NOISE AND CURRENT-VOLTAGE CHARACTERISTICS
OF NEAR-BALLISTIC GaAs DEVICES
ROBERT ROY SCHMIDT
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
The author wishes to express his sincere gratitude to
Dr. C. M. Van Vliet and Dr. G. Bosman for their research guidance and
aid in improving drafts of the work, and to Dr. A. van der Ziel,
Dr. E. R. Chenette, and Dr. A. Sutherland for their helpful suggestions
and kind interest. He wishes to thank Mark Hollis for fabricating the
Finally, the author appreciates the help of his fellow students
in the Noise Research Laboratory, especially Bill Murray for drawing
most of the figures contained herein.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . .
ABSTRACT . . . .
I INTRODUCTION . . .
II THEORY OF VERY SMALL LAYERS IN GaAs .
III EXPERIMENTAL PROCEDURES AND MEASUREMENT CIRCUITS .
3.1 Current-Voltage Measurements .
3.2 The 0.24 Hz to 25 kHz Correlation System .
3.3 The 50 kHz to 32 MHz System .
IV MEASUREMENT RESULTS . .
4.1 Current-Voltage Characteristics ..
4.1a The n+n-n+ Device .
4.1b The n+p-n+ Device .
4.2 The n+p-n+ Device Noise . .
4.3 The n+n-n+ Device Noise . .
V DISCUSSION OF EXPERIMENTAL RESULTS . .
5.1 The n+n-n+ Device . .
5.1a Current-Voltage Characteristic
and Impedance .
5.1b Excess 1/f Noise .
5.1c High-Frequency Noise .
5.2 The n+p-n+ Device . .
5.2a Current-Voltage Characteristics
and Impedance .
5.2b Noise . .
VI CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK .
6.1 The n+n-n+ Device . .
6.2 The n+p-n+ Device . .
APPENDIX: COMPUTER PROGRAMS FOR THE HP 9825 ... 88
REFERENCES .. .. .. . .. ..... 93
BIOGRAPHICAL SKETCH . . . 96
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
NOISE AND CURRENT-VOLTAGE CHARACTERISTICS
OF NEAR-BALLISTIC GaAs DEVICES
Robert Roy Schmidt
Chairperson: C. M. Van Vliet
Major Department: Electrical Engineering
+ + + +
Conduction processes in novel submicron n n n and n p n mesa
structures in GaAs are investigated. The widths of the n-type and p-
type layers are 0.4 pm and 0.47 im, respectively. These small devices
are of interest due to the possibility of ballistic (collision free)
transport which leads to picosecond switching times at femtojoule
power levels, since the velocities of the carriers may be much greater
than the collision-limited drift velocity.
Three noise measurement systems are described, covering the
frequency range 0.2 Hz to 64 MHz. The first system, for frequencies up
to 25 kHz, features a spectrum analyzer with a dual-channel fast-
Fourier transform algorithm. By exploiting the correlation feature,
the system,when combined with very low-noise preamplifiers, has a
background noise level for a low-impedance source of less than 0.3 ohms
noise resistance. The other two systems for radio frequencies use a
tuned step-up transformer to bring the noise of the very quiet n-typF
device to a level above that of the RF preamplifier. One is a conven-
tional single-channel system. The other uses RF mixers before the
dual-channel FFT analyzer to extend the range of the correlation system
to high frequencies, depending on the preamplifier frequency response.
Current-voltage measurements, DC, pulsed DC, and AC impedance,
are presented versus parameters bias level, temperature, and frequency,
as are noise measurements. The n-type device is linear and relatively
temperature independent exhibiting full thermal noise and, at low
frequencies, very low levels of excess 1/f noise five orders of magni-
tude less than for the bulk material. This suggests that collisions are
mainly absent from this device. The p-type device, conversely, is
nonlinear with large levels of excess low frequency noise. There is
a linear, noisy, and temperature-dependent low-bias region followed by
a transition to a less noisy temperature-independent high-bias regime
with large conductance. This may represent a transition from ambi-
polarly governed to near-ballistic transport.
There is great interest in very thin GaAs layers of lengths
less than 1 m. This is of the order of the mean free path lengths
of the dominant collision mechanisms for electrons. Under favorable
conditions, carriers may cross the layers undergoing few or no col-
lisions, which leads to very high velocities, much greater than the
collision-limited drift velocity. The resulting so-called ballistic or
near-ballistic transport leads to very fast-response devices for pico-
second switching at very low power or other new applications. These
new devices have been made possible by advances in fabrication tech-
niques such as electron beam lithography and, in particular, molecular
Such small devices enable us to investigate physical mechanisms
on a small scale for which the traditional models no longer apply. In
addition, practical knowledge of the performance limitations of these
new devices is obtained.
Early theories of these devices treated the ballistic motion of
the carriers as the dominant mechanism affecting its characteristics.
Recent measurements and later theories have shown that boundary condi-
tions, in particular the velocity dispersion of the carriers, have
much greater influence.
The organization of the chapters follows. In Chapter II some
theories of small n n n and n p n layers in GaAs are surveyed and
predictions are noted. Measurement techniques and procedures are
presented in Chapter III. In Darticular, a crosscorrelation noise
measurement system with a noise resistance less than 0.3 ohms suitable
for low-impedance low-noise devices such as the n n n diode is dis-
cussed. In Chapter IV, experimental results of measurements on two
devices are described. One is an n n n structure of length 0.4 pm.
The other is an n p n device of length 0.47 um. Current-voltage charac-
teristics, DC, pulsed DC, and AC to 25 kHz are presented, as are
measurements from 0.2 Hz to 32 MHz. The measurements are repeated at
77 K to investigate the effect of temperature. In some cases, T is
reduced to 12 K. Chapter V contains a discussion of the results.
Finally, conclusions and recommendations for further work are presented
in Chapter VI. An HP (Hewlett Packard) 9825A computer program used
to automate the noise measurements is recorded in the Appendix.
THEORY OF VERY SMALL LAYERS IN GaAs
In most semiconductor devices, the drift current is limited
by the rate of carrier collisions. However, for sufficiently thin
devices few or no collisions occur permitting ballistic or near-
ballistic transport. The resulting carrier velocities can be much
larger than in the collision-dominated case so that such parameters as
switching speed can be greatly increased. Advances in fabrication
techniques such as molecular beam epitaxy and electron lithography have
resulted in submicron gallium arsenide devices with dimensions the
same order of magnitude as the mean free paths of the dominant collision
mechanisms. Thus near-ballistic transport in these devices becomes
For polar optical phonon emission at room temperature, Eastman
et al.  report mean free path lengths in GaAs of about 0.1 pm for
electron energies near 0.05 eV to 0.2 um up to 0.5 eV. Phonon absorp-
tion is about four times less probable. They also report that the
change in the direction of motion due to a collision is small (5-10
degrees). Intervalley scattering becomes significant for higher elec-
tron energies than 0.5 eV. Shur and Eastman  calculated the mean
free path in the high-purity GaAs at 77 K to be 1.3 pm. Barker, Ferry,
and Grubin  have suggested some complicating factors even for
devices of length equal to the mean free path. First, in large area
devices, some carriers may move at angles to the length direction,
thereby increasing the distance traveled and the number of collisions.
Also, some of these carriers may collide with the device boundaries.
Third, space-charge effects may limit the current due to Coulomb
scattering. Finally, short devices may be dominated by contact effects
such as carrier reflection.
The theory for pure ballistic transport was revived from the
days of vacuum tubes by Shur and Eastman  based on a simple model.
They assumed a one-dimensional n-type device of length, L, neglecting
diffusion and electron scattering. Then the current density is
J = qnv (2.1)
where q is the electronic charge, n is the free electron density, and
the velocity, v, is found from
qVx m v (2.2)
where Vx is the voltage at x due to the applied potential, V, and m is
the effective mass. The initial velocity and the field at the injecting
contact are assumed to be zero. Poisson's equation
x 9 (n n) (2.3)
dx2 EOr 0
is then solved yielding Child's law
J / Er V3/2 (2.4)
/ m L
for large bias voltage and large consequent injected space charge. For
small applied voltages, the fixed charge due to ionized donors is
greater than that due to the injected carriers and an electron beam
drift region (J V1/2) results. The range of voltages for which
their model is valid is
-< V < (2.5)
where T is the lattice temperature and AE is the energy difference
between the main conduction band minimum and the secondary valley.
For very small voltages diffusion cannot be neglected. Intervalley
scattering is the cause of the upper voltage limit. Some measurements
[1,4] have been reported that appear to support this model, but their
interpretation has been questioned as will be discussed.
To take into account the effect of a few collisions, Shur 
and Shur and Eastman  have extended the theory. Frictional "drag
terms" to represent the collisions are added to the equations of
balance of energy and momentum. In general, the effective mass, m ,
and relaxation times, Tm and TE' are functions of energy so that the
balance equations are
dt qE --T (2.6)
dt qEv E (2.7)
Shur assumes a constant energy-independent effective mass and a single
momentum relaxation time, T, so that, neglecting (2.7), (2.6) is
m -t = qE (2.8)
Equations (2.1), (2.3), and (2.8) along with the boundary conditions
for the ballistic case are then solved analytically. For T much longer
than the transit time and sufficient applied voltage to justify
neglecting no, Child's law is again obtained. Conversely T much less
than the transit time yields (for V= -iE where i is the mobility) the
Mott-Gurney law for collision-dominated space-charge limited current
J EEr (2.9)
In the second paper, values of m*(E), v(E), Tm(E), and TE(E) are
obtained from Monte Carlo calculations. Steady state is assumed and the
boundary conditions are taken to be the initial field (and velocity)
equal to zero. Again letting TE and Tm become large yields Child's
law. For the general case, computer solutions are presented for various
lengths and doping densities which show small deviations from their
previous (ballistic) results.
The interpretation that current proportional to V3/2 indicates
ballistic transport has been seriously questioned by some authors.
Rosenberg, Yoffa, and Nathan  have shown the crucial importance of
the boundary conditions. For the ballistic case, they assumed a
simple one-dimensional model neglecting collisions. For each electron,
they solve equations (2.1), (2.3), and the energy-velocity relationship
S(v2 v) = q(Vi V) (2.10)
where vi and V. are the initial velocity and potential, respectively. A
displaced Maxwellian distribution of initial velocities characterized by
a temperature and mean velocity is assumed. A set of nonlinear equa-
tions in V result which are solved numerically for specified electric
field, E, initial carrier density, ni, and initial (temperature normal-
ized) mean velocity, v. They demonstrate that a wide variety of current
versus potential curves can be generated for various choices of initial
conditions [7, Figure 3]. The authors agree with others [3,8] that,
conversely with Shur and Eastman, the current-voltage characteristic may
be used to infer the boundary conditions for a device that has already
been shown to be ballistic by other means (such as noise behavior).
Another significant effect in short devices is "spillover" of
carriers from high- to low-doped regions. The result is that the
effective length of the low-doped region is shortened and hence the
resistance is less than expected naively even for devices many Debye
lengths long . Universal curves have been calculated by van der Ziel
et al.  from which the magnitude of the effect can be determined
for a particular device. The authors calculated the near-equilibrium
resistance for a 0.4 pm n-type device with doping densities Nd+ =
18 -3 15 -3
101 cm and Nd = 101 cm for liquid nitrogen and room temperatures.
They solve Poisson's equation including electrons and ionized donors
in the high- and low-doped regions, neglecting holes. They assume
n(x) = Nd+ exo fIq()l (2.11)
where Nd+ is the ionized donor density in the highly doped region and
,(x) is the potential. Reciprocal mobilities due to diffusion/drift
and thermionic emission are added to give an effective mobility which
agrees within 10/ of experimental results at room temperature. However,
a similar calculation for an n pn+ device is off by more than an order
of magnitude. They assumed that the electron spillover depletes the
holes in the p-region such that they (holes) may be neglected. This is
apparently not the case; the effects of the holes are important.
The simple theory of ballistic  and near-ballistic [5,6]
transport does not take into account the energy or velocity distribu-
tions of the carriers. Cook and Frey  have suggested the inclusion
of an electron temperature gradient term in the momentum balance
equation for this purpose. This may be sufficient for first order
effects such as the current-voltage characteristic. Their treatment
includes an average collective velocity dispersion term, in essence
treating the ensemble as a single particle for such effects as the
noise, a drawback they themselves point out in the simple theory.
For the noise, more adequate analysis should include a Langevin or
Monte Carlo approach based on the momentum and energy balance equations
which include terms necessary to account for the significant physical
mechanisms. Such a Monte Carlo calculation for a 0.25 pm n -i-n
diode at 77 K has been reported by Awano et al. . Ionized impurity
and intervalley and intravalley phonon scattering is included in their
model but not nonparabolicity of the band edges. Particles with a
distribution of velocities in equilibrium with the lattice at 77 K are
injected at one contact. They find that a large proportion of the
particles are transported ballistically. Groups of particles cor-
responding to one or two collisions and some backscattering from the
collecting contact is observed. For potentials less than 0.5 volts,
the current-voltage characteristic is surprisingly close to Child's
vacuum diode law.
Holden and Debney  have presented a calculation based on
ideas from Fry's theory for thermionic values . They assume injec-
tion from both n regions of carriers with Maxwell-Boltzmann velocity
distributions. Scattering is neglected. Following Fry, the free-
carrier charge density is found by an integration over the injected
carrier velocity distribution. A potential minimum due to injected
space-charge is assumed. They calculate current-voltage characteristics
for T = 77 K and lengths of 0.1, 0.2, and 0.5 um. The slopes at high
bias are less than 3/2 (L = 0.1 and 0.2 pm give ,1.3, L = 0.5 pm gives
<1.14). At low bias, the characteristics are somewhat more linear.
The authors conclude that ballistic effects do not lead to a particular
current-voltage power law and suggest that another method must be
found to determine ballistic effects.
The noise behavior of thin structures gives important informa-
tion on the extent of ballistic effects. Current-voltage character-
istics for these devices are dominated by events at the boundaries such
as the carrier velocity distribution. In addition, practical knowledge
of the performance limitations of the devices is obtained, as well as
useful insight into the physical mechanisms causing the various types
The noise is naturally divided into two frequency regions. At
high frequencies the dominant mechanism, variously called thermal,
velocity fluctuation, or diffusion noise is the electrical result of
the Brownian motion of the carriers. While the theory is not yet
complete, preliminary calculations have been made by van der Ziel and
Bosman [14,15]. For the ballistic case (collisions neglected) at large
bias, the device is modeled similarly to a dual-cathode vacuum diode
with opposing thermionic emission currents across the potential mini-
mum. Then correlated fluctuations in the current due to fluctuations
in the minimum due to the space charge result in a lowered (64%) level
of noise compared to the low-bias value of thermal noise of the AC
conductance. For the collision-limited case, at sufficiently large
bias, the device is modeled as a space-charge-limited solid-state
diode and the noise becomes twice the thermal noise of the AC conduc-
tance. Thus ballistic effects should reduce the noise and
collision-dominated transport should increase it if sufficient bias
levels can be achieved.
At low frequencies, excess noise characterized by a spectral
density with a 1/f frequency dependence dominates. According to most
recent theories [16,17] such noise is thought to be caused by mobility
fluctuations which represent fluctuations in scattering cross-sections.
The usual method to describe the noise is using Hooge's empirical
S-I(f) fN (2.12)
where I0 is the dc current, N is the number of carriers, f is the fre-
quency, and aH is Hooge's parameter.
This is accurate for a uniform sample. However, for a non-
homogeneous sample or a mesa structure, van der Ziel and Van Vliet 
have shown that the formula becomes
m 2 r L
maH 0 dx
S (f) H dx
S fAL2 nrx)
where m is the number of layers, L is the length of one layer, A is the
cross-sectional area, and n(x) is the electron density. The value of
aH was first thought to be constant (2 x 10-3). Later research has
found that aH depends on material variation, the dominant scattering
mechanism, and carrier heating  in Si. Thus the magnitude of aH
should give a good measure of the rate of collisions or lack of them.
EXPERIMENTAL PROCEDURES AND MEASUREMENT CIRCUITS
The procedures used in the measurement of both devices, n n n
and n p n are similar, but the actual circuits depend on the device
characteristics which are quite different. The p-type near-ballistic
diode (NBD) exhibited an impedance about 100 times that of the n-type
device at small bias. It also generated excess noise at low frequencies
orders of magnitude larger than the n-type NBD. Consequently, the noise
of the n-NBD was the most challenging measurement requiring an equiva-
lent noise resistance of the measurement system of about 0.2 ohms.
3.1 Current Voltage Measurements
Three I-V measurements were done on each diode: DC, pulsed DC,
and AC from 2.4 Hz to 25 kHz. A block diagram of the n-NBD circuit
is shown in Figure 3.1. A three-terminal measurement is required since
the resistance of the active region is comparable to that of the bonding
wire to the top surface of the diode (the devices were mounted in TO-5
cans). The resistance of the output wire, RL2, is negligible since it
is in series with the large input impedance of the oscilloscope. Then
V2 is the voltage across RX + RS which represents the series combina-
tion of substrate resistance and active region. The current through
the device is
I R R (3.1)
RB + RLl
Figure 3.1 Block diagram of n +current-voltage measurement
Figure 3.1 Block diagram of n n n diode current-voltage measurement
Pulsed measurements were done using an HP 214A pulse generator. The
pulse width was 1 psec and the repetition rate was 100 Hz.
The AC I-V measurement employed the HP 3582A spectrum analyzer.
The dual-channel feature was used to measure the transfer function as
a function of frequency from 2 Hz to 25 kHz and as a function of DC
bias. The circuit diagram of the AC resistance measurement is shown
in Figure 3.2. Taking into account the parallel resistances, RX is
found to be
V 1 + RS + R
V C R S RL S
R H= V- R-0R- L -(3.2)
X VO II RC1 (3.2
1 1 + T~\
VC t RB
The measurement for the p-type device is similar. Here, the
lead resistances may be neglected since the impedance is large; the
diode may be treated as a two-terminal device.
3.2 The 0.24 Hz to 25 kHz Correlation System
For the electrical noise measurement of low impedance devices
with resistances of the order of an ohm, the usual single-channel
method is not useful. Typical preamplifiers have noise resistances of
about 10 to 20 ohms. The device noise is masked by the preamplifier
noise. Therefore, the correlation method  is used as shown in Figure
A Hewlett Packard 3582A spectrum analyzer featuring a dual-
channel Fast-Fourier transform is employed. Low-noise preamplifiers
Ll i RL2
V Vo I MR
AC resistance measurement circuit for n-NBD
Correlation measurement setup
precede each channel from a common input. By measuring the coherence
(square of the correlation between the channels) the cross-spectra
can be calculated. The noise generated at the output of each channel
is uncorrelated with the other and therefore averages out in the final
reading. Only the noise generated at the input of each channel gives
a contribution to the final reading. Hence a better device noise
versus amplifier background noise ratio may be obtained.
The device under test (DUT) noise is compared to a known cali-
bration signal which is applied through a series resistor much greater
than the DUT resistance. The bias current is applied in a similar
manner. An equivalent circuit of the measurement setup is shown in
Figure 3.4. To characterize the noise of the system, we first neglect
the effect of the device noise. The series resistors to the bias and
calibration sources are R' and Rs. The calibration source, v al,
transforms to a Norton equivalent, ic, where
ci vocal (3.3)
The source resistance is represented by RX. The preamplifiers are
assumed identical (with uncorrelated noise sources, vl, i1, v2, and i2)
with gain, G (assumed constant), and input resistance, Ri. The output
of the amplifiers, u1 and u2, are then multiplied together and averaged.
The measurement procedure is to compare the output for three con-
ditions. They are (1) shorted input (RX = 0) giving output reading M1,
(2) open input (RX = W, RS J R >> Ri) giving M2, and (3) open input
with calibration signal applied (i 3 0) which gives M,. The output
for each case is easily found to be
M =0 (3.4)
M2 G2 1(i* + i (3.5)
2 = l T4-
M3 G2 (ili i2 + ) (3.6)
In reality, M1 is not exactly zero. There is a residual back-
ground noise. This can be accounted for by introducing a correlated
background noise source, vb, to the input voltage sources so that
vI = vi + vb and v2 = v2 + vb. The primed portions are uncorrelated.
Then the analysis yields
Ml =G2 VbV (3.7)
S __ ___ R2-
=G2 v (i i* + i (8)
M2 = bVb ( + i2i) (3.8)
M3 = 2 vb + (i i* + 2 + (3.9)
Writing the mean square averages as spectral densities, i.e.,
i i SiVc
S = 2 f etc., and noting Sc = allows the current and
voltage noise to be calculated.
M M S
M3 M2 SIc
K- M S SI (3.10)
M2 N11 Il + 12
SII + SI2 ,S (3.11)
SVb i VM (3.12)
2 M2 )
The current noise spectra of the two channels are SI and SI2 and the
background voltage noise spectrum is SVb'
A significant source of background noise, after such causes
as pickup of unwanted signal, ground loops, and power supply noise have
been eliminated, is the finite averaging time of the spectrum analyzer.
The sample coherence for shorted input versus number of averages is
shown in Figure 3.5. It is a large-side biased estimate inversely pro-
portional to the number of averages which is limited to 256. The
distribution of sample coherences is not easily described  for
1 10 100 10
NUMBER OF AVERAGES
HP 3582A sample coherence
for shorted input versus number
small expected value. The residual nonzero value is interpreted as
The system is used with two similar sets of preamplifiers
denoted PAl and PA2; PA2 features five parallel input stages like that
of PA1 but with larger bias current. They are shown in Figures 3.6
and 3.7; PA1 has larger voltage noise but extended low frequency
response suitable for excess 1/f noise measurement. The PA2 has been
designed for minimum voltage noise.
The PAl features a capacitively coupled common emitter transistor
first stage with shunt feedback. This reduces the input impedance but
does not affect the noise. The primary motivation for this circuit
is a practical one. The RC settling time of the base bias circuit is
substantially reduced compared to the usual configuration. The tran-
sistor (GE 82) is chosen for large and small series base resistance.
The second stage is a low-noise operational amplifier (Burr-Brown
OPA101BM) in noninverting configuration;12-volt automotive batteries
are used for the power supply.
An equivalent circuit of the input stage is shown in Figure
3.8. It is the low-frequency hybrid pi including source resistance,
feedback, and noise sources. The source resistance is RS. Thermal
noise of the series base resistance, rb, is vb. Shot noise of the
base and collector currents are denoted ib and ic, respectively. To
transform this circuit to a form similar to that in Figure 3.4, the
closed loop gain, the input resistance, and the noise sources must
be calculated. The closed loop gain is found by summing currents at
SINPU GE 8,
INPU I I
Figure 3.6. Model one (PAl) low-noise premplifier
v v. v.
i + o i 0, (3.13)
s RF 1 Rs
and at the output
V V. V
i. + 1 0- (3.14)
1 R R
where R = r R, i = gmv and the noise sources have been neglected
for now. Letting r = rb + r so i = the output equation gives i
in terms of v which, when substituted into the input equation allows i
to be expressed as a function of v Then, for RF -, the closed
loop gain, A, is found to be
A R- F (3.15)
RF + RC + r. + 1 +
S C 1 RF RSJ
The loop transmission is found by disconnecting the output current
generator, gmv and applying a test current generator, iT, there. The
output voltage, v is
v = iT [RC (RF + RS r)] (3.16)
The input voltage fed back is
r.RS (v v.)
v. RS 0 (3.17)
i r + R RF
1 S F
(r + RS) RF
i = vR (3.18)
ri + RS) RF
Then, noting that gmv, = gvi gives
g v -_Rc
1 RV r-BR
T RF + RS+ir ri + r(s
C F R + r R
S il( S)
The input resistance is RS in parallel with Ri where, for RF >> RC and
RF >> ri/,
RC + R
R. = r. (3.20)
1 + r R g
The output resistance is R in parallel with RL where
R + r+ R-
R = r (3.21)
0 0 r.
B+ 1 +
Except for the noise, the circuit of Figure 3.8 now becomes that of
Figure 3.9 where the voltage gain is
fR + R
G = A R 1 (3.22)
For the case that RF >> RC, ri, Ri >> rb, RS, and (riRF)/RS >> BRC,
G -Fr (3.23)
The gain becomes open loop as the input is shorted by a small RS. To
transform the noise sources, the effect of feedback is neglected. Open
circuiting the inputs (RS = m) of Figures 3.8 and 3.9 and setting the
output voltages equal yields
S rb Vb + 9C
i =g rb m (3.24)
a b r + r rb + r,
Short circuiting (RS = 0) the inputs yields
a = Vb + + ibrb (3.25)
Substituting numerical values for components with RS = 5.6 ohms and
assuming 8 350 yields about 1200 ohms for the input resistance. The
measured value for two PAls in parallel is 660 ohms as shown in Figure
3.10. The input resistance of two PA2s in parallel is shown in Figure
3.10. For the gain the calculated value is about 51 decibels. The
result including the second stage is 90 decibels. The measured value
is 89.5 decibels as shown in Figure 3.12.
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The noise resistance of PA1 and PA2 were measured to be about
35 and r2.5 ohms, respectively. The five in parallel input stage of
the PA2 gives that factor of reduction in the noise resistance.
Another factor of three reduction comes from increasing the input bias
currents by that amount since, to first order approximations, the
voltage noise sources are inversely proportional to bias .
Using the correlation setup gives about a factor of ten reduc-
tion in the voltage noise. This is seen in the ploLs of voltage noise
resistance and current noise conductance for the two setups shown in
Figures 3.13 through 3.16. The noise resistance, Rn, is defined by
SVb = 4kTRn (3.26)
Similarly, the noise conductance is defined by
S1 + SI2 = 4kTGn (3.27)
The current noise of the PA2 is much larger than that of the PA1
as would be expected from larger bias currents and five in parallel.
For the sensitive measurements, the current noise is shorted by the
small resistance of the DUT. This is the full current noise which
remains in the correlation calculation. Of the voltage noise, only the
background level remains.
The device noise measurement procedure is very similar to
that for the amplifier. Three conditions are recorded. They are
(1) DUT on, (2) DUT off, and (3) calibration signal applied with DUT
off. Any change in DUT resistance between the on and off state must be
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- O (n) ONVI.onON0O o ,
-- 3SION IN3fnO ,
taken into account (replacing the device by a resistance equal to its
"on" resistance for the latter two measurements). The equivalent circuit
of the input can be drawn as in Figure 3.17. The DUT is represented
by the parallel combination of Rx, the AC resistance of the device,
StLf, the thermal current noise generator, and V^-'f the excess
current noise generator. The calibration signal is ^cal f. The ampli-
fier is characterized by Ra, /Sif and /VLf
For the three conditions, the outputs are
M = G2[(S + S + S)R2 + SI] (3.28)
1 x th A A
M2 = G2[(Sth + Si)R2 + SA] (3.29)
M3 G[(Sth + SA + Sal)R2 S] (3.30)
where G is the (constant) gain and R is the parallel resistance at the
input. Then, as before,
M1 M S
K 1 2 x (3.31)
M3 M2 Scal
so that the device noise current can be written
S = S +S = KS + (3.32)
DUT x th cal R
+ + dV
Note that for the nonlinear n p n diode, Rx d- and depends on the
bias current applied. An HP 9825A controller can easily automate this
measurement and be used to average many data sets for increased
accuracy. A program which does this for eight logarithmically spaced
points per decade is presented in the Appendix.
3.3 The 50 kHz to 32 MHz System
At radio frequencies, the same three-measurement procedure as
before is used for the noise. The circuit is more conventional, as
shown in Figure 3.8. A step-up transformer consisting of four trans-
mission line transformers in cascade with capacitance-tuned input and
output is employed for the n-type device. See the Radio Amateur's
Handbook for details. A Micronetics KSD20LEE solid-state noise source
is used for the calibration signal. Frequency selection is done by an
HP 8557A spectrum analyzer. The IF output signal from the spectrum
analyzer is passed through a 21 MHz bandpass filter and detected with an
HP 431C power meter.
The preamplifier, designed and built by Christopher Whiteside
of the noise research group, is shown in Figure 3.19. It employs two
stages of low-noise FETs (2N4393) in cascade configuration to obtain
30 dB gain with a noise voltage resistance of about 70 ohms. This is
less than the stepped-up noise of the DUT.
The HP 3582A spectrum analyzer can be used to make noise
measurements in the radio frequency range. This is accomplished by
mixing down the RF signal just before the analyzer as shown in Figure
3.20. Only a single channel is shown, although the correlation method
can be used just as easily. The bias and calibration signal are
applied as for the conventional RF system. The circuit for the n-type
device, using a tuned step-up transformer, is shown. The 60 dB radio
frequency preamplifier is actually two of the 30 dB preamplifiers
shown in Figure 3.19 in cascade. The large gain is needed to overcome
the poor noise performance of the mixer (Mini-Circuits ZAD-1). Using a
standard RF signal generator with output amplitude capability of
+7 dBm, the mixer has a frequency response of 100 kHz to 500 MHz.
The same signal generator can be used to supply both mixers
(correlation setup). Then two 60 dB preamplifiers are used and, if
series resistance or unwanted pickup of the step-up transformer is not
negligible, two of these also. Feedthrough of local oscillator har-
monics may overload the spectrum analyzer at some frequencies if a
bandpass filter similar to that shown in Figure 3.21 is not employed.
This simple filter had good (90 dB) attenuation to 100 MHz. The band-
width of a single FFT bin of the spectrum analyzer was extremely small
compared to the frequencies of interest, causing significant inaccuracy.
To reduce that, a program to average 80% of the bins to synthesize a
bandwidth of up to 20 kHz was written. It is shown in the Appendix.
The near-ballistic diode (NBD) is a sandwiched mesa structure
of five lightly doped p or n layers, alternating with heavily doped n
layers. A not-to-scale sketch of the p-NBD is shown in Figure 4.1.
18 -3 +
The doping densities of the various regions are 10 cm for the n
regions, approximately 2 x 10 cm for the n regions, and approxi-
mately 6 x 101 cm for the p regions. The diameter of the mesas is
100 pm. The devices were manufactured by molecular beam epitaxy at
the Cornell University Submicron Research Facility by Mr. M. Hollis.
The mesas have very low-noise ohmic AuGe contacts.
Current-voltage measurements of three types-DC, pulsed DC,
and AC-are reported. Also presented are noise spectra versus parameters
bias, frequency, and temperature.
4.1 Current-Voltage Characteristics
4.1a The n n n Device
The DC current-voltage characteristics of the 0.4 m n n n device
at room temperature and 77 K are shown in Figure 4.2 In contrast to
the device reported in Eastman et al. , there is no vV region.
The characteristic is linear for both temperatures up to very large
bias. Pulse techniques are used for currents greater than 100 mA.
The resistance of the active region is 0.75 ohms at room temperature
NJ 10 cm
Np- r 10 cm
Figure 4.1 P-type near-ballistic diode mesa structure
o 0 300 K
 77 K
0.1 mA '
O.ImV ImV lOmV
Figure 4.2 DC I-V characteristic of n n n 0.4 nm device
and 0.68 ohms at 77 K. This is confirmed by the AC impedance
measurement at 300 K for IDC = 75 mA shown in Figure 4.3. Low-
frequency equivalent circuits of the device at room temperature and
77 K are shown in Figures 4.4 and 4.5. The series resistances of the
gold wires of the TO-5 can are significant and must be taken into
4.1b The n p n Device
Conversely, the n p n structure is quite nonlinear. The DC
current-voltage characteristics of the 0.47 im n+p-n+ diode at 300 K
and 77 K are shown in Figure 4.6. The device is linear for both
temperatures up to about 100 mV. The characteristics then move through
transition to a temperature independent high bias regime in which the
slope falls off. The maximum slopes in the transition regions are
3 for the 300 K case and 4.5 at 77 K. The low-bias resistances at
300 K and 77 K are 90 ohms and 320 ohms, respectively. The measurements
of AC resistance for several bias currents at T = 300 K shown in Figure
4.7 and for T = 77 K shown in Figure 4.8, display no frequency
To compare the large and small signal resistances more easily,
the exponent, B, can be examined where I = V Differentiating both
sides and solving for g gives
S DC (4.1)
o 0 -
0.75 < R,
Figure 4.4 Equivalent circuit of n n n structure at 300 K showing
R LI RL2
Figure 4.5 Equivalent circuit of n n n structure at 77 K showing
0 300 K
ImV lOmV lOOmV IV lOV
Figure 4.6 DC I- characteristic of n- 0.47 m device
Figure 4.6 DC I-V characteristic of n p n 0.47 ,im device
< Ln <
[ > O
7 0> 0
oD 7 o
ED 7 0
cD 7 0
(u)i) na 0o 0v
1 I I
This is plotted in Figure 4.9 for small bias up to 34 mA. At higher
bias, pulsed DC but not AC measurements were done. The resistance
falls dramatically at high bias. This is seen more clearly in Figure
4.10 which presents the DC and pulsed DC conductance versus bias
voltage for several temperatures down to 12 K. The large-bias
conductance in the temperature independent regime rises to a limiting
value of about 0.33 Siemens. In the low-bias regime, the conductance
quickly falls from its 300 K value by about a factor of three at 150 K
to 200 K and remains nearly constant for further decreases in tempera-
4.2 The n p n Device Noise
The n p n 0.47 ;m structure exhibited large levels of excess
low-frequency noise. The room temperature noise current spectrum
(less than 25 kHz) for several bias currents is shown in Figure 4.11.
The frequency dependence for all bias currents is about .75. In
Figure 4.12 is shown the extension to 32 MHz of the spectra for bias
currents of 100 pA and 1 mA. The 100 1A spectrum is approaching the
thermal level at the high-frequency end. The turnover frequency to
thermal noise occurs in the GHz range for larger bias. Figures 4.13
and 4.14 display the complete spectra versus frequency for bias currents
of 34 mA and 68 mA, respectively. Both show slopes of -0.77 over many
decades. No turnover frequency to a different slope is found. These
spectra represent measurements in the low-bias regime and transition
region. Measurement in the high-bias regime requires pulsed techniques.
1 I 1 -
qo d- to() CiJ C
o F 0 a
o V, I n c o
0 O o
Q 0 0 ..,
u-i- "G 0 0o,
^ -a^ So->
A2 I 0r !- 0 0
N-/ /" U -\ 0 [-
0 3.4 mA
0 I mA
Figure 4.11 Low-frequency p-NBD room temperature current noise spectra
UIK lOOK IM IOM lOOM
Current noise of 0.47 pm n pn+ NBD at T = 300 K for
I = 100 IA and 1 mA
(ZH/VIs 10 10
S-O >- o
G- 0 L
S| LL z
-0 0 A
The room temperature current noise at 100 Hz is plotted
versus bias current in Figure 4.15. There is an 12 dependence at
lower currents up to a few mA. At higher bias the noise increases
less fast. The deviation from 12 behavior appears to coincide with
the transition region.
The low-frequency current noise spectra at 77 K for several
bias currents are shown in Figure 4.16. The levels of excess low-
frequency noise are again large. The slopes are somewhat steeper than
for the room temperature case, being approximately -0.85. Figure 4.17
displays the current noise at 100 Hz versus bias. Again, 12 dependence
in the low-bias regime with a fall-off in the transition region is
The temperature dependence of the noise in the low-bias regime
was investigated further. The low-frequency small bias (100 uA) noise
spectra were measured for several temperatures (300 K, 250 K, 200 K,
150 K, 77 K, and 12 K) down to 12 K as shown in Figure 4.18. The
magnitude increases with decreasing temperature down to about 200 K.
Thereafter, further lowering of the temperature does not affect the
magnitude very much, but the slope becomes more closely 1/f. The
other temperatures are not plotted since they only obscure the figure.
At 12 K, the slope is fully 1/f as shown in Figure 4.19.
4.3 The n n n Device Noise
The magnitudes of the noise levels of the 0.4 um n+n n struc-
ture, both thermal and excess low frequency, are very small. The
current noise spectra for several bias currents at room temperature is
10 10 I 10 o0o
Figure 4.15 Current noise at 100 Hz versus bias current for p-NBD
at T = 300 K
Y 10 0L A
FREQ UENCY (Hz)
Figure 4.16 Current noise of p-NBD at T = 77 K
1 x 71
1OU A lOOA ImA 10mA IO0mA I A
Figure 4.17 Current noise versus current of the p-NBD for f = 100 Hz
and T = 77 K
I I I i
Current noise of n+p n+ diode for I = 100 -A and three
1 0 -19
10 100 IK IOK lOOK
Figure 4.19 Current noise of n p n diode at T = 12 K and IDC = 100 IA
shown in Figure 4.20. Thermal levels and excess low-frequency noise
for some levels of bias can be seen. The frequency dependence of the
low-frequency noise is 1/f. The spectra from 1 to 25 kHz with the
1/f levels subtracted is shown in Figure 4.21. The lower three bias
currents result in approximately thermal noise. There is still excess
noise for 75 mA, however. Therefore, a spot noise measurement at
500 kHz for that bias was done. Less than J- deviation from the
thermal level was found. Values at 10 Hz obtained from the straight
line approximations to the 1/f noise are plotted versus bias current
in Figure 4.22. The expected behavior for 1/f noise, SI 12 is well
Spectra for T = 77 K and the same bias currents are plotted in
Figure 4.23. Excess low-frequency noise is found for all current
levels. The noise in the thermal region is difficult to determine
accurately because the expected value for full thermal noise (%0.17 2)
is below the background noise of even the correlation setup. Also, for
some bias currents, the noise is not yet flat at these frequencies.
The 1/f noise at 10 Hz is plotted versus bias in Figure 4.24. Again,
the I2 dependence of the magnitude is found.
-, 75 mA
10 L--- -
-19 K) r-n r-
10 00 IK OK JO0K
Figure 4.20 Current noise spectra of n 0.4 m NBD at T 300 K
Figure 4.20 Current noise spectra of n n n 0.4 pm NBD at T = 300 K
O 54 mA 2.5 x 1020
S27 mA S. (,VG.) I KHz 25 Hz
10 o mA 2.1 x -20,
C) ^ ^ ^ ^ ^------- -,
V THEFi.!AL ,'CISE-
Figure 4.21 Thermal (-like) noise of n n n device
SLOPE 'L 2
Figure 4.22 Excess 1/f noise of n+nn+ device versus current
25 2.5 25 250 2.5K 25K
Figure 4.23 Current noise of 0.4 nm n-NBD at T = 77 K
Figure 4.24 SI of n-NBD at 10 Hz versus bias current for T = 77 K
DISCUSSION OF EXPERIMENTAL RESULTS
5.1 The n nn+ Device
5.la Current-Voltage Characteristic and Impedance
The I-V characteristic of the n-type device is seen from
Figure 4.2 to be linear for bias voltages up to about 1 volt and
currents up to about 1 amp for both room temperature and 77 K. An
attempt to apply pulses at higher bias resulted in melting the gold
bonding wire at the top of the mesa. Higher bias was desired since a
slight nonlinearity appears at currents greater than 1 amp. Neverthe-
less, 1 amp corresponds to a current density of 12,800 A/cm2. No V1/2
or V32 dependence is found which suggests that theories with these
results are not adequate.
Similarly, the collision-dominated Mott-Gurney theory which
predicts V2 current dependence at high currents does not apply.
Indeed, sublinear current dependence at high bias seems to be indicated
by the sparse data. The more realistic theory of Holden and Debney
 gives a high-bias current dependence of V14 for a 0.5 im device
where collisions are neglected. At lower bias, their result appears to
be somewhat sublinear, similar to the V /2 region of Shurand Eastman's 
theory. The theory of van der Ziel et al.  gives linear behavior
for small bias. They include spillover from the highly doped regions
and calculate separately the mobilities due to diffusion-drift and
thermionic emission. Setting the calculated and measured values of
resistance at room temperature equal and solving for the diameter of
the mesa gives a 96 pm diameter which is very close to the reported
value of 100 jm. At 77 K, the measured value decreases 10%, the cal-
culated value decreases 23%. The impedance is purely resistive at
5.1b Excess 1/f Noise
In the 1/f noise region, we would like to apply Hooge's
empirical formula  which is Equation (2.12). For mesa structures
or nonhomogenous samples , Equation (2.13) replaces it and is
correct whether or not the transport is ballistic.
In a ballistic or near-ballistic device, many carriers do not
undergo any collisions at all. This is in contrast with a typical
semiconductor device in which every carrier collides many times.
Hooge's formula was developed for the second case, requiring that N,
the number of carriers in Equation (2.12) can be determined. In the
near-ballistic case, it is desired to exclude those carriers which are
transported ballistically, including only those that contribute to
the noise. This can be very difficult. Therefore, an alternative
expression to describe "noisiness," avoiding this problem, will also be
used. Noisiness is described as (S A(f)f)/I2 which is still dimension-
less unless the spectral slope is not -1. Substituting values gives,
at 300 K,
S = 1.6 x 10-15 (5.1)
and at 77 K,
2 1.4 x 104 (5.2)
If the slope is not -1, then just (S A(f)f)/I2 can be reported at a
If n(x) = n is a reasonable approximation despite the complex
nature of n(x), then Equation (2.13) becomes
Hb = 2 (5.3)
where the subscript, b, denotes validity for the ballistic case. If
the transport can be characterized by a constant mobility, i, the
measured resistance is
R m j n (5.4)
Then, for the collision-dominated case, Hooge's constant becomes
Hc = 2 (5.5)
Assuming that 300K = 0.74 mV- 14 mec A = 7.9 x 10 m2
aHc = 7.2 x 10-8 (5.6)
aHb = 5 x 10-8 (5.7)
At 77 K the values are
cHc = 3.7 x 10-8 (5.8)
aHb = 4.5 x 10-7 (5.9)
These values are five orders of magnitude smaller than the value
reported by Hooge et al.  for n-type bulk GaAs of 6 x 10-3. Thus
the number of collisions for this device is very small. The remaining
collisions involve polar optical phonon emission typically with a very
small deflection angle , 6. Handel's  quantum theory of 1/f noise
indicates that the magnitude of the relative 1/f noise goes as sin2
so that the residual noise is very low.
Comparing the ballistic and collision-limited case temperature
dependence of aH suggests that the device is not purely ballistic at
either temperature since the low temperature ccHb is nine times larger
than the value at room temperature. Further, the diffusion-drift
resistance calculated by van der Ziel et al.  is larger than the
thermionic emission resistance for both temperatures. However, the
values are within a factor of two of each other. The very low value
of aH suggests near-ballistic transport.
5.1c High-Frequency Noise
The device exhibits nearly 100% thermal noise at all currents
to 75 mA if sufficiently high frequencies are attained. This current
corresponds to a current density of 960 A/cm2. There is no detailed
theory for the noise as yet developed for all applied bias, just the
preliminary calculations of van der Ziel and Bosman [14,15]. For the
collision-dominated space-charge-limited diode at low bias, the noise
is due to diffusion noise sources which transform via Einstein's
relation to 4kT/R At high bias for which the Mott-Gurney law
For a bal-
(I V2) applies, the noise becomes 8kT/R where R For a bal-
x x di.
listic device the noise is due to shot noise. At sufficiently high
bias where soace charge effects dominate, correlations between current
components due to fluctuations in the potential minimum caused by the
space charge lead to subthermal noise.
In order to differentiate between the two models, high bias
must be achieved. Our measurements have found no deviations from
thermal noise. One possible reason for this is that the current density
of 960 A/cm2 is insufficient. Another is that the device is operating
in between the two regimes as suggested by the 1/f measurements so that
extreme bias may be required to see which effect dominates.
5.2 The n p n Device
5.2a Current-Voltage Characteristic and Impedance
The n p n device shows substantial nonlinearity. There are
two regimes with a transition region in between as shown in Figure
4.10. At low bias, the device is linear with a DC conductance at room
temperature 100 times smaller than the n-type device. It decreases
with decreasing temperature to a limiting value a factor of 3 below its
room temperature value. It reaches this value near 150 K and remains
constant thereafter down to 12 K. The high bias regime is temperature
independent and is also linear with a large conductance 4 times less
than the n-type device.
Due to the thinness of p-regions and the large doping density
of the n regions, the spillover of electrons into the p-regions is
not very different than for the n-type diode case . Then current
flow should be by nearly ballistic electron emission through the poten-
tial minimum. The resulting characteristic should be linear with a
large conductance and nearly temperature independent. This appears to
be a good model for the high bias regime. At low bias, the model
fails, however. One possible reason for this is that enough holes re-
main in the p-region to control the transport ambipolarly. The details
of such an effect are unclear, but a qualitative description by
Dr. C. M. Van Vliet follows. The motion is not strictly ambipolar,
since there is space charge, as indicated by the presence of the poten-
tial minimum , which even for V = 0 can be computed from Poisson's
equation. Therefore, near the potential minimum the excess electron
charge is small. Roughly speaking, only ambipolar pairs with energies
within kT of the potential minimum are able to cross the minimum.
If the injected carrier density An is less than p ata point (labeled x')
approximately kT greater in energy than the minimum on the injecting
side, then the current will be ambipolar (instead of ballistic).
Clearly, with decreasing T, p(x') decreases. Thus, with decreasing T
the ambipolar current decreases, and the transition to ballistic
behavior-which is independent of T-sets in at lower bias. The I/V
versus V characteristic is therefore as shown in Figure 4.10.
In any case, assuming that holes control the mobility for low
bias, and electrons at high bias gives a factor of 21 change in the con-
ductance at room temperature since typical values are pn 8,500 cm2
and p k 400 cm /V-sec . There still remains to be explained the
factor of 4 difference between the n-device conductance and the high
bias p-device conductance. The potential barrier is larger in the
p-type device . In the p- region, Poisson's equation is
2 q(n + N p)
where '(x) is the potential, n(x) the electron density, p(x) the hole
density, Na the acceptor density, and ee0 the dielectric constant. For
the n-device in the n region
d2 q(n Nd)
x Nd (5.11)
If p(x) is assumed negligible due to electron spillover,
I 22 dp
so that the n-device barrier is smaller. The above model of ambipolar
collision-dominated flow at low bias and near-ballistic electron
emission at high bias gives a qualitative explanation of the experi-
The n p n device showed much larger levels of noise than the
n-type device. The frequency dependence of the spectra for all
measured currents is about (1/f)75 for all measured bias currents at
room temperature. Then Hooge's parameter is not well defined since it
is not dimensionless (unless the slope is -1) and depends on frequency.
The noisiness at 10 Hz and 100 pA is
2 = 6 x 10-9
This is about 4 x 106 times
slopes do not change in the
magnitude of the noise does
seen at low bias, however.
with the low bias transport
the n-type device value. The spectral
transition from low to high bias. The
fall off at high bias from the 12 dependence
This suggests that the noise is associated
mechanism and that the high bias mechanism
is much less noisy. That is in good agreement with the conjecture
of ambipolarly governed flow at low bias and near-ballistic flow at
high bias. The -0.75 slope is not common although van de Roer 
has also found spectra going slower than 1/f in 6 im p n p punch-
through diodes. The spectra become more closely 1/f as temperature
decreases. At 77 K the slope is -0.85 which is common for intermediate
temperatures down to 12 K. The magnitude of the noise is
= 3.3 x 10-8
at 10 Hz and 100 pA.
at 10 Hz and 100 yA.
slope is unclear.
Finally, at 12 K, the slope is fully -1 with
The explanation of this temperature-dependent
CONCLUSIONS AND RECOMMENDATIONS
FOR FURTHER WORK
6.1 The n+n n Device
The n n n device is nearly ballistic. Carrier transport is
by both thermionic emission and by collision-based diffusion-drift.
Neither process can be neglected in a physical model. For the I-V
characteristic, it is desired to calculate n(x), v(x), and J(V) for
any applied bias, expanding on the calculations of van der Ziel et al.
 for small V. Alternately, the model of Holden and Debney 
should be further developed to investigate the effect of adding col-
lisions to their model. Also the temperature-dependence and the
effects of replacing the Maxwell-Boltzmann velocity distribution by
a Fermi-Dirac distribution should be investigated.
Since nonlinearity in the I-V characteristic appears at high
bias, very fast (1l nsec) pulse neasurements at yet higher bias
would be very interesting. The mechanism causing this nonlinearity
should be identified.
For the noise, the measured value of aH found was extremely
low. This is the best confirmation yet that lattice phonon scattering
causes 1/f noise. It would be valuable to repeat the measurement on
other mesas. Perhaps in such small devices Handel's  fundamental
theory can be tested.
In the thermal noise region, the results were inconclusive,
neither subthermal nor greater than thermal noise was found. Perhaps
the bias level was not great enough. In that case pulsed noise
measurements could be attempted. This may be difficult since the noise
is already very low. A detailed and complete noise theory for these
devices is desirable, including collision effects and velocity dis-
persion. A Langevin equation based on the momentum and energy balance
equations of Shur and Eastman [5,6] but including the above effects
should give accurate results.
6.2 The n p n Device
The p-type device was very intriguing, beginning with the
I-V characteristic. At present it is believed that at low bias the
carrier transport is ambipolar and collision-limited, centering about
the potential minimum. At high bias, the injected electrons overrun
the holes and near-ballistic electron flow results similar to the n-
type device. The conductance is less because the potential barrier is
greater. This model deserves further detailed investigation.
The noise is very large and shows slopes becoming progressively
less 1/f as temperature is increased. This interesting characteristic
suggests that subtle and complex mechanisms may be taking place that
are not well understood yet. To develop a theory that explains these
effects would be a great step forward in our knowledge of very small
devices. The 1/f noise extends to the GHz range to frequencies greater
than our measurement system so that thermal noise measurements have still
to be done. In addition, only these low-bias measurements have
been done; pulsed noise measurements in the high-bias regime are
underway; they may yield valuable information.
Investigation of this device has led to another novel device
. A p n p device with nonlinear characteristics is predicted to
have negative differential conductance. At low bias, electron-
controlled ambipolar flow should give a large conductance. At larger
bias, hole injection takes over with collision-limited flow resulting
in a low conductance. The transition region, therefore, should show
the negative differential conductance.
COMPUTER PROGRAMS FOR THE HP 9825
COMPUTER PROGRAMS FOR THE HP 9825
A.1 Correlation-System Three-Measurement Averaae
This program calculates equations for the current noise spectral
density of a device under test (DUT) using the three-measurement
technique. Actually, the magnitude of the calibration signal is also
recorded. The program calculates data for eight logarithmically equal-
spaced points covering one decade in frequency. It is used with the
HP 3582A spectrum analyzer which features a dual-channel Fast Fourier
transform algorithm for frequencies from 0.02 Hz to 25 kHz. Many data
sets can be averaged to increase the accuracy of the measurement which
is described in Chapter III.
0: "REPEATED-3 MEASUREMENT CORRELATION SYSTEM":
2: dim A,B,C,F,M,S8] 8],Q$,LS
3: dim MS[8,5];"MP12"-M$;"MP18"M$
7: ldf 1,A,B,C,D,A[*],B[*],C[*],F[*],M[*]
8: fxd 0;dsp A,B,C,D,F;beep;stp
9: fit 3
10: "n"-W$;ent "DUT ON (y/n)",QS;if Q$="y";gto "DUTON"
11: "n"Q$;ent "DUT OFF (y/n)",Q$;if Q$="y";gto "DUTOFF"
12: "n"-QS;ent "CAL ON (y/n)",QS;if Q$="y ;gto "CALON"
13: "n"-QS;ent "CAL MAG (y/n)",O$;if Q$="y";gto "CALMAG"
14: "n"-QS;ent "CALC NOISE (y/n)",Q$;if Q$="y";gto "NOISE"
15: "n"*Q$;ent "CLEAR DATA FILE (y/n)",Q$;if QS="y";gto "CLEAR"
17: rcf 1,A,B,C,D,A[*],B[*],C[*],F[*],M[*]
18: fxd O;dsp A,B,C,D;beep
19: Icl 7i1;end
21: for I=l to 8;gsb "GET"
22: if A=0;X-A[I];Y*B[I];Z-C[I];next I
23: if A0O;jmp 4
26: (Z+A*C[I])/(A+1)*C[I];next I
27: A+1-A;gto "DONE"
29: for I=1 to 8g:sb "GET"
31: if B=0;X-A[J];Y-B[J];Z-C[J];next I
32: if B=0:jmp 3
34: (Z+B*C[J])/(B+1)C[J];next I
35: B+1-B;gto "DONE"
37: for I=1 to 8;gsb "GET"
39: if C=0;X-A[J];Y-B[J];Z-C[J];next I
40: if C=0;jmp 3
42: (Z+C*C[J])/(C+1)C[J];next I
43: C+1-C;gto "DONE"
45: wrt 711,"AAIMN1MB1"
46: for I=1 to 8
47: wrt 711, "MP",S[I],"LMK";red 711,U,V
48: if A+B+C+D=0;V-F[I]
49: if V#F[I];beep;dsp "FREQUENCY MISMATCH";stp
51: if D=0;U-M[I];next I
52: uf D#0;(U+D*M[I])/(D+1)4M[I];next I
53: wrt 711,"AA0";D+1-D;gto "DONE"
55: ent "TEtFP",T;ent "DUT RESISTANCE",R
56: ent "CAL RESISTANCE",S;ent "DC CURRENT",U
57: gsb "LABEL"
58: for I=1 to 8;spc
63: prt "SI=",N;fxd 1;prt "FREQ=",F[I];flt 3
64: next I
65: spc ; spc ;gto "DONE"
68: for I=l to 8;0F[I]-1M[I];next I
69: for I=1 to 24;0-*A[I]-B[I]C[I];next I
70: gto "DONE"
72: gsb "DATA"
73: if A+B+C+D=0;V-F[I]
74: if V#F[I];beep;dsp "FREQUENCY MISMATCH";stp
75: asb "COH"
78: wrt 711,"AAlMNlMB1"
79: wrt 711,MS[I]
80: wrt 711,"LMK";red 711,X,V
81: wrt 711,"AA0AB1LMK";red 711,Y,V
82: wrt 711,"ABO";ret
84: wrt 711,"LFM,",76000+dto(4*S[I]),",4";red 711
85: for J=1 to 4;rdb(731)-U;rdb(731)-Z
86: ior(rot(U,8),Z)-X[J];next J
87: wrt 711,"LFM,",77000+dtoS[I],",1";red 711
89: wrt 711,"LFM,",75000+dtoS[I],",1";red 711
91: wrt 711,"LFM,",75200+dtoS[I],",1";red 711
93: wrt 711,"LFM,",77200+dtoS[I],",1";red 711
102: ent "Label",L$;spc ;prt L$
103: prt "DCI=",U;prt "TEMP=",T
104: prt "DUT RES=",R;prt "CAL RES=",S
105: prt "# SETS=",A
A.2 Wide-Band Filter Synthesizer
This program is written for the HP 9825 computer in conjunction
with the HP 3582A spectrum analyzer. The high-frequency 4/5 of the
FFT bins are averaged to synthesize a wide-band filter to use with the
radio frequency FFT system which utilizes a mixer just before the
spectrum analyzer. Without the use of this program, the accuracy
of a measurement is poor since the bandwidth is then very small com-
pared with the frequency of interest. A bandwidth of 20 kHz can be
generated by setting the frequency span on the 3582A to 25 kHz,
although the program displays the filter output in normalized dBV//Vz.
0: "Last 4/5'ths of display averager:
1: dim B,Y
2: wrt 711,"LFM,77454,5"
3: red 711
4: for I=1 to 10;rdb*711)-~[I]
5: next I
6: wrt 711,"LSP";red 711,S
7: if B>0;sfg 1
9: if H>127:H-128-H4
10: if H>63;H-64-H
11: if H>31;H-32-H
12: if H>15;H-16-H
13: if H>7;H-8-H
14: if H=0;250-B
15: if H>1;68.87+B
16: if H>3;166.6667-B
18: if H>127;H-128-H
19: if H>63;H-56.-H
20: if H>31;H-32-4
21: if H>15;H-16-*H
22: if H>7;H-8-4H
23: if H>3;H-4-+H
24: if H>2;sfg 2
25: 128-N;if flgl;256-N
26: if not flgl;B/2-B
27: if flg2;256-N
28: wrt 711,"LDS"
29: red 711
30: for I=1 to N;red 731,Y[I]
31: next I
32: Icl 711
33: if flg2;128+N
34: 0-A;fxd 4
35: gsb "calc"
36: if flg2;XYY;0+X;128-A;gsb "calc"
37: if flg2;prt 20*log(Y/.8N),201og(X/.8N);end
38: prt 201og(X/.8N);end
40: for I=A+N/5 to A+N;X+tnt(Y[I]/20)//(S/B)-X;next I
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