Title Page
 Table of Contents
 Literature review
 Experimental techniques
 Summary and conclusions
 Biographical sketch

Group Title: Microstructure/electrical property correlations for YBa2Cu3O7-x/barrier layer films deposited on Al2O3, silicon, and yittria-stabilized zirconia subst
Title: Microstructure/electrical property correlations for YBa2Cu3O7-x/barrier layer films deposited on Al2O3, silicon, and yittria-stabilized zirconia substrates
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Permanent Link: http://ufdc.ufl.edu/UF00090920/00001
 Material Information
Title: Microstructure/electrical property correlations for YBa2Cu3O7-x/barrier layer films deposited on Al2O3, silicon, and yittria-stabilized zirconia substrates
Series Title: Microstructure/electrical property correlations for YBa2Cu3O7-x/barrier layer films deposited on Al2O3, silicon, and yittria-stabilized zirconia subst
Physical Description: Book
Creator: Mueller, Carl Henry,
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Bibliographic ID: UF00090920
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
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        Page vii
        Page 1
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        Page 3
    Literature review
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    Experimental techniques
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    Summary and conclusions
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    Biographical sketch
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Full Text








Several people have helped me complete this thesis. I would like to thank my

advisor, Professor Paul Holloway for being an excellent role model and showing me

how a scientist solves problems. I am especially grateful for his guidance during the

early stages of the project, and for letting me choose my own directions as the project

matured. I was fortunate to have very talented people on my committee, and

Professors Abbaschian, Anderson, Connell, and DeHoff each provided insights into

materials properties which were important to this project and will be valuable

throughout my career.

I am grateful for the help I recieved from co-workers within our group, especially

Kelly Truman and Ludie Hampton. Much of the data was collected at the Major

Analytical Instrumentational Center at the University of Florida, and Eric Lambers,

Wayne Acree, and Richard Crockett did a superb job of keeping the instruments in

top condition, which made the data collection and interpretation possible.

I would like to thank Drs. Kul Bhasin, Felix Miranda, Mark Stan, and Crystal

Cubbage of NASA Lewis Research Center for their help. A large portion of this

thesis would not have been possible without their help.

My family provided a strong emotional base which allowed my to complete the

program. I would like to thank my parents, Gerhard and Lillian Mueller, for

stressing the importance of finishing a project. I would also like to thank my

brothers, Don, Lloyd, and Keith, my sister Jan, and their families for their

encouragement and for helping to keep things in perspective.

Finally, I would like to thank the friends who made my stay in Gainesville so

enjoyable. I will miss the Sunday afternoon soccer games.


ACKNOWLEDGEMENTS ..................................... ii

ABSTRACT ................................................ vi


1. INTRODUCTION ......................................... 1

2. LITERATURE REVIEW ................................... 4

D evices ............................................... 4
Microstructure/Superconductor Relations ..................... 18
W eak Link Behavior .................................... 27
Nucleation and Epitaxial Growth ........................... 35
Thermally Induced Stresses ................................ 46
YBa2Cu3O7. Film Growth ................................ 53
Barrier Layer Technology ................................. 67

3. EXPERIMENTAL TECHNIQUES ........................... 81

Film Growth by Laser Deposition ........................... 80
X-ray Diffraction ....................................... 84
Scanning Electron Microscopy ............................. 86
Scanning Auger Electron Spectroscopy ....................... 86
Electrical Resistance Measurements ......................... 90
Critical Current Density .................................. 94
Raman Spectroscopy .................................... 96
Millimeter-Wave Transmission Measurements .................. 99

4. RESULTS ......................... ................ 101

YBa2Cu3O. on (1i02) LaA10 ........................... 101

YBa2Cu307.x/Y-ZrO2 Films on Si, Y-ZrO2, and LaAO03 Substrates .108
YBa2Cu307./SrTiO3 Films on A1203 Substrates ................ 137
YBa2Cu307.x/LaA103 Films on Si and A1203 Substrates .......... 154
YBa2Cu307x/YA103 Films on Si and A1203 ................... 160
YBa2CuO37./Y203 Films on Si, Y-ZrO2, and SrTiO3 Substrates .... 173
YBa2Cu3O7./(YA103, LaA1O3, or Y203)/Al6Si2013 Films on
Si and A1203 ..................... ................... 180

5. DISCUSSION .......................................... 196

Intergranular Versus Intragranular Effects ................... 196
Effect of Y-ZrO2, Y203, and ZrO2 Barrier Layers on Jc Values .... 201
Dependence of To and J. on A1203 Substrate Orientation ........ 209
Estimate of Stress and Cracking Due to Differential
Thermal Expansion ................................... 211
Effects of Texture and In-Plane Alignment ................... 212
Millimeter-Wave Properties .............................. 214
Effects of Surface Energy ................................ 215
Effects of Lattice Matching ......................... ...... 217
Effects of Oxygen Pressure on SrTiO3 Growth ................ 219
LaA103 Barrier Layers .................... .... ........... 225
Y203 Barrier Layers ................... ............... 228
YA103 Barrier Layers ................................... 229
Al6Si2013 Barrier Layers .......................... ........ 231

6. SUMMARY AND CONCLUSIONS .......................... 236

FOR YBaCu30 ............................... 241


REFERENCES ........................................... 266

BIOGRAPHICAL SKETCH ................................... 276

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




December, 1992

Chairperson: Professor Paul Holloway
Major Department: Materials Science and Engineering

YBa2Cu3O7x and barrier layer films were deposited on single-crystal silicon (Si),

A1203, yittria-stabilized zirconia (Y-ZrO2), SrTiO3, and LaA103 substrates. A pulsed

laser deposition process was used to deposit the films at a substrate temperature of

730 750 *C, and the films were cooled in an oxygen ambient. The films were

characterized using resistance versus temperature, critical current density (Je), x-ray

diffraction (XRD), scanning electron microscopy (SEM), Auger electron spectroscopy

(AES), and Raman spectroscopy.

Growth of barrier layers on Si and A1203 substrates prior to the superconductor

suppressed chemical interdiffusion between the superconductor and substrate. For

(1102) A1203, the best barrier layer was a SrTiO3 film deposited at 200 mTorr of

oxygen. The YBa2Cu307. film had a zero resistance temperature of 83 K, and the

Jc was 2.5x106 amps/cm2 at 4.5 K. The surface resistance was 10-2 ohms at 36


On silicon substrates, YBa2Cu3O07 degradation is aggravated by thermal stresses

created by the difference in thermal expansion coefficients between YBa2Cu307- and

Si (13.2 versus 3.8x10-6/*C, respectively), which causes microcracking in the

YBa2Cu307.x films. Cracking and interdiffusion were minimized by depositing a

YA103 barrier layer prior to YBa2Cu3O7-.. The thermal stresses were relieved by

viscoelastic relaxation in the YBa2Cu3O7. film, and the To was 78 oK.

The Jc values of YBa2C3Cu307 films on Y-ZrO2 substrates were increased by

depositing Y-ZrO2 or Y203 barrier layers. YBa2Cu3O7-x/Y2O3 films on Y-ZrO2

substrates had Jc values of 9 10 and 1xl10 amps/cm2 at 77 and 4.5 K. The Jc of

YBa2Cu3O7. films deposited on a Y-ZrO2 substrate without a barrier layer was

6.8 x 103 amps/cm2 at 4.5 *K. The higher Jc values were attributed to pinning of the

magnetic flux by excess Y203 at high-grain boundaries.


There are several commercial and military application for thin films which are

superconducting at temperatures above 77 "K. Since most semiconducting

devices perform optimally near 77 K, the potential for high-speed devices with

low-attenuation superconducting interconnects is promising'. In another

electronics area, passive microwave and millimeter-wave devices patterned into

superconducting thin films dramatically outperform the resonators and filters

presently being used.2 As the technology for depositing superconducting films on

A1203 substrates improves, this performance will be further enhanced. Potentially,

the largest applications for superconducting films are in power applications.3

Transmission cables, motors, and high field magnets which are too costly to

operate at 4.5 K would be economically feasible at 77 *K. Progress in

fabricating superconducting wires has been difficult because the wires currently

being fabricated suffer from brittleness and low critical current density (J,) values

(3 x104 amps/cm2 at 77 K). A better technique for making superconducting

cables may be to deposit superconducting films on fibers such as yittria-stabilized

zirconia (Y-ZrOz) which are mechanically strong and have a similar thermal

expansion coefficient as the superconducting film.

For each of these applications, Jc values greater than 1l amps/cm2 are

required.3 The sensitivity of J, to interfacial phases and high-angle grain

boundaries in YBa2Cu3O7. is one of the most significant problems, and it has

inhibited commercialization of YBa2Cu3O7.x films. To date, YBa2Cu3O7. films

with JC values above 10s amps/cm2 at 77 K have only been deposited on single-

crystal substrates such as SrTiO3, LaA103, and Y-ZrO2 which nearly lattice match

YBazCu3O7x. The ability to deposit films with high Jc values on randomly

oriented or polycrystalline substrates would be a tremendous boost towards

commercialization, since this would allow a variety of substrates with different

shapes and sizes to be used.

In this thesis, the literature is reviewed in chapter 2 in order to provide a

background for this work. The experimental techniques used to deposit and

characterize the films are described in chapter 3. The data original to this thesis

is presented in chapter 4, and is discussed in detail in chapter 5.

Chapter 2 shows how superconductivity evolves. The temperature at which

the resistance disappears (To) and Jc are closely tied to the microstructure, and an

overview of the microstructural phenomena which most critically affects the

superconducting properties is introduced. The laser deposition process is

described, and the mechanisms which enable multicomponent films to grow with

the same stoichiometry as the target are presented. Chapter 2 concludes with a

survey of the work directed towards depositing YBa2Cu3O7 films on various

substrate materials.

Chapter 3 describes the film growth technique, and the methods used to

characterize the films. Each of the characterization tools relies on different

physical phenomena to probe the film microstructures, so different aspects of the

microstructures were uncovered. A brief description of the operating principles of

each of the probes is given in this chapter.

The experimental results are presented in chapter 4. The sections are

arranged so as to compare the effectiveness of each barrier layer to induce growth

of optimal quality YBa2Cu3O7. films on different substrates. The text explains

what information the data is providing, and points out the most notable features

in each figure.

Chapter 5 compares and contrasts the data in order to explain the observed

phenomena. The primary objective of this thesis is to uncover the microstructural

features which were primarily responsible for the normal state and

superconducting properties. By using a variety of experimental techniques, we

arrived at a more clear understanding of film microstructures than if only one or

two techniques were used; thus we were able to correlate the film microstructures

with the electrical properties.



Much of the interest in high temperature superconductivity is due to the large

number of applications which could benefit from replacing normal metals and

conventional solid state electronic devices with superconducting materials.

Basically, applications which could utilize high temperature superconducting thin

films can be divided into two categories: active devices which require one or

more weak link junctions, and passive devices which utilize the intrinsic properties

of superconductors for enhanced performance.

In superconductors, zero resistance and macroscopic quantization occur

because the wave functions of the electron or hole pairs are coherently coupled to

each other. This coherence enables calculations of the phase difference between

two different points of the superconductor to be made.4 Weak-link junctions are

thin insulating or normal metal regions which separate two superconducting

volumes, and the lower density of superconducting charge carriers causes a

gradient in the phase of the superconducting electron (or hole) wave function

across the weak link.

A Josephson junction is a special type of weak link junction in which the

relationship between the supercurrent, I,, and the gradient of the phase of the

superconducting wave function (AL ) is given by:s'6

1, = Isin (A Q) (2-1)

where I, is the maximum superconducting current which can travel through the

junction. For the rest of the discussion on devices, it will be assumed that the

weak links are Josephson junctions. The current vs. voltage behavior of a

Josephson junction is characterized by a zero resistance supercurrent which

persists when A~Q is constant, and a non-linear voltage which appears when A4Q
varies with time. The voltage, V, across a Josephson junction in this state is given


2eV= h a(A ) (2-2)
27r &t

where e is the carrier charge and h is Planck's constant.

The I-V plot for a Josephson junction is given in figure 2-1,7 and virtually

all of the active superconducting devices utilize the behavior predicted by

equations 2-1 and 2-2. A brief overview of some of the devices which use

Josephson junctions, and their operating principles, is presented below.

Oscillators are devices which generate a repeating voltage vs. time waveform.

Superconducting oscillators, in which the output voltage is controlled by the

frequency of the supercurrent travelling through the junction (equation 2-2), can


generate electromagnetic radiation at milliwatt-level powers,8 at frequencies up to

1012 Hz.

Critical Current

M ------ -------------


Figure 2-1. The current versus voltage characteristic of a Josephson junction.
Reference 7.

Radiation detectors are based on the principle that electronic radiation will

induce AC currents in the Josephson junction.7 Regardless of the orgin, currents

add algebraically, hence the DC critical current will be suppressed by the

radiation induced AC currents. In the finite voltage regime, the mixture of AC

Josephson supercurrent with induced normal state AC currents will produce sum

and difference harmonic currents within the junction. When the ac Josephson

frequency and radiation frequency are harmonics of each other, there is a mixing

harmonic, and a step in the current vs. voltage spectrum appears at zero

frequency and at the mixing frequency. By varying the voltage and thereby the

supercurrent frequency across the junction, a large range of frequencies can be

sampled via the conversion factor:

1 microvolt = 484 MHz. (2-3)

Surface Quantum Interference Devices (SQUID's) are used to detect weak

magnetic fields, and operate on the principle that the number of flux lines which

pass through a Josephson junction must be quantized.4'9 If the magnetic field

being detected is not a quantized number of fluxons, the J. of the junction will

change so that the magnetic flux from the magnetic field plus the flux generated

by the current through the junction is quantized (figure 2-2). The magnetic

intensity of a fluxon, o0, is given by:

Q = h = 2.07 x 10-15 Webers (2-4)

Thus the I V profile of a Josephson junction is modulated by the magnetic field.

In practice, the magnetic sensitivity of a de SQUID is significantly improved by

placing two Josephson junctions in parallel (figure 2-3), which makes the loop

defined by the film plus the two junctions the area through which the modulating

magnetic flux travels. This dramatically increases the area over which the flux is

measured. For two junctions placed in parallel,


1,(10) = I, o) cos0' )

The high sensitivity of SQUID devices make them attractive for a variety of

biomedical, geological, and military applications.




0 o 20
9oA 0oA

Figure 2-2. Periodic variations in the critical current density with increasing
magnetic field strength. Reference 4.

1/21X1 W 1/2 1 V

Figure 2-3. Schematic of a two-junction SQUID. Reference 4.

Because Josephson junctions can be changed from superconducting to

semiconducting and vice-versa by varying the current or magnetic field, they have

been used as switching devices in digital electronics. The intrinsic switching

speed of a Josephson junction is:

Switching speed = h (2-6)
2 rA (7)

where A(T) is the temperature dependent superconducting energy gap. The
intrinsic switching speed for niobium-based Josephson junctions is 0.22

picoseconds. As an example of the increased performance which can be achieved

by replacing semiconducting switching devices with superconducting Josephson

junctions,10 a four-bit data processor made with GaAs transistors had a clock

speed of 72 MHz, and a power dissipation of 2.2 watts. A processor which

performed the same functions using Josephson junctions had a clock speed of 770

MHz and dissipated 5 milliwatts. More recently, superconducting electronics were

used to fabricate a four-bit shift register using 3 um linewidths, which operated at
9.6 GHz and dissipated 40 microwatts. By comparison, devices made from GaAs

or Si which used 0.5 pm linewidths, dissipated approximately 100 milliwatts. The
lower power dissipation associated with Josephson switching devices is an

important advantage, since heat generation and removal limit the density and

bandwidth of circuits based on semiconducting electronics.

Superconducting devices employing Josephson junctions have great potential

and, in theory, could completely change the materials and operating principles on

which high speed electronics are currently based. However, reproducible and

reliable Josephson junctions are difficult to fabricate. Efforts to create high

speed, commercially acceptable switching devices based on low temperature

superconducting electronics have not been successful. Because the high

temperature superconductors are much more sensitive to microstructural defects

than their low temperature counterparts, it is unlikely that high temperature

superconductors will be used as switching devices in the near future. While

devices which utilize fewer Josephson junctions, such as electromagnetic detectors

and SQUID's are more feasible, difficulties in creating reliable Josephson

junctions remain formidable.

The materials challenges presented by the second group of devices based on

superconducting materials, passive devices, are more likely to be surmounted in

the near future. The first commercial applications for high temperature

superconductors will probably emerge from this group. The largest applications

of passive superconductors will be as transmission lines, delay lines, and filters for

receiving and transmitting electromagnetic signals.

The advantages gained by replacing normal metals with superconducting

materials are derived from the magnetic field penetration depth:"

(T) -- x(0)
[ 4-( ] (2-7)

where A(T) is the temperature dependent magnetic penetration depth, A(0) is the
penetration depth near 0 *K, T is the operating temperature, and To is the

highest temperature at which zero resistance is observed. The response of a

superconducting material to an applied magnetic field is shown in figure 2-4. For

a superconductor, A is a material property, so it is independent of the device
operating frequency.


Figure 2-4. Variation of magnetic flux density at the boundary of a
superconductor. Reference 4.

In microwave and millimeter-wave transmission lines, there is an electric field

induced in the superconducting line because of the inertia of superconducting

electron pairs to the electromagnetic field. A surface resistance results because

the normal-state electrons are excited by the electric field, and the surface

resistance is qualitatively a measure of how much of the electromagnetic signal is

lost as heat in the transmission line:6

Joule losses
Surface resistance = R= Joul losses, (2-8)

where Hsufa is the magnetic field intensity inside the superconductor. In

superconductors, the depth to which a magnetic or electric field can extend is

limited by the penetration depth, and the surface resistance (R,) is given by:6'12

R,(T,) = A2 exp-A (2-9)
T kT

where A is a constant, o is the frequency of the electromagnetic signal, T is the
temperature, kB is Boltzmann's constant, and A(T) is the superconducting energy


By contrast, the surface resistance of normal metals is given by:13

R,= ( o) (2-10)

where po is the magnetic permeability of the metal, and o = a1 + iO2 is the

complex electrical conductivity, with,

= 0 2 (2-11)
1 + M2r2


o= o (2-12)
1 + o22

a, and a2 are the conduction and displacement currents, and r is the mean time

between electron-phonon interactions. In normal metals, the skin depth (6) is the
distance into the metal which an electric field can penetrate, and is a function of

the electrical conductivity:

6 = (2-13)

where c is the speed of light (3x1010 cm/sec) and p is the magnetic permeability.

The dependence of the skin depth on electrical conductivity and hence

frequency means the dielectric constant of the metal changes with frequency. The

parameters pertinent to microwave signal transmission are contained within the

propagation constant, y,14 where

y=a+rjp (2-14)

a is the attenuation constant, and f is the wavenumber of the microstrip line. f
is given by:

S2 (2-15)

where Ag is the wavelength of the electromagnetic signal as it propagates in the

microstrip line. The speed at which electrical signals propagate through the metal

is given by the phase velocity, vp, where

v 1 (2-16)
p (pe).

p = PoUr and E = EoE, where Po and E, are the magnetic permeability and
dielectic permittivity of free space, and (uo0o)"5 is equal to the speed of light.

Given that /r and Er are the relative permeability and dielectric constant of the

microstrip material, the phase velocity of an electromagnetic signal propogating in

the metal is given by:

S c (assuming P, = 1) (2-17)

Changes in the electrical conductivity, and hence dielectric constant of the metal

as a function of frequency, will also result in phase velocities which vary with

frequency. This phenomena, termed dispersion, causes electrical pulses composed

of various Fourier components to become spread out as they propagate along a

transmission line, and is the primary reason why normal metal conductors are

inadequate for long transmission lines. Dispersion in metallic interconnect lines

makes them inadequate for delay times greater than 1 microsecond, or for

wideband lines carrying short pulses (figure 2-5). For example, assuming typical

dimensions for a VLSI microstrip line (thickness = 0.1 0.3 um, width = 1 3

jum, and length = 1 10 pm) dispersion necessitates that pulse lengths longer than
100 picoseconds must be used. However, a superconducting line of the same

dimensions would have negligible dispersion for pulses longer than 1



9 : Superconducting Line
>- 109

S107 Aluminum Line

U) 106

S105 I
0 2 4 6 8 10 12
LOG (Frequency)

Figure 2-5. Calculated phase velocities as a function of frequency for
superconducting and aluminum microstrip lines, at 77 K. Reference

The real part of the propagation constant, a, is the attenuation and results

from Joule losses within the microstrip line. In a superconducting material, the

penetration depth is constant, so a (decibel/cm) is linearly proportional to the

number of wavelengths/cm, and thus the frequency. In normal metals, a is

dependent on the skin depth, which is proportional to o0"5, so a increases more

slowly with increasing frequencies in metallic microstrip lines than it does in

superconducting lines. However, at microwave and millimeter wave frequencies,

the superconducting penetration depth is much less than the normal metal skin

depth, and it is only at w > 1012 Hz that attenuation in a superconducting

stripline approaches a for normal metals (figure 2-6).16'17

In semiconductor devices, the reduced attenuation and Joule heating provided

by superconducting interconnect lines would permit interconnect lines to be scaled

down considerably, thereby reducing chip to chip propagation delays.


. 10-2


L 10-4



1 10


Figure 2-6. Surface resistances of YBa2Cu30., (dotted line) and copper (solid
line) films deposited on LaAlO, substrates. Reference 17.

Microstructure/Superconductor Relations

The microstructure of a superconducting film has a large influence on the

electrical and magnetic properties, and understanding how the superconducting

properties are impacted by film microstructure will dictate the processing

procedures used to fabricate the films. In YBa2Cu3O7., the superconducting and

normal-state properties are anisotropic with respect to crystallographic direction,1

so film orientation is a critical parameter. The To and Jc of the film are

dependent on superconducting properties such as coherence length (4), and
penetration depth (A), which, in turn, are influenced by orientation, grain size,
and grain boundaries. Clearly, microstructural considerations play a large role in

defining the electrical and magnetic properties of the film. To understand the

relationship between microstructure and superconductive behavior, it is instructive

to review how superconductivity evolves. Although the physical processes

responsible for superconductivity in YBa2Cu30.x have not been uncovered, most

of the properties are well described by the microscopic Bardeen-Cooper-Schrieffer

(BCS) theory and the phenomenological equations which predate BCS, so the

properties of YBa2Cu30.x will be described in terms of conventional


In a normal metal, there is a repulsive energy between electrons, and the

energy levels are described by Fermi-Dirac statistics:19,2

( (E E) (2-18)
e +1

where f(E) is the probability that a given electron state is occupied, E is the

energy, Ep is the Fermi energy, k is Boltzman's constant, and T is the

temperature. In normal metals, electrical conductivity is possible because there

are empty electronic states at energies greater than Ep, into which electrons can

hop and thus move through the lattice. Current is transported through a material

because the applied electric field raises the electron energy level of one terminal

relative to the other, thus increasing the probability that electrons will hop from

the high potential to the lower potential region of the sample. Electrical

resistance arises from processes which transfer kinetic energy to the crystal lattice

by electron-electron and electron-phonon collisions.

The mechanisms for current transport in superconductors are different from

those observed in normal metals. Superconductivity is a cooperative phenomena

involving many electron or hole pairs, and is possible because of electron (hole)-

phonon coupling, which creates an attractive force between electrons (holes). The

potential energy caused by an electronic transition from an initial state k, to

another state k', is given by:6

V(q,0) [1+ q ] (2-19)
q2+2 k 02 2

where V (q,m)is the electron-electron potential, q is the wave-vector difference
between the k and k' states, wq is the phonon frequency at wave-vector q, and k is

the wave number of superconducting electrons at the Fermi surface. During an

electron transition between two states (k to k'), a phonon may be absorbed. If w
< Oq, and the transition lowers the potential energy of the system, the electron-

phonon interaction creates an energy gap in the energy vs. momentum spectrum,

and the most favorable way for two electrons with p > pf (p = momentum at the

Fermi level) to lower their energy below 2E, is to form a bound state, in which

electrons with equal and opposite moment combine to form Cooper pairs. The

wavefunction for a Cooper pair is given by:4

(iPp=e (2-20)

where is the amplitude of the wavefunction (also known as the "order
parameter"), multiplied by the travelling wave expression in which P = electron

momentum, r = position, h is Planck's constant, and I' 2 is the density of

superconducting electrons. Cooper pairs obey Bose-Einstein statistics, hence it is

energetically favorable for all the pairs can have the same momentum. Because

all the superconducting pairs have the same momentum, and thus the same

wavelength, superposition of the coherent waves results in another wave with the

same wavelength. Superconductors possess macroscopic quantization because all

the superconducting electrons have the same momentum. When a transport

current is impressed on the system, the quantum mechanical relationship

v,2m h(k +k2) (2-21)

(where v, = velocity of superconducting electrons, and k1 = k2 = k. for the

superconducting electrons) produces long range order in the momentum. There is

no resistance because the superconducting electrons are coupled together, and the

energy required to break a Cooper pair into excited electrons (quasiparticles) is

greater than twice the energy gap between superconducting and normal state

electrons (= 2A(T)).
The size of the superconducting energy gap is dependent on the fraction of

electrons which are superconducting, and this fraction varies with temperature.

Gorter and Casimer derived:

.=1-( 4, (2-22)
n To

where n/n is the fraction of superconducting electrons, To is the temperature at

which resistance vanishes in weak magnetic fields, and T is the temperature. The

variation of the superconducting energy gap (A(T)) with temperature is given by:2

A (7)TT=aTo(1-I) (2-23)

where a is constant equal to 3.06 if weak electron-phonon coupling is assumed.

The variation of the superconducting gap with temperature is shown in figure 2-7,

1.0 -...e A- 0o indium

SA A Tin
0.8 o *Lead I
0** BCS Theory oA
o 0.6 o



0 I I I
0 0.2 0.4 0.6 0.8 1.0

Figure 2-7. The superconducting energy gaps of lead, tin, and indium versus
temperature. Reference 4.

and shows the gap is a maximum at T = O *K. To illustrate the fraction of the

ideal superconducting bandgap which commercial high temperature

superconducting devices will be expected to operate at, we assume To to be 90

K, and the device operating temperature to be 77 K. These values correspond

to the temperature at which zero resistance is achieved in YBa2Cu3O7x, and the

boiling point of liquid nitrogen. Using equation 2-23, we see that A(T)/A(0)
drops to 0.38 at T/Tc = 0.86, and disappears at T = To. Increasing the

superconducting energy gap at 77 K is one of the prime motivations for studying

higher T, materials such as the bismuth and thallium-based superconductors.

A parameter which critically affects film and device quality is the coherence

length (i), which is the decay length for the wave function created by the

formation of Cooper pairs,7
W '. (2-24)

where vp is the velocity of electrons at the Fermi level and A is the size of the

superconducting energy gap. An equivalent definition is that the coherence length

is the minimum distance over which the density of superconducting electrons can

vary, and hence the minimum distance between superconducting and

nonsuperconducting regions. The coherence length (4) is much shorter in

YBa2Cu37O.x than it is in conventional superconductors such as Nb3Sn, and is

highly dependent on crystallographic direction (table 2-1). The short coherence

length in YBa2CU3O7-. (table 2-2) is primarily due to the small Fermi velocity of

the superconducting electrons, and an important consequence of the short

coherence length is that microstructural defects, such as grain boundaries,

impurity atoms, dislocations, or chemically unstable surfaces which create

imperfect or disordered regions of similar size to the coherence length, can

significantly alter the superconducting wave function, especially in the <001>

direction. By contrast, microstructural defects are considerably less degrading to

the order parameters of conventional superconductors.

Table 2-1. Normal state parameters of conventional metals (such as Nb3Sn) and
YBa2Cu3O7x. Reference 7.

Parameters Conventional YBa2zCU30OT
Metals (001) 1 (001)
m* 1-1.5 m, 5 me 25 mg
Ep (eV) 5-10 0.3 0.3
kF (cm)- 108 5x107 5x107
vp (cm/sec) 1-2x108 107 2x106

A final parameter which is important for understanding the magnetic and

electrical transport properties of superconductors is the magnetic penetration

depth, A, which is a measure of how deeply a magnetic field penetrates into a
superconductor. The depth to which a magnetic field can penetrate into a

superconductor is limited because the superconductor will generate circular eddy

currents, which create an internal magnetic field that nullifies the applied field. A
is defined as4

f B(x)d= Bo (2-25)

where Bo is the applied magnetic field, and B(x) decays exponentially as it enters

the superconductor (figure 2-4). By virtue of the Maxwell equation,21

VxB=E +4nJ, (2-26)

A is the maximum depth at which a transport current (J) can flow, hence it is
analogous to the skin depth in normal metals.

Table 2-2. Superconducting parameters of conventional metals (such as Nb3Sn)
andYBa2Cu307., Reference 7.

Parameter Conventional YBa2Cu307-
Metal (001) 1. (001)

To (OK) < 23 95 95
2A/kBTo < 4.4 5-8 2-3.5
A/E, 104 2x10-1 1xlO-1
o (A) 10'-10 15 7

The penetration depth varies with superconducting electron density, and hence

temperature. The Gorter-Casimir expression for A is:"

[1( 0o 1 (2-7)
T[-( ) 4 2

where A is the penetration depth at 0 K, and varies with film quality. For a
highly-(001)-oriented, 3000 A thick YBa2Cu3O0.. film grown on LaAIlO, 10 = 1800

A was measured.17 Films with larger fractions of non-(001) oriented grains, or

which contain high-angle grain boundaries, had larger penetration depths.

The way in which a superconductor responds to a magnetic field is dependent

on the Ginzburg-Landau parameter K, defined as4

K =0.966- (2-27)

The magnetic field may be applied, or may be induced by the transport current (a

self-field). Superconductors with K < j 2 are classified as Type 1, while those
with K > 2 are Type 2. In both types, there is a magnetic contribution which
increases the free energy density, AG, while the electron ordering associated with
the formation of Cooper pairs lowers AG. If the AG associated with electron
ordering occurs over a shorter distance from the surface than the magnetic

contribution ( as in Type 2 superconductors), there will be a minimum in the free

energy density at the surface, and it becomes energetically favorable to form an

interface between the normal and superconducting regions (figure 2-8). Thus

there are isolated circular regions in the sample which are normal, while the rest


of the sample is superconducting. The coexistance of normal and superconducting

regions (i.e. the mixed state) enables superconductivity to be maintained in much

higher magnetic fields in type 2 materials than are allowed in type 1. All of the

commercially useful superconductors are type 2 materials.

Normal Superconducting
&Number of

(a) Penetration depth and coherence range


S- -,-_-_ --- Electron-ordering

(b) Contributions to free energy


(c) Total free energy

Figure 2-8. Orgin of negative surface energy. Reference 4.

Weak Link Behavior

Because of the short coherence length, microstructural defects significantly

affect the electrical properties of YBa2CU3O7-.. Defects are regions in which the

amplitude of the superconducting wave function is depressed, and the density of

superconducting electrons is lowered. Since these defects reduce the

superconducting order parameter, reductions in To and J, result if the transport

current is forced to travel through the defects.6

Defects are classified as either superconductor-insulator-superconductor (SIS)

or superconductor-normal-superconductor (SNS), depending on the electrical and

magnetic properties of the junction.4 For the case in which two superconductors

are separated by a thin insulating layer, there is a finite probability that

superconducting electron pairs will tunnel through the insulator and a

superconducting current will be maintained. Because of the insulating layer, the

wave function is no longer continuous between superconductors, but there is a

phase difference, A,, between the wavefunction at each of the interfaces which
determines the maximum supercurrent, I,, which can pass through the insulator:5

,= i Ain A (2-1)

If the transport current exceeds i, A4 is no longer constant with time, and a

voltage appears across the junction. The currents which result from the time

varying A~Q and subsequent voltage across the insulator are given by:4

Ch o2(A) + h c(Ai) (2-28)
4xe at2 R44xe at

where C is the capacitance, h is Planck's constant, and R, is the normal state

resistance of the junction. Ambegaokatar and Baratoff derived an expression

which shows that JC is inversely proportional to the normal state resistance,2

J(T) = ()tanhT A()]. (2-29)
2eRn 2kT

where A(T) is the superconducting energy gap.
Coupling between the superconductor wavefunctions on each side of a

junction, and thus tunneling current density, are rapidly diminished by increasingly

thick insulator regions:2

S c "c e "c (2-30)

where s is the insulator thickness (nm), a = 0.1 (eV)'-/nm is the effective barrier

height, and 4D the electron energy gap between valence and conduction bands in
the insulator. Many devices, such as detectors and oscillators, could be made

using superconductors if SIS junctions were more reproducible. However, since

superconducting areas within a distance smaller than the coherence length, , of
the junction are often degraded, A(T) is not the energy gap for a perfect material
but is depressed because of defects near the junction. Thus Jc for a given junction

is difficult to control.

When two superconductors are separated by a normal metal (SNS structure),

superconductivity is induced in the normal metal via the proximity effect. The

proximity effect entails diffusion of superconducting electron pairs and normal

electrons across the interface to create a weak superconducting layer in the

normal metal. There is a coherence length for superconducting pairs in the

normal metal which is given by:2

wasorIM a v, (2-31)

where vF is the Fermi velocity of the normal metal, and the electron mean free

path is assumed to be longer than the coherence length ("clean limit").

Conversely, if the electron mean free path is shorter than the coherence length

("dirty limit"), the coherence length is given by:

S-_ hvl I. (2-32)

where 1 is the electron mean-free path. The critical current across an SNS

junction is given by:


where B is a constant, and a is the normal metal thickness.

The short coherence length in YBa2Cu3O7- is the primary reason why

microstructural defects have a significant effect on the superconducting properties.

Dimos et al. conducted a series of experiments designed to determine the

dependence of Jc and To on temperature and magnetic field, and reveal the types

of weak links responsible for reduced superconducting properties.2 For epitaxial

YBa2Cu30.x films grown on (100) SrTiO3 substrates, where two substrates were

sintered together so as to deliberately produce a misorientation angle O in the
film yet insure the <001> directions in the YBa2Cu3O7. film on both sides of the

sintered SrTiO3 junction were parallel, variations in J, as a function of grain

misorientation showed a dramatic drop as the grain boundary angle was increased.

Inside the grains, Jc values of 4x106 amps/cm2 at 5 K were measured. However,

across the grain boundaries Jc values dropped from 4 x 106 amps/cm2 at 00

misorientation to 0.16x106 amps/cm2 at 12.50 misorientation.

Further increases in resulted in similar or lower J, values, and did not

follow a systematic trend. The authors observed that Jbw/JC was approximately

proportional to 1/0 for O < 200, and proposed a model in which the dislocation
spacing was the predominant factor in determining J,. The dislocation array acts

as a partial barrier to superconducting electrons, or perhaps as an easy path for

flux flow, since the superconducting order parameter is depressed at the

dislocation cores. Although various studies have observed significantly larger Jc

values (> 5x106 amps/cm2 at 77 K) in epitaxial (001)-oriented films as opposed

to polycrystalline films, this study was the first to indicate that larger J, would be

observed in (001) films with in-plane epitaxy and low grain boundary angles,

compared to to (001) oriented films with random in-plane orientation.

Later experiments by Mannhart et al. on epitaxial, (001)-oriented YBa2Cu3O7.

films grown on (100) SrTiO3 substrates determined that the values of

intergranular J. as a function of temperature could be fitted by the

Ambegtaokatar-Baratoff equation for a SIS junction in which an energy gap A(0)

of 5 meV was assumed.25 However, the Ambegaokatar-Baratoff expression is also

valid for dirty SNS junctions, provided that significant changes in the phase of the

wavelength only occur near or in the normal layer; hence the observed gap could

represent the reduced order parameter inside the normal layer. The authors

concluded that grain boundaries were dirty SNS junctions because Jc(0) was a

factor of 10 less than values predicted by the SIS model. On the other hand, J, vs

B(T) for different orientations of the magnetic field indicated intragranular J,

values were limited by flux creep across the grains, and intragranular Jc values

were determined by the density and pinning energies of the flux-pinning sites.

Because the sensitivity of electrical properties in the superconducting and

normal states to film microstructure is very pronounced, a great deal of

information about the film microstructure can be obtained from the resistance vs.

temperature data. Zero resistance occurs when there is a continuous pathway in

which the wave function of the superconductor is phase ordered along the entire

path. If the wave function is strongly coupled between grains, the transition from

the normal to the superconducting state is abrupt, and the film To is close to the

transition temperature observed in bulk samples. However, if the film

superconductivity is localized, meaning there are isolated superconductor volumes

such as grains separated by barriers at which the intergranular coupling is weak,

or if the coupling strength varies randomly at the different grain boundaries, the

transition to the superconducting state will be percolative and there will be a

finite resistance at temperatures below Tot. Deviations from the ideal resistivity

and superconducting transition of a YBa2Cu307. film can be attributed to

microstructural defects such as high angle grain boundaries, interfacial phases at

the grain boundaries, and randomly oriented grains. An expression for the normal

state resistivity, p, of a single crystal YBa2Cu3O7. film free of microstructural

defects was proposed by Halbritter:26

p (7) = UcT+ p0, (2-34)

where the superscript i denotes intragranular effects, a1 is a parameter which

contains the temperature dependence of intragranular normal state resistivity, and

PoL is the intragranular resistivity exptrapolated to T = O OK. For single crystal
YBa2CU30.x films, Halbritter reported poi = 0 and a' = 0.5 ohmxcm/K.

However, many YBa2Cu3O7.x films, especially those grown on substrates which are

reactive or do not lattice match YBa2Cu3O7-, are polycrystalline and contain grain

boundaries or other types of weak links which increase the percolation distance of

the electrical conduction network. Using a technique similar to Eom et al.,7

deviations from the ideal resistance vs. temperature curve for YBa2Cu370x can be

attributed to specific types of microstructural defects. Halbritter expanded the

equation to separate the normal state resistivity into intergranular (e.g. grain

boundary or cracks) and intragranular contributions caused by electron scattering

from other electrons, lattice ions, or defects within the grain:

P (7) = (p, +p(a 'T+ pL (2-35)
where z(pg,) is the sum of the resitivities associated with all grain boundaries, and

(aiT + POLi) describes the intragranular resistivity. The percolation parameter, p,

accounts for increases in the percolation distance of the transport current resulting

from microstructural defects including grain boundaries and cracks. When pg is

small compared to p(a' + PoL'), intergranular defects have little effect on p, and

separation of inter and intragranular defects is difficult. If the current pathway of

lowest resistance is through the grain boundaries, the net effect of a change in pg

on R vs. T is to shift the curve to higher resistance values, without changing the

slope (p values) of the curve. Extrapolation of the curve to 0 OK will result in

higher values of 2(pg) when grain boundary resistance becomes larger, but not so

large as to significantly alter the current pathways. However, when 2(Po,) is

comparable to or greater than the intragranular resistivity, the percolation

distance of the transport increases as the current selects pathways which avoid

grain boundaries or other microstructural defects such as cracks, thereby

increasing p.

The same defects which increase normal state resistivity are responsible for

depressions in To and J.2829 Intragranular Josephson junctions resulting from

oxygen disorder or twinning locally depress the order parameter, and thus the To

within the grain. The most damaging defects are usually intergranular, and are

observed at high angle (0> 20 ) grain boundaries where dislocated regions often
have significant oxygen disorder.25 At high angle grain boundaries,

superconducting electrons are preferentially transported through the grain

boundaries at microbridges where the oxygen disorder is minimal (figure 2-9).

Interfacial impurity phases increase the separation between superconducting

regions, further degrading the interface and making it more difficult for

superconducting electrons to tunnel through the grain boundary. Because the

coherence length of superconducting electrons is longer in the <100> and <010>

than in the <001> direction, To and J, in (001) oriented films are not as sensitive

to grain boundaries as are films with other orientations. However, high angle

grain boundaries are highly dislocated regions where impurity phases tend to

accumulate, so the order parameter is depressed in (001) oriented films with

random in-plane orientation. By contrast, low angle grain boundaries are

generally free of interfacial phases and do not depress superconductivity. In

addition, 900 grain boundaries, which usually result from twinning or adjacent

(010), (100) and (001) oriented grains, generally do not contain significant

amounts of impurity phases, and hence do not reduce To or J, values.30


6I, CRO-


Figure 2-9. Intergranular defect with one microbridge. Cuprate regions near the
grain boundary are normal conducting, and the superconducting order
parameter is diminished in these regions. Reference 26.

Nucleation and Epitaxial Growth

The superconducting properties of YBa2Cu3O07, are very dependent on

microstructure. A general section which describes nucleation and growth

processes is presented in order to establish a framework in which the electrical

properties of the YBa2CCu3O7. films can be correlated with the growth processes.

Nucleation and growth of thin films is a large and complex subject, with many

variables which can potentially affect the microstructure and orientation of the

film. While it is difficult to obtain direct experimental evidence for many of the

parameters which determine growth mode, it is possible to speculate about the

forces which were operative during film growth by examining microstructural

properties such as surface morphology, grain orientation, and the distribution and

orientation of interfacial phases. Because superconducting and barrier layer films

have been deposited on several different substrates under a variety of growth

conditions, many of the growth mechanisms which determine film microstructure

can be deduced. In most deposition processes involving high temperature

superconductors in which the film is grown from vaporized constituents striking

the substrate, the experimental parameters which are varied include substrate

temperature, oxygen partial pressure, and the energies of the atoms and ions as

they strike the substrate. A general discussion of the fundamental processes

involved in film growth and how they are affected by growth conditions is

presented in order to establish a framework by which film microstructure evolves.

In the specific case of YBa2Cu3O7-. and barrier layer growth, correlations between

growth conditions and the underlying growth mechanisms will lead to an

understanding of how film quality can be optimized.

The crystallinity and orientation of a film can be manipulated by changing the

growth rate. In order to grow a film, more adatoms must stick to the surface than

are evaporated, hence there must be a flux causing a supersaturation of atoms or

ions reaching the surface and forming stable nuclei. The flux of atoms impinging

on the surface (0) is given by:31

atoms P(T)
0 ( atoms_ P(T) (2-36)
cm2xsec (2xmkT)o05

where P(T) is the vapor pressure at the substrate surface, m is the mass of the

impinging species at the substrate surface, T is the substrate temperature, and k is

Boltzmann's constant. To achieve epitaxy, it is essential that the atom be able to

move freely across the substrate until it reaches a potential minimum. The jump

frequency, o, of an adatom on a substrate is given by:

= v exp(-) (2-37)

where v = number of jump attempts/sec (typically 1013/sec), and ED is the

activation energy for surface diffusion. The mean stay time for an adatom is:32

1 Ed (2-38)
Ve = exp(p (2-38)

where Ed is the energy for desorption of an adatom from the substrate. The

mean distance an adatom diffuses before being desorbed is given by:

= 2aoexpl[ (E, (2-39)

where a0 is the single jump distance. This result shows that the surface diffusion

length increases with decreasing substrate temperature because the mean stay

time is increased. However, epitaxy is not necessarily improved by lowering the

substrate temperature because the jump frequency is lowered, hence the rate at

which equilibrium is reached is lowered. When the number of adatoms diffusing

across the surface at a given time approaches the density of surface sites, energy is

lost by adatom-adatom collisions, and adatom-substrate interactions are

diminished, thereby decreasing epitaxy. For the remainder of this study, we

assume that the flux of impinging species was low enough, and the substrate

temperature sufficiently high that the number of adatoms diffusing along the

surface was negligible compared to the number of surface sites, hence the

adatoms were able to reach their lowest energy configuration and equilibrium

conditions prevailed.

Until the nucleus reaches a critical size, it is more likely that the atoms will

dissociate and join a different nucleus or desorb, thus sub-critical nuclei do not

participate in the film growth process. In a real deposition system, the flux of

atoms striking the substrate consists of clusters of atoms as well as single atoms or

ions. Although it is difficult to determine what is the smallest stable nucleus size,

it is logical to expect that larger clusters striking the surface are more likely to

remain and form stable nuclei than are smaller clusters or atoms, since there are

more overlayer-substrate bonds formed. In addition, increasing the substrate

temperature is expected to increase the critical nucleus size, so the distribution of

clusters or atoms which eventually form stable clusters is further skewed towards

the higher cluster sizes.33

The relationship between critical cluster size and substrate temperature is

important because the orientation of the entire film can be heavily influenced by

the size of the original clusters from which stable nuclei are grown. Theoretical

and experimental data on face centered cubic metallic films deposited on NaCl

substrates indicates that for a critical cluster size of 3, the atoms will adopt a

triangular arrangement, and the film will grow with a (111) orientation.34

Similarily, when the smallest critical nucleus size is 4 atoms, the nucleus will

arrange itself in a square or rectangular mesh, and (100) oriented growth is

favored. In general, the first monolayer will grow with the surface mesh initiated

by the stable cluster, and subsequent layers will maintain this orientation and

grow with the closest packed planes parallel to the substrate. Based on this

analysis, face centered cubic films in which the critical cluster sizes are 3 or 4

atoms are expected to grow with (111) and (100) orientations, respectively. It has

been observed that several metallic films which grow with a (111) orientation at

low temperatures will adopt the (100) orientation when deposited at higher

temperatures.s Likewise, yittria-stabilized zirconia (Y-ZrO2) films deposited on

(1102) A1203 grow with mixed (111) and (100) orientations at temperatures below

780 *C, and are predominately (100) orientated when deposited at higher


The relative surface free energies of the substrate, film surface, and interfacial

layer are some of the most important parameters which dictate the film

morphology, and whether film-substrate epitaxy is possible. In a thin film, the

surface energy can be a substantial portion of the total energy of the system. For

a planar interface between two phases, a and f,37

a dA = dU'l _TdS' E i ,dn (2-40)

where a is the energy required to create a surface of area A, dUx"" and dS'"

are the energy and entropy associated with creation of the new surface, and pi and

dn, are the chemical potentials and excess surface concentrations of species i at

the surface. The general expression for the surface energy is:

dUXes = dUMt- _dUa -dUJp (2-41)


dU" = TdS" -PadV* +, ifdr (2-42)


dU = TdS -PPdVP + iAn, (2-43)

Substituting the expressions for dU" and dUf into equation 2-42, we obtain

odA = dU'- TdSPD- pn, + P" dV + PdV (2-44)

Assuming the volume of the system is constant, the Helmholtz free energy is


dF = -S"~dT+ E 1 II d,+ dA (2-45)


a aA .TSV (2-46)

For a crystal which is freely grown from its supersaturated vapor (i.e. no

substrate effects on nucleation, growth energetic, or kinetics), the equilibrium

shape is given by:3

al 02 03 a
= --- = = constant (2-47)
1t 2 "3 i,

where ai is the surface energy of the ith face and Ai is the distance from the center

of the crystal to the face. This result implies that a crystal will grow so as to

minimize its surface energy, and in the case of thin film growth on a substrate,

orientations with the lowest surface energies are the most energetically favorable

to grow.

The morphologies which a growing film adopts generally fall into one of the

following three categories.39 Film growth can be classified as two dimensional, in

which case the film completely covers the substrate before another layer is

nucleated, and the film grows at a uniform rate normal to the substrate. Films

can also grow by a three-dimensional growth process, in which case the film atoms

agglomerate into islands and the islands coalesce to form the film. A third option

is for the film to grow by a mixture of two and three-dimensional growth. The

first growth mode, termed Frank-van der Merwe, is characterized by two

dimensional growth of the film. This occurs when the surface energy of the film

is less than that of the substrate and interface:

oia < a + os ra1~e -fi Lrface (2-48)

In the Frank-van der Merwe growth mode, the surface free energy of the system

is lowered by replacing the substrate surface with a different surface which has a

lower surface energy. For most electronic applications, in which it is often

desirable to grow a thin film with the same structure and orientation as the

substrate, two dimensional growth is preferred because the adatoms will tend to

reside in potential minima along the substrate, thus preserving the pattern of the

substrate surface. The relative adatom-adatom or adatom-substrate bonding

energies also influence the film growth mode, with strong adatom-substrate

bonding favoring two dimensional growth. When the surface energy of the film is


afom > ,brae + abtrate filintrce (2-49)

the surface energy is minimized by the formation of three dimensional islands,

and the islands coalesce to form the film. This is known as the Volmer-Weber

growth mode, and is characterized by strong adatom-adatom bonding. The

orientations of these films are less influenced by the substrate than in the case of

two dimensional growth, and generally have more grain boundaries.

The third mode of film growth, Stranski-Krastanov, occurs when

ofia sbre 0 + Obte ilm inteface (2-50)

The Stranski-Krastanov mode contains features of both of the previous growth

modes, and is often characterized by two dimensional growth of the first

monolayer, followed by three dimensional growth of the rest of the film.

Assuming the film growth rate, surface energy, and adatom-substrate bond

strengths are such that two dimensional film growth predominates, the film will try

to minimize Osubstrate-film interface by growing epitaxially on the substrate, thus

eliminating the energy required to create an additional surface at the interface.

However, if the film has a different chemical composition than the substrate, the

lattice parameter of the film will be different and there will be a strain induced in

the film as it attempts to adopt the lattice spacings of the substrate. Once the

elastic limit of the film is exceeded, the strain is relieved via formation of

dislocations at the interface and the film is no longer completely epitaxial with the


There are a variety of methods by which the film will attempt to minimize

differences in lattice parameters with the substrate. Starting with the definition of

lattice misfit ( = f)40

lattice misfit (=f)= af b -asub (2-51)
where anim and asubstrate are the lattice parameters of the film and substrate. It has

been observed that the orientation which a film adopts with respect to the

substrate is primarily a function of lattice misfit, as well as the adatom-film and

adatom-adatom bonding strengths. If the lattice parameters of the film and

substrate are very close (generally < 1%) and both have the same crystal

structure, the film will align itself so the film directions in the plane of the

interface match those of the substrate. For larger mismatches, the film will adopt

an in-plane orientation such that the maximum number of lattice points will be

commensurate with the substrate.41 Theoretical and experimental data indicate

that the unit cell over which the film minimizes misfit and becomes commensurate

with the substrate may exceed 500 A, hence the correlation between film and
substrate directions is not always obvious or simple to deduce. One commonly

observed method of minimizing strains induced by dissimilar surface meshes is to

strain the lattice of the film so as to match row spacings in one of the directions.42

The Nishiyama-Wassermand and Kurdjumov-Sachs matching are shown in figure

2-10. The difference between the two orientations is the Kurdjumov-Sachs

orientation achieves better row matching by rotating the film surface mesh with

respect to the substrate mesh.

Figure 2-10.

Matching of atomic rows with epitaxial configurations of dissimilar
rhombic meshes. The substrate unit cell PQRS is drawn in solid
lines, and the overlayer unit cells in dashed lines. (a) Nishiyama-
Wassermand orientation, with overlayer PABC matching rows
parallel to PR, and overlayer PERF matching rows parallel to SQ.
(b) Kurdjumov-Sachs orientation; after rotating the overlayer mesh
relative to the substrate, overlayer PABC matches rows parallel to
PQ and PS. Reference 42.

As the lattice mismatch continues to increase, elastic strain within the film

exceeds the shear stress limit, and strain energy is released by the formation of

misfit dislocations.43 Misfit dislocations usually consist of edge dislocations with

the glide direction parallel to the interface. The elastic strain which can be

accomodated before misfit dislocations form is a function of the film-substrate

bonding, with strong bonding leading to larger elastic strain accommodation and a

reduced tendency to form misfit dislocations. The strain energy per unit length of

an edge dislocation line is given by:

E= Gb In (2-52)
4n(1 -v) r0

where G is the shear modulus of the film, b is the Burger's vector of the

dislocation, v is Poissons's ratio, R and ro denote the outer and inner radii of the

strain field over which the dislocation acts. In bulk materials, R can be

approximated as the distance between parallel misfit dislocations, b/f. In thin
films, the area over which a strain field acts is limited by the film thickness, and if

the film thickness is less than b/f thick, the strain energy of a dislocation can be

substantially reduced.

In films used for electrical applications, one of the most damaging aspects of

misfit dislocations is that they create grain boundaries which degrade the

electrical performance of the films. For pure edge dislocations, the angle between

two adjacent grains, 0, is given by:

sin 0 = b (2-53)

where D is the distance between dislocations. Misfit dislocations also reduce the

film-substrate epitaxy. During the initial stages of film growth, islands are highly

mobile and wil try to attain epitaxy with the substrate. If the substrate-film

bonding is weakened by misfit dislocations, there will be a tendency for the

islands to rotate slightly about the ideal in-plane epitaxial positions.52 The extent

of island rotation is given by:


0 =fO (2-54)

where 0 is the island rotation, f is the lattice misfit, and 0 is the rotation of misfit
dislocations. The maximum island rotation is obtained when 0 = 1, and hence q
= f. The result of island rotation is that films deposited on substrates in which

the lattice mismatch is severe will contain a much larger number of grain

boundaries than will films deposited on a more closely lattice matched substrate.

Several of the mechanisms responsible for film growth, and the energetic

parameters which dictate the orientation and microstructure of films, have been

presented in this section. Because several of the parameters are interdependent

and are difficult to observe experimentally, it is impossible to provide a

quantitative analysis of the effect of each variable. However, a general

understanding of the parameters necessary to promote two dimensional, epitaxial

growth provides considerable insight into what defects are likely to emerge from

various film processing techniques, and suggest methods by which film quality can

be improved.

Thermally induced stresses

Thermally induced cracking is a problem which plagues thin films deposited

on substrates. There is usually a difference in thermal expansion coefficients

between the film and substrate, so if the temperature of the film is changed after

the deposition, thermally induced stresses will be generated in the film and

substrate. The least desirable way for the film to relieve these stresses is by

cracking, because cracks severely degrade the electrical properties of the films.

Thermally induced stresses have a significant impact on microstructural features

such as microcracking and grain size, and the microstructural processes by which

thermally induced stresses are relieved will be introduced.

Cracks are formed when the strain energy due to stresses in the film is greater

than the energy required to create new surfaces.45 The stress required to

propagate a crack is given by:

oa- 2E (y, ,)lo (2-55)

where Ef is the Young's modulus for the film, y, is the surface energy of the new

surface created by the crack, yp is the work of plastic deformation per unit area,

and a is the initial crack radius. A key point is that the fracture stress is

considerably lower at points where pre-existing flaws are present, such as at the

film-substrate interface.4

The model frequently used to calculate the stresses induced in thin films by

differences in the thermal expansion coefficients between the substrate and film(s)

begins with the assumption that the strain is entirely elastic.47 The dimensions of

the substrate are presumed to be unaffected by the presence of the film, and the

film is required to alter its shape in order to match the surface dimensions of the

substrate. Shear forces are generated at the film/substrate interface because of

the differing thermal expansion coefficients, and these shear forces cause the

substrate and film to bow slightly (figure 2-11). Assuming there is no plastic

deformation in the film or substrate, nor any slippage at the film/substrate

interface, stress in the film (af) can be obtained by measuring the radius of

curvature of the film/substrate combination:4

S ESt (2-56)
/ 6(1-vs)R t

where t, and tf are the thicknesses of the substrate and film, v, is the Poisson's

ratio of the substrate, and R is the radius of curvature of the film/substrate

combination. There are two basic requirements imposed by continuum mechanics

which this model satisfies.49 First, the sum of the forces per unit width acting on

the film and substrate must be zero. The force per unit width is defined as aiti,

where i denotes either the substrate or one of the film layers. As an example of

how the stresses are distributed in the film and substrate, consider the case in

which the film stresses are tensile (figure 2-11). These film stresses will cause the

substrate to bow slightly, so the top of the substrate (adjacent to the film) will be

in compression. The magnitude of the forces will vary within the substrate, with

the maximum compressive stress observed at the top, and the maximum tensile

stress at the bottom of the substrate. Near the middle, there will be a plane

through which the stress (and therefore strain) is zero, and this is called the zero

strain plane. In the films, the stress is assumed to be constant throughout the

thickness of the each film layer. In this example, the tensile aiti forces contributed

by the film and the portion of the substrate below the zero strain plane must

balance the compressive ait, contribution of the upper part of the substrate,


-- Tensile Compressive ----

Mi M1

Figure 2-11. Cross-sectional side view of a two-layered film on a substate,
showing how elastic film stresses are accomodated by the substrate.
Reference 47.

between the zero strain plane and the film-substrate interface. The second
requirement is that the sum of moments about the axis which runs through
the zero strain plane must equal zero. Continuum mechanics requires that the
sum of moments induced by various mechanical forces acting on a common axis
must cancel each other in order for the axis to remain stationary. In our case, the
axis running through the zero-strain plane is common to all the forces acting on
the films and substrate.

Several features regarding the stress distribution in a multilayered film are

implicit in the continuum mechanics model. Since the ot, force for each layer of

film is significantly less than oat, for the substrate, each layer of film is required to

adopt the surface dimensions of the relaxed substrate if there is no plastic

deformation at the film-substrate interface, or between any of the film layers. A

consequence of the small ot force of the film relative to that of the substrate is
that the stresses induced in each layer result almost entirely from interactions

between the film and substrate. According to this model, the stress in any given

layer of a multilayered film is independent of the sequence in which the films

were deposited, and the thermally induced stresses in each of the layers is given


a=- (af -a,)AT (2-57)

where Ef and vt are the Young's modulus and Poisson's ratio for the film, af and

a, are the thermal expansion coefficients for the film and substrate, and AT is the

change in temperature to which the film-substrate combination is subjected. A

key assumption of this model is that the chemical composition of each layer is

uniform. Since the composition is uniform, the thermal expansion coefficient

within each layer is constant, so the dimensions of the top of each layer will be

the same as the bottom. This assumption, coupled with the assumption of no

plastic deformation at any of the interfaces, leads to the conclusion that it is not

possible to reduce the thermally induced stresses in the outermost film by

depositing intermediate layers in which the thermal expansion coefficients

gradually bridge the gap between the substrate and outermost film.

Film stresses can significantly affect microstructural features such as grain size

and porosity in thin films. Using an energy minimization argument, Chaudhari5

showed that tensile stresses can significantly reduce the average grain size of a

film. Because the atomic packing density is lower in a region containing grain

boundaries than in a crystalline region, tensile stresses are reduced in films with

small grain sizes. A quantitative energy minima for the film is given by the


AEfmn = AEtra AE~ bndY
E 1 1 aa EE~ 1 1 (2-58)
[( -7)(-)+Eo]- r ( )
1-v do d 2 1-v do d

where do is the initial grain size, d is the final grain size, Eo is the initial strain in

the film, and a is a normalized distance parameter used to compare the atomic
density of the grain boundary region with that of a grain. If the boundary region

has the same atomic density as the grain, then a is zero. If the boundary has a
monolayer of atoms missing, then a is 1. P is a geometrical factor used to
characterize the shape of the grains. For grains with a square cross-section, p =
2. y is the grain boundary energy. For films subjected to tensile stresses, there is
some combination of strain and grain boundary energies for which the overall

energy of the film is a minimum. For films subjected to compressive stresses,

there is no overall energy minima, and the total film energy decreases as the grain

size increases.

In brittle materials, film cracking is caused by the motion and accumulation of

dislocations, which creates regions of high elastic energy and ultimately fracture.

The film microstructure can significantly alter the magnitude of stress required to

move dislocations and initiate plastic deformation.46,4751 Numerous experiments

have shown that the stress at which plastic deformation is initiated is greater in

thin films than in bulk materials. This is because dislocations are pinned at the

film-substrate interface, thus increasing the stress required to move dislocations

through the film. The minimum stress required to move a dislocation in a film is

given by:4

S=A[ b fv ln(2.6h)] (2-59)
2n(1-vf)h (vf+v,) b

where A is a geometrical constant which accounts for the angle between the

applied stress and Burgers vector, b is the Burgers vector of the dislocation, vf and

v, are the elastic shear moduli of the film and substrate, and h is the film

thickness. For brittle films, the stresses required to move dislocations are

associated with the onset of microcracking. Equation 2-59 shows that the stress

required to move dislocations is inversely proportional to the film thickness, and is

the reason why there is often a critical film thickness which, if exceeded, causes

cracks to form.

Depositing a second layer on top of the initial film significantly increases the

stress in the initial layer. This seems to contradict the elastic continuum model,

which asserts that the stress in a given layer is only a function of the differences in

thermal expansion coefficients between the each layer and the substrate, and is

independent of the other layers. However, the top layer creates an additional

interface which pins dislocations. Hence plastic deformation in the initial layer is

suppressed, and the yield strength is increased.

The elastic continuum model is a popular model for predicting film stresses in

the elastic limit. However, the assumptions of perfect bonding at each of the

interfaces, and chemical homogenity within each layer are not realistic in most

cases. Microstructural features such as chemical bonding at interfaces, grain size,

and film thickness will affect the stress at which the mode of deformation changes

from elastic to plastic, and must be taken into account when interpreting the

stresses required to form cracks.

YBa, jQCQx Film Growth

Shortly after the discovery of superconductivity in YBa2Cu3O.x, the difficulty

of growing stoichiometric YBa2Cu3O.. thin films by conventional methods such as

sputtering52',3 and electron beam evaporation4 became apparent. Depositing a

film with the correct Y:Ba:Cu ratios is a difficult process using these techniques.

Pulsed laser deposition became a popular technique for growing superconductor

films because stoichiometric films could be readily grown from a target with the

same composition.55 6 Pulsed lasers have generated stoichiometric films over a

wide range of pulse energies, laser wavelengths, and pulse durations. Nd-YAG

lasers operating at 1064, 532, and 355 nm and pulse energies ranging from 0.6 to

3.0 J/cm2 have generated YBa2Cu3O7. films with the correct stoichiometry.57'859

YBa2Cu3O7. films were also grown using a pulsed CO2 laser (10.6 pm), but a

Y-enriched target was required to produce a stoichiometric film.6 By increasing

the pulse energy density of a CO2 laser, stoichiometric YBa2Cu3O7.x films were

grown from a stoichiometric target, but the film morphology and superconducting

properties were seriously degraded by large globules in the film.61 The best films

have been grown using pulsed excimer lasers which operate at ultraviolet

wavelengths. The main problems associated with laser deposition is the presence

of fragments in the films which are ejected from the target, and nonuniform film

thicknesses.62 Shorter wavelength excimer lasers are popular because the

particulate size is smaller in these films than in films grown with longer

wavelength lasers.57

The ease with which stoichiometric films can be grown, and the presence of

particulates in the films both result from the laser-target interactions. There are

two basic ablation mechanisms: thermal and electronic.63 Thermal processes

result from rapid heating of the target surface and subsequent evaporation and

sublimation from the surface. Evaporation occurs when the laser power density

(Qo) exceeds the minimum power density necessary for evaporation, Q:64

Qo -" PoU( )0. (2-60)

where po is the target density, D is the thermal diffusivity, U is the sublimation

energy, and r is the duration of the laser pulse.

Assuming the optical absorption depth (a1) of the target is small compared to

thermal diffusion length, the relationship a(2Dt)o0 > > 1 is valid. The

temperature rise of the target surface layer (where the thickness, t, of the surface

layer heated by the laser is defined as t = (2DT)o), can be approximated by

comparing the energy absorbed during the laser pulse with the thickness of target

surface heated by the pulse:

AT= (1-R) (2-61)
C, p (2Dt)o
where R is the target reflectivity, I is the power density (W/cm2), t is the duration

of the laser pulse, and C, is the specific heat.

Since the thickness over which laser energy is absorbed in the target is

inversely proportional to the absorption coefficient, target materials with high

absorption coefficients will attain higher surface temperatures because the energy

is confined to a smaller volume. The absorption coefficient is also a function of

the laser wavelength (A), and the absorption coefficient for YBa2Cu3O7-. increases

as A decreases.5 Congruent evaporation from a multicomponent target occurs

because the components cannot segregate over a region greater than the thermal

diffusive region (2DT)0s during the time over which the target is irradiated.

Because the temperature within the thermal diffusive region is high enough to

evaporate all the components, the entire region is evaporated and the film

stoichiometry is the same as that of the target.

Electronic mechanisms are also operative during laser deposition.66 Photons

with energies greater than the first ionization potential energies (7.726, 5.512, and

6.38 eV for Cu, Ba, and Y, respectively) will excite the target atoms, thereby

breaking bonds and causing ejection of ions. Experiments in which YBa2Cu3O7-.

film morphology and electrical properties of films grown at different wavelengths

showed conclusively that smoother films with fewer and smaller particulates, as

well as lower normal state resistivities and higher J. values, were obtained in films

grown at shorter wavelengths (figure 2-12).57

The smaller particulate sizes which are observed when YBazCu3O7.x films are

deposited using shorter wavelength lasers is largely attributed to the higher

absorption coefficients in YBa2Cu3O7.x targets with decreasing A. The absorption

coefficients are 1.2 x 105, 1.5 x 10s, and 1.7 x 10s cm- at 1064, 532, and 355 nm,

respectively.57 A higher absorption coefficient results in a thinner layer at the

surface into which the laser energy is coupled, thus creating a hotter

plume with finer fragments. However, the improved microstructures which result

from short wavelength radiation cannot be completely attributed to the slightly

larger YBa2Cu3O7.- target absorption coefficients. Strong absorption by

photofragments in short wavelength radiation, and subsequent fragmentation into

smaller particles, probably contributes to the smooth morphology of films grown

at shorter wavelengths.57

A great deal of effort has been made to understand the mechanisms by which

material is transferred from a YBa2Cu3OT., target to the substrate via laser

ablation, and to optimize the film growing process. The film thickness across the

substrate varies as cos9", (n 4),67 which indicates the ejected particle distribution

from the target is highly peaked. In addition, the cation ratios in the film are no

longer stoichiometric at lateral distances greater than 20 degrees from the target

50 100 150 200

250 300

Figure 2-12.

Resistivity as a function of temperature for three YBa2Cu307.x films
deposited on (100) SrTiO3 substrates by a Nd:YAG laser and it's
second and third harmonics. Reference 57.



normal.66 Apparently the highly peaked, forward-directed component is primarily

responsible for stoichiometry in the growing film. One explanation for this

behavior is that the laser generated plasma results in rapid evaporation from the

target surface.6 The gas is initially at high pressures because the rate of


is greater than the rate at which atoms and ions can leave the target surface. The

plasma expands into the vacuum, creating a supersonic molecular beam. Time-of-

flight measurements indicate that mean kinetic energies for Cu(1), Y(1), and

Ba(1) are 41.3, 43.4, and 47.9 eV, respectively for particles generated by a

193 nm laser.69 Time resolved optical spectroscopy measurements showed that at

oxygen partial pressures less than 1.3x104 Torr, the velocities of neutral and

ionized atomic species, as well as the diatomic species (such as YO, BaO, CuO)

were approximately 106 cm/sec. Increasing the oxygen pressure to 10'2 Tonr

reduced the velocities of the atomic and diatomic species to approximately

5x105 cm/sec.7

Although the ability to deposit a stoichiometric film is an extremely important

parameter for growing superconductor films with low surface resistivities and high

J, there have been other advances in film growth techniques which have

significantly improved the film quality. Optimization of the growth temperature

and oxygen pressure during deposition, as well as the oxygen pressure and cooling

rate after the deposition, have generated YBa2Cu3O7. films with nearly ideal

superconducting properties. Initially, amorphous films with the correct

stoichiometry were grown in vacuum (typically < 10-s Torr) onto unheated

substrates. The films were then post annealed in flowing 02 at 850 900 "C,

thereby forming the tetragonal YBa2Cu307- phase.5

During cooling from the high temperature tetragonal phase, YBazqCuO7.

undergoes large structural changes. Understanding what these changes are, and

how they are affected by temperature and oxygen pressure are critically important

for optimizing growth of YBa2Cu307.x films. The temperature at which

YBa2Cu307T. transforms from the non-superconducting tetragonal phase to the

superconducting orthorhombic phase is dependent on oxygen pressure.7 In 100%

oxygen, the transition occurs near 700 C. The oxygen content and change in

oxygent content as a function of temeprature are shown in figure 2-13 for bulk

YBa2Cu307-. in 100 % oxygen. If the oxygen pressure is lowered to 20% oxygen,

the tetragonal 6 orthorhombic transition temperature is lowered to 670 C, and
in 2% oxygen the transition is depressed to 620 C. Ordering of the oxygen

atoms into one-dimensional Cu-O chains along the <010> direction is the

primary mechanism responsible for the tetragonal orthorhombic transition.
The dramatic increase in the <010>, and decrease in <100> lattice parameters

as the orthorhombic phase is formed are shown in figure 2-14.

The temperature at which the transition occurs affects the kinetics of the

phase change. The transition occurs via a nucleation and growth process, in which

the ordering of oxygen along <010> and lengthening of the <010> lattice

parameter begins at a grain boundary or free surface.7 If the transition

temperature is suppressed by decreasing the oxygen pressure, growth of the

orthorhombic phase will be slow, and rapid cooling of the sample will result in

(a) Ox


bic Tetragonal


(b) dox

1 ^ -


-- c I I











400 600


Figure 2-13. Total oxygen content, and change in oxygen content as a function of
temperature for YBa2Cu3O7,.. Reference 72.



(a) 100% oxygen
[010] [10]t



0 3.86 -

3.84 -

3.82 1
0 200 400 600 800 1000

Figure 2-14. The [100] and [010] lattice parameters of YBa2CuO37.x versus
temperature for a bulk sample heated in 100% oxygen. Reference

incomplete growth of the orthorhombic phase. Rapidly cooled YBa2Cu3O7.

samples will be comprised of orthorhombic nuclei surrounded by an oxygen

depleted, tetragonal phase matrix. YBa2Cu307. films prepared by heating an

amorphous film to 850 900 C in oxygen, then slowly cooling through the

tetragonal-to-orthorhombic transition, have To values of approximately 85 "K on

nonreactive substrates such as SrTiO3, and To 75 "K on the more reactive A1203

substrates.55'56 Post-annealed films on (100) SrTiO3 substrates are polycrystalline,

but are preferentially textured with the (001) plane parallel to the substrate.

Major improvements in J, values were accomplished by depositing the films

in-situ at elevated temperatures and controlled oxygen pressures. Epitaxial

YBa2Cu307. films on (100) SrTiO3 and (100) Y-ZrO2 substrates were grown at

substrate temperatures ranging from 500 650 C and 200 mTorr 02, and

subsequently annealing the films at 450-500 C in 760 Torr 02 for 60 minutes.73'74

In-situ films grown on (100) SrTiO3 and (100) Y-ZrO, had Jc values of 5x106

amps/cm2 and 1x106 amps/cm2, respectively, at 77 K; both had To values of 90

K. In addition, films grown in-situ have much lower room-temperature

resistivities (160 /ohmxcm) than post-annealed films (- 1 milliohmxcm). This
behavior was attributed to the predominance of (001) orientation in the in-situ

film, whereas the post-annealed films contained a mixture of (001), (100) and

(010) oriented grains. The microstructures of in-situ films also formed an

epitaxial orientation with the substrate, whereas a "basket-weave" structure was

observed in post-annealed films.75 The basket-weave structure arises from the

growth kinetics of the (100) and (010) oriented grains. Both of these orientations

have the <001> axis, which is the slow growth direction, parallel to the substrate,

but the <100> directions are at 900 to each other.

For YBa2Cu30., films grown in-situ, the substrate temperature and lattice

mismatch at the film-substrate interface significantly affect the orientation of the

films.76 Films grown at 640 C on SrTiO3 and LaAIO3 substrates were primarily

(001) oriented, whereas films on MgO, Y-ZrO2, and A1203 substrates, which were

also deposited at 640 C, grew with an (001) orientation. Increasing the growth

temperature to 720 C resulted in (001) oriented films on SrTiO3 and LaA103

substrates. The variations in orientation were attributed to competition between

minimizing the surface energy of the film, which favors (001) orientation, and

minimizing structural coherence at the film-substrate interface during the early

stages of growth. Both SrTiO3 and LaA103 have the perovskite structure, as does

YBa2Cu307, and the lattice matching between these substrates and YBa2Cu30..

is reasonably close. At low growth temperatures, the reduced surface mobility

and possibility of film-substrate coherence is not as energetically favorable when

there is a large lattice mismatch between the film and substrate, which is the case

for YBa2Cu30., films deposited on MgO, Y-ZrO2, and A1203 substrates. Hence

the surface free energies are minimized by incoherent growth of the (001)

oriented grains.

Above 670 C, the tetragonal, oxygen depleted phase of YBa2Cu307. is

stable, and at a typical growth temperatures of 750 C the non-superconducting

YBa2Cu307. phase is formed. At 750 C, the perovskite lattice is

thermodynamically stable at oxygen pressures greater than 150 mTorr.7 Below

this pressure, YBa2Cu30.. decomposes into its component oxides, hence in-situ

growth is dependent on oxygen pressure, and is usually performed at a PO2 of

approximately 200 mTorr (figure 2-15). The tetragonal-to-orthorhombic transition

temperature is a function of oxygen pressure, with a maximum temperature of 700

C. This transition is usually induced by backfilling the vacuum chamber to 10 -

760 Torr 02 after the deposition, and slowly cooling to 450 C. The film is kept

at 450 "C for approximately 30 minutes to insure oxygenation of the Cu(1) atoms,

and ordering of the 0(1) atoms in the <010> direction. In the tetragonal phase,

0(1) and 0(5) sites are randomly occupied by O atoms, whereas in the

orthorhombic phase the 0(1) sites are completely full and the 0(5) sites are

empty (figure 2-16).7'79

YBa2Cu307. films deposited in-situ at 650 750 C have higher Jc values than

post-annealed films. In-situ films have a higher ratio of (001)/(100) oriented

grains, and have better in-plane epitaxy in the <100> and <010> directions. It

has been established that the penetration depth is increased, and Je values are

lowered by weakly coupled grains separated by high-angle grain boundaries or

non-superconducting interfacial phases. Hence the improved electrical properties

of films grown in-situ results from the reduction of weak links at the grain


900 800 700 600 500 400
YBa2C30Oy Ortho-2

S102 -y=6.0 y=6.5
1 \ Sputtering
CL y=6.9
W 0

ILI Y2BaCuO5 + Ablation
I BaCuO2
L BaCuO2 + Sputtering
-1 Cu20
C 100

Z Electron
(B- eam/Thermal
o C

10-2 I I I
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Figure 2-15. Oxygen partial pressure versus temperature plot showing the critical
stability line for YBa2Cu3O7-. at y = 6.0. Reference 77.



Figure 2-16. Crystal structure of YBa2Cu3O7., illustrating the CuO chains and
CuO2 planes.

Barrier Layer Technology

Because of the increased performance which could be realized by replacing

metallic interconnects and microstrip lines with superconductors, significant effort

has been expended towards finding deposition techniques which enable

YBa2Cu3O0.x films with high To and J. values to be deposited on silicon and A1203

substrates. Sapphire is an attractive substrate material for microwave applications

because it is relatively inexpensive, mechanically strong, and has a much lower

dielectric loss tangent (tan 6) than other substrate materials (table 2-3).17

Table 2-3. Dielectric properties of substrate and barrier layer materials.
Reference 17.

Material Dielectric Loss
constant tangent
Sapphire (A1203) 9.4 1 x 10-6
Silicon (Si) 12 1 x 10-3
Y-ZrO2 27 6 x10
LaAIlO 25 5.8 x 10-4
SrTiO3 305
MgO 9.65 4 x 104

Devices fabricated on Si substrates would benefit from the lower attenuation and

signal distortion which superconducting interconnects can provide. Because

silicon and sapphire are chemically reactive with YBa2Cu307., and attempts to

grow YBa2Cu3O7. films directly on these substrates result in interfacial phases

which damage both the substrate and film," substantial efforts to grow

intermediate barrier layers on the substrate prior to YBa2Cu3O7. film deposition

have been made. In order to understand why some barrier layers are successful

and thus obtain the expertise necessary to design better barrier layer structures, it

is helpful to characterize YBa2Cu3O7. films grown on inert single crystal

substrates. The first class of substrates are materials which are chemically inert to

YBa2Cu3O7 lattice match reasonably well, and have the perovskite structure.

SrTi03 is cubic with a0 = 3.905 at 25 "C,8 and LaA103 is rhombohedral with ao

= 7.586 and and included angle of 9001'. However, LaAO13 undergoes a cubic &

rhombohedral transformation at 430 C, and at 650 C LaA103 is cubic with ao =

3.818 A,82 so in-situ films are grown on a cubic perovskite LaA103 substrate.

YBa2Cu3O7. films grown at 650 *C on (100) SrTiO3 substrates show To at 89 K

and Jc = 7.5x106 amps/cm2 at 77 K. Cross-sectional transmission electron

microscopy indicates the interface is atomically flat and abrupt, and the film does

not contain any secondary phases.83'84'85 The films grew with the <001> direction

normal to the substrate, the films are heavily faulted, with staggered,

discontinuous (001) layers. Close to the substrate, Y or Ba combine with Cu and

O to form perovskite subshells which are epitaxial with the substrate.

Perpendicular to the substrate, each perovskite subshell contains both Y and Ba,

but Y and Ba segregate into different domains along the interface. Away from

the interface, the (001) layers become continuous, but very wavy. Increasing the

substrate temperature to 720 780 "C reduced the number of defects. Films

grown at the higher temperatures were completely (001) oriented, with less wavy

(001) layers, and Jc values of 2.2x 106 amps/cm2 at 77 K.

YBa2Cu3O7-. films with To = 90 K and J, = 1x106 amps/cm2 have been

deposited on (1102) LaAlO, at 750 C.86 These films were highly (001) oriented

during the first 4000 A of their growth. At greater thicknesses however, the
growth mode abruptly changed, and the dominant growth mode was with the

(100) and (010) planes parallel to the substrate. Computer simulations based on

nucleation densities and growth rates of (001) and (100)-oriented grains help

explain the experimentally observed film microstructures.87 Assuming the

nucleation density of (001)-oriented grains is 109/cm2, and for (100) and (010)

oriented grains is 2x108/cm2, and the growth rate in the <100> and <010>

directions is 10 times larger than in the <001> direction, a microstructure

emerges in which the film surface is initially dominated by (001)-oriented grains.

As the film thickens, the (100) and (010)-oriented grains, which have a high

growth rate normal to the substrate, coalesce and the film is covered by these


YBa2Cu307.x films have also been deposited on several substrates which have

distorted perovskite structures. The difference between these substrates and the

cubic perovskite materials (such as SrTiO3) is that the angle between the <100>

and <001> directions is not 90 0. YBa2Cu3O7- films with To values of 92, 89,

and 88 "K have been deposited on single crystal LaGaO3," PrGaO3,89 and

YbFeO39 substrates, respectively. In each case, the YBa2Cu307-. films were

strongly (001) oriented. Although each of these substrates contain elements which

are known to suppress superconductivity (La, Pr, and Fe), interdiffusion was not


Despite a large lattice mismatch, highly (001) oriented YBa2Cu307.x films with

To = 92 K have been deposited on LiNbO, substrates.91 The unit mesh of Y-cut

LiNbO3, onto which the YBa2Cu30-.x films were grown, is 5.148 x 6.932 A. The J.

values for these films were 2x10s amps/cm2 at 77 K, and the reduction in Je

(relative to YBa2CuO7.x films deposited on SrTiO3) was attributed to the high

concentration of Li in the film. The diffusion of Li was so rapid that the

concentration of Li within the YBa2CU3O7-. film film was peaked at the surface.

The second group of substrates are materials which are chemically inert to

YBa2Cu3O7., but do not lattice match nor do they have the perovskite lattice. Y-

ZrO2 amd MgO have been widely studied because high quality YBa2Cu3O7. films

have been grown on these materials. Despite the large YBa2Cu3O7.x/Y-ZrO2

lattice mismatch of 5.95 % in the YBa2Cu3OT7. direction,

YBa2Cu3O7 films with To = 88 K and J, = 1x106 amps/cm2 at 77 K were

deposited on (100) Y-ZrO2.92'93 Tietz et. al.94 proposed a model for

YBa2Cu307O. growth on Y-ZrO2 substrates which asserts that YBazCuO37. grows

in a manner which permits matching of the oxygen sublattices. This model also

proposes that the large lattice misfits are accomodated by 90 degree boundaries

and stacking faults. Norton et. al.92 reported that YBa2Cu3O7. films with To = 90

K and Jc = 11,000 amps/cm2 at 77 K were grown on a polished, randomly

oriented Y-ZrO2 substrate at 680 C. The films were strongly (001) oriented, and

the electrical properties of the films were more sensitive to the substrate

temperature during growth than were films grown on SrTiO3 and LaAlO3.

Increasing the growth temperature to 730 C resulted in YBa2Cu3O7. films with

Jc values of 1000 amps/cm2. The drop in Jc was attributed to increased chemical

interaction at the Y-ZrO2/YBa2Cu307. interface, with subsequent formation of

BaZrO3. Presumably, BaZrO3 diffused through the grain boundaries and reduced

intergranular conduction.

The lower Jc values for YBa2Cu307. films on polycrystalline Y-ZrO2 relative

to single crystal Y-ZrO2 was attributed to the presence of high angle grain

boundaries. Garrison et al.95 demonstrated that by altering the deposition

conditions, YBa2Cu3307 films could be deposited such that matching of the

YBa2Cu307-x <100>/Y-ZrO2 <100> or <110> directions could be induced. When one

or the other of these orientations was dominant, YBa2Cu3O7. films with Je = 106

amps/cm2 at 77 K were observed. However, if both orientations were present in

the same film, the Jc values were only 102 104 amps/cm2 at 77 OK. This

behavior was attributed to the high angle grain boundaries which resulted from

the mixed in-plane orientations of the YBa2Cu307.x films.

Films grown on (100) MgO substrates also showed To values of 89 K and J,

= lx106 A/cm2 at 77 OK.9697 Similar to Y-ZrO2, there is a large YBa2Cu3O-.x/

MgO lattice mismatch (5.9 and 4.2% in the YBa2Cu3OTx <1o> and <01o0/MgO,0o>

directions, respectively). YBa2Cu3O7-x films grown onto MgO at 670 C were

predominantly (001) oriented. Unlike Y-ZrO2, there was no evidence of

interfacial reactions at the YBa2Cu3O/7MgO interface. Similar to the case for

Y-ZrO2, it was speculated that YBa2Cu3O7., grows on MgO in a manner which

permits matching of the oxygen sublattices. The model also proposed that the

large lattice misfits are accomodated by 90" boundaries and stacking faults.

The third group of substrate materials is characterized by materials which

chemically react with YBa2Cu307x, thus making growth of high quality

YBa2Cu3O7.x directly onto these substrates very difficult. Unfortunately, the two

substrate materials most widely used for electronic applications--(100) silicon for

integrated circuits and A1203 (sapphire) for micro and millimeter-wave electronics,

belong to this group. A 1.5 pm thick YBa2Cu3O7-x film grown in-situ at 700 C

onto a Si substrate showed To = 70 K, and an interfacial reaction layer 0.5 pm

thick was observed.98 Auger electron spectroscopy detected Si at the film surface,

indicating Si diffusion through grain boundaries and microcracks. The poor film

quality was also attributed to microcracks generated by the large difference in

thermal expansion coefficients for Si (3.8x10-6/C) and

YBa2Cu307. (13.6x 10-6/C). Chourasia et al.99 showed that in a YBa2Cu3O7.

film deposited directly onto a Si substrate at room temperature, Si diffused into

YBa2Cu3O7, near the interface, and formed a Si suboxide which depleted oxygen

from the CuO planes. After annealing the film at 860 C for 3 hours, the Si

diffusion was much more extensive, and SiO2 was detected at the surface. The

authors concluded that oxidation of Si at the expense of CuO was the primary

reason that diffusion of Si into YBa2Cu307, degraded the superconducting

properties of YBa2Cu30,7.

Better films have been grown directly on sapphire. YBa2Cu37.,, films grown

on (1102) A1203 at 700 C showed To = 87 "K and JC values of 2x106 amps/cm2

at 4.2 OK.1 Attempts to deposit films at higher temperatures resulted in rapid

deterioration of the film because of interfacial reactions, probably BaO and CuO

reacting with Al203.

Because of the enormous technological advances which would result from

successful deposition of high quality YBa2Cu30.x films on Si and sapphire, a great

deal of research has been dedicated towards overcoming the interfacial reaction

problem. The most common approach has been to grow an intermediate barrier

layer prior to YBa2Cu307.-. The principal requirements of the barrier layer are

that it must be chemically inert to both the substrate and the YBa2Cu3O7. film,

and should lattice match YBa2CU3O7. and the substrate. The materials which

have been most successful as barrier layers have been the materials which are also

the best substrate materials, such as SrTiO3, Y-ZrO2, and MgO. Although

excellent quality YBa2CuO37., films have been deposited on single crystal LaAO03

substrates, LaA103 has not been reported to be a good barrier layer material for

growth of YBa2CU307. on either A1203 or Si substrates. Attempts to grow

LaAO03 films on a variety of substrates at 760 C showed that epitaxial films

could be deposited on SrTiO3 and LaAO03 substrates, while attempts to grow

LaAIO3 films on Si, A1203, and MgO substrates resulted in amorphous films.10

This indicates that matching both the lattice parameters and crystal structures at

the film-substrate interface are important parameters which critically influence the

crystallinity and orientation of the YBa2Cu3O7.x films.

Experiments in which LaAlO3 and YBa2Cu3O07. were simultaneously deposited

onto an MgO substrate showed that To gradually dropped as the fraction of

LaAO03 in the film increased.t10 YBa2Cu3O., films which contained no LaA103

had a To = 87 "K, while the transition temperature dropped to 77.5 and 30 K

for YBa2Cu3O7. films containing 9 and 13 mole percent LaAlO3, respectively.

When the transition from Tsen to To was determined by measuring the magnetic

response of the film to a magnetic field (inductive response), the transition

remained fairly sharp (< 5 K) for all the films. However, when measured by the

electrical resistance technique, the transitions became much broader as the

fraction of LaA103 in the films increased. Apparently, the formation of LaA103

at the grain boundaries decreased coupling of the superconducting wave function

between the grains. The discrepancies in the widths of the temperature ranges

over which the transitions occurred was attributed to the higher sensitivity of the

inductive measuring technique to intragranular conductivity, whereas the electrical

resistance technique is more sensitive to the presence of intergranular defects.

To date, Y-ZrO2 has been the most successful barrier layer for YBa2Cu307-x

films grown onto Si substrates. 1 pm thick YBa2Cu3O0.x films with To = 82 K

have been grown at substrate temperatures of 650 C, using 0.1 pm Y-ZrO2

barrier layers.83 The orientation of the Y-ZrO2 layer greatly influences the

orientation of YBa2Cu3O.7-, and the best superconducting films are grown onto

(100) oriented Y-ZrO, barrier layers.1" Fork et al. showed that the ratio of

(200)/(111) x-ray diffraction peaks from Y-ZrO2 is strongly influenced by the

depostion temperature, and to a lesser extent, the oxygen partial pressure during

growth. The conditions under which highly (100) oriented Y-ZrO, barrier layers

were grown on Si were at a substrate temperature of 780 "C and Po2 = 7 x 10

Torr. Growth of (100) Y-ZrO2 was also promoted by degreasing and cleaning the

silicon substrates in a flowing N2 hood, then transferring the substrates to the

deposition chamber via a N2 purged glove box, thus insuring a hydrogen

terminated Si surface. Thin YBa2Cu3OT7. films (305 A) deposited at 750 TC, and

grown on 500 A Y-ZrO2 layers have To = 86 88 oK, and Jc values of 2.2x106

amps/cm2 at 77 K. These values are comparable to those obtained from

YBa2CuO37x films deposited on SrTiO3 substrates. However, increasing the

YBa2Cu307-. film thickness to 1300 A reduced the Jc to 1.5 x 10 A/cm2 at 77 K.

Table 2-4 lists some of the more successful YBa2CU307.x/barrier layer structures

deposited on Si substrates, along with the film thicknesses. These data show that

reductions in To and J, as the YBa2Cu3O7-. film thickness increases result from

film cracking caused by tensile stresses in the YBa2Cu3O7-. films. The cracking

seriously degrades the superconducting film properties as the YBa2Cu3O7- film

thickness exceeds approximately 500 A.
In addition to the stress created by the thermal expansion coefficient

differences between Si and YBa2Cu307., stresses in the YBa2Cu307, films are

exacerbated because the thermal expansion coefficient of YBa2Cu307. is highly

anisotropic.14 Table 2-5 tabulates the thermal expansion coefficients of

YBa2Cu3O7.x in three directions, and in different temperature regimes. The

differences in thermal expansion coefficents in the <100> and <010> directions

are caused by ordering of oxygen atoms along the <010> direction, and

formation of the orthorhombic phase. The largest thermal expansion coefficients

are observed in the <001> direction. For YBa2Cu3O7T. films in which the <001>

direction is normal to the substrate, nucleation of a grain with the <010>

direction along a given direction parallel to the substrate will also result in

nucleation of another grain with the <010> direction orthogonal to the first

grain. This is the method by which the system minimizes the stresses caused by

differing thermal expansion coefficients in the <100> and <010> directions. If

an (001) oriented YBa2Cu3O7-. film is deposited on a substrate (such as SrTiO3 or

LaA103) in which the thermal expansion coefficient is close to the average

thermal expansion of YBa2Cu3O7-. in the <100> and <010> directions, film

cracking does not appear to be a problem. However, for substrates with lower

thermal expansion coefficients (Si and A1203), YBa2CuO37.x film cracking caused

by thermally induced stresses is a significant problem.

The cracking problems caused by the low thermal expansion coefficients of Si

have been circumvented by using a silicon-on-sapphire structure.105 YBa2Cu307-.

films grown onto a Y-ZrO2 barrier layer, which in turn was deposited on a Si film

grown on a sapphire substrate, had Jc values of 4.6x 106 A/cm2 at 77 "K for

YBa2Cu307.- film thicknesses up to 4000 A.

Y-ZrO2 has also been successfully used as a barrier layer for YBa2Cu3O7.x

films deposited on the (1102) plane of A1203. Highly (100)-oriented Y-ZrO2 films

were deposited on (1102) A1203 at substrate temperatures greater than 780 "C,

whereas growing the Y-ZrO2 layer at lower temperatures increased the ratio of

(111)/(100) Y-ZrO2 x-ray diffraction peak intensities.36 YBa2Cu3O7.. films

deposited on highly (100) oriented Y-ZrO2 barrier layers had To = 90 K, and J.

values of 1.2x 106 amps/cm2 at 77 K.

SrTiO3 has emerged as a very good barrier layer material for growth of

YBa2Cu307-. on (1102) A1203 substrates. 1.2 pm thick YBa2Cu307-. films grown

on a 4000 A SrTiO3 barrier layer, had To values of 86.5 K and Jc values of x 106

amps/cm2 at 77 K.106 X-ray diffraction indicated that the SrTiO3 layers

preferentially grew with a (110) orientation, although the (200) peak was

significant. The YBa2Cu3O7-, films were (001) oriented. Secondary ion mass

spectroscopy showed a drastic reduction of Al concentration in films grown on

Table 2-4. Superconducting transition temperatures and critical current densities for YBa2CU3O7dbarrier layer films
on silicon and LaAO03 substrates.

Substrate Barrier layer and YBazCu30,x Transition Critical current Reference
Thickness (A) thickness (A) temperature density
(K) (amps/cm2)
Si Y-ZrO2 (1000) 10,000 82 -- 83
Si BaTiO3/MgAl204 --- 70 -- 107
Si BaTiO3/MgAl204 1000 86-87 6x104 at 77 oK 108
Si Y203/Y-ZrO2 600 82-84 1x106 at 77 OK 109
Si Y-ZrO2 130 86-88 2x106 at 77 OK 103
Si Y-ZrO2 1350 --- 1x10 at 77 OK 103
LaAO03 --- 1300 88-90 5x106 at 770K 73

Table 2-5. Thermal expansion of YBa2Cu307Ox. Reference 104.

Thermal Expansion (xl06/OC). Dila-
<100> <010> <001> Average average

25-400 oC 14.3 5.8 25.5 15.2 12.9
400-610 oC 37.5 0.0 39.5 25.7 25
25-610 oC 22.6 3.5 30.3 18.8 16.6
25-800 oC 11.5 17.0 13.3 10.9

SrTiO3 barrier layers relative to superconducting films grown directly on A1203,

confirming that SrTiO3 is an excellent barrier to Al diffusion. Char et al.o10 found

that growth of the YBa2Cu3O7/SrTiO3 film on (1102) A1203 at 750 C produced

films with To = 86.5 "K and Jc values of 2x 106 amps/cm2 at 74 K. Higher

YBa2Cu3O7., deposition temperatures and hence better in-plane epitaxy, which

were made possible by the SrTiO3 barrier layers, were credited as the cause for

improved electrical properties, relative to YBa2Cu30. films deposited directly

onto (1102) Al203.


Film Growth by Laser Deposition

Barrier layer and YBa2Cu3O7. films were sequentially deposited at 730 750

C on silicon (Si), aluminum oxide (A1203), yittria-stabilized zirconia (Y-ZrO2),

lanthanum aluminate (LaAlO), or strontium titanate (SrTiO3) substrates using a

pulsed laser deposition system. A Questek model 2560 pulsed excimer laser,

using KrF gas and operating at 248 nanometers, 30 nanosecond pulses, and 5

pulses/second, was focused to 2.5 3.0 Joules/cm2 with a 50 centimeter focal

length lens onto a one-inch diameter YBa2Cu3O7. or barrier layer target. A

schematic diagram of the deposition system is shown in figure 3-1. The

stoichiometric YBa2Cu307 target was obtained from Ceracon, Inc. and was 96%

dense. The barrier layer targets were fabricated by mixing stoichiometric ratios of

the powders, calcining at 950 OC, then pressing the powders into disks and re-

firing at 950 OC for 12 hours. The barrier-layer targets were approximately 65%

dense. Up to three targets could be mounted on a stainless steel holder. By

rotating the target holder, sequential films were deposited without breaking


Excimer Laser
248 nm, 30 ns pulses

Figure 3-1. Schematic diagram of the pulsed laser deposition system.

vacuum or reducing the substrate temperature. This holder did not allow

continuous rotation of the target during deposition, but the target was moved

slightly every 800 pulses to expose a new surface to the laser radiation. The

deposition temperatures were measured by a thermocouple spot-welded to the

heater block. The barrier layer films were approximately 1000 A thick, and unless
specified otherwise, were grown in 40 mTorr 02. The YBa2CCu307 films were

2000 3000 A thick, and were always deposited at Po2 = 200 mTorr. After the

YBa2Cu30O7. films were deposited, the chamber was filled with oxygen, and the

temperature was maintained at 730 750 C for 20 minutes in order to facilitate

the tetragonal-to-orthorhombic transition. The films were cooled to 450 C over

60 minutes, held at 450 C for 45 minutes at approximately 300 Torr of oxygen to

ensure complete oxygenation, then cooled to room temperature.

All of the substrates used in this study were single crystal. The SrTiO3 and Si

substrates were cut parallel to the (100) planes, LaAO03 was cut parallel to the

(1102) planes, and Al203 was cut parallel to the (1102), (1210), or (0001) planes.

The Y-ZrO2 substrates were cut 5 12 degrees from the (100) planes, as

determined by Laue back-diffraction patterns. By depositing the YBa2Cu307.

films on off-axis Y-ZrO2 substrates, we increased the tendency for high-angle

grain boundaries to form in the barrier layer and superconducting films. This

feature enabled us to determine whether the barrier layers would passivate the

YBa2Cu307.x films from the defects introduced by these substrates, and allow

growth of superconducting films with high Jc values.

A variety of techniques were used to characterize the superconducting and

barrier-layer microstructures. Film orientation and interdiffusion at the barrier

layer/substrate and YBa2Cu307.,/barrier layer interfaces critically affected the

electrical properties of the YBa2Cu307. films, and evaluation of the interfacial

reactions and diffusion phenomena which promoted various types of

microstructures were required in order to correlate film microstructure with

electrical performance. Several analytical techniques, including x-ray diffraction

(XRD), scanning Auger electron spectroscopy (AES), scanning electron

microscopy (SEM), and Raman spectroscopy were used to evaluate the film

microstructures. Because the beam/sample interactions and detection techniques

were different for each of the measurement techniques, various microstructural

features could be examined. By understanding the mechanisms by which the data

was generated, the sample volume which was probed by each technique, and the

factors which were likely to reduce the validity of the data (such as electron

charging in AES), a complementary set of data were obtained which uncovered

many of the microstructural features which influenced the superconducting

properties of the films. Similarily, electrical and magnetic measurements provided

essential information about the film microstructures, and the suitability of the

YBa2Cu3O7-./barrier layer/substrate combinations for various devices. A basic

understanding of how the techniques work, and the potential sources of error are

essential in order to assess the data. In this section, a description of the various

experimental techniques, and the regimes in which they were used for this study,

is presented.

X-ray Diffraction

X-ray diffraction was initially used to verify that YBa2Cu307-. and barrier layer

films were being grown. Interfacial phases were also detected using x-ray

diffraction (XRD). A Phillips model APD 3720 x-ray diffractometer operating at

40 kilvolts and 20 milliamps was used to generate Cu Ka radiation of A = 1.54060
and 1.54439 1. A graphite monochromater filtered out most of the Cu 1kf
radiation. Peaks within the 20 range of 5 65* were detected, and the x-ray
detector was rotated at 3" per minute. Interplanar spacings were calculated using

the Bragg equation:"1

nAL = 2dsine (3-1)

where n is an integer, A is the photon wavelength, d is the interplanar spacing,
and is the angle (relative to the sample surface) at which the x-rays enter and

leave the sample. By matching the experimentally observed interplanar spacings

with those predicted by the Joint Committee of Powder Diffraction Standards

index, the phases and orientations of the films were determined. Although the

graphite monochromater eliminated over 99% of the Kfl radiation, samples which
produced extremely large Ka diffraction peaks, such as the single crystal
substrates, also produced measurable Kf x-ray diffraction peaks.
The orientations of the YBa2Cu3O7.. films were highly dependent on the

orientations of the barrier layer films. To determine whether phase information

about the barrier layer or interfacial phases buried beneath the superconducting

film could be obtained, the x-ray attenuation depths for the various films were

calculated. Assuming the x-ray intensity decreases exponentially as it enters the

sample, the attenuation for each compound was calculated using the expression:

S= exp[-() pt] (3-2)
o0 P

where I/I0 is the fraction of the incident x-ray intensity which penetrates to a

depth = t, (u/p) is the mass absorption coefficient for each phase, and p is the
density of the phase. (u/p) was calculated from the weighted fractions of the
mass absorption coefficients for the individual elements:

(!),I = wl([) + W2( ) + W3( ) + ...+ (1) (3-3)
P P P2 P3 Pn

where Wn is the weight fraction of element n in the phase, and (u/p)n is the mass

absorption coefficient for element n. For the calculation, the penetration depth at

which I/Io was equal to 0.368 was taken to be the absorption depth (= t). Of the

films examined in this study, YBa2Cu30. had the smallest absorption depth (= 9

/im). Since the YBa2Cu3O7x films were typically 3000 A thick, and the barrier

layer films were 1000 A thick, we concluded that diffraction data was obtained
from all of the films in the multilayered structure. The calculation of the x-ray

absorption depth for YBa2Cu30. is presented in appendix A.

Scanning Electron Microscopy

A JEOL JSM 35C scanning electron microscope (SEM) operated at 15 20

kilovolts accelerating voltage and 100 microamps beam current was used to

visually determine the surface morphology and microstructures of the films.

Microstructural features are readily imaged in the SEM because secondary

electron detection is highly sensitive to the angle between the ejected electrons

and detector, so the number of secondary electrons detected varies as the

topography of the film changes.112 YBa2Cu30 films deposited on highly reactive

substrates or barrier layers tended to be cracked or have rough surfaces, whereas

superconducting films grown on inert substrates were smooth and featureless.

Correlations between SEM micrographs and electrical data were instrumental for

clarifying the types of microstructures which resulted in YBa2Cu307-. film


Scanning Auger Electron Spectroscopy

Film uniformity and interdiffusion between the various layers and Si substrates

were analyzed using Auger electron spectroscopy (AES). A Phi model 660

scanning Auger microprobe, controlled by an Apollo domain series 3500

computer, was used to determine the film composition as a function of depth.

The operating parameters for the Auger were 5 kilovolts accelerating voltage, 25 -

35 nanoamps beam current, 132 volts emission voltage, and 40 60 microamps

emission current. Interdiffusion at the YBa2Cu3O.7x/barrier layer and barrier

layer/substrate interfaces was observed by ion sputtering a crater in the films, so

as to expose the barrier layer and substrate, then making a line scan across the

edge of the crater. With this method, errors induced by electrical charging and

Auger peak shifting in the insulating barrier layers were minimized.

Auger is often used to qualitatively measure the relative concentrations of

components within the top 10 A of the surface. The type of element is
determined by the energy of electrons emitted as a result of the Auger process.

The Auger process is started by an incident electron beam with sufficient energy

to remove an inner shell electron, which creates a core hole. The ion energy is

reduced by filling the core hole with an electron from a more shallow energy

level, and emitting another electron from a shallow energy level. The energy of

the emitted electron is given by:13

Kinetic Energy = EA E- Ec (3-4)

where EA is the energy of the core level electron, EB is the energy of the shallow

level electron which fills the core hole, and Ec is the energy of the shallow level

electron which is emitted. Although EA, Eg and Ec are all sensitive to the

chemical state of the atom, the time constant for Auger emission is short, so the

peaks are broad. Therefore the energies of electrons emitted via the Auger

process are less sensitive to the chemical state of the element than are electrons

emitted by other techniques, such as x-ray photoelectron spectroscopy. Hence

AES is widely used to determined which elements are present at the surface, with

limited determination of chemical state.

Quantification of the surface concentration is a difficult process because there

are many factors which influence the Auger yield. For an Auger transition from

species i at a site (x,y,z), where Ni is the background Auger count and dN, is the

number of Auger electrons resulting from the transition:114

dN, = (incident electron flux of energy Eprimary at xy,z)

x (ionization cross-section of EA for species i at E,)

x backscatteringg factor for Eprimary at the incident direction)

x (probability of decay of EA for species i to give the Auger


x (probability of no loss escape of electrons from region (x,y,z))

x (acceptance angle of analyzer)

x (instrumental detection efficiency).

To as much of an extent as possible, the Auger operating parameters were

kept constant in these experiments so that comparisons between the atomic

concentrations of different samples could be made. The incident electron flux was

dependent on the beam current, and was maintained at 30 40 nanoamps. The

ionization cross section is heavily influenced by the incident beam energy; low

beam energies are not adequate to produce core holes, and high beam energies

reduce the Auger yield from the shallow core levels. Generally, the optimal beam

energy is 3 5 times the binding energy of the deepest core level of interest. In

this set of experiments the beam accelerating voltage was always 5 kilovolts

because the sensitivity of the YLMM transition is highest at this accelerating


Atoms can be ionized by backscattered and secondary electrons as well as

primary electrons, and the backscattering and secondary-electron yields are

sensitive to the chemical environment and electrical properties of the sample.119

Discrepancies in ionization cross section resulting from different backscattering

yields of the same element in different compounds is the primary phenomena

which limits quantitative Auger analysis. In this set of experiments, interdiffusion

between YBa2Cu3O7-, the barrier layers, and the Si substrates were of interest.

Since the chemical environment and backscattering yields of each of the structures

were similar, semi-quantitative comparisons between the chemical compositions of

these structures could be made. Two final parameters which significantly effect

the Auger yield are the angle between the sample surface and the incident

electron beam, and the angle between the surface and detector. As the angle

between the beam and surface normal increases, the incident beam path length in

the surface region increases by a factor of sec 0,14 and the Auger yield increases.

Experimentally, this factor was kept constant by always keeping the angle between

the incident beam and surface normal at 60 .

Electrical Resistance Measurements

Electrical resistance versus temperature data were taken in order to correlate

normal state resistances, the onset of superconductivity (Tont), and the

temperatures at which the DC resistance dropped to zero (To), with YBa2Cu3O7.x

film microstructures. Resistance measurements were obtained using a four-point

probe apparatus in which current was transported through the film by the outer

two terminals, and the voltage drop was measured across the inner two terminals.

The four probes were mechanically pressed against the sample, and either 10 or

100 microamps were transported through the sample. To was determined when

the voltage drop was less than 1 microvolt (R < 0.1 or 0.01 ohms. Resistance vs.

temperature data were also obtained on many of the samples at NASA Lewis

Research Center. The system at NASA was more sensitive than the one at the

University of Florida; gold contacts leads were wire bonded directly to the

superconducting films, which increased the sensitivity in the low resistance regime

near the transition temperature. The criteria for superconductivity in this system

was R < 0.001 ohms. Despite the differences, both measurement apparatuses

produced very similar normal state resistance and transition temperature data

when the same samples were tested on both systems.

For thin films, resistivity rather than film resistance is usually plotted because

resistivity is a material property, and the calculations used to obtain resistivity

values take into account film thickness, probe spacings, and sample geometry. In

this set of experiments, resistance was documented because the variations in

resistance caused by microstructural features overshadowed the relatively minor

changes in resistivity caused by varying YBa2Cu3O7. film thicknesses and sample

geometries. An explanation of how resistivities are calculated, and how they are

affected by sample geometries is presented in order to support the hypothesis that

electrical resistance was the more appropriate parameter to monitor. Film

resistivity is given by:

p =FRt (3-5)

where F is a correction factor, R is the measured resistance, and t is the film

thickness. Assuming the probes are equally spaced, there are two correction

factors which will improve the accuracy of the resistivity measurements."1 The

first correction factor is given by the thickness correction factor, F(t/a). As the

sample length, a, becomes significantly greater than the film thickness, F(t/a)

approaches 1. Since the films were less than 3000 A thick, and the length of the
substrates were usually greater than 1 cm, F(t/a) had a negligible influence on the

measurement. The second correction factor, F2, is a geometric correction factor

which takes into account the increased current densities in the sample caused by

narrow samples with relatively large distances between the probes. Films

deposited on narrow substrates have large a/d ratios, where d is the sample width.

If we assume the YBa2Cu3O7. films were deposited on rectangular substrates in

which the length was twice the width (a/d = 2), the appropriate correction factors

for the film resistivity as the ratio of sample width to probe spacing (d/s) are

presented in table 3-1.

There were several practical difficulties which made calculating the

resistivities difficult. First, there was a trade-off between growing the highest

quality films and accurately assessing the film thickness, because masking off an

area of the substrate to create a step for profilometer analysis created thermal

gradients in the sample, which damaged the superconducting film quality. Second,

the substrates on which the films were deposited had a variety of shapes, so the

precise geometrical correction factor was difficult to establish. Although the

geometric factors were diverse, it is unlikely that they altered the resistivities by

more than +/- 50%, since the sample width/probe spacing ratios were

constrained by the design of the R vs. T measurement apparatus to be between 2

and 3. On the other hand, measured resistances often varied by an order of

magnitude or more, depending on the film microstructure and type of substrate

used. The additional information which could have been obtained by determining

the film resistivities would have been minor, and the fundamental

microstructural/electrical property correlations which controlled the electrical

properties were more fully uncovered by correlating data obtained by electrical

resistance measurements with other types of microstructural data.

Table 3-1. Resistivity correction factors as the sample width to probe spacing
increases. The sample length to width is kept constant (a/d = 2).

Ratio of sample width Resistivity correction
to probe spacing (= d/s) factor (= F2), assuming
a/d = 2.
1.50 1.4788
1.75 1.7196
2.00 1.9454
2.50 2.3532
3.00 2.7000
4.00 3.2246
5.00 3.5746
7.50 4.0361
10.00 4.2357
15.00 4.3947
20.00 4.4553
40.00 4.5129
00 4.5324

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