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INTENTITI‘ITT‘IT‘ITIWI'I‘TII‘I'TNTTI

3 1293 01581 2187

LIBRARY

Michigan State
University T

 

 

 

 

This is to certify that the

dissertation entitled

TEMPERATURE DEPENDENCE OF CONDUCTIVITY
AND MOBILITY 0F t3- ANDcK:SiC
FOR TEMPERATURE SENSORS

presented by

Nayef Muhamed Abu-Ageei

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in EleCtrica] Eng.

 

 

fl! flaw

Major professor

Date [0/30/51

 

MS U is an Affirmatiw Action/Equal Opportunity Institution 0 12771

 

PLACE IN RETURN BOX to remove thie checkout from your record.
TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-| i |
-[____

MSU le An Affinnetive Action/Equal Opportunity Inetituion
W

 

 

 

m1

 

 

TEMPERATURE DEPENDENCE OF CONDUCTIVITY AND MOBILITY OF B-
AND a-SiC FOR TEMPERATURE SENSORS

By

Nayef Muhammed Abu-Ageel

A DISSERTATION

Submitted to Michigan State University in partial fulfillment of the requirements for
the degree of

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering

1996

ABSTRACT

TEMPERATURE DEPENDENCE OF CONDUCTIVITY AND MOBILITY OF B-
AND a-SiC FOR TEL/IPERATURE SENSORS

By

Nayef Muhammed Abu-Ageel

Conductivity and Hall measurements of poly and monocrystalline B-SiC films
prepared by laser ablation and commercial a-SiC wafers were conducted in a
temperature range of 13-800 K. Polycrystalline B-SiC films and heavily doped a-SiC
wafers showed mobilities in ranges of 0.3-3 cmZ/Vs and 2-50 cmZ/Vs and electron
concentrations in ranges of IO‘9—4><1020 cm’3 and 5><10‘7-5><1019 cm'3, respectively,
whereas lightly doped a-SiC wafers showed higher mobilities (10-280 cmZ/Vs) and
lower electron concentrations (4>< 1012-1x10'9 cm'3) throughout the entire temperature
range.

Transport data of polycrystalline B-SiC films and heavily doped oc-SiC wafers
exhibited a Shallow activation energy of 35 meV below 1100 K. In this temperature
range, polycrystalline B-SiC data was analyzed in terms of impurity/defect band and
hopping models. At higher temperatures, two activation energies (9-20 meV and 75
meV) were obtained for polycrystalline B-SiC and one activation energy (80—84 meV)
for a-SiC. In case of heteroepitaxial B-SiC films deposited on Si substrates, two

models were presented to extract the conductivity and Hall data of B-SiC films from

measurements on the B-SiC/Si structure.

Measurements of Seebeck coefficient were obtained for polycrystalline 3C-SiC
films and monocrystalline a-SiC wafers in a temperature range of 300-533 K. The
resistivity and Seebeck coefficient data were investigated to assess the potential of
these SiC polytypes for thermal sensors such as temperature and heat flux measuring

devices.

ACKNOWLEDGEMENTS

I would like to extend my sincere appreciation to Professor Dean M. Aslam,
the principle adviser of this thesis, for his excellent guidance and constant
encouragement and to Dr. Lajous Rimai from Ford Motor Company for his excellent
and valuable supervision of this work.

I would like to thank the members of my oral committee, Professor J.
Asmussen, Professor D. Reinhard and Professor M. Thorpe for their time and
comments.

I would also like to thank the group at the Scientific Research Laboratories of
Ford Motor Company for the technical assistance. In particular I wish to thank: R.
Ager, R. Soltis, W. Vassell, A. Samman, D. Kubinski and J. Visser.

Finally, I would like to extend my special appreciation to my parents, whom
I have not seen for more than eight years, for their constant support since my early

school days.

iv

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

1

Research Motivation and Goal

1 . 1 Introduction

1.2 Objective of this Work

1.3 Organization of Dissertation

Background

2. 1 Introduction

2.2 SiC Properties

2.3 SiC Technology
2.3.1 Thin-Film Growth of SiC
2.3.2 Doping
2.3.3 Metallization

2.4 Characterization of SiC Films
2.4.] Structural Characterization
2.4.2 Electrical Properties

2.5 SiC Films as Temperature Sensors

2.6 Summary

Laser Ablation Technology

3.1
3.2
3.3

3.4

Introduction

Pulsed Laser Deposition Technique
Sample Fabrication

3.3.1 Deposition of SiC Film

3.3.2 Deposition of Metal Contacts
Summary

ix

woo—H

11
11
15
.. 16
17
.. 17
18
20
.. 21

22

22
23
23
23
26
.. 27

4 Measurement Techniques
4. 1 Introduction
4.2 Van der Pauw's Measuring Procedure
4.3 Seebeck Coefficient Measurement Technique
4.4 Summary

5 Conductivity and Mobility of SiC
5. 1 Introduction
5.2 Polycrystalline Cubic SiC Films
5.2.1 Experimental
5.2.2 Conductivity and Hall Measurements
5.2.3 Analysis of Intermediate and High Temperature Data
5.2.4 Analysis of Low Temperature Data
5.2.4.1 Hopping Conduction
5.2.4.2 Impurity/Defect Band Conduction
5.3 Monocrystalline SiC
5.3.1 Monocrystalline a-SiC Substrates
5.3.2 Monocrystalline B-SiC Films
5.4 Summary

6 Seebeck Coefficient of SiC

6. 1 Introduction

6.2 The Seebeck Coefficient

6.3 Results and Discussion

6.4 Applications
6.4.1 Thermoelectric Temperature Sensor
6.4.2 Heat Flux Sensor
6.4.3 Thermoelectric Generator

6.5 Summary

7 SiC Thennistors
7.1 Introduction
7.2 Resistivity of SiC
7.3 Summary

8 Summary and Future Research
8.1 Future Work

Multiple-Layer Resistivity Model

BIBLIOGRA PHY

vi

28

...28
...28
...30
...33

34

...34
...35
...35
...36
...39
...50
...51
59
...64
...65
...70
85

87

...87
...89
...93
100
100
102
106
.. 109

110

110
111
.. 121

122

.. 123

124

135

LIST OF TABLES

2.1. Comparison of semiconducting properties. 6

2.2. Lattice constants, energy gaps at 300K, stacking sequences, and thermal conductivity
of common SiC polytypes. 10

2.3. Electronic parameters of B-SiC“. m0 is the electronic rest mass. 19

5.1. Activation energies: ei (conductivity) and Bi (Hall data) and constants: a-

I

(conductivity) and Ai (Hall data) for five samples. 42
5.2. Thicknesses, deposition temperatures, deposition times, and pulse rates for five SiC
films. 71
5.3. Temperature range of n-type conductivity for samples of Table 5.2. 76

6.1. The electron concentration n=1/qRH, Fermi level location below E, and effective
mass estimated at 300 K for some polycrystalline B-SiC and a-SiC monocrystalline
samples. 97

6.2. Properties of some materials for thermoelectric generation applications. 11 is
calculated using Thigh=600K and Tlow=3OOK. 108
7.1. The temperature coefficient a at 300 K for some alloys, oxides, hexagonal SiC, and
polycrystalline SiC films. 118

7.2. Temperature coefficients of resistivity (TCR) of some polycrystalline 3C-SiC samples
evaluated over the corresponding temperature range. 119

7.3. Temperature coefficients of resistivity (TCR) of some polycrystalline and single
crystalline 3C-SiC films and heteroepitaxial 6H- and 4H-SiC samples evaluated over the
corresponding temperature range. Thicknesses and available carrier concentrations
obtained at room temperatures are also provided. 120

vii

LIST OF FIGURES

2.1. A close-packed layer of spheres with centers at points A. A second layer of spheres
can be placed over this, with centers over the points marked B. A third layer can be
placed over A and the resulting sequence is ABAB... (2H structure) or it can be placed
over C and the resulting sequence is ABCABC... (3C structure). 7

2.2. Possible respective orientation of Si and C atoms in tetrahedral bonding.
(a) Si-C group with adhering carbon and silicon atoms.
(b) Si and C atoms in eclipsed position (2H).
(c) Si and C atoms in staggered position (3C).
(d) The axes-system and the base of the unit cell. 7

2.3. Positions of atoms in (1120) planes.
(a) Relative position of Si and C atoms.
(b) Position of Si in 3C.
(c) Position of Si in 2H.
((1) Position of Si in 6H.
(e) Position of Si in 15R.
(f) Position of Si in 4H. 9

3.1. A schematic diagram of the pulsed laser deposition system. 25

4.1. A sample of arbitrary shape with four metal contacts along the circumference for
conductivity and Hall measurements. 30

4.2. Sample arrangement for Seebeck coefficient measurement. 31

5.1 Temperature dependence of conductivity of 3 polycrystalline B-SiC films with the fits
shown as solid lines. 37

5.2 Temperature dependence of the inverse of measured Hall coefficient, NR“, and the

corresponding carrier concentration, 1/qRH, of samples of Fig.5.] with the fits shown as
solid lines. 38

viii

5.3 Temperature dependence of the mobility derived from the Hall and conductivity data
as (SRH for samples of Fig.5.]. 40

5.4 The measured conductivity (hollow symbols) of 152B and fits (solid lines) obtained
in 3 different temperature ranges using Eq.5.4. Slopes and intercepts of these lines

represent activation energies and corresponding constants: (a) el and a1, (b) e2 and a2, and
(c) e3 and a3. 43

5.5 The measured electron concentration (hollow symbols) of 1523 and fits (solid lines)
obtained in 3 different temperature ranges using Eq.5.3. Slopes and intercepts of these
lines represent activation energies and corresponding constants: (a) El and A,, (b) E2 and
A2, and (e) E3 and A3. 44

5.6 Fermi level position computed using Fermi Statistics (Eqs.5.1-2) for 2 of the samples
of Table 5.1. 47

5.7 Inverse of measured Hall coefficient, 1/RH, for samples of Fig.5.6, with carrier
concentration fits obtained by the charge neutrality condition assuming no compensation
and considering 3 independent donor levels represented by activation energies shown in
Table 5.1. 49

5.8 Fermi level position computed by fitting the measured electron concentration n of 2
polycrystalline samples using Eq.5.5. In these fits, N,, N1] and Na: are treated as
parameters and (Na/Nd2)=33%. 54

5.9 Effective carrier concentration, l/qRH, for samples of Fig.5.8, with carrier concentra-
tion fits obtained by the charge neutrality condition assuming compensation ratio of 33%
and considering two independent donor levels represented by activation energies E] and
E2 as shown in Table 5.1. 55

5.10 Fermi level position for sample 194A computed using the charge neutrality condition
for compensation ratios of 10%, 33%, and 90% and considering two independent donor
levels represented by activation energies El and E2 shown in Table 5.1. 56

5.1 1 Inverse of measured Hall coefficient, 1/RH, for 194A with its fits using corresponding
Fermi level locations for the 3 different compensation ratios of Fig.5.10. 57

5.12 Energy band of SiC with two donor levels located at El and E2 below the bottom of
the conduction band EC. The impurity/defect band is located at (Ez-E3) below Be. The
energy levels in this figure are not drawn to scale and the intrinsic level Ei should not be
exactly in the middle of the bandgap. 6O

ix

5.13 Inverse of measured Hall coefficient, I/RH, with corresponding electron concentration
for some 4H- and 6H-SiC. The fits for samples A and H in the low temperature range are
shown as solid lines. 66

5.14 The Hall mobility (u=oRH) as computed from Fig.5.13 and Fig.5.15. 67

5.15 The temperature dependence of measured conductivity for 7 samples of 6H-SiC and
one 4H-SiC sample. 69

5.16 The measured Hall voltage of sample 362 in two temperature ranges. These results
are obtained using an input current of 0.1 mA and magnetic field of 8 kGauss. Interface-
Si structure represents the Si under the peeled off B-SiC film. 73

5.17 The measured Hall voltage in the high and low temperature ranges of some samples
of Table 5.3. These results are obtained using an input current of 0.1 mA and magnetic
field of 8 kGauss. 74

5.18 The measured resistance of two highly resistive films in the low and high
temperature ranges. The measurement was done on SiC/Si structure (solid symbols) and
on interface-Si structure after the removal of the SiC film (hollow symbols). 79

5.19 The measured resistance of 3 different films in the low and high temperature ranges.
The solid symbols represent the data of the SiC/Si structure. The hollow symbols
represent the data of interface-Si after removing the delaminated portion of the SiC film.
The dotted line represents the data of the Si substrate that was underneath the shadow
mask during deposition. 80

5.20 (a) A schematic of the sample used for Hall voltage measurement with 4 metal
contacts at the corners of the sample. (b) Equivalent cicuit of (a). 82

6.1 (a) Top view of the sample under test showing the metal contacts and the
thermocouples with T being the lower end temperature and AT being the temperature
difference between the two ends. (b) A schematic of the band diagram of the sample
showing the electrical field E and the Seebeck emf (i.e. qV). 91

6.2 Measured Seebeck coefficient for three polycrystalline 3C-SiC films (solid symbols)
and three hexagonal samples (hollow symbols) . 94

6.3 The measured (solid symbols) and calculated (hollow symbols) electron concentration
of 3 polycrystalline SiC samples. The calculated electron concentrations are obtained from
the measured values of Seebeck coefficient using Eq.6.2. 99

6.4 The absolute value of the Seebeck emf for B-SiC (solid symbols) and a-SiC (hollow
symbols) and a platinum thermocouple. 101

6.5 A schematic of n- and p-SiC cells connected serially. This schematic represents either
a thermoelectric generator with Thigh-Tlow is large or a heat flux sensor with Thigh-TIOW=AT
is very small. 105
7.] The resistivity of some B-SiC (solid symbols) and a-SiC (hollow symbols). 112
7.2 Two cycles of the resistivity of some polycrystalline B-SiC films. 114

7.3 (a) The sensitivity coefficient a for samples of Fig.7.]. (b) An expansion of the data
shown in (a). 116

A] A top view of the sample used in our model. The two metal contacts are shown in
dark color. 125

A2 A two dimensional plot of the imposed field in the Y direction at the surface (i.e.

Z=0). 126
A3 A two dimensional plot of the imposed field in the X direction at the surface (i.e.
Z=0). 127
A4 A three dimensional plot of the imposed field at the surface (i.e. Z=0). 128

A5 A three dimensional plot of the potential at the surface (i.e. Z=O) assuming that the
conductivity of the three layers is the same. 129

xi

CHAPTER 1

RESEARCH MOTIVATION AND GOAL

1.1 Introduction

There is a growing research and interest in wide bandgap materials because of
their potential use in high power, high temperature, and high frequency electronic device
applications. Silicon-based devices have limited operating temperature (below 150°C) and
their use for micromechanics is limited to temperatures below 600°C where Si starts to
deform plastically”. There is a need for a semiconductor, operable in a wide temperature
range, with high thermal conductivity and breakdown voltage. Although there are several
interesting wide bandgap materials such as diamond, SiC, GaAs, and other III-V
compounds, of these SiC is the most promising one. GaAs is not suitable for high
temperature applications since its bandgap is close to that of Si. Diamond technology is
still being developed and n-type doping and heteroepitaxy are not very successful7.
Technology of other wide bandgap materials is not well developed”. SiC technology is
much more advanced due to major improvements in bulk and film growth of SiC,

capability of n- and p-type doping, physical stability in an oxidizing atmosphere, the

2
possibility to grow relatively low-defect-density oxides on its surface2 and some degree
of compatibility with the existing Si technologys'g'm.

SiC has strong potential for electronic devices and sensors operating at high
temperatures and in chemically aggressive environments such as those prevailing in
automotive and jet enginess. This is due to the unique physical, chemical and electrical
properties of SiC such as its large band gap, large thermal conductivity and high
breakdown voltage.

Chemical vapor deposition (CVD) is the most successful technique so far for
(hetero and homo) epitaxial growth of SiC films onto Si, 4H-SiC and 6H-SiC substrates.
This technique usually requires a high growth temperature (1400°C) which is incompatible
with the existing Si technology and may lead to film contamination in addition to the
hydrogen incorporation inherent to the process”. Pulsed Laser Deposition (PLD) has

”"3 and monocrystallinews B-SiC films from

been used recently to deposit polycrystalline
ceramic SiC targets on Si substrates at 800°C and 900-1000°C, respectively, but these
films have not been fully characterized.

In this research the temperature dependence of conductivity and Hall coefficient
in the temperature ranges of 13-1275 K and 17-800 K, respectively, are reported for the
first time for laser-deposited polycrystalline B-SiC films. The temperature dependence of
Seebeck coefficient in the temperature range of 300-550 K is reported for the first time
for B-SiC and a-SiC. Furthermore, measurements of the conductivity and Hall coefficient

of monocrystalline B- and a-SiC in a temperature range of 13-800 K are also reported.

These results are analyzed to determine the potential of B- and a-SiC for temperature

sensor applications.

1.2 Objectives of this Work

The primary objectives of this research are to study the temperature dependence
of conductivity, mobility and Seebeck coefficient of B- and a-SiC in a wide temperature
range and to determine their potential for temperature sensor applications.

This requires deposition of the metal contacts needed for the measurements and
construction of the measurement systems. The obtained results have to be analyzed using
appropriate models, in order to assess the potential of SiC for thermal sensor applications

such as temperature and heat flux measuring devices.

1.3 Organization of Dissertation

A review of SiC properties, technologies, and SiC use for temperature sensors is
presented in chapter 2. The deposition process that we have used to prepare SiC films and
their metal contacts is explained in chapter 3. A description of the conductivity, Hall, and
thermoelectric measurements methods used in this research is presented in chapter 4.
Chapter 5 presents the measured conductivity and Hall concentration for polycrystalline
and heteroepitaxial 3C-SiC and monocrystalline a-SiC. Chapter 6 presents the
measurement of the Seebeck coefficient for SiC in addition to a discussion of the potential
application of SiC in thermoelectric sensors. Chapter 7 focusses on potential application
of SiC as a thermistor. Chapters 3-7 deal with the work performed in the present research.

Chapter 8 summarizes the results of this study.

CHAPTER 2

BACKGROUND

2.1 Introduction

The interest in SiC has been renewed since the introduction of the technology that
allows the growth of SiC films on Si substrates in the 1980's. In the late 1980's, a major
development in SiC technology was achieved as the commercial production of high-
quality 6H-SiC wafers started. Although there has been some success in preparing SiC
electronic devices, SiC technology still suffers from problems related to crystal growth,
doping and metallization. A review of the progress that has been made in SiC technology
is needed in order to investigate such problems.

The SiC general properties such as physical, chemical, and structural properties
compared to those of Si are discussed in section 2.2. In addition, this section contains a
summary of the methods used for bulk growth of SiC crystals. In section 2.3, SiC thin
film technology which includes thin film growth, doping, and metallization is discussed.
Structural and electrical characterizations of SiC films are presented in section 2.4. The
use of SiC films as temperature sensors is discussed in section 2.5.

4

2.2 SiC Properties

SiC is a vvide-band-gap semiconductor with outstanding physical and chemical
characteristics. Table 2.1 shows the properties of B- and 6H-SiC compared with those
of diamond, Si, and GaAs. This material possesses high hardness, high thermal
conductivity, superior resistance to fracture and deformation at elevated temperatures,
excellent resistance to corrosion, thermal shock and radiation damage, and is chemically
inerts'zw. Junction isolation problems limit the operation of silicon based devices to less
than 150°C.2 SiC based devices would remove this limitation. The electrical properties of
B-SiC films compare favorably with Si for minority, as well as majority carrier device
applications.

SiC is a stable compound of silicon and carbon. Each Si (or C) atom is surrounded
by four C (or Si) atoms tetrahedrally with sp3 hybrid bonds (covalency is about 88%)”.
Most of the valence electron-charge density in SiC is located near the carbon atom,
because of this asymmetric charge density SiC looks like a polar compound. SiC exhibits
a form of one-dimensional polymorphism called polytypism. Different stacking sequence
of double layers of Si and C atoms results in different polytypes structures. Each double
layer consists of a plane of close-packed Si atoms over a plane of close-packed C atoms;
one Si atom lies directly over each C atom in a double layer. Each successive double
layer is stacked on the previous double layer in a close-packed arrangement that allows
for only three possible relative positions for the double layers as shown in Fig.2.] and
Fig.2.2. These positions are normally labeled A, B, and C. Cubic, hexagonal, or

rhombohedral structures are produced as a result of different stacking sequence. According

6

Table 2.1. Comparison of semiconducting properties°'°.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Properties 3C-SiC 6H-SiC Diamond Si GaAs
Lattice constant (A) 4.358 3.567 5.430 5.65
Thoma] expansion 4.63 1.1 4.16 5.9
(XIO°°C)
Density (g.cm'3) 3.216 3.515 2.328
Melting point (°C) 2540* ** 1420 1238 )1800
Bandgap (eV) 2.2 2.9 5.45 1.1 1.43
Saturated electron 2.5 2.7 1.0 2.0
velocity VS (XI07cm s") ’
Mobility (cmZV"s")
Electron 1000 600 2200 1500 8 500
Hole 40 1600 600 400
Breakdown voltage 40 100 3 40
EB(X105V cm)
Dielectric constant K 9.7 5.5 11.8 12.8
Thermal conductivity 5 4.9 20 1.5 0.46
O'T(W cm"K")
Absorption edge (mm) 0.4 0.2 1.4
Refractive index 2.65 2.42 3.5 3.4
Hardness (kg mm'z) 3500 10000 1000 600
Z, (XI023W Q 5-2) 10240 73856 9.0 62.5
zK (x102w cm"s"°C) 90.3 444 13.8 6.3
Physical stability excellent excellent very good good fair
Bandgap type indirect indirect indirect indirect direct

"' Sublimes

** Phase change

ZJ =(EBVS/Tr)2
ZK =O'T(Vs/K)U2

 

 

Fig.2.]. A close-packed layer of spheres with centers at points A. A second layer of
spheres can be placed over this, with centers over the points marked B. A third layer can
be placed over A and the resulting sequence is ABAB... (2H structure) or it can be placed
over C and the resulting sequence is ABCABC... (3C structure).

[>130

>23

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if

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Fig.2.2. Possible respective orientation of Si and C atoms in tetrahedral bonding”.
(a) Si-C group with adhering carbon and silicon atoms.
(b) Si and C atoms in eclipsed position (2H).
(c) Si and C atoms in staggered position (3C).
(d) The axes-system and the base of the unit cell.

to Ramsdell the different polytypes can be characterized by their local symmetry
(C=cubic, H=hexagonal or R=rhombohedral) and the number of double-layers after which
the layer sequence is repeated. Thus, we have 3C for cubic SiC (known as B-SiC) and all
of the other polytypes are known as a-SiC. In these structures all atoms lie on symmetry
axes, and all symmetry axes lie in (1120) planes (in this notation the c (cubic 11]) axis
is (0001)) as shown in Fig.2.2(d). A (1120) plane therefore represents these structures
as shown in Fig.2.3(a). The different crystallographic polytypes of SiC are formed by
different zig-zag sequences of Si-C double layers as shown in Fig.2.3.

The band structure, and thus important electronic and optical properties vary
significantly from one polytype to another. The most important polytypes for applications
are 3C-, 4H-, and 6H-SiC due to layer production in pure form. Cubic SiC has the
zincblende lattice arrangement of GaAsS. Table 2.2 shows Ramsdell notation, lattice
constants, stacking sequences and energy gaps of some polytypes.

Acheson's method was the first process to produce bulk crystals of silicon carbide
(for grinding and cutting purposes). In this process a mixture of silica and carbon (sand
and coal) is heated according to a definite temperature-time cycle in air to produce silicon
carbide”. The development of a sublimation process for growing higher purity a-SiC
single crystals was reported by Lely in 1955. This process as it had been developed by
the early 1970's involves the heating of a polycrystalline SiC charge to about 2500 °C to
sublime the SiC which condensed on the slightly cooler parts of an inner hollow graphite
cavity. This cavity was formed initially inside the charge and lined with a porous graphite

tube.

 

 

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n {Z n u
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n 3 2 6 1 4
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of; L/ L/ ,.. mmssssa
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10

Table 2.2. Lattice constants, energy gaps at 300K, stacking sequences, and thermal
conductivity of common SiC polytypes.5'18

 

 

 

 

 

 

Type Constants (A) Gap Stacking sequence Conductivity
(eV) (W/cm.K)
a c
2H 3.076 5.048 3.3 ABAB 4.9
4H 3.073 10.053 3.3 ABACABAC 4.9
6H 3.08] 15.117 2.9 ABCACBABCACB 4.9
3C 4.360 ------ 2.2 ABCABC 5.0

 

 

 

 

 

 

 

 

Nucleation of individual crystals was uncontrolled, and the resulting crystals were
randomly-sized hexagonally-shaped a-SiC platelets. The platelets often exhibited a layered
structure of various 0L polytypes with the stacking direction of the atomic planes of these
polytypes being along the {0001} directions. Transition region of random stacking of
double layers (one-dimensional disorder) occurred between polytypes. Since these
polytypes have different energy bandgaps, undesirable heterojunctions were produced in

the crystals”. A seeded-growth sublimation process developed by Tairov et al.‘9'2°, Ziegler

21 I 22

et a] , and Carter et a produced bulk crystals of a single polytype of SiC at tempera-
tures of the order of 2200°C. The size of the crystals is limited not by the technique, but
by the ability to cut large diameters of this very hard materialg.

This sublimation process has been taken over by the groups at Siemens AG23 and

by a group at the North Carolina State University from which an industrial activity at

Cree Research was derived. Highly doped n-type 25 mm wafers of 6H-SiC and 4H-SiC

11

are now commercially available”. Since this sublimation growth technique produces
highly doped (up to 10‘9 cm") n-type wafers, an epitaxial layer has to be grown onto them
in order to realize active microelectronic devices. Recently, growth of bulk crystals of B-

(124.25. The seeds for the sublimation

SiC by the sublimation technique has been reporte
process were 6H-SiC substrates (Acheson- and Lely-grown) and free-standing
monocrystalline B-SiC films. Chemical vapor deposition technique was used initially to

grow monocrystalline B-SiC films on Si(100) substrates and subsequently the Si substrate

was removed.

2.3 SiC Technology
2.3.11 Thin-Film Growth of SiC

Because controllable quality SiC substrates are not available, the growth of SiC
thin films on foreign substrates in amorphous (a—), polycrystalline (pc-) as well as in
heteroepitaxial (c-) forms has been investigated extensively. Polycrystalline and
amorphous SiC have been grown on Si, thermally oxidized Si, glass and sapphire
substrates. Heteroepitaxial growth of B-SiC has been achieved on Si as well as on TiCx.
Single crystal growth of B- and 6H-SiC was achieved on 6H-SiC substrates (Acheson,
Lely and boule wafers)°.

Silicon substrates have been most frequently used as the substrate of choice for
the heteroepitaxial growth of B-SiC thin films because of the availability of the former
in well characterized and reproducible defect free and large area forms of controlled

purity9. Another interesting feature of Si substrates is that in spite of the large lattice

12

mismatch (20%) the cubic structure of the Si lattice automatically selects the cubic
polytype B-SiC. The heteroepitaxial growth of SiC on Si still has the following major
problems.
(1) The high defect density, which includes misfit dislocations, twins, stacking
faults, and antiphase boundaries (APB's), is present. The APB's are created
because of the growth of a non centrosymmetric (B-SiC) onto a centrosymmetric
substrate (Si) from a random distribution of nucleation sites. The density of defects
is higher at the interface where misfit dislocations and twins are usually found and
might extend to few pm from the interface. On the other hand the stacking faults
as well as APB's generally extend all the way to the film surface. These defects
might be caused by the mismatches in the coefficients of lattice parameters
(20%) and thermal expansion (8%) between the Si and SiC, or probably by the
nucleation processzw‘.
(2) The high concentration of residual donors and compensating acceptors. Hall
measurements indicate that while the net electron carrier concentration in un-
intentionally doped material could be as low as 5><10'°cm'3 , the actual donor and
acceptor impurity concentrations are often as high as 10'8 cm“3 (i.e. there is greater
than 90% compensation of the donors by acceptors). So far the evidence regarding
the origin of the donors and the source of the compensating acceptors points to
nitrogen and point defects in the material, respectivelyzg’”.
(3) Chemical vapor deposition (CVD) growth of B-SiC films on Si often requires

very high substrate temperatures (1360°C in many cases) which can lead to film

13

contamination by other impurities. Also some hydrogen incorporation inherent to

the process. The high substrate temperatures are close to the melting temperature

of Si (1412°C). Thus the compatibility with the existing Si technology is hard to
fulfill.

There have been numerous studies regarding the elimination of the above
problems. In order to reduce the high defect density caused by the lattice mismatch, TiCx
(less than 1% mismatch) substrates were investigated. Somewhat improved growth was
achieved, but great difficulties (3140°C growth temperature at pressure greater than 10
atmospheres) in producing defect-free single-crystal TiCx has hindered its use as a
substrate for SiC growth“.

Another way attempted to overcome the large lattice mismatch between SiC and
Si is to convert the Si surface layer of the substrate to a thin B-SiC layer by flowing a
dilute mixture of a hydrocarbon in H2 over the substrate as its temperature is ramped from
room temperature to the growth temperature (near 1400°C). This carbonization step
(buffer layer) is followed by the film growth using a flowing mixture of silane and a
hydrocarbon carried in hydrogen. This two-step B-SiC CVD process has been initially
reported by Nishino et al.32'33 and subsequently by numerous authors34'37. Heteroepitaxial
growth of B-SiC at “00°C on Si(] 11) and Si(100) has been recently reported by
Takahashi et 31'8_ Golecki et al.38 have recently reported heteroepitaxial growth of B-SiC
on Si at about 750°C using a single stoichiometric precursor (H3SiCH3) in their thermal
CVD process.

New deposition techniques of B-SiC films are now being investigated to determine

14

if the film quality can be improved. Fuyuki et a].39 have reported atomic layer-by-layer
control using gas source molecular beam epitaxy (Gas-source MBE) of the deposition of
B-SiC within the temperature range 1250-1320K on B-SiC(100) substrates previously

1.40 have reported the growth

prepared on Si(100) by the two-step CVD process. Sugii et a
of B-SiC(l]1) on Si(lll) oriented 4° toward <21_l_> using gas-source MBE at 1173K.
Photostimulated epitaxial deposition of B-SiC on sapphire (or-A1203)(000]) has been
achieved by Nakamatsu and coworkers“"2 using an ArF laser, C2H2: and Si2H6 within the
temperature range of 1253-1425K, and a pressure of 10'2 Pa. Deposition of
polycrystalline B-SiC films on Si using an electron cyclotron resonance (EAR) plasma
(v=2.45 Hz) discharge in a gas mixture of Sh4, C4, and H2 in the temperature range 680-K
have been reported by Cohere et al.43. Electron beam evaporation of a-SiC has been used
to deposit polycrystalline SiC films on [11]] Si and sapphire substrates, within a
temperature range of 600-900°C, but these films contain a-SiC‘4'45. Other techniques such
as sputtering can also produce SiC films on Si or some other substrates, at lower
temperatures than those used in the CVD process, but the films are usually amorphous
or microcrystalline“. The laser ablation technique more recently has been used to deposit
polycrystalline”l3 and epitaxial”IS SiC films from ceramic SiC targets on Si substrates
at 800°C and 900-] 150°C, respectively.

In an attempt to substantially reduce the concentrations of all defects
simultaneously, growth of B-SiC(l 11) on the Si(0001) and C(OOOI) faces of commercial
(Acheson-derived) 6H-SiC single crystals substrates has been investigated within the

temperature range of 1683-K at l aim total pressure‘7‘50. In contrast to films grown on Si

15

substrates, few defects were observed in these films when examined by cross sectional
transmission electron microscopy (XTEM), however, examination in plan view revealed
the presence of double positioning boundaries (DPB's). DPB's are usually created when
the orientation of the film growth is not the same at all nucleation points. High quality
6H-SiC films have been grown on "off-axis" 6H-SiC wafers that were produced from
sublimation-grown boulessms. The low defect density was verified by extensive plan view

TEMSI.

2.3.2 Doping

The capability of shallow n- and p-type dopings of SiC is essential if the material
is to reach its full potential for electronic device applications. SiC film growth by various
techniques including chemical vapor deposition (CVD) leads usually to highly n-type
doped films with no intentional introduction of dopants. Analysis of the temperature
dependence of the experimental Hall data shows an activation energy of 15-22 meV.
Some authors have suggested that the residual shallow donor is nitrogen56 and others
related the presence of the shallow activation energy to structural defects that behave as
shallow donors9.

Although SiC films are unintentionally doped, controlled n- and p-type dopings
can be achieved by in situ doping (gas phase during growth or diffusion sources) or ion
implantation. Al and P are usually used to dope SiC p-type and n-type, respectively.
Nitrogen is used also to obtain n-type conductivity by replacing a C-site. For 6H-SiC the

shallowest acceptor observed is Al on Si-site with an activation energy of 200 meV’. For

l6

3C-SiC the activation energies for A] acceptors3o and nitrogen donors57 are 160 and 34-37

meV, respectively.

2.3.3 Metallization

High temperature stable and low resistive contact structures are essential for
development of SiC devices. Several contact structures have been investigated to date,
however most results point at difficulties to fabricate low resistivity ohmic contacts with
good adhesion. Although diffusion of the metal and chemical reaction produces good
mechanical adhesion, excessive diffusion at the high temperatures results in spiking and
might cause electrical shorting of the device”.

Evaporation and sputtering techniques are usually used to metallize Sing’“. Ni
is widely used to form ohmic contacts to SiC upon high temperature annealing (900°C).
This results in formation of Ni silicides“. Ni, Au-Ta, Ti, Mo and Cr form ohmic contacts
on n-type B-SiC upon annealing. Mo/B-SiC contact has been reported to be thermally
stable up to 970°C with contact resistivity of 4.02><10'2 flcm2 after annealing at 970°C“.
For p-type B-SiC, Al,64 Al-TaSi2 and Ni form ohmic contacts upon annealing with
contact resistivity of Ni/B-SiC contact of 3.l9><10'2 (1cm2 after annealing“. Several
metallic elements (e.g. Ta, Ti, Mo), refractory silicides (eg. TaSiz, TiSiz, MoSiz), and
interstitial compounds (i.e. carbides, nitrides, and borides) have been developed as ohmic
contacts for 6H-SiC with somewhat high specific contact resistivity (10'3-10“ Q.cm2)°7.

Ti-W alloy makes a good high temperature low resistance ohmic contact to n-type Si face

of 6H-SiC°8. MeSi2/n-6H-SiC contact has been reported69 to be stable at high temperatures

17

with contact resistance less than 10" Q.cm2.

2.4 Characterization of SiC Films
2.4.1 Structural Characterization

There are several methods to identify polytypes in SiC. One simple method is to
observe the luminescence under ultraviolet light at liquid nitrogen temperature and then
again as the sample warms up. Although this method determines only the predominant
polytype in a mixed polytype crystal, it is useful as a quick way to examine a large
number of films in a short time. Electron and x-ray diffraction methods can be used to
identify a single polytype and provide more exact information about the presence of
multiple polytypes in a film. X-ray and reflection electron diffraction techniques are used
to obtain information about the surface being examined. Transmission electron
microscopy (TEM) is used to study and identify the buried layers of the material.
Furthermore, TEM is used to provide information about the epitaxial relation between film
and substrate in case of heteroepitaxial growth. However, TEM, x-ray and electron
diffraction techniques give little or no information about the non-crystalline phases that
might be present in the material”.

Further information about the non-crystalline phases can be obtained from Raman
spectroscopy. Cubic (3C) SiC film shows the characteristic Raman peak position of the
transverse-optic (TO) and longitudinal-optic (LO) at relative wave numbers of 796 and
973 cm", respectively. Well ordered graphitic material has only one Raman peak at z1600

cm" and the presence of disorder or small crystallite size gives rise to peak at 1355 cm‘

l8

‘.”’"'" Although TEM, Raman spectroscopy, and x-ray and electron diffraction techniques
are used to study the crystalline nature of the films and to identify polytypes, they are not
useful for studying the morphology of SiC films. Scanning electron microscopy (SAM)
is a very useful tool for morphology and visual analysis and provides information about
films in terms of voids, cracks, dislocations, uniformity of surface, and film-substrate
interface, etc. Optical-absorption spectra can be used to estimate the lowest indirect gap

of the material being studied and thus to identify polytypes”.

2.4.2 Electrical Properties

Although epitaxial and amorphous films have been the focus of many studies”
7929‘”, less work has been reported on polycrystalline SiC‘s'so'”. Polycrystalline SiC is easy
to prepare at lower temperatures than epitaxial SiC, and is more stable than amorphous
SiC”. In earlier studies of electrical properties of polycrystalline SiC, the films were

45'8"”. The reported parameters are conductivi-

deposited directly on insulating substrates
ties, charge carrier concentrations and Hall mobilities.

The carrier concentrations are generally computed assuming one type of carriers
in the conduction band that contributes to the electrical transport. Polycrystalline n-type
SiC films with no intentional doping, grown on thermal oxidized SaO2 and fused quartz
glasses by plasma enhanced chemical vapor deposition (PECVD)8', showed Hall mobility,
carrier concentration and conductivity in the ranges of 10 cmZV"s", 10‘°- 10‘8 cm“3 and

0.1-1 Q"-cm", respectively. Hall mobility showed a weak dependence on deposition

temperature from 600 to 900 C, but the deposition temperature had no effect on the room

19

temperature carrier concentration. In another study, polycrystalline SiC films deposited
on sapphire by electron beam evaporation”, showed n-type conduction with no impurities
added intentionally. Carrier concentrations and Hall mobilities were in the ranges of
5.0x10‘°-5.0x10l7 cm’3 and 2-20 cm2V“s", respectively. The Hall mobility and room
temperature carrier concentration increased with the deposition temperature for deposition
at 700-900°C and were independent of temperature for deposition at 600 - 700 °C‘5'32.
The conduction mechanism in polycrystalline SiC and the temperature dependence of
conductivity and Hall coefficient have not been reported.

Single crystalline B-SiC has electron mobility of 1000 csz"s‘l in spite of its

wide-bandgap energy (2.3 eV)“, and a calculated saturation drift velocity of 2.7x 107 cm.s‘

' (at 2><105 V.cm") for electrons”. Table 2.3 shows the electronic parameters of B-SiC.

Table 2.3. Electronic parameters of B-SiC“. m, is the electronic rest mass.

 

Transverse mass of electrons (m,) 0.247m0

 

Longitudinal mass of electrons (ml) 0.677mo

 

Density of states effective mass of electrons [m,‘=(m,m,)"3] 0.346mo

 

Number of equivalent minima in the conduction band (MC) 3

 

Effective mass of holes (mh') unknown

 

 

 

 

The electrical properties of single crystalline B-SiC were reported by many

author329‘30'45‘58'87‘". For single crystalline B-SiC films grown on Si substrates by chemical

20

vapor deposition, formation of an impurity band was observed. These films are highly
compensated and show electron concentration, Hall mobility and conductivity at room
temperature in the ranges of 10‘°-10”cm'3, 200-600 csz"s" and 1-10 Q'cm",
respectively. The reported activation energies computed from Hall data are in the range
of 0014-0025 eV58'87'88. The values reported for conductivity data are in the range of
0025-0032 eV”. The activation energy associated with the hopping conduction was not

observed.

2.5 SiC Films as Temperature Sensors

SiC single-crystal thermistors were developed by the Carborundum Company as
a high-temperature sensor. These thermistors exhibit high electrical stability under
conditions of continuous 1000-h exposure to 450°C and repeated thermal shocking from -
100 to 450°C. SiC thin films are considered to be applicable for manufacturing SiC
thermistors as a hi gh-temperature sensor while the silicon carbide thermistors are not easy
to manufacture because the silicon carbide single crystals cannot be precisely cut and
polished due to their hardness”. A thermistor using an RF-sputtered SiC film has been
developed as a temperature sensor for cooking products with stable thermistor properties
over a temperature range of 0-500C89'92. There have been no reports about SiC-based heat

flux sensors and thermoelectric generators.

21

2.6 Summary

Laser ablation technique has been recently used to deposit B-SiC films. Studying
the electrical properties of these films is essential to determine their potential for
temperature sensor and electronic device applications. Consequently, this study may
indicate the potential of the laser ablation technique for deposition of high quality B-SiC

films.

CHAPTER 3

LASER ABLATION TECHNOLOGY

3.1 Introduction
Pulsed-laser deposition (PLD) technique has been used to produce high-quality
films of high-Tc superconducting oxides and a number of other materials such as metals,

”'9‘. However, deposition of epitaxial layers of

piezoelectrics and ferroelectrics
semiconductors by PLD has not received the same attention, although there is potential
for growth of high-quality (hetero)epitaxia1 films at moderately lower temperatures (near
1000°C) than those of other techniques'5'95. The laser ablation technique has been used to

3 and epitaxial'“5 SiC films from ceramic SiC targets on Si

deposit polycrystalline'z"
substrates at substrate temperatures lower than those generally used in the CVD process.
Since this technique has been employed for the deposition of thin SiC films in this
research, features of this technique and details of the deposition system are discussed in
this chapter.

The characteristics of laser ablation technique for thin film deposition are

explained in section 3.2. Deposition and metallization of SiC films and sample

22

23

fabrication are presented in section 3.3.

3.2 Pulsed-Laser Deposition Technique

PLD is an attractive technique for thin film deposition because it has the following
advantages over other standard techniques:
(a) The localization of the ablation process at the target surface due to the very short
pulse duration (nanosecond) and to the very small size of the laser spot (2X3 mmz)‘3
provides a well controlled ablation of the material and high growth rate (0.2 nm/pulse)”.
(b) This technique has the advantage of producing highly energetic species that can lead
to (hetero)epitaxial growth of high-quality films‘s's’s'96 and provides control over the kinetic
energy of the evaporated particles (10-200 eV) by changing the laser parameters and the
external bias. This large kinetic energy of ablated species is comparable to that of charged
particles obtained by the ion beam technique. Compared with other thermal growth
techniques such as molecular beam epitaxy (MBE), this one produces species with kinetic
energies 2-3 orders of magnitude larger97'98.
(c) This technique is suitable for growth of multicomponent and multilayered thin films

and for in-situ deposition and metallization of semiconductors94‘99.

3.3 Sample Fabrication
3.3.1 Deposition of SiC Films
A schematic diagram of the PLD system for the growth of SiC thin films is shown

in Fig.3.]. A stainless steel vacuum system is equipped to prevent cratering of the target

24

surface by allowing the rotation of the target. The vacuum chamber is evacuated by a
turbomolecular pump to a base pressure of 5><10'6 Torr before starting the deposition
process. The surface of the target is illuminated by the laser beam over areas ranging from
2X]0 to IXS mm2 at a variable angle of 0-90° from an excimer laser of wavelength 193
nm (ArF) or 35] nm (XeF). The pulse energy at the target can be adjusted between 100
and 400 m] corresponding to fluences from 2 to 8 J/cmz. The angle between the target
and the substrate normal can be adjusted in a range of 0-90°. The distance between the
target and the substrate is another variable to be optimized. The ablation targets are 99.5%
pure SiC stoichiometric ceramics (Angstrom Corp). The substrates are Si wafers, fused
quartz microscope slides approximately 0.5 mm thick, and slightly thicker sapphire R-cut
plates. Immediately before use they are ultrasonically cleaned for 15 min each in (i)
distilled water with detergent (liquinox); (ii) distilled water; (iii) 2-propanol, and finally
dried in flowing nitrogen. The substrate and a boron-nitride-coated graphite resistive
heater (trade name lBoralectric, from Union Carbide) are enclosed in a tantalum radiation
shield with a square opening, 2.5 cm on the side for plume access”.

Temperature during deposition is monitored with near-IR (Ircon model V-15C10)
through a sapphire access window to the vacuum system. The pyrometer has a relatively
narrow wavelength passband, from 1.0-0.9 pm. It views a circle of less than 1 mm
diameter, over which one expects relatively constant film thickness. The viewing aperture
is small (leSO) implying small beam divergence. Under these conditions oscillations
corresponding to standing waves in the growing film can be clearly observed in the

pyrometer reading. Such oscillations allow the monitoring of the film growth rate,”100 but

 

 

25

H: Heater

R: Radiation Shield
S : Growing Film
M: Shadow mask

 

 

 

 

Fig.3.]. A schematic diagram of the pulsed laser deposition system.

26

alter the interpretation of the signal in terms of temperature. Thus, the temperatures are
taken from the readings just prior to start of deposition. Whereas for Si substrates, which
is optically thick, this initial pyrometer reading (using the appropriate emissivity of Si)
yields the actual substrate temperature for the optically thin quartz and sapphire substrates,
after correction for the substrate reflectivity and using the emissivity of boron nitride it
yields the heater temperature. A tantalum shadow mask can be placed on top of the

substrate to pattern the deposited film.

3.3.2 Deposition of Metal Contacts

The in-situ deposition of SiC films and metal contacts by pulsed laser deposition
method eliminates the required cleaning steps prior to deposition of the ohmic contacts
and might lead to a better adhesion to SiC films due to the large kinetic energy of the
ablated atoms and molecules upon arrival at the film surface. This attractive method is
described as follows. Once the SiC film is deposited the metal contacts can be deposited
either in the pulsed laser deposition system described above. The ablation targets are high
purity metals and are irradiated from an ArF or XeF excimer laser. Radiation is focused
near the surface of the target. The substrate rests on a boron-nitride-coated graphite
resistive heater (or a flat alumina heater) and the substrate normal is either at 0° or 45°
to the target surface. A shadow mask is placed on substrate surface to allow selective
deposition of the contacts. Ni and Pt are deposited (base pressure 5XI0'° Torr) in a range
of deposition temperatures between room temperature and 500°C. Cleaning of the films

is not needed as long as the replacement of the targets and the placement of a shadow

27

mask is done in a short period of time. The temperature is monitored either with a
thermocouple attached to the alumina heater or with near-IR pyrometer as described

earlier.

3.4 Summary
The potential of the pulsed-laser ablation technique for deposition of high-quality
SiC films is great. In addition, the deposition system and SiC sample fabrication process

are simple.

 

CHAPTER 4

MEASUREMENT TECHNIQUES

4.1 Introduction

This chapter deals with the experimental techniques used in this research to
measure conductivity, Hall coefficient, and Seebeck coefficient of SiC. In section 4.2,
van der Pauw's procedure for conductivity and Hall coefficient measurement is explained.
In section 4.3, the methods that are usually used for Seebeck coefficient measurement

are explained.

4.2 Van der Pauw's Measuring Procedure

It was shown by van der Pauw in 1958 that four electrodes are needed along the
circumference of a plane-parallel sample with arbitrary shape to perform conductivity and
Hall measurements. Two transfer resistances R1 and R2 can be evaluated in the following
way. If a current 1,2 is applied between electrodes 1 and 2, a voltage V3,, will appear
between electrodes 3 and 4 (see Fig. 4.1).

In a similar way, applying a current I23 between electrodes 2 and 3, a voltage V”

28

 

29

will appear between electrodes 1 and 4. This leads to R1=V3,,/I12 and R2=V,4/123.

According to van der Pauw the resistivity p is given by‘o'

=<

 

p= )(RllR2)f<%), ...<4.1)

1! d
1n2 2 2

OIH

where d is the sample thickness in cm; 0 is the conductivity in Q'cm"; RI and R2 are
in Q; and f(R,/R2) is a dimensionless and monotonically decreasing function with the
increasing RIIRZ. f(R,/R2) values range between 0 and 1 depending on R,/R2 where f(1)=1
and f(oo)=0. If the sample has a square shape and homogeneous, f(R,/R2) will be equal to
1. The same electrodes can be used to evaluate the Hall coefficient RH. If a current IB is
passed between 1 and 3, a voltage V24 appears between 2 and 4. Considering this situation
if a magnetic field perpendicular to the sample is applied, an additional voltage VH
between 2 and 4 appears.

The total voltage between 2 and 4 with the presence of magnetic field is
V*=V24iVH. When the magnetic field is reversed, the same voltage VH appears between
2 and 4 with opposite polarity. The total voltage between 2 and 4 with the presence of
opposite magnetic field is V'=V2,, TV". This voltage V“, the Hall voltage, can be expressed
as VH=(V*-V‘)/2. The Hall coefficient RH is related to the current II3 and the magnetic
induction B by

av,
BI13

 

RH=10° , ...(4.2)

where d is in cm, VH is in volts, B is in Gauss, RH is in cm3Coulomb'l and I,3 is in Amps.

30

Fig.4.l. A sample of arbitrary shape with four metal contacts along the circumference for
conductivity and Hall measurements.

4.3 Seebeck Coefficient Measurement Technique

There are two methods for measurement of Seebeck coefficient. In one technique,
one end of the sample under test is held at a certain temperature such as boiling helium
or nitrogen during the measurement. The temperature of the other junction is changed to
the required temperature T and the Seebeck emf E(T) is measured. The Seebeck
coefficient Q(T) is calculated as 6E(T)/6T '02. The other technique is the so called
differential technique.

In our work, we used the differential technique”? In this case, both ends are first

3]

brought to the required temperature T and then the temperature of one end is further
increased by a small increment AT~1K. Measurement of the small Seebeck emf AB

between the two ends leads to the Seebeck coefficient Q at T+(AT/2)Wthh is given by

AT _AE
Q(T+-—2— —AT' ...(4.3)

 

The first technique requires only the measurement of T and E(T) whereas T, AT,
and AE are to be determined in the second one. On the other hand, the first technique

requires more data processing to obtain Q(T).

 

 

A B
Pt Pt
Sample X

T T+AT
D Pt+13%Rh Pt+13%Rh

Fig.4.2. Sample arrangement for Seebeck coefficient measurement”)?

32

One experimental arrangement to obtain T, AT, and AB is shown in Fig.4.2. Two
thermocouples (e.g. Pt and Pt+13%Rh) are connected to the two ends of the sample
through metal contacts. The metal contacts have negligible effect on the measurements
since the Seebeck coefficient of metals is one order of magnitude lower than that of
semiconductors. A small heater can be used to raise the temperature of one end of the
sample by AT relative to that of the other end. The temperature of the entire sample can
be brought to T by inserting the sample into a low or high temperature measurement
system.

T and (T+AT) can be obtained using the thermocouples A-D and B-C, respectively,
while holding their outside junctions at a constant temperature. This leads to an estimate
of AT. The Seebeck emf AE between the two junctions can be measured directly using a
voltmeter. The Seebeck coefficient can be evaluated using Eq.4.3.

T, AT, and AE can be obtained in another way where two Seebeck emfs can be
measured between the two ends of the sample (i.e. AEAB and AEDC). The difference between
these two measurements leads to

AEAB_AEDC= [ (QPt-QX) ‘— (QPt+13%Rh_QX) ] AT!

’ [Qpc'QPunsRh] AT!
=QPC,Pt+13%Rh AT! - ' - (4 ° 4)

where , Qp,,,3%R,,, and Qx are the absolute Seebeck coefficients of Pt, Pt+13%Rh, and
sample X, respectively. Since the relative Seebeck coefficient of Pt and Pt+13%Rh (i.e.

Qp,‘p,,,3./,Rh) is available, AT can be evaluated using Eq.4.4. QX can be obtained using

33

MAB-Ag”; (Opt-Ox) AT, .. . (4 .5)

since OP, is also available in standard charts.

4.4 Summary

The measurement techniques used in this research are explained in this chapter.
The measurement of the conductivity and Hall coefficient allows the calculation of the
mobility and carrier concentration using a suitable model. The Seebeck coefficient
measurements coupled with the Hall measurements are used to explain the conduction
process in SiC and thus to determine the potential of SiC for temperature sensor

applications.

CHAPTER 5

CONDUCTIVITY AND MOBILITY OF SiC

5.1 Introduction

Measurements of fundamental electrical properties, such as carrier concentration,
conductivity, mobility, etc., of SiC are essential in evaluating its potential for electronic
device applications. Low temperature measurements are useful in determining types and
precise locations of shallow impurity levels. High temperature measurements are needed
in locating deep impurity levels and studying conduction process at such temperatures.

Electrical properties of B-SiC (i.e. cubic SiC) films deposited on either Si or
insulating substrates by laser ablation of ceramic stoichiometric SiC targets have not been
reported. On the other hand, there have been many reports about conductivity and Hall
carrier concentration of monocrystalline a-SiC.

In this chapter, measurements of conductivity and Hall voltage of polycrystalline
B-SiC and monocrystalline B- and a-SiC are discussed. For polycrystalline B-SiC films
deposited on insulating substrates and for a-SiC (6H and 4H) wafers, carrier concentra-

tions and mobilities are evaluated from the measured data assuming that carriers in a

34

35

single band are responsible for electrical transport. For monocrystalline B-SiC films
deposited on Si substrates, the measured conductivity and Hall voltage represent the
combined structure of the B-SiC film, interface and Si substrate. Multiple-layer
conductivity and Hall voltage models are used to obtain a simple understanding of the
relation between the conductivity and Hall data of the B-SiC film and those of the Si

substrate.

5.2 Polycrystalline Cubic SiC Films
5.2.1 Experimental

Polycrystalline B-SiC films were deposited on 3x2 cm2 quartz substrates using
laser deposition method as described in chapter 4. The film thicknesses and deposition
temperatures ranges are 1000-4500A and 1189-1298°C, respectively.

These polycrystalline films show the optical properties characteristic of the 3C
polytype of SiC (i.e. B-SiC). Analysis of optical transmission spectra of these films shows
a lowest-energy gap near 2.2 eV which is the value for cubic SiC. The films deposited
above 800°C show (111) and (222) x-ray-diffraction bands from crystal planes parallel
to the substrate. Selected-area electron-diffraction transmission patterns of these films
show predominant crystallite orientation with the 1]] axis normal to the substrate. The
crystallite dimension for the films deposited at ~1150°C is in the order of 50 nm'°°.

Samples were cut in l><l cm2 sizes and cleaned with acetone, isopropanol and
deionized water. Using a shadow mask, 2000A thick layers of Ni and Pt were sequentially

sputtered as 1.6 mm diameter circles, at the four comers to provide the contacts. The Pt

36

layer was needed to protect the Ni against oxidation and to allow wire bonding. No
annealing was done as low contact resistance was not critical for Van der Pauw
procedures.

The measurements in the 13-300K range were done in a closed-loop helium
cryostat, whereas above 300K a stainless-steel chamber evacuated by a turbomolecular
pump to 8x10'°torr was used. The sample was attached to a flat alumina resistive heater
using ceramic paste. The sample temperature was monitored by a chromel-alumel
thermocouple. An electromagnet provided a magnetic field of 8 kGauss for the Hall
measurements, which were obtained by averaging the 8 readings corresponding to the

switching of contacts and the direction of magnetic field and current.

5.2.2 Conductivity and Hall Measurements

Fig.5.] illustrates the temperature dependence of the conductivity of laser
deposited films for 3 samples. The film thickness and deposition temperature ranges are
1000-4500 A and 1189-1298°C, respectively. The conductivities increase monotonically
with temperature and are an order of magnitude larger than those reported for
polycrystalline SiC films prepared by plasma enhanced chemical vapor deposition and
electron beam evaporation “"5.

The Hall coefficient RH was measured in a temperature range of 17-729 K. The
effective carrier concentration n and mobility it were calculated assuming that electrons

are the sole carriers. Fig.5.2 shows the temperature dependence of 1/RH and n for samples

of Fig.5.]. The inverse Hall coefficient l/RH increases monotonically with temperature

37

 

 

    

O 1523

A 194A

D 164B
A Fitted data
.7 70 T T T T l T T T T Tm T T T l T T T T_
_. a
'E _
tn:
8 —t
z ' ‘ = -
E 10 E E
i" : .~. :
U h a ..
D A
C T ' T
Z .
o l
U lllllllllLillLAIIIHI

 

 

 

C)

20 4O 60 80
1000/TEMPERATURE (K'l)

Fig.5.] Temperature dependence of conductivity of 3 polycrystalline B-SiC films with the
fits shown as solid lines.

38

0 15213
A 194A
D 164B

— Fitted data

 

 

, O

70 3.

w

E

A Pi

-= w

5 10208

g 2

U10 (1:1
to .

IE 2

U '-i

= 5

a: :2

: C2D

E1019?

11.111111111.11l111r111..7 5"»

 

 

 

1o 20 30 4o 50
1000/TEMPERATURE (1(1)

Fig.5.2 Temperature dependence of the inverse of measured Hall coefficient, HR", and
the corresponding carrier concentration, l/qRH, of samples of Fig.5.] with the fits shown
as solid lines.

39

and ranges between 3 and 65 cm'3Coulomb. As seen in Fig.5.3, it varies slowly with T
and only occasionally (as for 194A) it shows a clear T dependence (below 200K). There
is no correlation between this temperature dependence and deposition temperature or film
thickness. Due to short mean free paths (discussed below), surface scattering is negligible
even for such thin sample (1000 A) and thus cannot explain such lack of temperature

dependence.

5.2.3 Analysis of Intermediate and High Temperature Data
Assuming that there is a number of donor (ground) states Ndi per unit volume of
degeneracies 13, at energy levels E, within the bandgap, the charge neutrality condition

gives"’1 '9:

N“ .(5.1)

 

IF):

1 1+0? exp (11+ei)
where n, the electron concentration in the conduction band, is given by

I): 2NC 61/2d6 I
VI?» ‘0 l+€Xp (6'11)

 

(5.2)

e,=E,/kT, n=(Er-Ec)/kT, Ef is the Fermi energy level, E, is the bottom edge of the
conduction band, k=0.86174><10"‘eV/°K, T is temperature, and Nc is the density of states
in the conduction band. The number of terms in the sum of Eq.5.1 is equal to the number
of the donor energy levels. Each term gives the number of ionized donors at the

corresponding energy level.

40

 

3TIIIIIIIIITIITIIIIIIII

 

 

_ A A A _

A
“A '- $% A A -
'7: £52 _
N 2 _
E - O 1523 -
3 — A 194A -
E - D 164B -
:1 0 ‘
m 1 —-
. a o D _
2 Cl [:1 @ 0%0 [U ..
D 1 IE] 1 -

 

O 200 400 600 800
TEMPERATURE (K)

Fig.5.3 Temperature dependence of the mobility derived from the Hall and conductivity
data as (SRH for samples of Fig.5.].

41

For a nondegenerate semiconductor with (nfiJZZ, a special case of Eq.(5.1) can

be written as”°

E.
n=ZAjCXp(—-k—'}')l ...(5-3)

where A,= BiNdiexp(-n). Thus a set of activation energies Ei can be obtained by fitting the
measured carrier concentration with Eq.(5.3) if we assume that Ai are temperature
independent

If we could define a temperature independent effective mobility u, the same set

of activation energies e,- should be obtained by fitting the measured conductivity data

with132

o =Zaiexp(-%), ...(5.4)

where o=qpn, a,=qu, and e,=E,.

Three exponentials were needed to fit the measured effective Hall carrier
concentrations and conductivities using equations 5.3 and 5.4, respectively, leading to
three sets of values for E,, A,, ei and ai as shown in Table 5.1. The activation energies ei
and constants ai are obtained as follows. The smallest activation energy e3 and the
constant a3 are obtained from the slope and intercept of log(o) versus ]/'T in the
temperature range of 17-40 K as shown in Fig.5.4(a) for sample 1528. Next, the calcu-
lated values of o3=a3exp(-e3/kT) are subtracted from the actual experimental conductivities
at corresponding temperatures, and the slope and intercept of log(G-0’3) versus I/T in the

50 to 150K temperature range yield e2 and a2 (see Fig.5.4(b)). Repeating this once more

42

Table 5.1. Activation energies: ei (conductivity) and Ei (Hall data) and constants: a,
(conductivity) and Ai (Hall data) for five samples.

 

Sample Activation energies (meV) Constants

(dimensionless) (Coulomb)

 

 

e1 32 63 E1 E2 E3 31 32 as in qu qAa

 

140A 76 8 0.8 75 7 0.8 40 9 12 45 3.7 8
152B 80 9 0.4 80 9 0.9 42 8.5 18 65 9.5 28
194A 74 14 1.5 74 11 1.4 30 14 11 11 2 5
164B 69 12 1.7 69 12 2.5 45 ll 10 T 70 7 20
]93A 69 19 1.9 69 20 3.8 30 l7 13 15 7 9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

yields el and al for the conductivity component activated above 250K as shown in
Fig.5.4(c). The activation energies Bi and constants Ai are obtained in the same way. The
corresponding slopes and intercepts are shown in Fig.5.5 for sample 1523. With three
terms Eq.5.4 yielded the fit shown by the solid line in Fig.5.]. The data could not be
fitted with two terms and no clear improvements was seen with more than three terms.
Hall data are also fitted in the same way using Eq.5.3 and yielded three pairs of constants
A, and E,. The fits of the Hall data are not as good as those of the conductivity data, but
still they are acceptable as shown by solid lines in Fig.5.2.

These fits, shown by solid lines, are valid if it is assumed that the density of states
is temperature independent. Within the data accuracy, E,=e,=74.5i5.5 meV for all films
and the quality of the fits is quite good. This result indicates that at the higher

temperatures electrons in the conduction band with temperature independent mobility are

 

 

43

 

010)
00

00-5
OO

N
O

 

 

CONDUCTIVITY (Ohm‘1.cm'l)

 

 

.3
O

20 40 60 80
1000/r (K")

(b) (C)

V'U'UUUIY'UIIEU

 

 

IUIT

  
 

....r.
O
-L
.3
O
A
T T TTTITi'I

100

_x
O
O
T rrnm]

 

jlllllllLLLllll

10 20 30 4o 0 5 10
1000/T (K") 1000/F (K")

 

CONDUCTIVITY (ohnr'l.cm'l)
CONDUCTIVITY (ohm‘1.cm'1)

_r1
Q
Q

Fig.5.4 The measured conductivity (hollow symbols) of 1528 and fits (solid lines)
obtained in 3 different temperature ranges using Eq.5.4. Slopes and intercepts of these
lines represent activation energies and corresponding constants: (a) el and a,, (b) e2 and
a2, and (c) e3 and a3.

ELECTRON CONCENTRATION (cm 3)

A

O
.5
(D

ELECTRON CONCENTRATION (cm'3)

Fig.5.5 The measured electron concentration (hollow symbols) of 1523 and fits (solid
lines) obtained in 3 different temperature ranges using Eq.5.3. Slopes and intercepts of
these lines represent activation energies and corresponding constants: (a) EI and A,, (b)

5x1 020

(a)

44

 

TIITTFTIIIITIIII

WWUU‘
O

 

..(

 

 

 

 

f1111l1111l1111

E3'A3
1020 1 1 1 1 11 1 1 1 O 11 1 l
0 15 30 45
1000/T(K'1)
(b)
I I l l I T Pl 1 I I I l T
_ Q .1
O
1020 @

IIJllll

 

 

 

O

4 8 12

1000/T (K'l)

E2 and A2, and (c) E3 and A3.

)

e? 1020

ELECTRON CONCENTRATION (cm

—8
O
_L
(D

(C)

 

 

 

 

JIIIIIIIIITTLfi
I 0 Z
_ o _
: OE"A‘ :
O

Illllllllllll
1 2 3l 4

1000rr(1<‘)

45

mainly responsible for the conductivity.

Polycrystalline films deposited by different techniques‘s'so's' had mobilities below
10 cmst even at carrier concentrations below 1018 cm'3. The low mobility and large
carrier concentration in our samples even at temperatures as low as 17 K, seem to imply
large concentrations of electrically active impurities or defects leading to concentrations
in the range of 10'9-1020cm’3 and a short carrier mean free path. For example, at 800 K,
Rutherford scattering by such densities of singly charged centers107 yields mean free paths
in the range of 6-20 A, which become even shorter at temperatures below 800 K. Surface
states associated with the grain boundaries change the bulk properties of the grains to
depths of 4 to 27 A (Debye screening length) at effective carrier concentrations found in
these films. Therefore, in our films with grain sizes'°° of 150 to 500 A the effect of
surface scatterring on bulk transport may be negligible. However, our results do not rule
out the possibility of grain boundary conduction.

The energy E, which activates conduction above 250K might be related to
transitions from donors to conduction band. This being the case, before extracting El
using Eq.5.3, the data should be corrected for the T3’2 dependence of the density of states.
The data corrected for this yields E,=55:t:5 meV. As SIMS analysis of our films showed
a density of nitrogen donors in excess of 1019 cm", this activation energy may be related
to nitrogen donors. Activation energies in the range of 53-54 meV have been seen in the
transport and electron paramagnetic resonance (EPR) data of high mobility
monocrystalline SiC” ”"32, even at nitrogen donor concentrations in the range of 10'7-1019

cm”. Our 13I values are also comparable to the values obtained by photoluminescence

46

”4 and to those obtained from Seebeck

spectroscopy for nitrogen donors in single crystals
coefficient measurements (see chapter 6).

The activation energies E2 and e2, although the same for each film except 194A,
exhibit some variation among the films and the quality of the fits is not as good as those
of E,=e,. For 194A,E2¢e2, which might be due to the dependence of its mobility on
temperature in this range. E3 and e, differ from each other and vary appreciably from film
to film, ranging from 0.4 to 3.8 meV. These results indicate that conduction at low
temperatures may not predominantly take place in the conduction band and the mobility
may not be temperature independent and therefore the assumptions made in the above
analysis may not be valid in this temperature range.

To investigate the validity of the assumption of single band conduction, the
location of Fermi level was determined through out the entire temperature range by fitting
measured effective carrier concentration with Eq.5.1. Fermi statistics was used since the
lowest activation energy is in the order of 1 meV and, thus, degeneracy is expected at
least at low temperatures. Fig.5.6 shows that the computed Fermi level Eris located within
the conduction band, indicating degeneracy, even at the lowest temperature, and Er moves
deeper in the conduction band as temperature increases. The strong temperature
dependence of measured 11 and 0 especially at high temperatures is hard to explain if our
films become strongly degenerate as temperature increases suggesting that the fitted it
might be exaggerated.

Using the obtained locations of 13,, the measured effective carrier concentration

was fitted with Eq.5.l assuming that 3 independent impurity levels exist. A degeneracy

 

 

 

 

 

 

47
I I I I I I I I I I I I I I I I I I I I I I I I
9 l 0 15213 - _
°’ e
E - ‘ 194A - _
m" .
m 100 -— O -
> E e E
o : :
at: _ e .
<1 _ _
5'3 ‘1 ' l
>
Lr-l T A . -
J T— ‘ —.
E _ _
ES _ A e _
g A
10 :- j
:1 l l l l l 1 1 1 I l l l I I l l l l I L‘, l 1‘
0 10 20 30 40 50

1000/TEMPERATURE (K'l)

Fig.5.6 Fermi level position computed using Fermi Statistics (Eqs.5.1-2) for 2 of the
samples of Table 5.1.

48

of 2 was used for each of the energy levels given by the activation energies of Table 5.1
and the donor densities were treated as parameters. The resulting fits are only good in the
high temperature range as shown in Fig.5.7 and require very high donor densities
(N,,,==N,,2=1021 cm" and N,l3 in the order of 1022 cm'3 for both 1643 and 1523) for the
heavily doped films, with the total donor density of the 3 donor levels being in the range
of 1022 cm’3. These donor densities seem to be comparable to the densities of atoms in
SiC (9.7><1022 cm'3) as the x-ray-diffraction studies indicate a crystalline structure within
the grains of our SiC films‘°°, such high donor densities are unreasonable and might
indicate that the measured carrier concentrations are too high. On the other hand, the fits
for the films with lower electron concentrations yield reasonable donor densities in the
order of 1020 cm'3 (N,,1=N,,,2=1020 cm'3 and Nd3=2.8><102° cm’3 for 194A). Generally, the fits
are best in the high temperature range (See Fig.5.7, sample 194A) indicating that the
contributing carriers are in the conduction band. The low temperature fits are generally
unacceptable and attempts to increase the donor density Nd3 do not alleviate this problem
indicating that single band conduction assumption is not valid in the low temperature
range. For example, in case of 194A, taking Nd3=4><1022 cm‘3 leads to a carrier
concentration of 5.2><10’8 cm‘3 at T=23K which is one order of magnitude less than that
derived from the Hall constant.

The low temperature data seem to indicate more complicated conduction processes

”9. Hopping conduction requires

such as impurity/defect band formation and hopping
compensation to occur whereas impurity/defect band conduction does not. In what follows

we present our analysis Of the low temperature data for both of these mechanisms.

49

 

  
   
    

 

 

 

O 1523
A 194A
—— Fitted data
—. . fl . . t . 4 q n
70 : T > .
‘ w
. E
... 0 :11
"g 0 :1
c A 1020 0
'3' 4 O
c I 2
U 10 ,- ~ ('3
"1’ ; i E
E». ’ i g
I >
E d
I 3
1019 ,3
1 i 1 act»

0 10 ~ 20
1000/TEMPERATURE (K'l)

Fig.5.7 Inverse of measured Hall coefficient, l/Rn, for samples of Fig.5.6, with carrier
concentration fits obtained by the charge neutrality condition assuming no compensation
and considering 3 independent donor levels represented by activation energies shown in
Table 5.1.

 

50

5.2.4 Analysis of Low Temperature Data

The phenomenological analysis introduced above was implicitly based on the
assumptions of temperature independent mobility and single band conduction. The
inconsistency of low temperature results shows that these assumptions might not be valid
in the low temperature range. Assuming that 3 independent impurity levels exist, the
location of Fermi level and thus the corresponding carrier concentration in the conduction
band can be determined for any set of donor densities, activation energies and degeneracy
factors using the charge neutrality condition. A degeneracy of 2 was used for each of the
energy levels represented by the activation energies of Table 5.1. The donor densities
were treated as parameters in order to fit the measured carrier concentrations.

Boltzmann statistics can be used only if the Fermi level Ef is several kT below the
bottom of the conduction band 13,. Since the lowest activation energy is in the order of
1 meV, degeneracy is expected at least at low temperatures. Using Fermi statistics, 3 fit
to the effective carrier concentrations obtained from the Hall data of some of the films
requires very high donor densities (Ndlr—Ndf—IO‘Zl cm'3 and Nd3 in the order of 1022 cm'3
for both 1643 and 1523) for the heavily doped films, with the total donor density of the
3 donor levels being in the order of 1022 cm‘3. These donors are either impurities or
electrically active defects and should be less than the densities of atoms in the host crystal
in order to preserve the crystalline structure. The atomic density in a SiC crystal is
9.7><1022 cm'3 and x-ray-diffraction Studies indicated the crystalline structure of our
polycrystalline SiC films within the grains'“.

Therefore, such high donor densities are unreasonable and might indicate that the

51

measured carrier concentrations are too high. Even with such high donor densities the
obtained fits are only good in the high temperature range. On the other hand, the fits for
the other films yield more reasonable donor densities (N,,,=N,,2=1020 cm'3 and Nd3=2.8><102°
cm‘3 for 194A), with their total being in the order of 1020 cm'3. Generally, the fits are best
in the high temperature range as shown in Fig.5.7 indicating that there the contributing
carriers are in the conduction band. The corresponding Fermi level Eris located within the
conduction band, indicating degeneracy, even at the lowest temperature and increases
monotonically with temperature as shown in Fig.5.6 for samples 1523 and 194A.

The low temperature fits are generally unacceptable and attempts to increase the
donor density Nd3 do not alleviate this problem (For 194A, taking Nd3=4><1022 cm'3 leads
to a carrier concentration of 5.2><1018 cm'3 at T=23K which is one order of magnitude less
than that derived from the Hall constant) indicating that single band conduction
assumption is not valid in the low temperature range. The possibility of impurity/defect

conduction either by hopping or impurity/defect band formation is considered below.

5.2.4.1 Hopping Conduction

Hopping conduction might proceed by direct or thermally activated tunneling.
Thermally activated hopping occurs when an electron tunnels from one localized and
occupied state to another localized and unoccupied state which has a different energy by
exchanging energy with the lattice vibrations. In direct hopping, an electron will tunnel
from an occupied state to an unoccupied state of some energy with no need for assisting

phonons. If hopping is thermally activated, conductivity tends to zero at very low

52

temperatures. In our measurements, it was not possible to go to such low temperatures to
check this condition and thus the scatter in the low temperature data prevents an
unambiguous conclusion about the type of hopping that might exist. The presence of
empty donors is a necessary condition for hopping conduction. At low temperatures this
condition can be fulfilled only by compensation. As the concentration of compensating
sites goes to zero, so does the concentration of empty sites leading to zero conductivity
at the lowest temperature.

Hopping conduction does not occur unless Fermi level is in the vicinity of the
impurity/defect band or hopping level. Therefore, one way to exclude some of these
possibilities without getting involved in details of the conduction process is by
determining the location of Fermi level'°7"°8.

Assume that in addition to El a level E2 of lower activation energy exist, with the
smallest activation energy B, being responsible for hopping. Since we do not have any
information about the density of compensating acceptors, we investigate the effect of
acceptor concentration on the location of Fermi level. Probability of hopping from full to
empty sites depends on densities of both full and empty sites, being highest when full and
empty sites have, approximately, equal occupations (E2 ~Ef).

The charge neutrality condition now has to include as a parameter an acceptor

concentration N, as follows:

53

N .
mi: _1 d1 +N, ...(5.5)
1 1451 exp(n+€i)

 

This acceptor level will be occupied by electrons from the donor states or the
valence band requiring an increase in the donor density to fit the measured carrier
concentration in the high temperature range. Fermi level IEf locations are determined by
fitting the measured carrier concentration using Eq.5.5. N,, Nd], and Nd2 are treated as
parameters. E3 contributes to conduction in the hopping band but not in the conduction
band. The obtained Fermi level locations Ef and the corresponding fits of the measured
carrier concentration for two samples are shown in Fig.5.8 and Fig.5.9, respectively. Both
samples show degeneracy above 100 K where Ergoes deeper within the conduction band.
For TSIOOK, the Fermi level stays in the vicinity, in terms of kT, of the intermediate
energy level E2 for compensation ratio N,/Nd2near 33%. As temperature increases above
100K, Fermi level moves away from E2.

For sample 194A, the effect of the compensation ratio on Ef is shown in Fig.5.10.
The obtained fits which correspond to these Fermi level locations are shown in Fig.5.] 1.
As the compensation ratio moves away from 33% the pinning of the Fermi level at E2
disappears. As compensation ratio increases more electrons fall into the acceptor states
from the conduction band or the donor states requiring an increase in the donor density
to fit the high temperature effective carrier concentrations.

The pinning of Ef even at 100K shows that donor sites at B2 are, approximately,

half empty indicating that in this model even at this high temperature there is significant

54

 

N
.3
O

—i
—
—
—(
‘

Ill] 1

A

G)

O

I.-
l

" 164B
194A

..L

01

o
I
F

120

NO)
CO

C

I
’lllllllllilllllllllllllllllllllll11

AA

FERMI LEVEL RELATIVE TO Ec (meV)
CO
C
IIIIIITTIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIT’
I
I

ll

.—
_
1—

11111111

10
1000/TEMPERATURE (K'l)

 

 

do
0

 

A

Fig.5.8 Fermi level position computed by fitting the measured electron concentration 11
of 2 polycrystalline samples using Eq.5.5. In these fits, Na, Ndl and Nd: are treated as
parameters and (Na/Nd3)=33%.

55

 

      

 

 

 

1021IIIIIIIIIIIII1IIIIIIII1:
'E '2
e, I 164B ‘
g A 194A ‘
E- I ' 5
E AAA ‘ I -
o ‘ ‘
Z A
O 19.. _
o 10 5 s
a: : I
E _ ..
z _ _
K _ _.
<
01018111]lllllllllllllllllll

10 20 30 40 50
1000/TEMPERATURE (K'l)

Fig.5.9 Effective carrier concentration, l/qRH, for samples of Fig.5.8, with carrier
concentration fits obtained by the charge neutrality condition assuming compensation ratio
of 33% and considering two independent donor levels represented by activation energies
EI and E2 as shown in Table 5.1.

56

 

 

 

 

E 60 E ..l I I I I 17 II I I I E
E 50 :7 l 0 10% I E

9 : I. . I
3 4° F I I 33% E
' I: 3° 5' A . A 90% T;
> 20 E A "o E
"" E A :
E; 10 :_ I O _:
v-l - I :
m E A . . Z
"'1 E A I . :
E -10 :- A I I I E
‘33 E A:
i '20 :— ‘ A 'E
2 a. A A 3
a: '30 : A E
E _40 : I I I I I I I II I I I -

1 1O
1000/TEMPERATURE (K‘)

Fig.5.10 Fermi level position for sample 194A computed using the charge neutrality
condition for compensation ratios of 10%, 33%, and 90% and considering two
independent donor levels represented by activation energies E] and E2 shown in Table 5.1.

57

 

 

 

 

 

I I I I l I I I I

- O

E

s _ 53
A

E A A A A ‘ 8

a A“ 2

«9 A Q

IE 194A _ 2

e, ---- 10% E

g: -— 33% :

.... \ ............ 90% — 1019 a

\\ g

\ - u

I\ I I I l I I I I V

5 1O 15

1000/TEMPERATURE (K'l)

Fig.5.]] Inverse of measured Hall coefficient, l/RH, for 194A with its fits using
corresponding Fermi level locations for the 3 different compensation ratios of Fig.5.lO.

58

contribution to conduction from this level. The exact location of the acceptors energy
level below midgap has no significant effect on the Fermi level location.

The donor density Ndl at energy level EI has to be in the order of 1022 cm’3 and
1021 cm‘3 for 140A, 1523, and 1643 and for both of 193A and 194A, respectively. The
donor density Nd2 at E2 has to be in the range of 4x 1019-1 ><102°cm'3 for all samples. Such
high donor densities are unreasonable (1022 cm'3) or exaggerated (102' cm") probably
indicating that the carrier concentration can not be directly derived from Hall effect in the
hopping region. In the high temperature range the fits of the effective carrier concentra-
tions were acceptable as shown in Fig.5.11 whereas in the low temperature range the
discrepancy is much larger than the previous case shown in Fig.5.7 due to the introduction
of compensation and elimination of the smallest energy level E3.

Thus, for the lightly doped samples, 193A and 194A, hopping conduction might
account for the discrepancy between measured and calculated carrier concentrations at
TsIOOK with a compensation ratio of about 33%. Whereas as in the high temperature
range the data can be explained by single band conduction of carriers mainly activated
from E, and E2 energy levels with donor densities being in the range of lOz'cm'3. For the
other films, a fit to the high temperature data with two energy levels requires
unreasonably large donor densities on the range of 1022cm'3 and thus single band
conduction in this case is ambiguous.

The carrier concentrations in the conduction band at low temperatures might be
much lower than those calculated from the measured Hall coefficient as l/qRH if hopping

conduction is taking place. Calculation of hopping electrical parameters such as Hall

59

coefficient and mobility is not possible since hopping theory provides only a qualitative
description of the conduction mechanism. A quantitative model requires the development
of the Hall coefficient considering the effect of magnetic field on carrier wave functions

as they tunnel from occupied sites to empty ones"5"'9.

5.2.4.2 Impurity/Defect Band Conduction

Impurity or defect band conduction is an alternative mechanism to hopping without
the requirement of compensation. Impurity/defect band formation requires sufficient
overlap of the localized electron wave functions of the defect or impurity centers to cause
significant energy broadening. It may be assumed that the excited states of
impurities/defects form this impurity/defect band. At absolute zero, this band and the
conduction band are assumed to be empty. In this band the density of states including
degeneracy of excited states should be large enough to accommodate the excited carriers
so they can move with finite mobility.

Although we assume that the impurity/defect band is located between Ec and E2
as shown in Fig.5.l2, it may also be between E2 and E,. In the former case electrons can
be excited from El and E2 into the impurity/defect band whereas in the latter case only
electrons at EI can be excited into the impurity/defect band. In both cases electrons can
be excited into the conduction band from both E, and E2 levels. The smallest activation
energy E3 is assumed to be the activation energy needed to excite carriers from E2
(considering the former assumption) or E1 (considering the latter assumption) into the

lower edge of the impurity/defect band. According to our measurements, the largest

60

Impurity/defect band

 

 

 

>1
31K—
A5
{11
—>1 re"
.55

 

 

Intrinsic level

 

 

E

V

Fig.5.12 Energy band of SiC with two donor levels located at El and IE2 below the bottom
of the conduction band EC. The impurity/defect band is located at (El-E3) below Be. The
energy levels in this figure are not drawn to scale and the intrinsic level B, should not be

exactly in the middle of the bandgap.

61

activation energy E1 is equal to 74.5:l:5.5 meV. The intermediate E2 and smallest E3 ones
are in ranges of 7-20 meV and 0.8-3.8 meV, respectively. In order to study the two cases
mentioned above, the measured electron concentration n=1/qRH has to be fitted with the

following equation as obtained using the charge neutrality condition9'”9:

 

 

 

n= Ndl
1+9;1 exp (11 +6011) +95; exp (fl+€d23)
+ _1 ”dz _1 , ...(5.6)
1+B2 exp (n+ed2) +323 exp (New)
where
2 °° 1/2
n= NC 6 d5 . . . (5 .7)

vf'ff 0 1+exp(e-n)

is the carrier concentration in the conduction band and n=(ErEc)/kT. N, is the density of
states in the conduction band. There are Nd, and Ndz donor (ground) states per unit
volume of degeneracies B, and [32 at El=ed,kT and E2=ed2kT, respectively. The energy
separation between the ground state of E2 and the impurity/defect band (or the excited
state of E2 ) is given by E3=ed3kT Thus, the impurity/defect band is located at E23=(ed2-
ed3)kT=ed23kT below Ec with its degeneracy being [323. The Fermi level may be any where
above midgap. Nd, and Ndz are used as parameters to fit the measured carrier
concentration.

The density of electrons in the impurity/defect band is equal to the density of

donors with electrons trapped in the excited state E23, which is given by”9 :

62

_ [[33 exp (n+ed23] Ndl
nd_ —1 -1
1+[31 expm +ed1) +stexpm+€dzal
[Br-a; exp<fl+€d23H Nd;

+ .
1+Bglexp (n+ed2) +l3§§exp (n+6d23)

 

...(5.8)

 

The impurity/defect band will contribute to conduction only if Fermi level is in
the vicinity of this band. The location of the Fermi level can be calculated using the
charge neutrality condition (i.e. Eq.5.6) with the donor density and degeneracy factor [323
being used as parameters. As the donor density increases the degeneracy factor has to be
increased also in order to have the Fermi level in the vicinity of the impurity/defect band
(e.g. for donor density Nd in the order of 10‘5cm'3, B2328 whereas for Nd ~10'9cm'3,
(32321000).

Considering that the impurity/defect band is above E2, fitting the effective carrier
concentrations of samples 1528, 1643 and 140A (Nd is in the range of 102°-1022cm'3)
leads to Ef far from the location of the impurity/defect band at low temperatures unless
degeneracy of the excited state is extremely high and unreasonable. Furthermore, it was
not possible to fit the measured carrier concentration at high temperatures (even if
B2321000) since most of the excited carriers tend to stay in the impurity/defect band even
at high temperatures. For samples l94A and 193A, fitting the carrier concentration at the
lowest temperatures resulted in Nd] in the order of 102°cm'3 and carrier concentrations in
the impurity/defect and conduction bands at high temperatures in the order of 102°cm’3 and

10'9cm'3, respectively, with the effective carrier concentration l/qRH at high temperatures

63

being several times larger than the one calculated using Eqs.5.6-8. Thus, this case is ruled
out.

Considering that the impurity/defect band is between E2 and E,, fitting the effective
carrier concentrations is not possible with donor densities NH and Nd2 in the range of the
atomic density in SiC (9.7x 1022cm'3) even at high temperatures. Therefore, impurity/defect
band model does not explain our results.

Impurity/defect band conduction requires high degeneracy to provide enough
empty states for the carriers so they can move with finite mobility whereas hopping
conduction requires compensation to produce such empty states. The existence of either
conduction mechanism in our case depends on the compensation and donor density.
Impurity/defect band mechanism leads to an unreasonably large degeneracy and seems to
indicate that the effective carrier concentration is exaggerated. Hopping mechanism does
provide a reasonable explanation of part of our data but with exaggerated donor densities
indicating the need for a quantitative analysis to obtain the actual carrier concentration
from the measured Hall coefficient in the hopping range.

Measured Hall coefficient of highly compensated semiconductors might lead to an
exaggerated estimate of the carrier concentration. Therefore, this case is considered here.
When both electrons and holes contribute to conduction, the Hall coefficient RH can be

expressed as

2- 2
RH=-1- p“ ““9 ...(5.9)

CI (puunueV'

 

where u, and uh are the electrons and holes mobilities, respectively, and n and p are the

64

electron and hole concentrations, respectively. According to the above equation the Hall
coefficient will be smaller than 1/qn if puzh is comparable to npzc. Therefore, the Hall
coefficient associated with highly compensated films (i.e. the Fermi level is near the
intrinsic level and accordingly electron concentration is, approximately, equal to the
concentration of intrinsic carriers) leads usually to an exaggerated carrier concentration
if estimated as l/qRH‘”. If electron and hole concentrations are near the intrinsic
concentration, fitting the measured conductivities of our films with o=q(u,n+u,,p) will
require unreasonably large mobilities (2106 cm2 V's"). Therefore, this phenomenon does

not explain the existence of high effective carrier concentration.

5.3 Monocrystalline SiC

In addition to depositing polycrystalline B-SiC films, laser ablation technique was
used to grow monocrystalline B-SiC films on Si substrates. As these monocrystalline films
(thickness 3 lum)‘“ have wide potential device applications, measurements of their
conductivity, mobility and carrier concentration is needed to assess that potential.

Since the polycrystalline B-SiC films were deposited on insulating substrates, their
electrical properties were measured with no need for separating the film from the
substrate. Usually B-SiC films (0.7-50 pm thick) grown on Si by chemical vapor
deposition (CVD) are prepared for electrical characterization by chemically etching the
Si substrate30'87. However, etching the substrate is not needed in case of laser-deposited
monocrystalline B-SiC on Si since these films seem to be isolated from the substrate by

a highly resistive (porous) interface‘“.

65

Since the quality of monocrystalline a-SiC substrate wafers is good, studying their
electrical properties might shed some light on the results obtained for polycrystalline B-
SiC and the potential of both poly and monocrystalline B-SiC prepared by laser ablation
for certain applications such as temperature sensors. In the next section, measurements of
conductivity, mobility and carrier concentration of both of these monocrystalline SiC

polytypes are presented.

5.3.1 Monocrystalline a-SiC Substrates

Van der Pauw measurements were conducted on commercially available 6H- and
4H-SiC wafers. The wafers were cut in l><1 cm2 sizes to obtain square samples suitable
for the available measurements systems. The thickness of these samples is in a range of
0.0569-0.1 143 cm. The measurement systems and method of measurement were similar
to those described earlier in 5.2.1. Fig.5.13 shows the temperature dependence of the
inverse Hall coefficient l/RH and electron concentration (n=l/qRH) of one 4H-SiC
sample and some 6H-SiC samples in a temperature range of 50-300K. The electron
concentration increases monotonically with temperature and ranges between 10'2 and 102°
cm'3. As shown in Fig.5.l4, the mobility of these samples (u=oRH) increases with
temperature reaching its maximum then goes down as temperature increases due to lattice
scattering. The maximum of the mobility for all samples ranges between 25 and 280

csz"s’l and occur in a temperature range of 150-300K. It is obvious that the mobility

66

‘ A(6H) O D(6H) V G(6H)
O B(6H) O E(4H) I EH63) _
D C (6H) A F(6H) —— Fits

 

100 _
10-1
1o-2
10-3
10-4

l/Rll (cm'3Coul0mb)

10-5
106;

_ i r:
10—7.....IHH1....1....1....1 ~1~'~=1O12§.

0 3 6 9 12 15 18 V“
1000/ma)

 

 

 

 

Fig.5.13 Inverse of measured Hall coefficient, l/R“, with corresponding electron
concentration for some 4H- and 6H-SiC. The fits for samples A and H in the low
temperature range are shown as solid lines.

67

O A (6H) 0 D (611) V G (611)
0 B (6H) 0 E (4H) I H (6B)
Cl C (6B) A F (6H)

 

 

 

 

 

350 ’- T—I I I l I I I I l I I I I 1 I I -1
t 1
300 :— o o ‘2
: 0,6 v0 :
7A 250 C' ' O 1
~m - C] V 3
N5 : V ' "
E 200 r o 1
3 : :
E 150 :— -3
._-_J : D [:1 I 2
g 100 3' C] 0 j
_ A A .
2 - A v _
; Cl .2
50 : co 0 4| :
.- .. . . .1
0 Z. . . Q I.“
: l l l 1 1 l L l l l J 1 l l l l l :

O 5 10 15

1000/UK")

Fig.5.l4 The Hall mobility (u=oR”) as computed from Fig.5.l3 and Fig.5.15.

68

values decrease as the donor density increases due to the increase in impurity scattering.
For example, sample A has the lowest mobility and highest donor density compared to
other samples.

The temperature dependence of the conductivity 0’ for samples of Fig.5.13 is
shown in Fig.5.15. 0' increases with the increasing temperature for Ts300K and starts
decreasing as temperature exceeds 300K due to the sharp decrease in mobility at those
temperatures.

The activation energy for these substrates can be obtained by fitting the data using
Eq.5.3 with two activation energies for samples A and B or one activation energy for the
rest of the samples. The obtained fits shown as solid lines for samples A and H in
Fig.5.l3 are good except at very low (below 60K for sample H) temperatures which might
be due to impurity/defect conduction. The shallow activation energy E2 for samples A and
B is 5 meV which is comparable to the shallow activation energy of the polycrystalline
B-SiC films reported in this chapter. These polycrystalline films have high carrier
concentrations and low mobilities with values comparable to those of samples A and B
especially at low temperatures. The deep activation energy El for all samples is in a range
of 80-84 meV assuming temperature independent density of states. Recalculating this deep
activation energy assuming T3’2 dependence of the density of states leads to values in a
range of 58-60 meV. The activation energies calculated using Hall measurements in a
temperature range of 90-1000K are 81-84 meV and 52.1 meV for 6H-SiC and 4H-SiC,

28,229.88

respectively whereas photoluminescence (PL) studies indicated a higher value of 170

meV'”. Activation energy of 81-84 meV was obtained from Hall electron concentration

69

O A (6H) 0 D (6H) ' G (6H)
0 B (6H) 0 E (411) I H (6H)
D c (an) A F (6H)

 

 

 

 

 

T T I I f
102 ‘=
A O
1' 101 O i
o :
"r ' ,
5100 fi
-= I
2 0 ’ 3
:101 A T
5
:10“2 ~ 0 -:
8 ‘ ' D
510’3 F “
8 E - 2
104% v E.
L- D 3
AID-Si .1 .mn. J . .4 1 .i i 1 i.

4 8 12 16 20
1000/T (K‘l)

Fig.5.15 The temperature dependence of measured conductivity for 7 samples of 6H-SiC
and one 4H-SiC sample.

70

of (10”cm'3 at 100K“. In our case, wafers (samples C to H) that showed a single
activation energy (80-84 meV) have comparable electron concentration of (10‘7cm°3 in
the same temperature range. On the other hand, samples A and B that showed a shallow
activation energy have electron concentration of at least one order of magnitude larger
than that of other samples especially at T_<_100K. It seems that the shallow activation
energy is associated with impurity conduction at low temperatures as it was found for
polycrystalline B-SiC earlier in this chapter. This impurity conduction is noticed at TSéOK
in case of sample H (low donor density) and extends to 120K for samples A and B (large
donor density). Impurity conduction and dependence of activation energy on the donor

density have been reported in earlier studies of B-SiCm”.

5.3.2 Monocrystalline B—SiC Films
Epitaxial B-SiC films were deposited on single-crystal Si wafers by laser ablation
of ceramic stoichiometric SiC, carbon, or alternating silicon and carbon targets

l03,l44

described elsewhere . X-ray diffraction spectroscopy and transmission electron

microscopy indicated the crystalline cubic structure (i.e. B-SiC) of these films and

alignment with the Si substrate'“

. The film thicknesses, deposition temperatures and
times, and pulse rates are shown in Table 5.2.

Even though the deposition time of 177 is approximately one order of magnitude

larger than that of other samples, the thickness of 177 is comparable to the thickness of

71

Table 5.2. Thicknesses, deposition temperatures, deposition times, and pulse rates for five
SiC films.

 

 

 

 

 

 

Sample Thickness Dep. Temperature Dep. Time Pulse Rate
(A) (°C) (min) (H2)
177 10000 1 166 60 5
306 5 500 l 188 7 20
307 6000 1 193 4 20
315 5500 1195 5.5 20
362 6500 1216 2.5 20

 

 

 

 

 

 

 

other samples. This discrepancy might be due to the lower pulse rate (5 Hz) and
deposition temperature (1166°C) of 177 compared to those (20 Hz and 21 188°C) of other
samples.

Since shadow masks were used for selective area deposition, SiC growth occurred
only within the openings of the shadow mask. The portion of the Si substrate underneath
the mask did not receive any of the ablated material (i.e. the plume) and no SiC growth
was noticed on the surface of this portion. The initial stages of epitaxial growth of SiC
on Si seem to proceed by the reaction of carbon in the plume with Si outdiffusing from
the substrate. As the growth of the film on top of the Si substrate continues, voids are left
behind and the contact between the growing SiC film and the substrate is maintained over
a progressively reduced area. Thus, some thick portions of the SiC film peel off due to
the loss of contact surface with the substrate‘“ leaving part of the film-substrate interface

on top of the Si substrate.

72

Three different samples of each Si substrate were prepared for resistance and Hall
measurements. First sample was cut from the part of the substrate that was exposed to the
plume. This sample has the sandwich structure, SiC-interface-Si, with the metal contacts
being on the surface of the SiC film. A second sample was prepared from the part of the
Si substrate that was underneath the shadow mask during deposition. A third sample was
prepared from the remaining Si after the removal of the delaminated SiC film from the
top. This SiC film broke into small pieces and was too thin to be used for the
measurement. In our discussion, we will refer to these 3 samples as SiC/Si, interface-Si
and Si, respectively.

Samples were cut in l><l cm2 sizes and the preparation of the metal contacts and
samples for van der Pauw measurements were done as described in 5.2.1. The
measurements in the low (13-300K) and high (T2300K) temperature ranges were done in
the measurement systems described in 5.2.1.

Figs.5.l6-l7 show the measured Hall voltage of the SiC/Si, interface-Si and Si
structures for samples of Table 5.2 in the low (below 300K) and high temperature (above
300K) ranges. The magnitude of the Hall voltage in the low temperature range is much
larger than that in the high temperature range for most samples. For temperatures below
300K, the Hall voltage of the SiC/Si structure is at least one order of magnitude lower
than that of the interface-Si structure for all samples except 306. This might be due to a
lower interface resistivity (i.e. less voids with smaller size) which results from either
lower deposition temperature (1188°C for 306 compared to ll93-1216°C for other

samples) or lower deposition time (7 min for 306 compared to 60 min for 177).

73

O 362C (interface-Si)
. 362B (SiC/Si)

 

 

 

 

 

 

 

 

1 r l T
A 0 r ©© ©© © . O _
> n-type O O
E ’ o
E O
O
3 O
S 4
O O O
>
O 1
j 0
<
=1 O
-1 1 1 ‘ ‘ ‘
1 2 3
1000/TEMPERATURE (K'l)
V—fi r r f l r
102 E o o O -
S‘ E O
E. L O
m 101 E O . . fl
3 $9 . ' p-type
E- L {g o .
-l 100 0 a
O a
> if .
:3 10-1 > ‘=
< -
I 0
10-2 1 l i i i i 1 4 i i i
10 20 30
1000/TEMPERATURE (K")

Fig.5.16 The measured Hall voltage of sample 362 in two temperature ranges. These
results are obtained using an input current of 0.1 mA and magnetic field of 8 kGauss.
Interface-Si structure represents the Si under the peeled off B-SiC film.

74

 

 

 

 

 

 

 

 

1oo_....,....,.T.:
5‘ E. E
5 50 I .0 .
8 o :— I E 29 I I---I--~§
E5 E % 2
5‘ -50 '— Q ' -E
> .. 1
j -100 _— O -:
E = -
-150 _- O "
g 00 ‘ O interface-Si (307B)
-200 1 . 1 _ .
1 2 3 4 . SiC/S1 (307A)
K-l . .
1000/TEMPERATURE( ) D Interface-SI ( 17 7B)
5 _. ' SiC/Si (177A)
10 1 1 11 [1 1 1 6 1 1 1 161 ‘6'
A 80 O w v interface-Si (306B)
> 104 88 v V O . .
3 v V SIC/SI (306A)
(1.1
U ........... Si (177C)
3
g 10 .. .. 51 vi
..1 C] . Cl .
S 102 D _
.1 O 3
:21 :
= 101 j
100 411111111111 1 iii 1 1 "‘
4 1O 16 22 28
1000/TEMPERATURE (K4)

Fig.5.l7 The measured Hall voltage in the high and low temperature ranges of some
samples of Table 5.3. These results are obtained using an input current of 0.1 mA and
magnetic field of 8 kGauss.

75

As temperature increases above 300K, the Hall voltage values decrease and
become negative (n-type conductivity) at temperatures given by Table 5.3. For both the
interface-Si and SiC/Si structures of samples 362 and 307, these negative values exhibit
a minimum with the lower values (larger magnitude) being those of the interface-Si
structure. As temperature increases above 500°C, Hall voltage values for both structures
approach the same value (-10uV).

Even though the Si substrate had n-type conductivity, after deposition the
conductivity of the SiC/Si, interface-Si and Si (front and back sides) was p-type for
temperatures below 345 K and above 35 K (see Table 5.3). This indicates the formation
of a p-type layer on the outer surface of the n-Si substrate. The formation of this p-type
layer on the front and back sides of the n-Si substrate might be due either to loosing
enough phosphorous from the outer surface of the substrate so that the native acceptor
concentration becomes relatively larger or to doping the substrate with an acceptor
available in the deposition system. This acceptor might be coming out of the resistive
boron-nitride-coated graphite heater used in the deposition system to heat the n-Si
substrate. Since the diffusion coefficient of boron and phosphorous in Si is very small
(2.51><10‘l2 cmz/s at 1200°C), this p-type Si layer is expected to be very thin (few
1000 A).

As temperature decreases below 300K, the positive Hall voltage shows a maximum
then decreases for all samples and becomes negative at TS35K for some samples. Usually,
the Hall voltage increases as the carrier concentration decreases with the decreasing

temperature. Therefore, the decrease in the Hall voltage at low temperatures might be due

76

Table 5.3. Temperature range of n-type conductivity for samples of Table 5.2.

 

 

 

 

 

 

 

 

 

 

 

 

Sample Temperature range

177A [SiC/Si] T2631K , 100K STS 130K and TSB4K
177B [interface-Si] T2544K

177C [Si] low temperature data shows p-type"
306A [SiC/Si] low temperature data shows p-type*
306B [interface-Si] at T=28K*

307A [SiC/Si] T2393K

307B [interface-Si] T2393K and TS35K

315A [interface-Si] T2363K and TS31K

315B [SiC/Si] T2363K

362A [SiC/Si] T2379K and T=23K

362C [interface-Si] T2345K

 

 

 

 

* No high temperature data is available.

77

to an increasing contribution to conduction from the n-Si substrate as the thickness of the
depletion layer of the p-n junction decreases with the decreasing temperature. The change
of the conduction type from p to n at temperatures 33 SK might be due either to
predominant contribution to conduction from the n-Si substrate or to impurity/defect band
conduction within the p-SiC film and the p-Si thin layer.

It seems that predominant conduction takes place in the n-type Si substrate at high
temperatures (above 300K) as the steep decrease in the Hall voltage shows in Figs.5.16-
17. For temperatures below 300K, more conduction seems to occur in the SiC film as a
result of the existing pn junction and the highly resistive interface between the SiC film
and the n-Si substrate. The SiC/Si structure of sample 177 shows lower Hall voltage
values compared to those values of the same structure of other samples for T53 00 K. This
might indicate that the SiC film of 177 is more isolated from the substrate compared to
other samples and thus the measured low Hall voltage values of the SiC/Si (177A) is
mainly that of the SiC film for TS300K. Table 5.3 shows that only for sample 177, the
change from p- to n-type conductivity for the SiC/Si structure occurs at a higher
temperature compared to that for the interface-Si structure (631K and 544K for 177A and
177B, respectively) supporting the view that the SiC film is well isolated from the
substrate.

A better isolation between the film and substrate is obtained for longer deposition
times as the contact surface between the SiC film and Si substrate reduces and the
thickness of the p-n junction increases with deposition time, respectively. Thus, this

isolation might be due to a longer deposition time of 60 minutes for 177 compared to that

78

of 37 minutes for other samples (Table 5.2). The low values of the measured Hall voltage
of 177A indicate that this SiC film is highly compensated and therefore shows n-type
conductivity in a temperature range of 100-130K whereas the interface-Si shows p-type
conductivity in this temperature range.

The transfer resistance was measured using van der Pauw method as described in
chapter 4. Figs.5.18-l9 show the measured resistances of the SiC/Si (solid symbols) and
interface-Si (hollow symbols) structures for samples of Table 5.3 in addition to the
measured resistance of the Si structure for sample 177 (dotted line). The measured
resistance of both the SiC/Si and interface-Si structures is at least one order of magnitude
larger than that of the Si structure at temperatures below 300 K which might be due to
defects and voids that exist in the SiC film and the interface, respectively. These voids
in turn lead to an increase in the resistance of interface-Si structure compared to that of
the SiC/Si structure (few times) for all samples at TS300K. Above 300K, the SiC/Si and
interface-Si resistances for all samples show sharp decrease with temperature and
approach the same value.

The resistance data coupled with the Hall voltage data indicate that conduction
takes place predominately in the n-type Si substrate above 300K. At lower temperatures,
SiC film contributes more than both the p-type interface and the n-Si substrate to
conduction. Therefore, the low temperature data of the SiC film needs to be extracted
from the combined measured data of the SiC/Si structure using appropriate resistivity and
Hall coefficient models. Multiple-layer models for Hall coefficient and resistivity are

discussed below.

79

 

 

 

 

 

 

105 . . . fl 1 1 1 ' 1 ‘ 1 T ' T 5
E o 3
104 :— O Q -:
I O O E
g Q .0 O i
<3. 103 z ‘=
m I E
U .
z .
f. .
:2 1o2 , ‘=
a : 0 interface-Si (3 15A) 3
a: O SiC/Si (31513) 3
101 ” O interface-Si(362C)
= . SiC/Si (362B)
100 l r 1 1 L L 1 1 1 1
10 20 30
1000/TEMPERATURE (K4)

Fig.5.l8 The measured resistance of two highly resistive films in the low and high
temperature ranges. The measurement was done on SiC/Si structure (solid symbols) and
on interface-Si structure after the removal of the SiC film (hollow symbols).

80

' SiC/Si (307A) v SiC/Si (306A)

0 interface-Si (3078) v magmas, (306B) .
l SiC/Si (177A) ........... Si (177C) ,

Cl

interface-Si (177B)

 

 

 

 

: ' ' ' ' ' ' ' 'F i' ‘ :
E 8 08 3
_ v o V ,
E M9999 q:
A i o o ‘ 1
an ..
E ” 00“. ‘
O 2 _ D -
g; 10 s O.
u E . D 1
.2. D *
1- % C1D “
V) DD
g 101 ,- CED I I I. ‘=
‘3‘ E I 5
: l.-'-' 3
10° :- 7:
DD 2
10-1 1 1 1 1 1 1 1 1| 1 1
1 10

1000/TEMPERATURE (K‘l)

Fig.5.l9 The measured resistance of 3 different films in the low and high temperature
ranges. The solid symbols represent the data of the SiC/Si structure. The hollow symbols
represent the data of interface-Si after removing the delaminated portion of the SiC film.
The dotted line represents the data of the Si substrate that was underneath the shadow
mask during deposition.

81

When the Hall voltage of two-layer structure such as SiC/Si is measured, the Hall
voltage of the SiC film need to be extracted from the measured data. This section presents
a model that deals with two layers with a resistive interface between them.

Fig.5.20(a) shows a schematic diagram of a symmetrical two-layer sample prepared
for Hall voltage measurement using van der Pauw method. The equivalent circuit of this
sample during the application of a magnetic field perpendicularly to the surface of the
sample. The input current I AC is applied between A and C. The effective Hall voltage of
both layers is measured between B and D. As shown in Fig.5.20(b), R, and V, represent
the resistance and Hall voltage of the upper layer, respectively, whereas R2 and V2
represent those of the lower layer. The interface resistance coupling the two layers
together is represented by R3 and R,. If the interface is homogeneous, R3 will be equal
to R,.

If the two layers are not identical, the Hall voltages developed within each layer
will be different (i.e. V,¢V2) leading to a current flow between the upper and lower layers
through the interface. This current is negligible for very large values of R3 and R,
compared to R, representing a case of well isolation of the upper layer (p-type and n-type
layers with nonleaky p-n junction). Large current flows through the interface if R3 and R4
are very small compared to R, representing a case of a conducting interface (two n-type
layers with different resistivities). Intermediate current flows through the interface if R3
and R4 are comparable to R, corresponding to a case of leaky p-n junction when it is

reverse-biased. This p-n junction becomes conducting if it is forward-biased.

82

 

 

 

 

 

 

 

 

 

 

I I
I I
B C
Cb)
UPPer Layer (Hype)
E R1 : D
Interface 5: R, 5: R,
R, ' : +

 

Lower Layer (n-typc)

Fig.5.20 (a) A schematic of the sample used for Hall voltage measurement with 4 metal
contacts at the corners of the sample. (b) Equivalent circuit of (a).

83

Using the equivalent circuit of Fig.5.20(b), the effective Hall voltage is given by

= V1 [R21'1‘-"3+R‘1:I “V2 [R1]

V
DB R1 +R2 +R3 +R4

(5.10)

 

The applied current IAC splits between the upper and lower layers as I, and 12,
respectively, with their values being dependent on the resistance of both layers and that
of the interface. The ratio of these currents can be obtained using the equivalent circuit

of Fig.5.20(b) with zero magnetic field (V,=V2=0) as

A=—l=—‘"‘—i—i, ...(5.11)

The Hall voltages of the upper and lower layers are given by

 

_ BI A
VI-EWRHJI I I I (5.12)
and
_ BI A
V2_—d-2_' A+1RHZI I I I (5.13)

where B is the applied magnetic field. d, and d2 are the thicknesses of the upper and
lower layers, respectively. RH, and RH2 are the corresponding Hall coefficients.

Substituting Eqs.5.l l-13 into Eq.5.10 leads to

 

R3112_R32

d d2
VD=BI 1 . 5.14
D (1+1), ( )

Since the thickness and Hall coefficient of n-type Si and the thickness of the B-SiC film

are known, the measured Hall voltage can be fitted with Eq.5.14 to obtain the Hall

84

coefficient R,,, of the B-SiC film. It was not possible to fit the measured data using this
model. This might be due to using a temperature independent interface resistance (R3 and
R4) and ignoring the p-type silicon thin-layer on top of the n-Si substrate. This model
needs to be developed in order to include voltage and temperature dependent resistance
to represent the nonlinearity of the p-n junction.

The possibility of extracting SiC data from sandwich measurements is enhanced
by considering "spreading resistance" effects. These effects require model like that in
appendix which provides a more accurate estimate of 71.

The measured resistance of a multiple-layer structure can be calculated using van

der Pauw method (see chapter 4 for details) as

R1

 

p=Y( £12,) f(%), ...(5.15)
1

where y is the thickness correction factor, R, and R2 are the measured transfer resistances,
and f(R2/R,) is a known correction factor for symmetry. For single layer structures,
y=(1td/ln2) where d is the film thickness.

As shown in the appendix, this correction is given by:

y: , ...(5.16)

mls

where E is the applied potential at two adjacent contacts (E=I/0' where I is the applied
current and o is the conductivity) and V is the potential at the other two contacts

calculated using the model in the appendix.

85

In case of SiC/Si structure, the resistance (or resistivity) of the Si substrate is
known and that of the interface can be treated as a parameter. One way to model the
resistivity of this interface is to consider it as an intrinsic or doped layer of a
semiconductor. By varying the bandgap and d0ping level of this layer, the interface
resistivity varies. The measured resistance of the SiC/Si structure can be fitted now to
obtain the resistance of the SiC layer. The results of the fit show that the resistance of the
SiC film dominates (RS,C«R5,) below room temperature whereas the Si substrate dominates

above room temperature.

5.4 Summary

Measured conductivity and Hall coefficient of polycrystalline SiC films deposited
on quartz by laser ablation of SiC targets showed strong temperature dependence even at
carrier concentrations in excess of 102°cm‘3. Phenomenological analysis produced three
well separated activation energies, high carrier concentration and low mobility over the
whole temperature range. Fits of the high temperature data of the films that show
effective carrier concentrations in the order of 1020 cm'3 at high temperatures require
unacceptable donor densities (i.e. ~1022cm’3). Hopping mechanism does provide a
reasonable explanation for films that show effective carrier concentration in the order of
lO'S’cm'3 but with exaggerated donor densities. For those films hopping process seems to
be associated with the intermediate energy level E2 with the smallest activation energy E3

being the hopping activation.

86

The resistance and Hall voltage data of the 3C-SiC heteroepitaxial films grown on
Si substrates show that the Si substrate dominates conduction for temperatures larger than
room temperature. The electron concentration of a-SiC substrates varies between 10‘2cm'3
and 2><10'8cm'3 in a temperature range of 50-800 K. Our Hall measurements of a-SiC
showed for the first time a very shallow activation energy of 5 meV which seems to be

responsible for impurity conduction.

CHAPTER 6

SEEBECK COEFFICIENT OF SiC

6.1 Introduction

SiC has strong potential for sensors operating at high temperatures and in
chemically aggressive environments such as those prevailing in automotive and jet
engines“. The progress that has been achieved in bulk and thin-film SiC preparations, n-
and p-type doping, and 8102 growth coupled with some degree of compatibility between
SiC and Si technologies makes SiC an attractive material for microsensor applications.
In particular, thermal microsensors which utilize the Seebeck effect to measure nonthermal
signals are very promising due to both their reliability and functional simplicity. In this
case, a nonthermal signal such as heat transfer rate, gas flow velocity, pressure, kinetic
energy and radiant energy is first converted into an on-chip temperature gradient inducing
an electrical signal that can finally be measured'”.

Metal or alloy thermocouples and thermistors are most frequently used to measure

132

the temperature. Metal or alloy thermocouples have large temperature range (-240 to

2300°C), linear response, and low sensitivity whereas thermistors90“"2"33'134 have lower

87

88

temperature range (-100 to 900°C), nonlinear response, and high sensitivity.
Semiconductor thermistors such as diamond also have been investigated. Although
diamond thin film thermistors have high sensitivity and fast response time, they suffer
from oxidation problem at temperatures above 600°C”. Other types of temperature
sensors show either poor sensitivity (resistance temperature detectors) or very limited
temperature range (IC sensors).

Most of the surface heat flux measurement techniques suffer from slow response
times which do not allow the measurements of transient heat fluxes. In addition, heat flux
gages might cause surface disruptions leading to significant flow and thermal disturbances.
These disturbances are compounded when gage cooling is required at high temperatures.

Higher response times and less surface disruptions have been obtained using thin
film technology. In this case, a thin metal film is deposited on a material surface where
the transient heat flux is measured by measuring either the dissipated power in or the
resistivity of the film. To measure the dissipated power, an external current is passed
through the thin film which is maintained at a constant temperature using a feedback
control system such as a constant temperature anemometer controller. This technique
suffers from a limited frequency response (i.e. below 100Hz)”8. In addition, the transient
response of the gage might be degraded if the resistance of the gage does not cover the
entire gage surface”. Using thin film technology a layered heat flux microsensor has been
recently developed'”. The total thickness of this gage is less than 2 pm and its time

I36

response is, approximately, 20 usec . Therefore, this microsensor can be used to measure

both transient and steady components of the heat flux.

89

There is current interest in developing temperature and heat flux sensors that have
large temperature range, linear response, high sensitivity, fast response time, and high
chemical stability. As the Seebeck emf of semiconductors is higher and the response time
for thin-film temperature sensors is faster than that of metal and alloy combination, it is
important to determine the possible advantages of using SiC thin films as the active
material for thermoelectric temperature sensors. There have been some reports about SiC
temperature sensors based on the measurement of SiC resistance”92 but there have been
no reports about the measurement of SiC Seebeck coefficient versus temperature.

In this chapter, measurements of the Seebeck coefficient of polycrystalline B-SiC
films and monocrystalline a-SiC substrates in a temperature range of 300-533 K are
presented for the first time. It is found that Seebeck emf of the B- and a-SiC is larger
than that of the standard platinum thermocouple. Application to temperature and heat flux

sensors and thermoelectric generators is investigated.

6.2 The Seebeck Coefficient

When a temperature gradient is established along an extrinsic semiconductor slab
(film), corresponding gradients in the carrier concentration and diffusion coefficient
usually appear in the same direction. Carriers (either electrons or holes) in the presence
of this temperature gradient will diffuse from the hot to the cold ends under open circuit
and will establish an electric field which tends to force carriers motion in the opposite
direction. At equilibrium, the flux of carriers caused by this field is equal to that caused

by the diffusion process. Although the number of carriers passing through any cross-

90

section of the semiconductor in a unit time in both directions are equal, carriers coming
from the hot end will have higher energies than those coming from the cold end.

Phonons and charge carriers contribute to the continuous transfer of heat from the
hot end to the cold one. However, heat is mainly transferred by phonons in SiC in the
temperature range of interest due to its high thermal conductivity'”. Since measurement
of the Seebeck emf is a steady state measurement, heat conductivity does not matter.
However, phonons may contribute to the Seebeck emf by dragging a larger number of
electrons from the hot end to the cold end. This drag effect was discovered by Gurevich
in metals'”. In semiconductors, phonon contribution to the Seebeck emf is negligible in
the transition and intrinsic ranges compared to the electronic contribution. This drag effect
has very large values below room temperature at least in Si and Gem'm. For example,
the contribution of this effect to Seebeck coefficient in Si at temperatures of 100K and
300K is as large as 6 mV/K and 0.43 mV/K, respectively.

If an intrinsic semiconductor (concentrations of electrons and holes are equal) is
subjected to temperature gradient, still an electrical field will be established due to
differences in the effective masses, energies and mobilities of electrons and holes,
respectively. In this case, more electrons than holes diffuse toward the cold end due to
the higher electrons mobility establishing an electrical field that accelerates the holes and
decelerates electrons. This process continues until the drift and diffusion currents of holes
and of electrons all add up to zero leading to equilibrium. As shown in Fig.6.], the

potential (Seebeck emf) that appears between the hot and cold ends is equal to qV where

91

 

T T+AT

 

Fig.6.] (a) Top view of the sample under test showing the metal contacts and the
thermocouples with T being the lower end temperature and AT being the temperature
difference between the two ends. (b) A schematic of the band diagram of the sample
showing the electrical field E and the Seebeck emf (i.e. qV).

92

q is the electron charge. The Seebeck coefficient is defined as the potential difference
between the two ends per 1°C.

Assuming that electrons are the sole carriers that contribute to the Seebeck emf
(n-type semiconductor) and the mean free time between carrier collisions I can be

expressed as t~E" where E is the carrier energy, and s=l/2 for phonon scattering and S:-

l22 l22,123

3/2 for ionized impurity scattering , the Seebeck coefficient Q can be evaluated as

 

=_1t2k kT i_i
Q —q (—Ep)(2 38), ...(6.1)
and
=_£ 2- =__§ §__EF
Q ql2 s+ln<NC/n)] q[2 s kT], ...(6.2)

for degenerate and nondegenerate cases, respectively. n and u, are the concentration and
mobility, respectively, of electrons in the conduction. EF is the Fermi level location
relative to the bottom of the conduction band edge E, with the assumed condition of
(EF/kT))0 for Eq.6.l and the Boltzmann distribution for Eq.6.2. T is the absolute
temperature, h is the Planck constant, k is the Boltzmann constant and q is the electronic

charge. The density of states in the conduction band is given by‘22

21:ka
N =2 (———’i—)3/2M

c 122 c ...(6.3)

where m, is the density-of-state effective mass for electrons and M, is the number of

equivalent minima in the conduction band which is equal to 3 for SiC. If holes in addition

93

to electrons contribute to conduction, Eq.6.2 has to be modified in order to obtain the net
contribution of electrons and holes to the Seebeck coefficient. The measured Q can be
used to determine the Fermi level location EF relative to the bottom edge of the
conduction band E, and consequently the carrier concentration in the conduction band can
be determined.

The sign of the measured Seebeck coefficient can be used to determine the
conduction type of a semiconductor. However, if the semiconductor is highly
compensated, there is a possibility of obtaining the incorrect sign of Q within a certain
range of temperature depending on the effective masses, mobilities and relative
concentrations of holes and electrons. The Seebeck coefficient for metals and degenerate
semiconductors is highly reduced compared to nondegenerate semiconductors since it is
assumed that i(E,./kT)»l. When mobility of electrons is much larger than that of holes as
it is in SiC, electrons become the major contributor to the Seebeck emf with its value

being dependent on the concentration and effective mass of electrons.

6.3 Results and Discussion

The measurement technique of the Seebeck coefficient is explained in chapter 4.
F ig.6.2 shows measured Seebeck coefficient versus temperature for some polycrystalline
3C-SiC (hollow symbols) and some monocrystalline 4H-SiC and 6H-SiC samples (solid
symbols) in a range of 27-260°C. These values of the Seebeck coefficient range from -9
to -30 uV/°C for the cubic samples and from -108 to -20 uV/°C for the hexagonal

samples. The Seebeck coefficient shows n-type conduction for all samples which is in

94

 

 

 

 

_; 0 -I I I I I I I T I r I I I I I I j -
e> : I I l 2
'c L I.
a '20 - I o 0 °9 3’ I33 . -
a: _ w v V. a
m t v _
B _ O _

-40 — O _
2 : o :
2 Z I
a: - — _
E- 60 _ fl
0 - I l94C d
1:: - O V 164A ‘
A - ..
g -80 :- O 0 14013 -—_
E _ O sample6 (4H) -
a: I 0 sample1 (6H) I
r$3400 _— O sample5(6H) f
[— "1 1 O 1 1 1 1 L 1 1 1 1 i 1 1 1 1 '1

300 400 500 600

LOWER END TEMPERATURE (K)

Fig.6.2 Measured Seebeck coefficient for three polycrystalline 3C-SiC films (solid
symbols) and three hexagonal samples (hollow symbols) .

95

agreement with the conduction type obtained from Hall measurements in this temperature
range.

The Seebeck coefficient of the monocrystalline hexagonal samples is higher than
that of the polycrystalline 3C-SiC samples near room temperature. However, as
temperature increases the absolute value of the Seebeck coefficient of the hexagonal
samples decreases due to the increase in the electron concentration and approaches that
of the polycrystalline samples. The hexagonal sample A with the highest electron
concentration (~10‘9 cm'3 at 23°C) has the lowest Seebeck coefficient of -30 uV/K
compared to -80 uV/K and -108 uV/K for samples E (~10'7 cm‘3 at 23°C) and D (~1016
cm’3 at 23°C), respectively.

Analysis of the measured Seebeck coefficient data coupled with the analysis of the
Hall data is crucial in understanding the electronic properties of SiC for sensor
applications. The phonon drag effect is negligible in our case since as we will see the
measured Seebeck coefficient can be fitted assuming only electronic contribution (using
Eq.6.2 with n being the measured Hall electron concentration).

Since the electron concentration of the polycrystalline B-SiC films is as large as
1018 cm'3 even at 20 K, these films might be degenerate. If this case, so. Eq.6.l can be
used to obtain the location of EF. As the measured Q ranges from -9 to -30 uV/K, Eq.6.l
leads to (BF-E,) in a range of 17-50 kT for phonon scattering and 33-100 kT for ionized
impurity scattering.

Using Fermi distribution, the carrier concentrations in the conduction band 11 for

the above locations of the Fermi level are found to be in the range of (l - 4)><102| cm'3

96

and (4 - 10) XIO‘” cm'3 for phonon scattering and ionized impurity scattering,
respectively, in a temperature range of 300-550 K. These values of carrier concentration
are one order of magnitude larger than the ones obtained from the Hall data and they
require donor densities in the range of the atomic density of SiC (i.e. 9.7><1022 cm”). As
the conduction process seems to be predominately within the grains (chapter 5) and since
x-ray-diffraction studies indicate the crystalline structure of our films within the grains,
the possibility of having degenerate SiC films has to be excluded'“.

The Fermi level EF location for samples of Fig.6.2 is estimated at 300 K using
Eq.6.2 with s=l/2. For the polycrystalline samples, EF-E, ranges from -l.7 kT to -l.9 kT
(~-45 meV at 300 K) whereas for the hexagonal samples it ranges from -l.42 kT to -
1.92 kT (from -27.6 meV to -42.9 meV at 300 K) as shown in Table 6.1. Boltzmann
approximation can be used as long as (E,-E,.)»kT. For the polycrystalline samples,
Boltzmann and Fermi statistics were used with the obtained results in both cases being
very close. The values of EF obtained from the measured Seebeck coefficient and the
electron concentration 11 obtained from the measured Hall coefficient RH as l/qRH can be
used to estimate the quantity m,/m,, where m, is the density-of-states effective mass and
m, is the free electron mass, by fitting 11 with N,exp(-E,./kT). For sample D, EF-E, ranges
from -0.74 kT to -1.92 kT in a temperature range of 300-533K and thus Fermi statistics
is used in the fitting.

At 300 K, the obtained values of mn/m, are shown in Table 6.1. These values are
different from the ones determined by cyclotron resonance measurements for single

crystalline B-SiC (mu/m,=0.346) and a-SiC (mn/m,=0.45)88. For B-SiC samples and 6H-

97

Table 6.1. The electron concentration n=l/qR,,, Fermi level location below E, and
effective mass estimated at 300 K for some polycrystalline B-SiC and a-SiC
monocrystalline samples.

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample 11 EF-E, mn/m,
(c133) (meV)

a-SiC: sample 1 (6H) 1><10'9 -42.9 0.787
sample 5 (6H) 6XI0'° -19.2 0.0156
sample 6 (4H) 2x10” -27.6 0.0391

B-SICI 1403 1 x1019 -48.6 0.912
164A 1 x1019 -43.2 0.794
1949 1x10” -45 0021

 

SiC (sample A), having a large effective mass (mn/m,=0.787 to 0.912) might be due to
the very large donor/defect concentration ()1020 cm"). In addition, the anisotropy of the
a-SiC crystals might lead to variations in the measured values of the effective mass.

For sample 1 (6H-SiC) and sample 6 (4H-S1C), the estimated effective mass values
mn/m, are 0.0156 and 0.0391, respectively. These values are much lower than the
measured one for a-SiC (m,/m,=0.45) and this might be caused by the anisotropic a—SiC
crystal where the effective mass varies between the basal plane of the crystal and the c-
axis'39'”°. This means that the angle between the temperature gradient along the sample
and the c-axis affects the values of the measured Seebeck coefficient and the effective
mass.

The analysis of the Hall data of the polycrystalline 3C-SiC films (see chapter 5)

shows that the electron concentration obtained as l/qR,, might be exaggerated. Therefore,

98

using such electron concentrations in fitting the measured Seebeck coefficient will lead
to a high estimate of the effective mass (m,/m,=0.79 to 0.91) as shown in Table 6.1. In
this situation, the measured Seebeck data can be used to estimate the electron
concentration assuming that the electron effective mass is known. Fig.6.3 shows the
estimated electron concentration for some polycrystalline 3C-SiC films using Eq.6.2
assuming that the effective mass of electrons is equal to that of single crystalline B-SiC
(mn=0.346m,) and phonon scattering is predominant (s=1/2). The obtained electron
concentration increases monotonically with temperature and is in the range of 2X10”-
7><10'8 cm'3.

The activation energy E, obtained from the calculated electron concentration of
Fig.6.3 is, approximately, equal to 54 meV. Correcting the data of Fig.3 for the T3’2
dependence of the density of states leads to an EszO meV. This activation energy agrees
with the obtained value of E, from Hall data (chapter 5) and is very close to the binding
energy of nitrogen (i.e. 53-54 meV) reported in earlier studies of monocrystalline SiC’“.
This result might indicate that measured Seebeck coefficient can be used to'obtain the
carrier concentration in the conduction band in cases where Hall data provides an

exaggerated one.

99

 

 

 

 

A - I I I I I I I T I I I I I I I I I I I _
E ' v ‘
Z 1020 _ . V .' ‘ . ‘—
O : 2
Id -- -1
g : :
E ' El 194C d
8 r v 164A ‘
O 1403
Z __
8 1019 :— Z
: O I
Z ~ 53 o r
3 : °® a ‘
1. °E .3
U ,_ —
m
:1 1018 1 1 1 L I 1 1 1 L l 1 1 1 1 i 1 1 1 1
1.5 2.0 2.5 3.0 3.5

1000/T (K')

Fig.6.3 The measured (solid symbols) and calculated (hollow symbols) electron
concentration of 3 polycrystalline SiC samples. The calculated electron concentrations are
obtained from the measured values of Seebeck coefficient using Eq.6.2.

100

6.4 Applications
6.4.1 Thermoelectric Temperature Sensor

Metal-alloy thermocouples measure temperature by measuring the Seebeck emf
between two junctions where one junction is held at a known reference temperature such
as room temperature and the other junction is exposed to the unknown temperature. Each
junction consists of two metals (or alloys) that have different Seebeck emf values. If the
Seebeck emf values of the two metals are the same, both emfs generated between the two
measuring leads will cancel out and the net emf detected will be zero. This means that
the difference in the work functions of the two metals at one junction relative to that at
the reference junction (A¢(T)—A¢(T,,,)) is used to measure the Seebeck emf. The measured
Seebeck emf between two ends coupled with a reference temperature such as the
temperature of the cold end can be used to obtain the unknown temperature of the other
end.

The Seebeck emf E(T) of thermocouples and semiconductors reflects their potential
for temperature sensors. F ig.6.4 shows the obtained output voltage E(T) of some
polycrystalline B-SiC and monocrystalline a-SiC and that of a platinum thermocouple (Pt-
lOIr versus Ptm). The Seebeck voltage E(T) of SiC is obtained by integrating the Seebeck
coefficient Q(T) over the corresponding temperature range assuming T,,,=300 K.

a-SiC has higher Seebeck emf compared to B-SiC and platinum. Two B-SiC
samples show higher Seebeck emf than that of the platinum thermocouple. This indicates
that SiC has a good potential for temperature sensing at least in a temperature range of

300-533 K.

10]

 

 

 

 

 

 

100 I I T I I I I T I I I I I I l I I I I I . I I-I
: Pt :
- 0 1403 ~
’ (Q O V 164A ‘
.— 0 ..
A (p O O I l94C
> " -1
E
h-
E Q S; O
o 10 ~— 63 1
a: . g -
u _ -
1:3 - .
a - .
a: I 0 A (6H) .
m I'
l O D (6H) -
_ O E (4H) -
1 1 1 1 1 J 1 1 1 1 l L 1 L 1 l L 1 1 r I 1 1
200 400 600 800 1000

TEMPERATURE (K)

Fig.6.4 The absolute value of the Seebeck emf for B-SiC (solid symbols) and a-SiC
(hollow symbols) and a platinum thermocouple'z“.

102

6.4.2 Heat Flux Sensor

Heat Flux sensors measure the heat transfer per unit area that usually takes place
between two materials if their temperatures are different. The application of this sensor
is limited to the case where one material is a solid body such as a metal plate and the
other one is a fluid material such as water or air. The sensor is usually placed at the
surface of the solid material. Measuring the gradient of temperature at the surface
provides information about the heat flux if the appropriate analytical model is used.
Therefore, the resistivity or Seebeck effect of SiC can be used to obtain the temperature
and thus the heat flux.

There are three modes of heat transfer: radiation, conduction, and convection.
Radiation heat transfer occurs when heat is transferred through electromagnetic radiation
with no need for a material medium. Heat transfer by conduction occurs when a
temperature gradient exists within a material. The heat flows from the high-temperature
region to the low-temperature region. Convection heat transfer takes place when a moving
fluid contacts the surface of another material. In this case the rate of heat transfer depends
on the velocity of the fluid. The velocity of the fluid is reduced to zero at the surface of
the material due to viscousity. Thus the heat is transferred only by conduction at the
surface. Since heat transfer rate and temperature gradient below the surface depend on the
velocity of the fluid, measurement of the heat transfer at the surface gives not only the

conduction heat transfer but the overall convection heat transfer.

103

The overall heat flux is given by Newton's law:

q=h (Ts-T1.) +qmd, . . . (6 .4)

where h is the convection heat-transfer coefficient. (T,-T,) is the temperature difference
between the surface and the fluid. The radiation heat flux qrad is usually negligible
compared to convection heat flux and can be ignored. A direct measurement of the heat
flux requires measurement of the temperature difference (T,-T,). Measuring the
temperature only at the surface leads to indirect measurement of the heat flux using the
appropriate analytical model.

A layered heat flux microsensor with a fast response time has been recently
developed'”. Heat flux is obtained directly by measuring the temperature difference
between the surface and the flowing fluid above it (T,-T,). This microsensor consists of
a thin thermal resistance layer sandwiched between two temperature sensors. Each
temperature sensor consists of two thin metal strips which overlap at the middle of the
resistor's width forming one thermocouple. These two thermocouples (i.e. above and
below the resistor) are connected in series outside the resistor to obtain the temperature
difference across the resistor.

The layered heat flux microsensor suffers from some problems. This microsensor
consists of five layers, one thin film resistor layer sandwiched between two thermocouples
where each thermocouple consists of two layers. Since the heat flux passes through the
gage itself into the surface of the material, flow and thermal disruptions result. These
disruptions can not be eliminated completely but can be minimized significantly by

reducing the thickness of the sensor which in turn improves the time response. For

104

thicknesses above 25 pm, the time response of the layered heat flux microsensor is larger
than 20 ms'“ and for thicknesses less than 1 pm, the time response is less than 100 115'”.

Since SiC can be used for high temperature applications, its thin film technology
is well developed and its Seebeck coefficient is higher than that of metal thermocouples,
investigating simpler structure of this microsensor to improve its performance utilizing
thin film SiC technology is of interest. Our proposed structure has not been fabricated,
however, it is discussed here in order to highlight its potential for a better performance.

The new structure uses many pairs of n- and p-type SiC cells connected serially
as shown in Fig.6.5 in order to obtain a larger output signal. This is also the structure of
a thermoelectric generator (see next section). In this structure only three layers are needed
compared to five layers in the original structure. Having only 3 layers leads to a smaller
thickness and thus thermal and flow disturbances are reduced. In addition, a thin layer of
an insulating material that has a high thermal conductivity such as undoped polycrystalline
diamondM3 can be deposited on the bottom and the top of this microsensor. This leads to
homogeneous distribution of the temperatures T, and Tf on the top and the bottom of the
microsensor, respectively, and thus to a more accurate measurement.

The fabrication of this proposed structure requires only 4 major steps using laser
ablation technology (see chapter 5). Firstly, a patterned metal layer is deposited using a
shadow mask. Secondly, p- and n-SiC layers are deposited in sequence using appropriate
shadow masks to obtain the p-type and the n-type cells. Thirdly, an insulating layer is
deposited between the n- and p-type cells. SiC is insulating if deposited at room

temperature and thus can be used for deposition between cells. Finally, a patterned metal

105

Meta] contacts

T... //
/.

/

 

n-SiC p-SiC

 

 

 

 

 

 

 

low

Fig.6.5 A schematic of n- and p-SiC cells connected serially. This schematic represents
either a thermoelectric generator with Th,g,,-T is large or a heat flux sensor with T1031:
T =AT is very small.

low

low

106

layer is deposited on the top of the structure.

The fabrication process of this structure is easier than that of the original structure
since the former has less number of layers. Laser ablation technology, in particular, can
be used for in-situ deposition of the metal layers and the SiC layer. In this case, the high
energy of the ablated plume usually leads to better adhesion between the deposited metals
and the SiC film compared to other techniques. Moreover, the Seebeck emf signal of SiC

films is usually larger than that of alloys and metals at least at high temperatures.

6.4.3 Thermoelectric Generator

A thermoelectric generator utilizes the fact that the Seebeck effect allows the
generation of electrical power from thermal power. A thermoelectric device consists of
a serial connection of cells as these of Fig.6.5. These cells might be made of similar or
different semiconducting material. A metal contact at the top connects both cells. At the
bottom, a metal contact is attached to each cell separately as shown in Fig.6.6. This
device can work as a current generator or as a cooling couple. If a temperature difference
(ngh-wa) is maintained between the two ends of the device, this device will function as
a voltage generator. On the other hand, if a current is externally supplied through this

device, this device will function as a cooling couple.

107
The ratio M of the optimum load resistance R, to the internal resistance R,- of the

device will be given by126

R
59:12,: [14”; (Thigh—T103!) ] 1/2’ ' ' ' (6 '5)
1

where Z=Q20/K, o is the electrical conductivity, K is the thermal conductivity and Q is
the Seebeck coefficient. If load resistance is equal to R,, a current I flows in the circuit
leading to maximum transfer of electrical power (I2 R,).

The ratio of electrical power lost in the optimum resistance R, to the thermal
power supplied at the heated end is defined as the efficiency. Assuming that both cells

have the same properties (i.e. o, x, and. I Q I ), the efficiency of a thermoelectric generator

is given by'mI27

Thigh- Tlow M—l

, . . . (6 .6)
Thigh M+ [Tlow/ Thigh]

 

n:

The efficiency 11 of a thermoelectric generator increases as the Seebeck coefficient
and the ratio of electrical to thermal conductivities (i.e. o/K) of the material increase.
Since the ratio O/K for metals is five orders of magnitude higher than that for SiC, the
potential of having an efficient SiC thermoelectric generator is weak.

Table 6.2 shows 0, Q, 1:, Z, and 11 of monocrystalline 4H- and 6H-SiC,
polycrystalline 3C-SiC and some other materials that are used for thermoelectric
generation. Since K for our polycrystalline SiC films has not been measured, the
efficiency of these films is calculated using the thermal conductivity of monocrystalline

SiC. This might lead to a smaller efficiency since thermal conductivity of monocrystalline

108

Table 6.2. Properties of some materials for thermoelectric generation applications. 1] is

 

 

 

 

 

 

calculated using Th,,,,=600K and T,,,,=300K.
Material 6 IQ I K Z 11
(Q'lcm'l) (uV/K) (w/cm K) (K')

Metals'25 105-10° 10 0.2-4.0 55 ><10“4 (1.2%
Boron 400 320 0.05 8.2x 10" 1.9%
Carbide'26

4H-SiC l 80 5 l.28><10'9 3.2><10'°%
6H-SiC 1-100 110 5 2.42><10'7 6.1><10“°/o
3C-SiC 30 10-30 , 5 5.4x10'9 1.4x10'5%

 

 

 

 

 

 

 

 

materials is usually higher than that of polycrystalline materials. However, even if thermal
conductivity of polycrystalline 3C-SiC films is two orders of magnitude lower than that
of monocrystalline films, the efficiency of our 3C-SiC films will be 3 orders of
magnitude lower than that of metals.

The efficiency of 6H-SiC is larger than that of 4H-SiC and 3C-SiC by at least two
orders of magnitude due to its high electrical conductivity and Seebeck coefficient.
However, this high efficiency is still two orders of magnitude less than that of metals.
Therefore, the potential of SiC for thermoelectric generators is not promising compared
to the other materials that are currently used (e.g. metals) or investigated (e.g.

semiconductors).

109

6.5 Summary

As the Seebeck coefficient of B- and a-SiC in temperature range of 300-533 K is
large their potential for temperature and heat flux sensor applications is excellent. Further
investigation of the Seebeck coefficient of SiC in a larger temperature range is needed
especially for applications at high temperatures. In addition, studying the effect of

anisotropy of a-SiC on the Seebeck coefficient will permit its maximization.

 

CHAPTER 7

SiC THERMISTORS

7.1 Intruduction

The change of resistivity with temperature of semiconductors can effectively be
used for temperature sensing through devices known as thermally sensitive resistors (i.e.
thermistors). Materials that are usually used to sense temperatures include metals, alloys,
insulators, and semiconducting materials such as compressed metal oxides, Si, diamond,
...etc. The magnitude of the sensitivity of metal oxides is larger by approximately an order
of magnitude than that of metals or alloys. Alloys usually have higher resistivities and
better physical properties compared to metals but these improvements are usually achieved
at the expense of reduced sensitivity. The platinum resistance thermometer is still a
temperature standard in range of 0-600°C‘23.

Thermistors (i.e. semiconductor-based temperature sensors) have a limited use as
compared to alloys-based temperature sensors in spite of their higher sensitivity. This is
due to some disadvantages related to the properties of the host material of the thermistor

compared to those of alloys. Those disadvantages include a limited temperature range (e. g.

110

111

Si), oxidation of the host material which prevents reproducibility of resistivity (e.g.
Diamond at T2600°C), and not withstanding high pressure that might change the structure
and thus the resistivity of the material (e.g. compressed metal oxides). Although the
resistance range of insulators is very high (i.e. 21010 (2), it is possible to use them as
temperature sensors at very high temperatures (T2600°C) as their resistance becomes
practically measurable. Since the available temperature sensors operate over limited
temperature ranges, it is of interest to investigate some other materials such as SiC that
can operate in harsh environments and over a wider temperature range.

In this chapter, the resistivities of polycrystalline and single crystalline 3C-SiC and
heteroepitaxial 4H- and 6H-SiC are discussed to determine the potential of these SiC
polytypes for temperature sensors. Among those materials, polycrystalline 3C-SiC films
showed a unique potential for temperature sensing over a wide temperature range of 13-

1277 K.

7.2 Resistivity of SiC

The resistivity of SiC is measured using van der Pauw method (see chapter 4).
Fig.7.] shows the measured resistivity of polycrystalline and single crystalline 3C-SiC and
monocrystalline a-SiC in a temperature range of 20-900 K. The single crystalline 3C-SiC
film (6000 A thick) was deposited on Si substrate using laser ablation technique (see
chapter 5 for more details). The measured resistance of the combined structure SiC/Si is
an effective resistance of both the SiC film and the Si substrate. The resistivity of this

SiC/Si structure is calculated from the measured resistance assuming that the thickness

112

 

 

 

105 _ . . . . , . . . - , . . . - , f ,
: ,3 V 152B (polycrystalline 3C- SiC) 3
105 F 0 307B (single crystalline 3C- SiC/Si) ‘;
D 0 sample E (4H-SiC) ‘
E 1 04 r C] sample H (6H-SiC) _:
q D 0 sample B (6H-SiC) j
E :0 :
5 103 E— j
.2 .02: i
z : ‘.   :
9 101 5 1:1 . ‘I
(I) E 3
Ii] 00 .. 1:] [I E] C]
O: O D *3. U D
1 O O O O O .5. p O
10‘ o 0 GD 0 0 I —.
w V V V V V
10-2........OQOOOOQ'..OO

 

0 200 400 600 800
TEMPERATURE (K)

Fig.7.] The resistivity of some B-SiC (solid symbols) and a-SiC (hollow symbols).

113

is equal to the sum of the SiC film and Si substrate thicknesses (~0.04 cm).

The resistivity of polycrystalline B-SiC decreases monotonically with the
increasing temperature over the entire temperature range whereas the resistivity of the
single crystalline B-SiC decreases with temperature in general but sometimes increases
slightly with temperature over short temperature ranges. The resistivity of a-SiC decreases
with the increasing temperature for TS3OO K and increases as temperature goes above
300 K. In the low temperature range (i.e. below room temperature), a-SiC resistivity
varies over a wider range (10"-106 Qcm) compared to single crystalline B-SiC (~101
(2cm) and polycrystalline B-SiC (~10'l Qcm). In the high temperature range, single
crystalline B-SiC (307B) has strong temperature dependence (10"-102 (1cm) whereas all
other samples have weak temperature dependence. This might be due to the low resistivity
of the Si substrate which shorts the SiC film at high temperatures.

The resistivity of all a-SiC samples shows strong temperature dependence below
room temperature whereas weak temperature dependence is obvious above room
temperature. Sample B, in particular, shows weaker temperature dependence than the other
two samples. This might be due to the large carrier concentration (~1018 cm‘3 at 300 K)
of this sample compared to that of the other two samples (10‘6 and 10‘7 cm‘3 for samples
H and B, respectively, at 300 K).

Fig.7.2 shows two cycles of the resistivity of some polycrystalline B-SiC films in
a temperature range of 13-1277K. The hollow symbols show the cycle that starts from
the low temperature and goes to the high temperature whereas the solid symbols show the

cycle that goes from high to low temperatures. The resistivity of these films has stronger

114

 

#IIIWTIW—TIIIIIITIIIIITTITITIIITIIIll

 

)— -4
A V O 1523
g V 193A
5 0.10 ~37 :-
E _
2. ..
[_ _
m
a _
In]
a: _

 

 

 

 

0.011111i1111i111111111i1111i1111i1111
0 200 400 600 800 1000 1200 1400

TEMPERATURE (K)

Fig.7.2 Two cycles of the resistivity of some polycrystalline B-SiC films.

115

temperature dependence at TSZOOK. Their resistivity is very low (0.01-0.4 (1cm)
compared to the single crystalline B-SiC and a-SiC samples especially at temperatures
below 200 K. This might be due to the large carrier concentration of these films even at
very low temperatures ()10'8 cm'3). Even though some films were not initially annealed,
the results were reproducible. The resistivity of the single crystalline B-SiC and or-SiC is
also reproducible in the entire temperature range.

Resistivity of SiC can be used in temperature sensing. An important figure-of-merit
of temperature sensors is their sensitivity to temperature change. This sensitivity can be

studied in terms of the temperature coefficient or defined as120

259
poT’

 

a = ...(7.1)

where p is the resistivity and T is the temperature. The temperature coefficient or is
suitable for sensitivity comparison of materials that have comparable resistance R values.
Otherwise, the quantity AR/AT can be used as a figure-of-merit.

Fig.7.3(a) shows the temperature coefficient or for the samples of Fig.7.]. All
polycrystalline and single crystalline B-SiC samples exhibit a negative or through out the
entire temperature range whereas a-SiC shows a negative or at low temperatures and
exhibits a change of sign near room temperature. This is not a desirable characteristic of
a temperature sensor since it limits its use to either the positive or negative temperature
range of at to insure obtaining a single calculated value of temperature for a single value

of measured resistivity.

116

 

 

 

 

 

 

 

 

 

0.02 I l l l I l l 1 l I l l I I I l 1 l 1

TE :
E- - .
E 000 5% v 1523(3c-51C)
g r O 193A(3C-SiC)
Ln - . . .
E: o“. O 3O7B(3C-SlC/S1)
8 002 V BE] .. LU sampleE(4H-SiC)
a ' - P6013 .‘ -0 sampleH(6H-SiC)
a [OCH . :0 sampleB(6H-SiC)
é - fl -
E -0.04 — —
E >— ..

._ . -
E-

R i

_006 l l l 1 i l 1 l l L l l l l i l l 1 l
0 200 400 600 800
TEMPERATURE (K)
A0.004_111U]111T8ED11111_
"E 5 [35b OED?) 8:ng
f: 0.002 :— Cl —_
E : O O O O :
.. — O O ..
2 0.000 ;— D ‘ ‘1
E: 5 . v';§""¥o°'o"o “ :
g -0.002 r:— v 0" ‘09 T:
U :o' ’ CI 0 :
g; -0 004 _—. v [3 O . -;
D Z O . I
E- _' Q ..
E E ‘ 0 a
:5 '0.008 5 . O . T:
E—_O_O1OE_1_91114111144111411:
0 200 400 600 800

TEMPERATURE (K)

Fig.7.3 (a) The sensitivity coefficient a for samples of Fig.7.]. (b) An expansion of the
data shown in (a).

117

In general, all samples show higher sensitivities at lower temperatures due to the
steep change in their resistivity at those temperatures. These sensitivities do not show any
scattering throughout the whole temperature range except for single crystalline B-SiC.
This scattering in sensitivity is not desirable and might be due to changes in resistivity
values of SiC-Si interface.

Fig.7.3(b) shows that the temperature coefficient for a-SiC at T23OOK (0.002-
0.004K'l for samples B and E) has a larger magnitude than that of polycrystalline B-SiC
(0.0005-0.002K"). Since or for the former material becomes very small and approaches
zero within a temperature range of 200-3OOK, the use of this material for temperature
sensing in this temperature range should be avoided.

Table 7.1 shows that or-SiC and B-SiC have temperature coefficients comparable
to those of platinum and tungsten. Therefore our polycrystalline SiC films can be a
potential alternative for the commercially available platinum and tungsten temperature
sensors since they have comparable sensitivity, negligible oxidation rate even at 1000°C,
chemical inertness to corrosive atmospheres, radiation immunity and excellent mechanical
properties. Hexagonal SiC suffers from a limited temperature range compared with our

polycrystalline SiC films which have negative or through out the temperature range.

118

Table 7.1. The temperature coefficient at at 300 K for some alloys, oxides, hexagonal SiC,
and polycrystalline SiC films.

 

 

 

 

 

 

Material or (/°K) Material 0t (/°K)
Platinum +0.0037 4H-SiC (sample B) -0.0015
Tungsten +0.0052 6H-SiC (sample B) -0.004

Nickel oxide -0.044 B-SiC (307B) -0.0l44
Manganese oxide ~0.044 193A (poly. [3-SiC) -0.0026
6H-SiC (sample H) +0.00014 1528 (poly. B-SiC) -0.0028

 

 

 

 

 

 

For comparison of sensitivity of other semiconductor temperature sensors, the
temperature coefficient of resistivity TCR is usually used. TCR is basically a crude

average of or over the specified temperature range (i.e. an-T) and defined asm

 

TCR_ 1 p(T)-p(T,,f)

1’0") (T—T,, , ...(7.2)

where p(Tmf) is the measured resistivity at a reference temperature, usually taken as the
lowest temperature in the operating temperature range of the sensor. p(T) is the measured
resistivity at the highest temperature T in that range.

Table 7.2 shows TCR for some polycrystalline 3C-SiC films over the entire
temperature range. The sensitivity of sample 1528 is one order of magnitude smaller than
that of 193A and 160A as shown in Table 7.2. Samples 1528 and 193A have comparable

carrier concentrations in the entire temperature range, comparable thicknesses (Table 7.3)

119

and large difference in their sensitivities (one order of magnitude). For sample 193A,
evaluating TCR over a narrower temperature range of 13-774 K leads to higher TCR
values since the sensitivity of polycrystalline B-SiC films decreases with temperature.
Since TCR exhibits a change of sign with temperature for a-SiC samples, it is
necessary to evaluate TCR in this case over a temperature range where sensitivity has no
sign change. Taking this range to be the high temperature range (i.e. above room
temperature) provides a possibility for us to compare our results with the published data
which is only available in this temperature range. Table 7.3 shows TCR for the
polycrystalline and single crystalline 3C-SiC, heteroepitaxial 4H- and 6H-SiC, and Si with

the corresponding temperature range and carrier concentration.

Table 7.2. Temperature coefficients of resistivity (TCR) of some polycrystalline 3C-SiC
samples evaluated over the corresponding temperature range.

 

 

 

 

 

Sample TCR (%/K) Temperature (K)
1523 (poly. B-SiC) 0.069 13-1277

160A (poly. B-SiC) 0.111 295-1016

193A (poly. B-SiC) 0.130 13-774

 

 

 

 

Table 7.3 shows that above room temperature the sensitivity of our polycrystalline
3C-SiC films is comparable (160A) or one order of magnitude less (1528 and 193A) than

that of Si. This difference in sensitivity might be due to an approximately three orders of

120

Table 7.3. Temperature coefficients of resistivity (TCR) of some polycrystalline and single
crystalline 3C—SiC films and heteroepitaxial 6H- and 4H-SiC samples evaluated over the
corresponding temperature range. Thicknesses and available carrier concentrations
obtained at room temperatures are also provided.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample TCR (%IK) Thickness Concentration Range (K)
(A) (cm‘3)

1523 (poly. B-SiC) 0.049 3500 1020 295-1277
160A (poly. B-SiC) 0.111 1200 295-1016
193A (poly. B-SiC) 0.092 3000 1020 293-774
H (6H-SiC) 0.202 1121 x10“ 5x1016 294-757

B (6H-SiC) 0.084 845.82x10‘ 6.8x1018 498-738

E (4H-SiC) 0.227 568.96x10‘ 3.2x10l7 314-735
3C-SiC* 0.091 10S »1017 623-823
Si“ substrate 0.72 10'7 300-923

 

*[lzll

 

121

magnitude variation in the carrier concentrations. These polycrystalline films have
comparable (1528 and 193A) or larger (160A) sensitivities than the single crystalline 3C-
SiC as shown in Table 7.3. In addition, they have a major advantage over Si and single
crystalline 3C-SiC since they can be used as temperature sensors over a much wider
temperature range with an acceptable sensitivity. The hexagonal samples show the same
potential but over a smaller temperature range compared to the polycrystalline 3C-SiC

films.

7.3 Summary

Polycrystalline 3C-SiC shows a negative temperature coefficient on over the entire
temperature range which permits its use for temperature sensing over a wide temperature
range (13—1277 K) with a single sensor. a-SiC exhibits a sign change in or in a
temperature range of 200-300 K which limits its use to either high or low temperature
range. The temperature coefficient of the single crystalline 3C-SiC shows some scattering
in a temperature range of 200-600 K which prevents its use as a temperature sensor in

that range.

CHAPTER 8

SUMMARY AND FUTURE RESEARCH

The objective of this research was to provide an understanding of the transport
properties of SiC films deposited by Pulsed Laser Deposition technique and to study the
potential of these films for temperature and heat flux sensors.

Conductivity and Hall measurements were conducted in a temperature range of 13-
800K. In case of polycrystalline 3C-SiC films deposited on insulating substrates, Hall
mobilities, carrier concentrations, and activation energies were obtained from these
experimental measurements using a phenomenological model. Furthermore, the low
transport data for polycrystalline 3C-SiC films were analyzed in terms of impurity/defect
band and hopping models were used for the first time. In case of heteroepitaxial 3C-SiC
films deposited on Si substrates, conductivity and Hall voltage models were used to
extract the conductivity and Hall voltage of 3C-SiC films from measurements on the 3C-
SiC/Si structure. In addition, data and analysis are also presented in chapter 5 for
commercially available 6H- and 4H-SiC substrate wafers.

The Seebeck coefficient was also investigated for polycrystalline 3C-SiC films and

122

123

monocrystalline 4H- and 6H-SiC wafers to determine the potential of these SiC polytypes
for thermoelectric generators and temperature and heat flux sensors. The measured
Seebeck emf of our polycrystalline SiC films is comparable or larger than that of platinum
thermocouple and thus has a good potential for temperature sensing as well as surface
heat flux sensing. However, polycrystalline SiC films show a weak potential for

thermoelectric generation compared to other materials.

8.1 Future Work

The Seebeck coefficient of polycrystalline 3C-SiC and monocrystalline a-SiC was
obtained over a limited temperature range and the results showed good potential for
temperature and heat flux sensors. Therefore, it would be interesting to measure the
Seebeck coefficient of SiC over a wider temperature range including investigation of
anisotropy for or-SiC polytypes. In addition, fabricating the proposed heat flux sensor
using SiC technology is of interest. Further development of the presented conductivity and
Hall coefficient models considering the nonlinearity of the p-n junction is needed to
extract accurately the conductivity and Hall data of the B-SiC thin film from the SiC/Si

structure.

APPENDIX

APPENDIX

Multiple-Layer Resistivity Model

In this model, it is assumed that we have a three-layer rectangular sample with
26,326, size. The thicknesses and conductivities of the top, intermediate, and bottom
layers are t,, t:, and t3, and 00, 0,, and 0'2, respectively. The current I is applied into the
top layer through rectangular contacts with 2c><2d size as shown in Fig.Al.

A two dimensional plots of the imposed field in the y and x directions are shown
in Figs.A2 and A3, respectively. A three dimensional plot of the same field is shown in
Fig.A4. Fig.AS shows the potential ¢(X,Y,Z=0) for the applied field of Fig.A4. The
amplitude of this potential varies between -0.1 and 0.1 for 00=01=02 and from -0.9 to 0.9

for 61:62 and (ol/o(,)=0.1, respectively.

124

 

 

 

 

   

 

 

 

 

 

125
7r
28,
AL
11 \l
l‘ ’l

28,.

Fig.A.l A top view of the sample used in our model. The two metal contacts are shown
in dark color.

126

The imposed field E,(X,Y) through the contacts at the top layer can be expressed
in terms of Fourier series in two dimensions as E,(X,Y)=F(Y)G(X). In the Y direction the
applied field F(Y) is an even function at both contacts whereas this field in the X
direction G(X) is an odd function at both contacts. Fig.AZ and Fig.A3 show Fourier
expansion of the imposed field in the Y and X directions, respectively, using 200 terms.

The imposed field E,(X,Y) is shown in Fig.A4.

 

.F- - {1.1-All.

 

E(Y)

 

 

 

 

L l J
‘1 '0.5 0 0 S 1
Y

Fig.A.2 A two dimensional plot of the imposed field in the Y direction at the surface (i.e.
Z=O)

127

 

(3in 0

 

 

 

 

Fig.A.3 A two dimensional plot of the imposed field in the X direction at the surface (i.e.
Z=0).

1’-

128

 

 

 

 

 

Fig.A.4 A three dimensional plot of the imposed field at the surface (i.e. Z=0).

129

 

   

 

 

 

Fig.A.5 A three dimensional plot of the potential at the surface (i.e. Z=0) assuming that
the conductivity of the three layers is the same.

130

Since the space charge is assumed to be zero, Poisson's equation reduces to

Laplace's equation:

v2¢(X,Y.Z)=0, ...(1)

where ¢(X,Y,Z) is the potential at any point, X=x/5x, Y—jI/Sy, and Z=z/5x. Solving this

differential equation by separation of variables leads to:

(b1 (X) =alsin(1cX) +blcos(1cX) , ... (2a)
¢2(Y) =azsin(lY) +b2cos(AY) , . . . (2b)
(1);, (Z) =a3exp(-yZ) +b3cos (yZ) . . . . (2c)

where K)», and y are constants with yz=1<2+23 Since the current is applied through one
contact and comes out of the other one, (1)1(X) and ¢2(Y) are odd and even functions of
X and Y, respectively, leading to bl=a2=0. Imposing zero current at the boundaries of the

sample (i.e. thi)l(:1:25x):0 and v,,¢2(125y)=0) leads to:

 

x=(2m+1)%-51;, .(3a)

1 112 by, . (3b)
’5 2 2

Y2=[ ((421721): +:2]1t2, ...(3C)
x y

where m and n are integers 20. The general solution of Laplace's equation can be written

as:

(,X Y, 2):;215’," nsin[ (2m+1)%X] cos(nrtY) , ...(4)

where

131

Fm,n-¢;,n<1)exp<y2) +¢;,n<1)exp<—ym, ...(5)

where l is the layer number and (V and (b' are constants that have to be determined in each

layer of the sample using the boundary conditions.

The electric field EZ=VZ¢ is:

EZ(X, Y, Z) =2 Hm’nsin[(2m+1)—123X] cos (nrtY) , . . . (6)
where
Hm”: 6 [(l),+,,,n(1) exp(yZ) -d),’,,,n(l) exp(-yZ)] , . . . (7)

X

The imposed field at the top layer E,(X,Y,Z=0) can be expressed in terms of

Fourier series as follows:

E, (X, y, 2:0) =DZAmsin [ (2m+1) gxl
m

+2 Amanin[ (2m+1) g—X] cos(nrrY) . . . (8)

17120 no

where

132

4sin [ (2m+1) gxo] sin[ (2m+1) go]
A = ...(9a)

- m I

(2m+1)-12-t
: 25in(nttD) . . . (9b)

12 '

I1“

 

R

 

where X0=x0/8x, C=c/6,,, and D=d/5y. For simplicity, it is assumed that the thickness of
the third layer of the sample is very large compared with these of the first two layers
resulting in ¢+(2)=0. This leaves us with 5 unknowns (i.e. d>+(0), ¢‘(0), ¢+(1), (13(1), and
<|>'(2)) to be determined by the boundary conditions. The 5 boundary conditions are:

at z=0, the imposed field E,(X,Y,Z=O) is equal to EZ(X,Y,Z=0).

at z=dl, the tangent field is continuous.

at z=d2, the tangent field is continuous.

at z=d,, the perpendicular current is continuous.

at z=d3, the perpendicular current is continuous.

Applying these boundary conditions lead to the following set of equations:

_61[¢;m(o)-¢;,'n(0)]=AmBn, . . . (10a)

[¢,;,n<0) exp(YT1) +<l>;,n(0) exp(-Y T1)] =
1012,).(1)exp(YT1)+¢£.,n(1)exp(-yT1)] , . - . (10b)

[¢;,n(l) exp<YT2) +<l>;z,n(1) eXP(-YT2)1 =
[<l>;.,n(2)exp(-yT2)1, ...(10c)

 

133

001(1),}...(0) exp<YT1)-¢;i.n(0)exp(-YT1H =
o1 10;,ntl) expo/T1) -¢;.,n(1) eXp(-YT1)1. . . . (10d)

01 [¢;,n(l) exp (7 T2) -<l>;z,n(1) exp(-Y T2) 1 =
[-02¢;,n(2)exp(-7T2)], ...(10e)

where T,=t,/5x and T3=t:/5x. Solving the above 5 equations leads to:

¢*(O) =(b‘(2) K‘exp(—2~{T1) , . . . (11a)
¢'(O)=¢’(2)K‘, ...(11b)
¢+<1>=—:-¢-(2)<1-—:3)exp<-2yrz), ...(llc)

¢~<1>=§0‘<2) (1+ :2

 

), ...(11d)

1

134

 

 

5..
(Amen) —-
¢‘(2)= Y , ...(1le)
K*exp(-2'yT1) -K‘
where
+_'_1_ O _O _
K ——4-[(1+—O—:) (1 B—jlexpmym T2))
+(1-$)(1+°2)], ...(12a)
(’0 1
-—1r —3l —3_2. —
K —Zt(l OO)(1 allexp(2y(T1 T2))
+(1+—°—1)(1+3%)l, ...(12b)
00 1

The solution of Laplace's equation is now complete. The thickness correction

factor is given by:

 

= Cd
C.F. ¢(—6x,6y,0)-<b(6,,,6,,.0)’ ...(13)

where 20d is half the area of the contact that supplies current into the whole sample.
Since the current density 0Ey(X,0,Z)=0, the total applied current splits in half between the
upper (i.e. y20) and the lower (i.e. y<0) portions of the sample. Thus our rectangular
sample can be considered as being composed of two square and separate samples.

This allows the calculation of current distribution in the three layers. Since the
intermediate layer is highly resistive, the current I] will be very small and negligible
compared to I0 and 12. Therefore, the current ratio 1:12/ I] can be calculated using this

model.

 

 

BIBLIOGRAPHY

BIBLIOGRAPHY

(1) TR Chow and Ritu Tyagi, "Wide Bandgap Compound Semiconductors for superior
High-Voltage Power Devices", in the 5th International Symposium on Power
Semiconductor Devices and IC's, page 84, 1993.

(2) G. Muller and G. Krotz, "SiC as a new sensor material", in The 7th International
Conference on Solid-State Sensors and Actuators, Yokohama, Japan, p. 948, 1993.

(3) E0. Jhonson, RCA Rev. 26(163), 1965.
(4) KW. Keyes, Proc. IEEE 60(225), 1972.

(5) J.A. Powell and LG. Matus, "Recent Development in SiC (USA)", in Amorphous and
Crystalline Silicon Carbide and Related Materials, Springer Proceedings in Physics Vol.
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(6) Z. Li and RC. Bradt, J. Amer. Cer. Soc., 70(445), 1987.

(7) R. Helbig, "Progress in New Materials for Power Electronics: SiC", in the 5th
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