistivity of the CNT film. As the device length (L ) approaches the length of individual nanotubes ( lCNT), the statistical distribution of nanotubes in the film can result in short conduction paths consisting of only a few nanotubes connecting source to drain, decreasing the total resistivity of the film [99,175] The simulation plot of resistivity versus device length shown in the inset of Fig. 6 3 (a) for the simulation dataset in the main panel of Fig. 6 3 (a) illustrates this point. As can be seen, while resistivity decrease with decreasing device length is quite significant for L < 8 m, its variation is less than 10% for L > 8 m, and the resist ivity almost saturates for L > 10 m. For very small device lengths, the decrease in resistivity increases the amount of current in the device for a fixed applied bias (in addition to the increase due to the length shrinkage), which in turn increases the total 1/f device noise at a rate faster than

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119 that observed for larger device lengths, as implied by Eq. ( 6 4). This increase in 1/ f noise causes the critical exponent to increase for small values of L as evidenced by the deviation from the dashed power -l aw fits in Figs. 6 4 (a) and (b). The effect of the change in resistivity at small L (due to percolation) on the noise amplitude A can be illustrated further by re -plotting the data in Fig. 6 3 (b) for the CNT film with t = 16 nm as A L versus resistivity, as shown in Fig. 6 4 We have seen above that the simulation data for the t = 16 nm curve in Fig. 6 3 (b) exhibits approximately 2~ /L R A which indicates that A L is a constant if is constant. As a result, by plotting A L versus in Fig. 6 4 any explicit dependence of A on L is eliminated, except for an implicit dependence through resistivity, since ) ( L as seen in the inset of Fig. 6 3 (a). The simulation data in Fig. 6 4 can be fit by a power law relationship given by L A with an extracted critical exponent of = 0.4. Since the resistivity is almost constant for many of the data points, they fall on top of or close to each other in Fig. 6 4 ; however, t he scaling trend can still be observed. This observed power law behavior is in agreement with previous results observed for percolation systems [172,183,184] and is a direct manifestation of percolation affecting the 1/ f noise in the CNT film. Up to this point, based on the relative noise amplitudes chosen to fit the experimental data, it is assumed tha t the tube -tube junctions dominate the 1/ f noise in the CNT film. In contrast, the inset in Fig. 6 4 shows the loglog plot of A L versus resistivity, when nanotubes are assumed to be the only sources of 1/ f noise in the film (tube -tube junction noise amplitudes are set to zero, i.e. a = 0). There are two striking differences between the results in the main panel and the inset in Fig. 6 4 First, the noise amplitude A has dropped more than 3 orders of magnitude when I exclude the junction noise. In other words, the noise amplitude chosen for an

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120 individual nanotube ( l R An/ 100 10 ) based on the experimental results for single tube devices [179] results in a total noise significantly smaller than the experimental values observed for the CNT film. This reduction is expected in my simulations, as the noise amplitudes An of the tube tub e junctions are significantly larger than those of the nanotubes themselves due to the larger resistance associated with the junctions. Secondly, A L scaling with resistivity now exhibits a power -law decrease, which is in sharp contrast to the power -law increase observed in the main panel of Fig. 6 4 for the simulations that fit the experimental data shown in Fig. 6 3 Furthermore, power law increase of 1/ f noise with resistivity is commonly observed for CNT films and other systems when a particular para meter is changed to modify the resistivity close to the percolation threshold [169,172,183,184] I will later show that my simulations exhibit a similar power -law increase of 1/ f noise with resistivity, when the CNT film thickness is the parameter that causes the change in resistivity and 1/ f noise, in agreement with experimental data [172] Taken together, the above results strongly suggest that tube tube junctions, and not the nanotubes themselves, dominate the overall CNT film 1/ f noise. This finding is in analogy to previous experimental and theoretical results [113,175] which show that the resistivity of the CNT film is also dominated by tube -tube junction resistance, and not the nanotube resistance. As long as the electronic mean free path is larger than about 100 nm, the nanotube noise remains negligible compared to the junction noise. Effect of Device W idth Noise scal ing trends with other device parameters also confirm the above results. In particular, I next study the effect of device width. The resistivity scaling with device width close to the percolation threshold has been experimentally observed to be significan tly more pronounced than that with device length [113,175] This point is also evident in the simulation

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121 data shown in the in set of Fig. 6 5 (a) for a device with L = 5 m, t = 16 nm, and other parameters kept the same as in Fig. 6 3 (b). (These parameters have been used for the rest of the sim ulations presented in this chapter ). In this inset, for 2 W m, resistivity is almost constant, while at submicron width range, it depends strongly on W We have also performed simulations to investigate the scaling of 1/ f noise with device width in the CNT film, which has not been experimentally studied before Th e main panel of Fig. 6 5 (a) shows 1/ f noise amplitude versus device width W in which two regions can be distinguished. For 2 W m, A is inversely proportional to W (the power law exponent extracted from the dashed line fit to the data i s W1.1). This variation is expected, since N A / 1 and the number of carriers N increases linearly with device width and the resistivity is constant in this regime as seen in the inset of Fig. 6 5 (a). However, for W < 1 m, there is a strong power law relationship between A and W with a critical exponent extracted from the fit equal to 5.6. This shows that the variation of resistivity has a strong effect on the noise in this region. To investigate this variation further, the inset of Fig. 6 5 (b) shows A vs. for the same data as in the main panel of Fig. 6 5 (a). As can be seen, presenting the data in this way results in a non -linear curve and its interpretation becomes difficult, since this data includes the effect of b oth W and on the noise. Once again, to separate these two dependencies, A can be multiplied by W which eliminates the explicit dependence of A on W The main panel of Fig. 6 5 (b) shows the loglog plot of A W (noise amplitude normalized with device width) versus resistivity. Similar to the length case, the simulation data can be fit by a power law dependence on resistivity, W A where the extracted critical exponent for width is = 1.7. Th is critical exponent is different from the one extracted for noise scaling with resistivity that was due to the change in device length. This result shows that the

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122 noise -resistivity critical exponent is not a universal invariant, rather it depends on the parameter that is causing the change in the 1/ f noise. Effect of Device T hickness and T ube Alignment A ngle As we have seen in Fig. 6 3 (b), CNT film thickness has a strong effect on the noise scaling with device length. Several studies have shown that film t hickness t also has a strong effect on the CNT film resistivity, especially for extremely thin films [62,113] Recently, Soliveres et al. ha ve experimentally studied the dependence of the 1/ f noise amplitude on film thickness [172] Next, I investigate this dependence by my simulations. The left inset of Fig. 6 6 (a) shows log -log plot of resistivity versus number of layers (i.e. thickness) where resistivity is almost constant for films with 10 layers or more, while strong inverse power law dependence of resistivity on thickness exists for thin films near the percolation threshold. As a result, like device width, film thickness can be expected to have a strong impact on noise, as shown by the experimental results of Soliveres et al. [172] T he main panel of Fig. 6 6 (a) shows the loglog plot of the noise amplitude normalized by thickness A t versus resistivity computed for the same CNT film device as in the inset. Similar to the width case, the normalized amplitude A t is used because A varies with thickness linearly in the regime when resistivity is constant. The simulation data can be fit by t A where the extracted critical exponent is = 1.8. These results can be compared to the experimental data of Soliveres et al. [172] Although they report a critical exponent for A not A t renormalization of their data gives = 1.1. The disagreement in the simulation (1.8) and experimental (1.1) critical exponents reported is most likely due to differences between other device/nanotube parameters, such as density per layer, and the film properties such as the purity and homogeneity of the deposited CNT film.

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123 As a confirmation of how the two possible noise sources (nanotube and junction) affect the noise results, the right inset in Fig. 6 6 (a) shows log -log plot of A t v ersus resistivity, but with tube -tube junction noise amplitudes set to zero, (i.e. nanotube -dominated noise). Similar to the case of device length, not only the noise amplitude A drops by orders of magnitude, but also the critical exponent becomes negative, which is in sharp opposition to the positive value observed in experimental data [172] These results once again imply that the tubetube junctions dominate the 1/ f noise in CNT films. It is worth mentioning that there is slight deviation of the simulation data from the dashed line fit for the highest r esistivity value (very thin films) in Fig. 6 6 (a). This is due to the decrease of the percolation probability below unity near the percolation threshold [175] and can be observed for noise scaling with nanotube alignment very close to the percolation thre shold as well [Fig. 6 6 (b)]. Finally, I study the effect of alignment of nanotubes making up the film on the scaling of 1/ f noise amplitude to show that even internal parameters of the film can strongly affect the 1/ f noise. I have used the same definition for alignment angle a as in chapter 4 (also illustrated in the inset of Fig. 62 (b) ). Therefore when a = 90o, the nanotubes are completely randomly distributed (which is the case for all the previous simulations), whereas when a = 0o, they are completely aligned along the horizontal axis. As a reminder from chapter 4, t he inset in Fig. 6 6 (b) plots resistivity versus nanotube alignment angle obtained by simulations. With a decrease in a, t he resistivity initially decreas es, reaches a minimum (at Min a ), and then starts to increase significantly, as observed experimentally and explained in chapter 4 [110] The main panel of Fig. 6 6 (b) shows the 1/ f noise amplitude A versus resistivity, where the high resistivity section of the curve corresponds to a film with well aligned nanotubes (i.e. small

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124 a). Unlike external device dimensions L W and t the alignment angle a changes device resistance R and noise magnitude A only implicitly by changing and the nature of the conduction paths. As a result, A is not normalized in this figure. Interestingly, it is evident from Fig. 6 6 (b) that CNT films with the same resistivity values can have two different noise amplitudes, depending on their alignment angles. As the alignment angle decreases from 90, the resistivity becomes smaller, but A remains approximately constant. However, below Min a [about 45 in the inset of Fig. 6 6 (b)], the noise amplitude starts to increase strongly with resistivity. A power law fit to the noise data with an amplitude higher than 7107, i.e. A yields a critical ex ponent of = 1.3. It can be inferred from the trend in Fig. 6 6 (b) that other parameters being constant, partial alignment of nanotubes at the minimum resistivity angle, Min a gives the lowest resistivity -lowest noise configuration; hen ce in order to optimize a device design, it is better to have the nanotubes partially aligned in the film rather than perfectly aligned. Experimental R esults In order to understand the noise mechanisms in CNT films better, I have analyzed the resistance and 1/ f noise trends in these films as a function of temperature. Figure 6 7 shows the log log plot of resistivity ( ) versus temperature ( T ) for one of the devices in Set 1 with L = 1500 m and W = 50 m (This device will be called D1 from now on). It is clear that increases over one order of magnitude as T decreases from 300 to 1.2 K. For CNT films, the temperature dependence of depends strongly on parameters such as the doping of the film, the density and structure of t he nanotubes (e.g. diameter and length), and device dimensions [101,108] For example, while highly doped thick CNT films were found to show metallic behavior with very

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125 weak dependence on T lightly doped or undoped thi n CNT films depicted strong localization behavior with close to zero conductance values at very low temperatures [101,108] Although the CNT films in my study are not intentionally doped, nitric acid, which is used for p urifying the nanotubes, unintentionally dopes the CNT films to some extent. However, as I have previously shown in chapter 3 nanotubes are subsequently de -doped during the processing steps associated with the four point -probe structure patterning, result ing in weakly doped films. The resistivity shown in Fig. 6 7 for device D1, therefore, depicts insulating behavior due to strong localization of carriers at low temperatures, which can be explained by variable range hopping (VRH). The temperature dependence of in the VRH regime can be written as ] ) / exp[( ) (0 0 pT T T ( 6 5 ) where 0 is a constant, T0 is the characteristic temperature which is proportional to the energy separation between the available states, and p = 1/ ( d +1) for Mott VRH [185] where d is the dimensionality of the hopping conduction. As is shown in the right inset of Fig. 6 7 p can be extracted from a plot of reduced acti vation energy W defined as T d T d T W ln )) ( ln( ) ( (6 6 ) versus T The p value (equal to the slope of the fit in this plot) I have extracted is 0.29, which is very close to the theoretical value of 0.25 expected for 3D VRH [i.e. d = 3 in Eq. (6 5 )]. The slight deviation from 0.25 could be related to the strong localization of carriers that cause a transition form Mott VRH to cou lomb gap (CG) VRH (For CG VRH, the exponent p should have a value close to 0.5) [108] More analysis of the CNT film resistivity dependence on electric and magnetic field in the VRH regime is presented in the appendix.

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126 The value extracted for T0 by fitting the experimental data with Eq. (6 5) as shown in the main panel of Fig. 6 7 is 39 K The extraction is performed by fitting a linear curve to ) ln( vs. pT 1 plot and calculating T0 from the slope of the fitted curve VRH is responsible for transport when T << T0. At higher temperatures, fluctuation induced tunneling (FIT) can describe the transport in the CNT film, as the conduction paths are formed by very conductive nanotubes in series with resistive tunneling junctions between them [12 3,186] The expression for the FIT controlled resistivity can be written as: ) exp( ) ( T T T C Ts b (6 7 ) where C is a constant, kTb reflects the order of magnitude of the barrier energies (where k is the Boltzmann constant) and the Ts to Tb ratio determines the increase of resistivity at lower temperatures. The values of C and Tb can be extracted directly from the data by plotting versus 1/ T (assuming Ts is small) and then Ts can be found from a fit to the data, as shown in the main panel of Fig. 6 7 From this fit, I get Tb = 24 K and Ts = 14 K. The values reported for Tb and Ts in the literature vary over a large range [62,187] and the ones extracted here are within that range [187] Ts is an important parameter here because the FIT model only explains the resistivity results for temperatures that are well above Ts. Therefore, Ts together with T0 (from the VRH model) suggest that at low temperatures VRH is the main transport mechanism, whereas at high temperatures, FIT begins to dominate. I will show next that this is also in agreement with my results on the temperature dependence of 1/ f noise in CNT films. The main panel of Fig. 6 8 shows a loglog plot of the noise amplitude A versus T for two devices, namely D1 (the device for which the resistivity is shown in Fig. 6 7 ) and one device in Se t 2 (with L = 50 m and W = 0.4 m, which will be called device D2). Based on a careful

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127 analysis of the noise spectrum at low frequencies, no features other than 1/ f behavior were detected over the range of measured temperatures (except for slight fluctuations in the exponent as T varies, as shown in the inset of Fig. 6 9 ). Due to the high resistance of D2 at low temperatures, I was able to perform noise measurements only down to 77 K for this device. The temperature dependence of A in Fig. 6 8 follows t he same pattern for both D1 and D2 for T > 77 K. However, there is roughly four orders of magnitude difference in the absolute value of A in these samples, which will be discussed later when I consider the effect of device dimensions on noise. At high tem peratures close to 300 K, A is a weak function of T however, as T decreases down to 77 K, A starts to decrease for both D1 and D2. The value of A for D1 reaches a minimum at around 40 K and then starts to increase significantly at lower temperatures. Thi s trend is strikingly different from the one that has been recently observed for individual semiconducting nanotubes [176] where A continuously decreases as T goes down to 4 K. Due to the insulating behavior of the CNT film at low temperatures ( A and both increase significantly when T decreases), the noise behavior might be determined by two separate mechanisms at high and low temperatures. For D1 at T << 40 K, A exhibits a power law dependence on T in the form T A with = 1.53. It has been suggested that for Mott VRH systems in which A increases as T decreases, a power law -based relationship with an exponent close to 1.5 exists between A a nd T [188] The exponent v extracted from my data is very close to this value. Another interesting feature is the position of the noise minimum in the A vs. T curve for D1, which is ~ 40 K. This temperature is very close to the T0 value in the VRH model extracted from the vs. T data. These observations imply that VRH theory applies to the temperature dependence of both resistivity and noise in my CNT films at low temperatures ( T << 40 K).

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128 The T dependence of A at temperatures above the VRH regime can provide further information about the energy distribution of the fluctuators. More specifically, Dutta and colleagues have suggested that for an inhomogeneous system with random fluctuations, if the energy distribu tion is broad compared to kT the relationship between D ( ), density of fluctuation states, and A can be written in the form [189] T T A D ) ( ) ( (6 8 ) W here ) 2 ln(0 f kT and 0 is a characteristic attempt time with a value inverse of phonon frequency. For most materials, 1014 < 0 < 1011 s [190] but the val ue of is not very sensitive to the absolute value of 0 The main panel of Fig. 6 9 shows D ( ) versus for D1 and D2, based on Eq. (6 8) with 0 = 1013 s. This value of 0 is chosen to provide the best fit of Eq. (6 9) to the values extracted experi mentally, as explained below. The similarity in the dependence of A on temperature for the two devices results in a similarity in the dependence of D on As can be seen, both curves show broad peaks in the range 0.3 to 0.6 eV. These peaks are broad enough to satisfy the assumptions made in writing Eq. (6 8) and they are responsible for most of the noise at high temperatures [189] As mentioned before, similar peaks have also been observed for individual semiconducting tubes [176] Based on the energy range of the peaks, sources of noise such as electronic excitations within the tubes or structural fluctuation of the defects within the CNT lattice have bee n ruled out [176] For CNT films, due to the presence of the tube tube junctions, the picture is even more complicated. However, a possible source of the noise could be fluctuation with in or at the surface of the SiO2 substrate underneath the nanotubes [176] In fact, it has been shown that removing the oxide underneath the tubes can improve (reduce) their noise ampli tude up to an order of magnitude [191,192] Therefore, similar to the individual

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129 semiconducting na notube case, a significant portion of the noise observed at room temperature in CNT films can also be related to the fluctuation of trapped charges in the oxide. Based on Dutta et al. [189] there should also be a relationship be tween the frequency scaling exponent and the dependence of A on temperature in the form [189] 1 ln ln ) 2 ln( 1 10T A f (6 9 ) In order to check the accuracy of Eq. (6 8 ) for CNT films, the inset in Fig. 6 9 compares the values of as a function of T that are extracted from the experimental results and calculated from Eq. (6 9) The agreement between the two sets is very good for T > 40 K (above the VRH regime) and so the relationship between the energy distribution of fluctuations and the temperature scaling of the noise amplitude stated in Eq. (6 8) is correctly established. As mentioned before, the value of A at room temperature is about 4 orders of magnitude larger fo r device D2 compared to D1 (see Fig. 6 8 ). This difference is due to two reasons: First, the dimensions of D2 ( L = 50 m and W = 0.4 m) are significantly smaller compared to those of D1 ( L = 1500 m and W = 50 m). As I have shown above for CNT films, A is almost inversely proportional to the total number of carriers ( N) and hence inversely proportional to both L and W in the region that film resistivity is constant (i.e. well above the percolation threshold) [169,193] As a result, the large difference between the dimensions of the two devices can partially explain the difference in their A values. As a reminder, Fig. 6 10(a) shows the strong dependence of the noise amplitude normalized to resistance ( A / R ) at room temp erature versus device length ( L ) for four devices in Set 1. Also shown in this figure are my Monte Carlo simulation results, described in detail previously. This f igure is similar to the one that is shown in Fig. 6 3 (b). T he

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130 critical exponent extracted fr om the power -law fit (i.e. L R A / ) to the simulation dataset is 1.9, which is very close to the theoretical value of = 2 [169] The second reason for the huge difference in the A values between D1 and D2 is the nonconstant resistivity. The device width W of D2 is very close to percolation threshold and hence its resistivity is much higher compared to D1. The increase in results in a further increase in A i.e. A dependence on W becomes significantly stronger than an inverse relationship. To better demonstrate the relationship between A and I have measured A for the devices in Set 2 with various widths, and the results are plotted as A W versus in Fig. 6 1 0 (b). If A is inversely proportional to W A W should remain constant as W and hence changes. However, as can be seen in this figur e, A W depends strongly on following a power law relationship with in the form W A where is extracted to be 2.5. This strong A dependence is due to the percolative nature of the transport in CNT films, as predicted by my comp utational results above (refer to Fig. 6 5 to compare the scaling of resistivity between computational and experimental results) Based on the above discussion, both the dimensions of the device and the resistivity of the film are responsible for the large differences observed in the noise levels of my samples.

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131 Figure 6 1 Effect of device length and film thickness on experimentally measured noise: (a) Log log plot of A / R versus L taken from [169] The dashed line represents A / R = 1011 1 and the solid line is a least -squares power law fit to the experimental data. (b) Log lin plot of A as a function of the number of deposited layers nL, taken from [172] The inset shows v ariation of A as a function of the conductivity with a line fitted to the experimental data

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132 Figure 6 2 Experimental and computational analysis of noise: (a) AFM image of a nanotube film with an approximate thickness of t = 15 nm where nanotubes are randomly distributed. (b) A 2D nanotube network generated using Monte Carlo simulations for a device with length L = 4 m, width W = 4 m, nanotube length lCNT = 2 m, and nanotube density per layer n = 10 m2. Semiconducting and metallic nanotubes are shown in cyan and blue color, respectively. The inset illustrates the alignment angle a, explained more in chapter 4. (c) L oglog plot of current spectral density ( SI) versus f for a device in Set 1 with L = 1000 m and W = 50 m (open circles), demonstrating the 1/ f type behavior at low frequencies and saturation of the noise at high frequencies. The black line in this inset is a fit to the low frequency regime with a slope of 0.99.

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133 Figure 6 3 Effect of device length on noise: (a) Log log plot of the noise amplitude normalized by resistance ( A / R ) versus device length ( L ) for a nanotube network. Experimental data points from Snow et al [169] is shown by the filled circles. S imulation data points for devices with W = 2 m, lCNT = 2 m, n = 5 m2, and L ranging from 2 to 20 m are shown by the open circles. The exponent obtained from the fit to the simulation data for 8 < L < 20 m is ~1.3 The inset shows log -log resistivity versus L for the same device as the main panel. (b) Log -log plot of A / R versus L for multi layer nanotube films. Filled circles represent measurements of devices in Set 3 Open circles and squares are simulation data points for devices with t = 16 nm (8 layers) and t = 6 nm (3 layers), respectively, other simulation parameters are W = 2 m, lCNT = 2 m, n = 1.25 m2, and L ranging from 2 to 14 m. The extracted critical exponents from the dashed line fits to these two simulation datasets above L > 6 m are 1.9 and 0.8, respectively. The inset shows the distribution of A in 500 simulated devices, all with L = 2 m, t = 16 nm, and the other parameters same as above fitted by a log -normal distribution

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134 Figure 6 4 Effect of resistivity change due to device length on noise: Main panel is a l oglog plot of computed A L versus resistivity for the device shown in Fig. 6 3 (b) with t = 16 nm. The change in resistivity is a result of the change in device length. The extracted critical exponent of the dashed line fit is 0.4. The inset shows log-log plot of A L versus resistivity for the same device as in the main panel, but without any noise sources at the tube tube junctions. The extracted critical exponent is 2.9 in this case.

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135 Figure 6 5 Effect of device width on noise: (a) Loglog plot of computed A versus W for a device with L = 5 m, t = 16 nm and other parameters same as in Fig. 6 3 (b). There are two separate scaling regimes. The extracted exponent of the dashed line fit for large widths (where resistivity is constant) is 1.1. The extracted exponent of the dashe d line fit for small widths is 5.6. The inset shows loglog plot of resistivity versus device width for the same device as in the main pane l. (b) Log log plot of computed A W versus resistivity. The change in resistivity is a result of change in device width. The extracted critical exponent in this case is 1.7. The inset shows loglog plot of A versus resistivity for the same device.

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136 Figure 6 6 Effect of device thickness on noise: (a) Log log plot of computed A t versus resistivity. The change in resistivity is a result of change in the t The extracted critical exponent in this case is 1.8. The left inset shows loglog plot of resistivity versus device thickness for the same device. The right inset shows log log plot of A t versus resistivity for the same device, but without any noise sources at the tubetube junctions. The extracted critical exponent is 0.8 in this case. (b) Log log plot of computed A versus resistivity. The change in resistivity is a result of change in the nanotube alignment angle a. It is evident that CNT films with the same resistivity values can have two different noise amplitudes, depending on their alignment angles. A power law fit to the data points (dashed line) with noise amplitudes A higher than 7107 yields a critical exponent of 1.3. The inset shows the log -log plot of resistivity versus alignment angle for the same device, in which the resistivity minimum at about 45 is evident.

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137 Figure 6 7 Effect of temperature on resistivity: Main panel is a log -log plot of versus T for device D1. Black squares a re experimental datapoints, while red and blue lines are fits to the experimental results based on the VRH and FIT models, respectively. The right inset is a log log plot of reduced activation energy ( W ) versus T for the same device. The red line in this inset is a power law fit to the data with an exponent 0.29. Figure 6 8 Effect of temperature on noise: Main panel is a l oglog plot of A versus T for devices D1 (left y axis) and D2 (right y axis). Due to th e high resistance of D2 at low temperatures, noise measurements could be performed only down to 77 K for this device. A power -law fit to the three leftmost D1 datapoints yields an exponent of 1.53. The black lines are drawn as a guide for the eye. The inse t is a log log plot of current spectral density ( SI) versus f for a device in Set 1 with L = 1000 m and W = 50 m (open circles), demonstrating the 1/ f type behavior at low frequencies and saturation of the noise at high frequencies. The black line in thi s inset is a fit to the low frequency regime with a slope of 0.99.

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138 Figure 6 9 Dependence of density of states on energy: Main panel is a l og -log plot of (arbitrary units) versus for devices D1 and D2 directly obtained from the A versus T results in Fig. 6 8 The black lines are drawn as a guide for the eye. The inset is a linear log plot of versus T for D1 either experimentally obtained (open circles) or directly calculated from the A versus T results in Fig. 6 8 Figure 6 1 0 Exper imental observation of the effect of device length and width on noise: (a) Log log plot of measured (filled circles) and simulated (open circles) A / R versus L Measured values are for devices in Set 1. The extracted critical exponent from the dashed line power law fit (i.e. A/R L) to the simulation dataset is 1.9. (b) Log log plot of A W versus experimentally measured for devices in Set 2 (with L = 50 m and W = 0.3, 0.4, 0.7, 1 and 2 m). The critical exponent extracted from a fit (in the form A W ) to the results is 2.5.

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139 CHAPTER 7 CONCLUSIONS AND FUTU RE WORK S S ummary of R esults The main scope of this work was to study CNT film electrical properties using both experimental and simulation approaches and to further evaluate its potential as a transparent conductive electrode for applications such as optoelectronics and flexible electronics. In chapter 2, I developed the nanolithographic patterning capability that would open up significant opportunities for fabrica ting and integrating single -walled nanotube films into a wide range of electronic and optoelectronic devices. I demonstrated the a bility to efficiently pattern CNT films with good selectivity and directionality down to submicron lateral dimensions by photolithography or e -beam lithography and O2 plasma etching using an ICP RIE system. I systematically studied the effect of ICP RIE etch parameters on the nanotube film etch rate and etch selectivity. Decreasing the substrate power from 100 W to 15 W, decrea sed the nanotube film and resist etch rates by about a factor of 10. Decreasing the chamber pressure from 45 mTorr to 10 mTorr increased the nanotube film and resist etch rates by a factor between 1.7 and 3.5. It also increased the etch selectivity betwe en the nanotube film and the resist masks On the other hand, increasing the chamber pressure from 45 mTorr to 100 mTorr did not change the etch rates of the nanotube film and resists significantly. Similarly, increasing the helium flow rate (which activ ely cools the substrate) from 10 sccm to 40 sccm did not produce a significant ch ange on the etch rates of the C NT film and the thr ee resists. Furthermore, the C NT film etch rate was found to be independent of the line width etched for linewidths ranging from 50 m down to 100 nm. In addition, by comparing the etch rates of CNT film and the three resists in an ICP RIE system to those in a conventional pa rallel plate RIE system, I demonstrated that using an ICP RIE system provides significant advantages, such as faster etch rates and better etch

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140 selectivity, over conventional parallel plate RIE plasma systems, making it possible to pattern lateral features as small as 100 nm in nan otube films. Furthermore, I showed that a wide range of nanotube film etch rates can be obtained using an ICP -RIE system by changing the substrate bias power and chamber pressure. Chapter 3 was dedicated to characteriz ation of the CNT film resistivity. By fabricating standard four -point -probe structures using the patterning capability developed in chapter 2, we demonstrated that the resistivity of the films is independent of device length, while increasing over three orders of magnitude compared to the b ulk films, as their width and thickness shrink. In particular, resistivity of CNT films started to increase with decreasing device width below 20 m, exhibiting an inverse power law dependence on width in the sub-micron range. These results suggested that the resistivity scaling is an important effect that require s consideration when fabricating small devices. I also show ed that different resist processes result in different CNT film resistivity values due to partial de -doping of the acid purified nanotubes during lithography. In addition, the resistivity of nanotube films increased between two to three orders of magnitude after partial etching by the O2 plasma, indicating that the remaining film is significantly damaged during the etch. I used a Monte Carlo simulation platform in chapter 4 to model percolating conduction in single -walled carbon nanotube films. I exhibited that this simple model can fit the experimental resul ts on resistivity scaling as a function of device width. In addition, I demonstrated that geometry -dependent resistivity scaling in single -walled carbon nanotube films depends strongly on nanotube and device parameters In particular, I studied the effect of four parameters, namely resistance ratio, nanotube density, length, and alignment on resistivity and its scaling with device w idth. Stronger width scaling is observed when the transport in the nanotube film is dominated

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141 by the tube tube contact resista nce. Increasing the nanotube density decreases the film resistivity strongly, and results in a higher critical exponent for width scaling and lower critical width WC. Increasing the nanotube length also reduces the film resistivity, but increases both and WC. In addition, the lowest resistivity occurs for a partially aligned rather than perfectly aligned nanotube film. Increasing the degree of alignment reduces both and WC. Furthermore, when the nanotubes are strongly aligned, the film resistivit y become s highly dependent on the measurement direction. Consequently, I studied the effects of nanotube length, nanotube density per layer, and device length on the scaling of CNT film resistivity with nanotube alignment and measurement direction. I found that longer nanotubes, denser films, and shorter device lengths all decrease the alignment critical exponent and the alignment angle at which minimum resistivity occurs, and increas e the measurement direction critical exponent However, the amount of increase or decrease is different for each parameter I systematically explained these observations, which are in agreement with previous experimental work, by simple physical and geometrical arguments. All these results confirm that near the percolatio n threshold, the resistivity of the nanotube film exhibits an inverse power law dependence on all of these parameters, which is a distinct signature of percolating conduction. However, the strength of resistivity scaling for each parameter, represented by the corresponding critical exponent, is different. I also studied the effect of length distribution (instead of a fixed length) on the resi stivity scaling with CNT length and have compared the results for CNT films with films in which the resistance of t he elements is significantly larger than their junctions (unlike CNT films). I observed that network resistivity correlates well with RMS length for CNT films and with average leng th for element -dominated film s. In the latter case, percolation effects driv e the

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142 correlation towards RMS length for short average lengths. Furthermore, in each case, alignment of nanotubes/elements in the network places increasing weight on the longest elements, shifting the correlation to higher power means. These results emph asize the importance of taking the nanoelement length distribution into account when using these films in potential device applications. In chapter 5, I fabricated and characterized MSM photodetectors based on CNT film GaAs and CNT film -Si Schottky contacts. After reviewing the fundamentals of the MSM photodetectors, I extracted the Schottky barrier height of CNT film contacts on GaAs and Si by measuring the dark I -V characteristics as a function of temperature. The results show ed that at temperatures above ~ 240260 K, thermionic emission of electrons with a barrier height of ~ 0.54 eV for GaAs junctions and barrier heights of 45 0 Bn eV and 51 0 Bp eV for n type and p type Si junctions w as the dominant transport mechanism, whereas at low er temperatures tunneling began to dominate, suggested by the weak dependence of current on temperature. Assuming an ideal M -S diode, these barrier height s correspond to a CNT film workfunction of about ~ 4 .6 eV, which is in excellent agreement with previously reported values. Furthermore, I observed that dark currents of the MSM devices scale rationally with device geometry, such as the device active area, finger width, and finger spacing. Finally, I obse rved that in the case of GaAs devices, while the photocurrent of the CNT film MSM devices is similar to that of the metal controls (resulting in a comparable responsivity), their significantly lower dark current results in a much higher photocurrent to -dar k current ratio relative to the control devices. Si based devices also exhibit a higher photo current -to -dark current ratio at high applied voltages relative to metal control devices.

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143 Finally, in chapter 6, I first used Monte Carlo simulations and noise modeling to systematically study the 1/f noise in CNT films I demonstrated that my computational model can fit previous experimental results on the scaling of 1/ f noise amplitude in CNT films My results show that the 1/ f noise ampl itude depends strongly on device dimensions and on the film resistivity, following a power -law relationship with resistivity near the percolation threshold after properly removing the effect of device dimensions. Furthermore, the noise -resistivity and noi se device dimension critical exponents extracted from the power law fits are not universal invariants, but rather depend both on the parameter that causes the change in resistivity and noise, and the values of the other device parameters. In addition, the simulation fit to the experimental data strongly suggests that tube tube junctions, and not the nanotubes themselves, dominate the overall CNT film 1/f noise. I then studied experimentally the variation of resistivity and 1/ f noise as a function of temp erature and concluded that at very low temperatures (< 40 K) 3D variable range hopping is the dominant mechanism for both resistivity and 1/ f noise. At temperatures above 40 K, however, the fluctuation induced tunneling model explains the resistivity behav ior. The noise amplitude exhibit ed a minimum at around 40 K and then start ed to increase with increasing temperature. In th e high temperature regime, the density of fluctuators as a function of energy, extracted from the temperature dependence of noise a mplitude depict ed a peak at around 0.3 0.6 eV. The fluctuations within or at the surface of the SiO2 substrate underneath the CNT film could be the source of this peak and therefore the dominant source of the noise at high temperatures. Future W ork s T he work presented in earlier chapters open up the possibility to further study various aspects of CNT film properties. F irst, the model developed for the CNT film in chapter 4 can be

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144 improved in several ways For example my model ignores non -linear effects at high bias voltages [133] by assuming a fixed nanotube resistance independent of bias voltage. Th e dependence of nanotube resistance on the node voltage can be included by solving the current continuity equation self -consistently with the Poison equation in a recursive manner. In addition a more accurate model can be developed for MS Schottky junctions by taking into account the variation of the depletion region in the semiconducting nanotube with the voltage at the contact node [123] Second, in chapter 5, I studied the junction between CNT film and semiconductor substrates such as Si and GaAs by fabricating and analyzing metal -semiconductor -metal structures There are two back to back Schottky junctions in these structures, which make the analysis of the transport over the barriers rather difficult. As a result, it would be advantageous to fabricate and study CNT -film/Si hetero -structures directly. Final ly my computational and experimental approach for studying CNT films can be applied to similar materials that are composed of nanostructures. One example would be to study nanocomposites and films composed of sheets/pallets of graphene Similar to CNT films, th ese materials are transparent, conductive and flexible and therefore have potential to be used in various electronic and optoelectronic applications. My Monte Carlo simulation approach might be appropriate for modeling the transport in these structures and the experimental techniques can also be used for characterizing the transport as a function of various device parameters

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145 APPENDIX : ELECTRIC AND MAGNETIC FIELD DEPENDENCE O F THE CNT FILM RESISTIVITY IN THE V RH REGIME In the VRH regime, resistivi ty of my CNT films depicts strong electric and magnetic field dependences. The inset in Fig. A 1 shows I V characteristics at three different temperatures for device D1 ( refer to chapter 6 ). While the nonlinearity in the I V curve at 1.2 K is considera ble, at 10 K it is almost non -existent. To better present the effect of electric field ( E ), the main panel of Fig. A 1 depicts differential device resistance ( R ) versus E for temperatures similar to the ones in the inset. As can be seen, the magnitude of nonlinearity decreases and the electric field required for the onset of nonlinearity ( En) increases as the temperature increases. The resistance at 10 K is almost constant in the whole range of electric field, indicating Ohmic behavior above this temperatur e. Also shown in Fig. A 1 is the R T dependence for D 1 ( refer to Fig. 6 8 in chapter 6 ) that is shifted to fit the other three curves in the high electric -field region. In VRH regime, the temperature and electric field dependences of the resistance are c orrelated by [194,195] : ) 8 3 0 ( 2 ) 0 ( qEa R T k RB ( A 1 ) where q is the electron charge and a is the localization radius, estimated from the fit to be ~800 nm. This large value suggests that the conductance of the nanotubes is quite high even at low temperatures and the long length of tubes results in the observed localization radius. This estimat ion is confirmed by considering the relationship between En and T which follows 2 0 / T k a qEB n [194,195] Fig. A 2 shows magnetoresistance (MR) data for D1 at three different temperatures. As can be seen, while at higher temperatures, MR is negative and decreases with magnetic field ( B ), at very low temperatures it reaches a negative minimum and then starts to increase and finally

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146 obtains positive values at high B The positive second derivative of the MR ( i.e. 2 2dT MR d ) at T 0 is a sign of insulating behavior in this sample, which confirms the previous observations [196] and the results presented in chapter 6 One possible origin for the positive contribution to the MR at very low temperatures is wavefunction shrinkage This contribution can explain the appearing of the positive MR when the B is high or the vanishing of the positive MR as temperature increases (which results in the MR minimum shifted towards h igher B values) [108]

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147 Figure A 1 Effect of electric field on resistance at very low temperatures: Main panel is a l inear log plot of the R versus E for D1 at 3 different temperatures. Open circles are R versus T experimental datapoints (also shown in Fig. 6 8 in chapter 6 ) plotted on the same panel and scaled to fit the R versus E results. The inset shows I V characteristics of device D1 for the 3 temperatures at which the main panel curves are shown. Figure A 2 Effect of magnetic field on resistance at very low temperatures. Main panel is a l inear linear plot of magnetoresistance ( R/R ) versus B for device D1 at 3 different temperatures.

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159 BIOGRAPHICAL SKETCH A shkan Behnam was born in Tehran, Iran in 1981. He received Bachelor of Science and Master of Science degrees in e lectrical e ngineering from University of Tehran, Iran, in 2003 and 2005, respectively. His research before 2005 was mainly on heat/stress -based crystallization of amorphous silicon for fabricat ion of field -effect transistors in addition to the modeling and optimizat ion of submicron device structures In 2005, he began his work towards Doctorate of Philosophy degree at University of Florida. During this period, t he focus of h is research has been on fabrication, characterization, and modeling of thin films and networks composed of nanoscale materials such as carbon nanotubes and graphitic nanoribbons, as well as fabrication and characterization of various electronic and optoelectronic devices based on these materials