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ELECTRICAL PROPERTIES OF THIN NANOCRYSTALLINE
DIAMOND BASED SCHOTTKY BARRIER DIODES AND
OTHER TWO-TERMINAL STRUCTURES

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ELECTRICAL PROPERTIES OF THIN NANOCRYSTALLINE DIAMOND BASED
SCHOTTKY BARRIER DIODES AND OTHER TWO TERMINAL STRUCTURES

By

Mitchell Douglas Parr

A THESIS
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Electrical and Computer Engineering

2005

ABSTRACT

ELECTRICAL PROPERTIES OF THIN NANOCRYSTALLINE DIAMOND BASED
SCHOTTKY BARRIER DIODES AND OTHER TWO-TERMINAL STRUCTURES

By

Mitchell Douglas Parr

Diamond possesses many unique characteristics that make it attractive for a
number of applications. Research in electronics has seen the development of diamond-
based devices over recent years but they have, for the most part, remained structurally
flat. This thesis presents a preliminary study on the fabrication potential of ﬂexible
diamond electronics. Undoped nanocrystalline diamond (nanodiamond) ﬁlms grown
from a microwave plasma-enhanced chemical vapor deposition (MPECVD) process
ranging from 0.25 — 1.0 pm in thickness were used in the fabrication of electronic devices
and current-voltage characteristics were investigated. Both freestanding nanodiamond
ﬁlms and substrate-mounted ﬁlms were studied. For the latter, Schottky barrier diodes of
a zirconium-nanodiamond-silicon conﬁguration were fabricated from nanodiamond ﬁlm
of varying thickness and rectiﬁcation ratios up to 1.1 x 104 at i 80 V were observed.
Temperature dependence of both the Schottky junction and ﬁeld-activated conductivity
following a Poole-Frenkel reduction in ionization energy was studied. This thesis also
includes a preliminary investigation into the unintentional development of what is
speculated to be a nanodiamond/carbon-ﬁlament based Schottky barrier diode. Current-
voltage characteristics were studied under varying nanodiamond ﬁlm thickness and

temperature where rectiﬁcation ratios up to 1.69 x 105 were observed at i 10 V.

Cepyright by
MITCHELL DOUGLAS PARR
2005

ACKNOWLEDGEMENTS

I would like to begin by thanking the Fraunhofer Center for Coatings and Laser
Applications for funding this research. I would also like to thank Michael Becker for his
generous help in metal deposition, which was necessary for the fabrication of the devices
studied in this thesis. My deepest gratitude is extended to my committee members, Dr.

J es Asmussen, Dr. Tim Grotjohn, and Dr. Donnie Reinhard for their valuable input.
Finally, I would like to express my utmost appreciation to my advisor, Dr. Donnie

Reinhard, for his patience and excellent guidance throughout this research.

iv

TABLE OF CONTENTS

List of Tables ....................................................................................... viii
List of Figures ....................................................................................... ix
Chapter 1 Introduction .............................................................................. 1
1.1 Research motivation ............................................................................ l
1.2 Thesis organization .............................................................................. 3
Chapter 2 Background .............................................................................. 5
2.1 Introduction ....................................................................................... 5
2.2 Why diamond for electronics? ................................................................. 5
2.3 CVD diamond .................................................................................... 7
2.4 Field-activated conductivity .................................................................... 9
2.5 Schottky barrier diodes ........................................................................ 11
2.6 Previous studies of Schottky barrier diodes ................................................ 16
2.7 Flexible diamond .............................................................................. 18
Chapter 3 Experimental Methods ............................................................... 19
3.1 Introduction ..................................................................................... 19
3.2 Diamond Films ................................................................................. 19
3.3 Metallization .................................................................................... 21
3.4 Back-Etch ....................................................................................... 22

3.5 Electrical sample conﬁgurations ............................................................. 24

3.6 I-V measurement setup — HP4145B semiconductor parameter analyzer . . . . ..27

3.7 I-V measurement setup — Tektronix 577 curve tracer .................................... 34
3.8 Transmission spectroscopy ................................................................... 35
Chapter 4 Experimental Results of Zirconium/Nanodiamond Diodes on Silicon ....... 39
4.1 Introduction ..................................................................................... 39
4.2 I-V characteristics of initial-state diodes vs. thickness at 300 K ........................ 39
4.3 I-V characteristics of initial-state diodes vs. thickness and temperature ............... 46
4.4 Reverse breakdown voltage vs. thickness for initial-state diodes ........................ 55
4.5 Initiation of a change in initial-state diode characteristics ................................ 57
4.6 I-V characteristics of phase-change diodes vs. thickness at 300 K ..................... 58
4.7 I-V characteristics of phase-change diodes vs. thickness and temperature ............ 62
Chapter 5 Analysis and Discussion .............................................................. 69
5.1 Introduction .................................................................................... 69
5.2 General model .................................................................................. 69
5.3 Poole’s Law .................................................................................... 72
5.4 Field-activated conductivity in forward-biased rectifying structures ................... 74
5.5 Temperature dependence of forward-biased rectifying structures ....................... 77
5.6 Temperature dependence of reverse-biased rectifying structures ........................ 83
5.7 Modeling of phase-change rectifying structures ........................................... 87

vi

Chapter 6 Conclusion and Recommendations for Future Research ......................... 96

6.1 Introduction ..................................................................................... 96
6.2 Two-terminal nanodiamond based structures .............................................. 96
6.3 Nanocrystalline diamond based Schottky barrier diode results .......................... 97
6.4 Phase-change material Schottky barrier diodes ............................................ 98
6.5 Recommendations for future research ...................................................... 98
APPENDD( HP4145B I-V Measurement Software ......................................... 101
BIBLIOGRAPHY ................................................................................. 107

vii

LIST OF TABLES

Table 2.1 Physical properties and ﬁgures of merit for common semiconductors ........... 7
Table 4.1 Diamond thickness values for the ﬁve fringes ....................................... 40
Table 4.2 Observed breakdown voltages and electric ﬁelds for the ﬁinge diodes .5......6
Table 5.1 Calculated Poole’s Law variables for the ﬁve fringe thicknesses ............... 75
Table 5.2 The Poole slope, a, calculated for each fringe and temperature .................. 79
Table 5.3 The Poole conductivity, 0'0 , calculated for each fringe and temperature ....... 79

Table 5.4 Separation, s, and barrier height, (0,, calculated for each ﬁinge thickness ...... 81

Table 5.5 Table of (pH calculated for each diamond ﬁinge thickness ........................ 84
Table 5.6 Fringe 1 phase-change diode resistances under reverse bias ..................... 90
Table 5.7 IS and n values for Fringe l phase-change diode ................................... 91

Table 5.8 R, values versus temperature for Fringe 1 phase-change diode .................. 93

viii

LIST OF FIGURES

Figure 2.1 Energy band diagram for (a) n-type equilibrium (b) n-type Schottky barrier

formation (c) p-type equilibrium ((1) p-type Schottky barrier formation .................... 14
Figure 3.1 Nanodiamond/silicon Schottky barrier diode structure ........................... 25
Figure 3.2 Freestanding diamond ﬁlm sandwiched by two washers ........................ 26
Figure 3.3 Flexible nanodiamond wrapped around stainless steel tube ..................... 27

Figure 3.4 HP414SB I-V zirconium/nanodiamond/silicon measurement apparatus ...... 29

Figure 3.5 Example zirconium/nanodiamond/silicon I-V plot ............................... 29
Figure 3.6 Representative I-V plot for freestanding nanodiamond structure .............. 31
Figure 3.7 Conductance versus voltage plot for freestanding nanodiamond ............... 31
Figure 3.8 Representative I-V plot for freestanding ultrananodiamond .................... 33
Figure 3.9 Representative I-V plot for nanodiamond wrapped tube structure ............. 33
Figure 3.10 Transmission spectroscopy measurement apparatus ............................ 37
Figure 3.11 Example plot of relative transmission vs. wavelength .......................... 37
Figure 4.1 I-V plot of typical Schottky barrier diode located on Fringe 1 .................. 41
Figure 4.2 I-V plot of fringe area diodes in forward bias ..................................... 43
Figure 4.3 I-V plot of fringe area diodes in reverse bias ...................................... 43
Figure 4.4 I-V plot of ﬁinge area diodes in both forward and reverse bias ................. 44
Figure 4.5 Rectiﬁcation ratios calculated for initial-state diodes vs. fringe ................ 45
Figure 4.6 I-V plot of a Fringe 1 diode under forward bias versus temperature ........... 46
Figure 4.7 I-V plot of a Fringe l diode under reverse bias versus temperature 4..7
Figure 4.8 I-V plot of a Fringe 2 diode under forward bias versus temperature ........... 49
Figure 4.9 I-V plot of a Fringe 2 diode under reverse bias versus temperature ............49

ix

Figure 4.10 I-V plot of a Fringe 3 diode under forward bias versus temperature ......... 50

Figure 4.11 I-V plot of a Fringe 3 diode under reverse bias versus temperature .......... 50
Figure 4.12 I-V plot of a Fringe 4 diode under forward bias versus temperature ......... 52
Figure 4.13 I-V plot of a Fringe 4 diode under reverse bias versus temperature .......... 52
Figure 4.14 I—V plot of a Fringe 5 diode under forward bias versus temperature ......... 53
Figure 4.15 I-V plot of a Fringe 5 diode under reverse bias versus temperature .......... 53
Figure 4.16 I-V plot of Fringe 1 diode for both temperature extremes ..................... 54
Figure 4.17 I-V plot of Fringe 5 diode for both temperature extremes ..................... 55
Figure 4.18 Reverse bias breakdown curves for diodes of varying thickness .............. 56
Figure 4.19 I-V plot of a phase-change Schottky barrier diode .............................. 59
Figure 4.20 I-V plot of phase-change diodes under forward bias versus fringe . ...59
Figure 4.21 I-V plot of phase-change diodes under reverse bias versus ﬁinge ............ 60
Figure 4.22 Rectiﬁcation ratios calculated for phase-change diodes vs. fringe ............61
Figure 4.23 Rectiﬁcation ratios calculated for phase-change diodes vs. fringe ............ 61
Figure 4.24 I-V plot of Fringe 1 phase-change diode in forward bias vs. temp ....62
Figure 4.25 I-V plot of Fringe l phase-change diode in reverse bias vs. temp ............ 63
Figure 4.26 I-V plot of Fringe l phase-change diode in forward bias vs. temp ............64
Figure 4.27 I-V Plot of Fringe 2 phase-change diode in forward bias vs. temp ............65
Figure 4.28 IN plot of Fringe 2 phase-change diode in reverse bias vs. temp ............ 65
Figure 4.29 I-V plot of Fringe 2 phase-change diode in forward bias vs. temp ....66
Figure 4.30 I-V plot of Fringe 5 phase-change diode in forward bias vs. temp . .......67
Figure 4.31 I-V plot of Fringe 5 phase-change diode in reverse bias vs. temp ............ 67
Figure 4.32 I-V plot of Fringe 5 phase-change diode in forward bias vs. temp ............ 68

Figure 5.1 General model for two terminal rectifying structure .............................. 70

Figure 5.2 IV plot of rectifying junction (dashed) and ﬁeld-activation (solid) ........... 71
Figure 5.3 IV plot of two-terminal rectifying structure with series resistance ............. 71
Figure 5.4 I-V plot of diamond based Schottky barrier diode ................................ 72
Figure 5.5 Conductivity vs. electric ﬁeld plot versus fringe thickness ...................... 75
Figure 5.6 Plot of a versus diamond thickness ................................................. 76
Figure 5.7 Conductivity vs. electric ﬁeld plot for Fringe 1 diode ........................... 78
Figure 5.8 Conductivity vs. electric ﬁeld plot for Fringe 5 diode ........................... 78
Figure 5.9 Plot of a versus inverse temperature for Fringe 1 ................................. 80
Figure 5.10 Natural log of 00 versus inverse temperature for Fringe 1 ..................... 81
Figure 5.11 Natural log of Is versus inverse temperature for Fringe l ...................... 84
Figure 5.12 Barrier height, (03, versus fringe thickness ....................................... 85
Figure 5.13 DC model of the phase-change diode ............................................. 88
Figure 5.14 Reverse bias I-V plot of Fringe 1 phase change diode at 300 K ............... 89

Figure 5.15 Natural log resistance vs. inverse temp for Fringe 1 phase-change diode. . ..91

Figure 5.16 Natural log I, vs. inverse temp for Fringe 1 phase-change diode ............ 92

Figure 5.17 I-V reverse bias plot of phase-change diodes showing linearity at 300 K ...95

Figure 5.18 I-V reverse bias plot of Fringe 2 diode vs. temperature showing linearity ...95

xi

Chapter 1

Introduction

1.1 Research motivation

Over the past 15 years, diamond has been of increased interest to researchers in
chemistry, physics, material science, and engineering due to the unique characteristics
that this rare material possesses and the availability of new methods of synthesizing it.
One oﬁen touted application of diamond is in electronics. Diamond has qualities that
make it ideal for high power, high frequency, and high temperature electronic
applications such as high breakdown ﬁeld, high saturation velocity, high thermal
conductivity and more [1,2]. Past research has demonstrated the development of
diamond-based vacuum tubes, Schottky banier diodes, ﬁeld-effect transistors (PET), and
other electronic switches [3,4,5]. Perfecting the development of these fundamental
devices is crucial for the development of more complex circuits. Though currently only
in a preliminary stage, advancements in diamond grth technology through research
here at Michigan State University and elsewhere continuously close in on the realization
of diamond-based electronics in our everyday life.

As an extension to current research into diamond based electronics, this thesis
introduces the idea of ﬂexible diamond based electronics. Thin sheets of diamond ﬁlm
have already been shown to have the capability to conform to curved surfaces and

maintain this shape without fracturing or breaking [6]. This thesis presents a preliminary

step in the investigation of electronic devices fabricated from thin diamond ﬁlms that
maintain this degree of ﬂexibility. Doped and undoped polycrystalline and single
crystalline diamond on the order of a few micrometers thick have been used in past
research for electronic device fabrication; however, diamond and contact thickness may
limit or prevent ﬂexibility.

The research presented in this thesis utilized undoped nanocrystalline diamond
ﬁlm (nanodiamond) with grain size on the order of tens to hundreds of nanometers in
diameter and ﬁlm thickness down to a quarter micrometer to aid in ﬂexibility. Simple
freestanding nanodiamond based devices behaving as voltage-controlled resistors were
fabricated. Pressures up to 15-20 psi were applied to two-terminal devices formed on
nanocrystalline membranes. Also, zirconium-nanodiarnond-silicon Schottky barrier
diode conﬁgurations were fabricated with nanodiamond ﬁlm ranging in ﬁlm thickness
from about 250 — 770 nm. Testing was completed on the Schottky barrier diodes at
temperatures of 300 — 425 K to investigate temperature dependence of the Schottky
junction and electric ﬁeld-activated conductivity. The latter follows a Poole-Frenkel
reduction in ionization energy associated with Coulombic centers in the nanodiamond. A
DC model was developed for these diodes based on device characterization. Also,
investigation into the unintentional, but fortuitous, development of a Schottky diode with
improved rectiﬁcation along with a developed DC model and subsequent device

characterization for this device is presented in this thesis.

1.2 Thesis organization

This thesis is divided into six main chapters with the next chapter providing
background material as an aid to the reader. The reason for interest in diamond, different
types of chemical vapor deposition (CVD) diamond, ﬁeld-activated conductivity,
Schottky banier diodes, previous diamond studies, and ﬂexible diamond are the topics
covered in Chapter 2.

Chapter 3 presents the experimental methods used in this research. Several types
of contact metals along with a few different sample conﬁgurations were considered.
These electrical sample conﬁgurations along with details on nanocrystalline and
ultrananocrystalline diamond ﬁlm growth, contact metallization, silicon back-etching,
current-voltage measurements, and diamond-ﬁlm thickness measurements are presented
in this chapter.

Chapter 4 presents the experimental results of the nanocrystalline diamond based
Schottky diodes investigated in this thesis. Current-voltage measurements on these
“initial-state” diodes were performed at various temperatures and with varying diamond
ﬁlm thickness and the results are presented in this chapter. Also, this chapter provides
results on modiﬁed diodes resulting from an unexpected “phase-change” through high
voltage/current combinations. Results from current-voltage measurements on these
“phase-change” diodes performed at various temperatures and with varying diamond ﬁlm
thickness are presented in the later part of Chapter 4.

Chapter 5 goes through an analysis of the experimental results of Chapter 4 in an

attempt to model both the initial-state and phase—change diodes through device

characterization. A proposed DC model along with the investigation and calculation of
the barrier height, saturation current, and voltage activated conductivity following a
Poole-Frenkel reduction in ionization energy is presented. Also, a DC model for the
phase-change diodes and subsequent device characterization giving rise to an estimated
banier height, forward bias and reverse bias resistance, reverse bias activation energy,
saturation current, and ideality factor follows in the last section of Chapter 5.

Finally, Chapter 6 follows with a conclusion and recommendations for future

research.

Chapter 2

Background

2.1 Introduction

This chapter presents background information to aid the reader in the
understanding of this research. The reason for interest in diamond for electronic
applications along with the different types of polycrystalline diamond currently being
used in the fabrication of electronic devices is presented in the ﬁrst two sections. F ield-
activated conductivity is discussed along with a short explanation on the construction and
operation of Schottky barrier diodes follows in the next two sections. Finally, a
discussion on previous diamond Schottky diode research along with a discussion on

ﬂexible diamond is presented in the last two sections of this chapter.

2.2 Why diamond for electronics?

Diamond has many properties that make it desirable for use in solid-state
electronics such as: wide band gap, high breakdown electric ﬁeld, high saturation
velocity, high hole and electron mobility, and the highest thermal conductivity of any
room temperature solid [1,2]. Collectively, these properties make diamond a potentially

suitable material for use in high power, high frequency, and high temperature electronic

applications. In addition, due to diamond’s natural chemical inertness and radiation-hard
physical properties, such diamond-based electronics could be realized for applications in
extremely harsh environments.

Two ﬁgures of merit, Keyes’ ﬁgure of merit (KFM) and the Johnson ﬁgure of
merit (JFM), provide an indication of a material’s suitability in electronic applications.
The KF M addresses the thermal limitations of a material for high-frequency applications
[7] and is given by:

l

KFM = 2|: “’3 F [2.01]
47:8,

 

where )t is the thermal conductivity, c is speed of light, vs is saturation velocity, and a, is

dielectric constant. The IF M addresses the potential of a material for both high-

frequency and high-power applications [8] and is given by:

EMvs 2
JFM = — [2.02]
27!

where E M is breakdown ﬁeld. A large value for KFM or JFM indicates a material to be

more suitable than materials of a lesser value.

Both Johnson and Keyes ﬁgure of merit calculated for diamond and a few other
semiconductors are shown in Table 2.1, along with some electronic properties commonly
compared among semiconductor materials. Values for the ﬁrst six rows in the table are
from a variety of sources and are used to calculate the values in the last two rows.
Diamond exceeds all other semiconductors in both ﬁgure of merits and in the speciﬁc
case of silicon, diamond is up to several orders of magnitude higher by comparison.

Other studies have shown the same trend in comparison with other semiconductors

besides those listed in Table 2.1 [2,9,10] with the exception of the JFM calculated for
AlN in reference [9]. However, it should be noted that the researchers chose to use a
smaller breakdown ﬁeld [9] in the JFM calculation instead of the maximum used in the
table below. A recalculation using the maximum breakdown ﬁeld present in Table 2.1

produces a relatively larger JFM for diamond.

 

 

 

 

 

 

 

 

 

Property Si SiC-4H GaN Diamond Units
EG 1.12 3.2 3.4 5.5 eV
EM 0.3 3 5 ~ 10 M V / cm
)1" 1450 900 2000 4500 [11] cm2 ”,3

2. 1.5 5 1.3 20 W / ch

Vs 1.0 2.0 2.5 2.7 107cm/S

5,. 11.8 10 9.0 5.5 no units

KFM 1.0 5.1 1.57 32 no units
(normalized)

JFM 1.0 400 1736 8,101 no units
(normalized)

 

 

 

 

 

 

 

 

Table 2.1 Physical properties and ﬁgures of merit for common semiconductors

2.3 CVD diamond

Over the years, several different deposition processes have been developed and
used by researchers to grow diamond ﬁlm. All ﬁlms grown for this study were produced
using the microwave plasma-enhanced chemical vapor deposition (MPECVD) process

which appears to be one of the more popular alternatives today for creating good quality

diamond. Depending on the substrate, both single crystalline or polycrystalline diamond
can be grown using this process. For the purpose of this thesis, only polycrystalline ﬁlms
were investigated.

By varying the growth conditions and seeding procedure for diamond ﬁlms,
different polycrystalline diamond ﬁlm variations are possible using the MPECVD
process and are classiﬁed as; microcrystalline, nanocrystalline, and ultrananocrystalline
diamond (UN CD) as described by Reinhard et a1 [6]. Microcrystalline diamond ﬁlm is
comprised of a multitude of diamond grains each on the order of a micrometer to several
micrometers in diameter bonded together to form a diamond sheet. Nanocrystalline
diamond ﬁlm is similar except it contains diamond grains on the order of tens of
nanometers to hundreds of nanometers in diameter. The difference in grain size between
these two ﬁlms is a result in substrate seeding methodology. Depending on nucleation
density from different seeding methods, a diamond ﬁlm with smaller grain sizes
(nanocrystalline) results with a higher nucleation versus ﬁlms with larger grain sizes
(microcrystalline) resulting from a smaller nucleation density.

UNCD ﬁlms require different deposition chemistry all together. The
microcrystalline and nanocrystalline diamond ﬁlms mentioned above are produced from
a H z/CH4, with optional oxygen containing, gaseous environment. Excited with plasma,
the end result is a diamond ﬁlm on the surface of the substrate as described by Celii and

Butler [12]. However, if an Ar/CH4, with optional hydrogen containing, gaseous

environment is used, a UNCD ﬁlm is deposited on the substrate surface as described by
Gruen [13]. A UNCD ﬁlm contains grain sizes on the order of a few nanometers to tens

of nanometers in diameter. Therefore, by varying the diamond nucleation and deposition

chemistry, the MPECVD process has the potential to produce polycrystalline ﬁlms

ranging in grain sizes from a few nanometers to tens of micrometers.

2.4 Field-activated conductivity

Due to the grain boundaries of polycrystalline diamond, the electrical
conductivity can be different from that of single crystalline material. Grain boundary
effects give rise to electron transport phenomena that have the potential to dominate the
electrical conductivity within the material under speciﬁc conditions. A very noticeable
transport phenomenon in undoped polycrystalline diamond is electric ﬁeld-activated
conductivity according to Poole’s Law as ﬁrst noted in polycrystalline diamond ﬁlms by
Huang and Reinhard [14]. Other sources have since observed and veriﬁed the same ﬁeld
dependent conductivity [1 5,1 6,1 7].

Defects in the crystal lattice, impurities, and grain boundaries can give rise to
localized Coulombic potentials that behave as canier traps. Associated with the
Coulombic potentials is an ionization energy required to free trapped carriers. When a
bias is applied, a reduction in ionization energy with rising electric ﬁeld results in a very
noticeable decrease in trapped carriers and subsequent increase in carrier concentration
[14]. At low ﬁelds, the I-V relationship is primarily ohmic because the electric ﬁeld is
not large enough to appreciably lower the barrier, so there is no change in carrier
concentration and conductivity remains constant. However, as the electric ﬁeld

increases, conductivity increases due to an increase in carrier concentration resulting

from a reduction in the ionization energy of Coulombic potentials. When the Coulombic
potentials are non-overlapping, the ﬁeld-activated conductivity follows the Poole-Frenkel

effect which goes as:

(q3E/8)1/2
o- = 0'08 W [2.03]

where 0'0 is the conductivity resulting from thermionic emission, E is electric ﬁeld, a is
the dielectric constant of the ﬁlm, k is Boltzmann’s constant, and T is temperature [18].

When the Coulombic potentials are overlapping, the ﬁeld-activated conductivity follows

Poole’s Law and goes as:
0' = ooeag [2.04]
where a is a function of temperature and spacing between Coulombic potential centers

[18]. Therefore, the total conductivity of the sample including the ohmic

conductivity, 0'00 , becomes:

a = 000 + ooeaE [2.05]
The total ﬁeld-activated conductivity according to Poole’s Law has been
experimentally observed in polycrystalline diamond ﬁlms at electric ﬁelds on the order of
105 V/cm and higher [14,15,17]. At sufﬁciently high enough ﬁelds, the ﬁeld-activated
conductivity was reported to dominate the electrical conductivity of the polycrystalline
diamond ﬁlms. Since ﬁeld-activated conductivity was observed in the diamond ﬁlms in

this study, Poole’s law will be examined in more detail in Chapter 5.

10

2.5 Schottky barrier diodes

The primary focus of this research was developing diamond—based Schottky
banier diodes; therefore, a brief background on Schottky barrier diodes is presented for
the reader. As with any topic in solid-state electronics, the details behind the inner
working of realized solid-state devices is long and detailed and the topic of Schottky
banier diodes is no different. This section only presents fundamental relations and
properties of Schottky barrier diodes and the curious reader is advised to reference any of
a number of solid-state text books available for a more advanced analysis of Schottky
barrier diodes. In particular, much of the information contained in this section has been
referenced from Casey’s introductory text [19].

As a quick reminder to the reader, semiconductors have distinct energy levels
where electrons reside due to the periodicity of atoms in the crystal lattice. For current
ﬂow, only the electrons inhabiting the outer two energy bands are involved. We
designate the outer most energy band the “conduction” band and the carriers are
electrons. The energy band directly below is called the valence band and the carriers are
“holes”, or electron vacancies. At zero Kelvin, the conduction band is free of electrons
and the valence band is completely full resulting in no current ﬂow, characteristic of a
semiconductor. As temperature increases, electrons gain enough energy to cross the
“bandgap” on into the conduction band, leaving behind a vacancy in the valence band, or
hole as deﬁned above. Both carrier types are free to move about their respective bands,
and under the inﬂuence of an electric ﬁeld, provide the means to conduct current through

the material.

11

One such device that takes advantage of the unique properties of a semiconductor
is a Schottky barrier diode. The construction of a Schottky barrier diode is essentially a
metal to semiconductor junction. If conditions are right, a “built-in potential” will form
around the interface of the two materials, allowing current ﬂow of primarily one carrier
type in, ideally, only one direction. Formation of a Schottky barrier is essential in these
devices and is dependent on the work function of the materials. A work function is the
amount of energy required to raise an electron from the Fermi energy to zero energy
vacuum level where there are no longer any forces acting on the electron leaving it
energy free. Thus, in both metals and semiconductors, the work function is the potential
difference between zero energy vacuum level and the F errni level. In metals, the Fermi
level is ﬁxed and known for each metal. However, in semiconductors, the Fermi level is
dependent on the doping concentration and, for nondegenerate semiconductors, falls in
between the conduction band and valence hand.

To produce a built-in potential, the work functions of the two materials must be
considerably different to form a signiﬁcant barrier at the metal-semiconductor junction.

The built-in potential is the difference between the metal work ﬁrnction, (Dm , and the
semiconductor work function, (D3 , deﬁned as:
Vb,- =(Dm —<Ds [2.06]
where (D3 is given as the following for an n-type semiconductor:
(1)3 =X+[EC—Ef]/q [2.07]
and p-type semiconductor:

(D, = X + [Eg — (Ef — Ev)]/q [2.08]

12

In this expression, EC is the bottom of the conduction band, Ev is the top of the valence
band, E [is the Fermi energy, E8 is the bandgap, and X is the electron afﬁnity. The

electron afﬁnity, X, is deﬁned as the difference in potential energy between vacuum level

and the bottom of the conduction band, EC.

The built-in potential “blocks” carriers of a particular type from crossing from the
semiconductor and into the metal. Carriers coming from the other direction, crossing
from the metal into the semiconductor, are blocked by a potential called the “banier

height”, 023 , and is deﬁned as:

61603 = 61(9)»; - X) [209]
for an n-type semiconductor and:

W3 = qX + Eg —q<r>,,, [2.10]

for a p-type semiconductor. The built-in potential and barrier height are essential to these
devices and govern the forward and reverse I-V characteristics that deﬁne their
functionality.

The best way to visualize the built-in potential and barrier height along with
corresponding energy levels is through the energy-band diagram. Shown in Figure 2.1
are the before and after joining representative energy-band diagrams for both a metal to
n-type semiconductor and metal to p-type semiconductor. Figure 2.1(a) shows the two
materials in equilibrium. Upon initial contact, the electrons in the n-type
semiconductor’s conduction band will transfer to the metal where the energy is lower
until the Fermi energy levels align and the subsequent built-in potential develops and
blocks any more electrons from transferring. The resulting energy diagram can be seen

in Figure 2. l (b). The same process follows for the p-type semiconductor in

13

 

I Vacuum Level I I

 

 

 

 

 

 

 

      

 

 

 

 

 

 

 

 

 

 

 

 

qX (1(1);-
q¢m * EC
E i n-type semiconductor
f Metal E
V
T \ Vacuum Level
,, t t
q m qX q¢s
l “I E
C
E f ______
Ef
Ef

 

 

 

(a)

(b)

(C)

(d)

Figure 2.1 Energy band diagram for (a) n-type equilibrium (b) n-type Schottky barrier

formation (c) p-type equilibrium ((1) p-type Schottky barrier formation

14

Figure 2.1 (0), except holes transfer to the metal upon initial contact and continues to do
so until the Fermi energy levels align and subsequent built-in potential develops and
prevents anymore holes from transferring as shown in Figure 2.1 (d).

Upon application of an electric ﬁeld across the device, with an applied voltage V,
the energy bands of the semiconductor will increase or decrease depending on orientation
of the ﬁeld. If the electric ﬁeld is applied in a manner to counter-act the built-in potential
(forward bias), the built-in potential will decrease as q(Vb,- — V) and majority carriers will
move from semiconductor to metal inducing a current ﬂow through the device. An
electric ﬁeld applied in the direction of the built-in potential (reverse bias) will only
increase the built-in potential as q(Vb,- + V) and only a small current ﬂows under this
condition. The following expression deemed the “Schottky” diode equation relates the

applied voltage to the current ﬂow induced within the device and is given as:

I =13[exp(—q£9—)-l:l [2.11]
nkT

where Va is applied voltage, positive for forward bias and negative for reverse bias, n is
ideality factor, k is Boltzmann’s constant and T is temperature. The saturation current, 15,

is the relatively small current arising from majority carriers in the metal possessing
enough energy to overcome the barrier height, (03 , and cross into the semiconductor.

The saturation current is given as:
* 2 “(WE
I = AA T ex 2.12
s p( kT ) I I

where A is cross-sectional area and A * is the effective Richardson’s constant.

Therefore, using the I-V relationship deﬁned above along with the

15

aforementioned relations and others not covered in this brief overview, several properties
can be extracted from experimental data to help characterize a fabricated device. These
properties include but are not limited to: saturation current, the ideality factor, the barrier
height, the built-in potential, activation energy, depletion capacitance, bulk resistance and
the cross sectional area of the device. The inclusion of these properties into a generalized
Schottky diode model allows one to accurately predict the behavior of the fabricated
device. For complete device characterization, both an AC model and DC model are
commonly developed; however, the focus of this research was DC analysis and

subsequent DC modeling of the diamond-based Schottky barrier diodes.

2.6 Previous studies of Schottky barrier diodes

Due to the difﬁculty in doping diamond n-type [20], most research on diamond-
based electronic devices has focused on unipolar structures such as Schottky banier
diodes and ﬁeld effect transistors (F ET). Preliminary studies of diamond as
semiconductor devices began as early as 1955 with Brophy [21] where the Hall Effect,
electrical conductivity and point contact rectiﬁcation was examined on natural diamond.
Reports of Schottky barrier diode fabrication and extensive study of the capacitance-
yoltage characteristics of Schottky barrier diodes formed on laboratory grown, boron-
doped single crystalline diamond was reported as early as 1973 by Grover [22]. With the
later development and interest in polycrystalline ﬁlms deposited through the chemical

vapor deposition (CVD) process, interest in diamond electronics increased. Schottky

16

banier diodes fabricated from these ﬁlms were ﬁrst reported in 1988 by Gildenblat et al
[23]. A subsequent review of the progress in device fabrication from polycrystalline
diamond ﬁlms in that era was published by Gildenblat a few years later [10].

As mentioned in section 2.5 above, Schottky banier diodes rely primarily on the
transport of one carrier type which can be inﬂuenced by doping. Diamond based
Schottky barrier diodes have been p-type where diamond plays the role of a p-type
semiconductor. This p-type behavior comes either from intentional boron doping of
diamond or from a highly conductive p-type surface layer resulting from defect acceptor-
like states present at or near the surface of the diamond. The details of this latter
phenomenon are currently not well understood [24,25]. Devices speciﬁcally utilizing this
unique surface conductivity have been realized to develop Schottky banier diodes and
F ETs with one such example of a PET coming from Glueche et al in 1997 [5]. It should
be noted that alteration of this p-type surface layer by exposing the surface to hydrogen
and oxygen through hydrogenation, cleaning, and oxidation modiﬁes the behavior of
metal to semiconductor interfaces [26] and is therefore an important variable in diamond
Schottky barrier diode fabrication.

Development of diamond based Schottky barrier diodes has continued to the
present as represented by a recent report by Butler et al on the development of a Schottky
barrier diode fabricated on boron-doped, single crystalline diamond with a breakdown
voltage over 6 kV [4]. Thus, diamond-based Schottky barrier diodes currently represent
one of the leading contenders for an electronic device that takes advantage of diamond
potential for high temperature and high power devices. Indeed, as noted by an article

recently published in Science Magazine titled “A dawn for carbon electronics?” there is

17

currently high interest in diamond based electronics [27].

2.7 Flexible Diamond

A novel approach to the research presented in this thesis was the development of
ﬂexible diamond-based electronics. Research into fabrication of diamond membranes
and sheets and application to curved surfaces was reported by Reinhard et al [6]. The
diamond sheets developed in this research were drapable, capable of being wrapped
around cylinders as demonstrated in the paper. Several thin diamond ﬁlms of varying
grain sizes were produced with thicknesses on the order of 1-3 pm and as large as several
cmz. The ﬁlms were then ﬂoated on an aqueous solution were they could be applied to
stainless steel frames as freestanding ﬁlms. Due to the ﬁlms ﬂexibility and limp behavior
when wet, the authors were able to successfully wrap the diamond ﬁlms around a
stainless steel tube. Although no electrical devices were produced from these ﬂexible
diamond ﬁlms, the research demonstrates the potential for eventual electronic device

fabrication.

18

Chapter 3

Experimental Methods

3.1 Introduction

This chapter reports on the methodology employed for Schottky barrier diode
fabrication, sample preparation, current-voltage and diamond thickness measurements
completed for this thesis. Nanocrystalline and ultrananocrystalline diamond ﬁlm growth,
contact metallization, silicon back-etching, electrical sample conﬁgurations, I-V
measurement using an HP4145B semiconductor parameter analyzer, I-V measurement
using a Tektronix 577 curve tracer, and diamond-ﬁlm thickness measurement using

transmission spectroscopy are all discussed in the following sections.

3.2 Diamond Films

The Schottky barrier diodes fabricated for this work were primarily developed
from nanodiamond grown on silicon wafers by Booth [28]. The nanodiamond ﬁlm was
grown inside a Microwave Cavity Plasma Reactor (MCPR) designed by Asmussen et a1.
and built at Michigan State University [29]. Microwave Plasma-Enhanced Chemical
Vapor Deposition (MPECVD) was the growth process from which the diamond ﬁlms

were created. MPECVD is the technique of mixing a number of reactive gases in a

19

microwave-induced plasma environment where the byproduct is, ultimately, deposited on
the surface of the substrate. Details of the MPECVD process used speciﬁcally for
diamond growth are explained by Asmussen et a1 [29].

A Booth nanodiamond sample, denoted as F823, was used principally for this
work. This particular diamond sample was reported to have been grown under the
following conditions: a substrate temperature of 660°C, deposition pressure of 33 Torr,

H2 gas ﬂow of 200 sccm, C02 gas ﬂow of 8 sccm, CH4 gas ﬂow of 3 sccm, 700 W of

absorbed microwave power, and a deposition time of 7 hours. The nanodiamond ﬁlm
was grown on a 3” diameter (100) p-type silicon wafer with a resistivity of 1-10 ohm-cm
and a thickness of approximately 250 pm. For more details of the nanodiamond growth
process for the FB23 sample, the reader is referred to the work completed by Booth [28].

Additionally, preliminary studies were performed on ultrananocrystalline
(UNCD) diamond ﬁlms. The UNCD ﬁlms were grown by Angela Moon in Professor
Grotjohn’s research group using the same MCPR reactor and MPECVD diamond growth
process mentioned earlier but with a different chemistry [30]. The UNCD sample used
for this work, denoted as A9, was reported to have been grown under the following

conditions: a substrate temperature less than 650°C, deposition pressure of 120 Torr, H2
gas ﬂow of 1 sccm, Ar gas ﬂow of 100 sccm, CH4 gas ﬂow of 1 sccm, and 1.1 KW of

absorbed microwave power.

20

3.3 Metallization

Metallization studies in this work included indium, gold, titanium/ gold, graphite
based “paint”, zirconium, and pressure contacts against tungsten, platinum, and stainless
steel. Metallization was performed on both diamond ﬁlm on silicon and freestanding
diamond. Metallization issues with contact reliability, consistency, and I-V behavior led,
ultimately, to zirconium as the chosen Schottky metal contact. Speciﬁc issues
encountered included inconsistent I-V behavior with pressure contacts and poor surface
adhesion with melted indium pellets. Aluminum has previously been reported as a good
Schottky metal contact for diamond. However Al was not investigated in this study after
the initial success with zirconium. Non-Schottky (ohmic) contacts on diamond were
formed primarily with gold. In one case, a titanium/ gold ﬁlm was sputtered on a
freestanding diamond ﬁlm; however the ﬁlm broke and curled after the process,
presumably due to stresses in the ﬁlm after the addition of the sputtered layers.

The use of gold for ohmic contacts requires further comment. A perfect ohmic
contact is one that has zero contact resistance. A practical ohmic contact is one for which
the contact resistance is small relative to the bulk or series resistance of the device to
which contact is being made. For the diamond ﬁlms used in this study, gold was a
practical ohmic contact so long as the diamond thickness was on the order of a
micrometer. For such structures, with gold as one contact and silicon as the other, the I-
V curves were symmetric, i.e. the rectifying ratios were essentially unity. However, for
very thin diamond, i.e. on the order of 0.25 pm, the rectiﬁcation ratio could be as high as

200. Thus, gold acted as an ohmic contact only if the diamond was sufﬁciently thick to

21

have a substantial bulk series resistance.

As mentioned above, zirconium was the chosen metal for contact metallization in
fabricating the Schottky barrier diodes. The zirconium metallization was performed by
Mr. Michael Becker of the Fraunhofer Center for Laser Coatings and Applications. Due
to the difﬁculty in producing zirconium metal in vapor form, a simple sputtering physical
vapor deposition (PVD) process could not be used. A PVD Arc process provided the
necessary means for zirconium deposition. A shadow mask with over 400 circular, 500
mm diameter holes was fastened to the diamond surface and the metal was deposited
through the mask. The zirconium was deposited under the following conditions: a
pressure of 1.13 x 10'2 Torr, two cathodes each with a current of 90 A, a sample bias of
-50 V, and a deposition time of 3.3 min. The metallization process resulted in distinct
zirconium contacts, each with a diameter of 450 um (i 25 um) and a height of

approximately 50 nm.

3.4 Back-Etch

Since the principal motivation of this research was to explore issues related to
“ﬂexible” diamond-electronics, various degrees of silicon back-etching were desired
throughout this research. The nanodiamond/silicon sample was submerged in an acid
solution and the acid was allowed to breakdown the silicon wafer leaving the diamond
ﬁlm and a portion of the silicon wafer if desired. The principal acid solution used was

mixed from quantities of the following chemicals: ﬁve parts HNO3, 4 parts H20, and 2

22

parts HF. The silicon side of the sample was scratched with sand paper to expedite the
silicon etching process and then placed, silicon side up, into a Teﬂon holder and then
both were placed in the acid solution. The acid solution, containing the diamond/silicon
sample, was then placed on a hotplate to raise the solution temperature to about 50-60°C.
The sample remained in the solution for approximately 30 minutes. After visual
conﬁrmation that silicon had been etched away, the sample was placed into de-ionized
water (1 uS/cm), providing a clean acid wash and a non-destructive environment for
maneuvering the fragile diamond ﬁlm onto a substrate if all silicOn was removed.

Two degrees of silicon back-etching were performed on the diamond/silicon
samples. The ﬁrst degree of silicon back-etching was limited to etching only half of the
silicon substrate, leaving the other half for the same diode fabrication mentioned above.
The reasoning for this particular etch was to research the affect of the acid etch treatment
on the chemical structure of the diamond surface. Chapter 2 discussed the importance of
the chemical structure of the diamond surface in regard to band-bending and Schottky
barrier formation with a metal. If the chemical structure of the surface was altered, then
diodes fabricated out of that particular sample would, most likely, not behave the same as
diodes fabricated from an as-grown diamond/silicon sample. The actual result from this
etch was no apparent change in diode behavior compared to un-etched samples. It was
concluded the acid etch treatment did not have a signiﬁcant affect on the chemical
structure of the diamond surface.

The second degree of silicon etching was complete removal of the silicon
substrate. Two types of nanodiamond/silicon samples were etched. One sample

contained no zirconium contacts (the zirconium was deposited after the silicon was

23

 

removed) and was etched using the HNO3 solution mentioned above. The other sample

had zirconium contacts already deposited on the diamond surface prior to silicon removal
and required the use of a KOH etch to prevent damage to the zirconium contacts. The

KOH silicon etch consisted of a 44/56 weight percentage KOH/HZO solution and was

performed at a temperature of 55-60°C. The reasoning behind etching a sample that
already contained zirconium contacts was to provide protection to the chemical structure
of the diamond surface covered by the metal contact. If the acid etch treatment did alter
the surface, the hypothesis was that the diamond surface under the contacts would not be
altered and any Schottky banier present would be protected.

However, both of these samples presented experimental difﬁculties. For the
sample of which zirconium was deposited on the diamond after complete silicon removal,
the zirconium contacts appeared faint, bubbly, and had poorly deﬁned edges. For the
sample of which zirconium was deposited prior to silicon removal, a majority of the
zirconium contacts came off during the silicon etch. A few contacts did survive but when
the ﬁlm was placed on a ﬂat copper coated circuit board for microprobing the probes
cracked the ﬁhn and prevented measurement of those remaining contacts. Thus both the
metallization procedures for thin freestanding (S 1 pm) ﬁlm and the subsequent testing of

such structures requires further development and investigation.

3.5 Electrical sample configurations

For measurements of Schottky banier diodes on nanodiamond ﬁlms still attached

24

to the silicon substrate, the following procedure was used. After contact metallization, the
silicon surface of the nanodiamond/silicon sample was attached to an aluminum plate
using a graphitic-carbon and water paste commonly referred to as “carbon paint”. The
carbon paint solidiﬁed and created a low resistive connection, relative to the highly
resistive diamond, between the silicon and aluminum plate. This provided a back contact
to the Schottky barrier diodes which was approximately ohmic over the current-voltage

range investigated. A drawing of the ﬁnal structure is shown in Figure 3.1.

Nanodiamond Carbon Paint

Zirconium Contact

22/

 

 

 

oooooooooooooooooooooooo

ooooooooooooooooooooooo
IIIIIIIIIIII

...........
IIIIIIIIIIII

iiiiiiiiiii

 

oooooooooooo
ooooooooooo
IIIIIIIIIIII
lllllllllll
............
IIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIII

 

   

Aluminum Plate ’

 

 

 

Figure 3.1 Nanodiamond/silicon Schottky barrier diode structure

Electrical samples were also formed from freestanding ﬁlms. Using the back-etch
procedure mentioned in the previous section; silicon was removed from samples of both
nanocrystalline-diamond/silicon and ultrananocrystalline-diamond/silicon samples.

While still in the de-ionized water bath, the diamond ﬁlm was maneuvered onto a steel
washer. An insulating washer, comprised of a neoprene washer and plastic washer, was
then attached to the exposed surface of the diamond ﬁlm using epoxy. The holes in each
of the washers were aligned with each other to form a diamond ﬁlm window in the center

of this structure. Gold was then deposited on both sides of the washer-diamond-washer

25

 

sample. The gold overlapped onto the steel washer surface providing one electrical
contact, Electrode 2. The gold covering the surface of the insulating washer was
removed to ensure no conductive path between gold layers on both sides of the diamond
ﬁlm. A metallic pin was inserted into the top of the insulating washer. A gold wire was
then attached to the gold deposited on the insulating washer side of the diamond ﬁlm
with silver paste and connected to the pin. This provided another electrical contact,
Electrode 1, insulated from the other contact via the insulating washer. A drawing of the

ﬁnal structure for this second device conﬁguration is shown in Figure 3.2.

A 3rd sample conﬁguration involved wrapping a ﬂexible 1.6 pm thick
nanocrystalline diamond ﬁlm around a 6.35 mm diameter stainless steel tube, with the
metal tube providing one electrode (Electrode 2) and graphite paint providing the other
(Electrode l). A picture of this device is shown in Figure 3.3. As shown in the ﬁgure,

the carbon paint contact is connected to Electrode 2 via a gold wire.

Electrode 1 Gold Wire Insulating 4 m
I Washer

   
   

   
 
 

Gold Wire

    

Silver Paste

 

 

 

  

, , Steel Washer .

Figure 3.2 Freestanding diamond ﬁlm sandwiched by two washers

26

 

 

Figure 3.3 Flexible nanodiamond wrapped around stainless steel tube

3.6 I-V measurement setup — HP4145B semiconductor parameter analyzer

The majority of the Schottky barrier diode current-voltage (I-V) data collected for
this work was performed by an HP414SB semiconductor parameter analyzer. The
HP414SB is speciﬁcally designed to measure the DC characteristics for a variety of
semiconductor devices. The device has the capability to perform arithmetic calculations,
display measurement results on a built in CRT, perform graphical analysis, and provide

various measurement options due to a number of voltage controls and connections. The

27

 

HP4145 is limited to a maximum power output of 2 Watts with an absolute maximum
voltage of 100 V. These limitations were reached several times throughout this study,
eventually, resulting in the need of another I-V measurement apparatus, which is
discussed in the following section.

Software developed to communicate with the HP414SB via a connected computer
provided the means for automated measurement and data storage to aid in this work
[Appendix]. A wafer probing station was used to provide the necessary contact
connections while providing shielding from electromagnetic interference. Two of four
available Stimulus/Measurement Units (SMU) on the HP4145B were connected to the
probe station providing the necessary source and ground electrical contacts to the sample.
Using the computer, the HP414SB was sent the necessary instructions for measurement
setup including: measurement type, SMU connection information, starting sweep voltage,
ending sweep voltage, and voltage increment. The HP4145B then proceeded to perform
I-V measurements on the sample and when ﬁnished, the data was transmitted to the
computer and stored as a text ﬁle.

The HP4145B measurement apparatus for the zirconium/nanodiamond/silicon
sample, including electrical connections to the sample, is shown in Figure 3.4 and an
example I—V plot is shown in Figure 3.5 for a diamond ﬁlm approximately 0.25 pm thick.
Due to the p-type behavior of the Schottky barrier diodes, a negative-bias voltage
dropped across the diode from the zirconium contact to the aluminum plate put the device
into forward bias. To represent the diode in forward bias using a more traditional
positive-voltage scale, SMU] and SMU2 were respectively chosen to be the “negative”

and “positive” connections to the HP414SB.

28

 

 

, HP414SB
Nanodiamond

 

  
 
   

Zirconium Contact

MUl I:
1:1

Olll

SMU2

 

 

 

 

 

O
:5; ShieldedCable_’

 

 

   

Computer System

 

Aluminum Plate

 

 

Carbon Paint D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

__ _ _LL
Probe Shielding Box
Figure 3.4 HP4145B I-V zirconiuuu’ " J ’silicon measurement apparatus
20015-02 ]
|
l
1.50E-02 -
l
2 l
E
g 1001-3-02 l
5
5.00E-03
-100 -80 -60 -40 -20 0 20 40 60 80 100
Voltage (V)
Figure 3.5 Example ' ' ’ 4' J ’silicon I-V plot

 

29

For the diamond ﬁlms mounted on steel washers (Figure 3.2), a similar HP4145
measurement apparatus to that of Figure 3.4 was used for this sample. The
zirconium/nanodiamond/silicon sample was replaced with the washer sample and SMUl
and SMU2 were connected to Electrode 2 and Electrode 1, respectively. In this case, the
samples are basically resistors. The conﬁguration allows one to test for piezoresistive
effects, however with applied differential pressures up to about 15-20 psi no discemable
effects were observed in both the ultrananocrystalline and nanocrystalline diamond.
Piezoresistivity is generally associated with boron-doped diamond, and ﬁlms in this study
were undoped.

A representative plot of I-V data collected from the diamond/washer sample is
shown in Figure 3.6 for a diamond ﬁlm approximately 1 pm thick. As shown in this
ﬁgure, the negative I-V data plotted in the negative quadrant very closely mirrors the data
in the positive quadrant. This relationship shows that both the top and bottom
gold/nanodiamond contact have the same I-V characteristics. As will be described, the
nonlinear l-V behavior in Figure 3.6 can be attributed to a physical phenomenon present
in the nanodiamond ﬁlm rather than contact effect.

As noted in chapter 2, high electric ﬁelds can induce ﬁeld-activated conductivity
in the diamond-ﬁlrn. Poole-Frenkel lowering of Coulombic trapping potentials was
discussed as one such phenomenon that has been observed in diamond. For a ﬁxed ﬁlm
thickness, the conductance of a material associated with Poole’s Law has an exponential
relationship with voltage. As shown in Figure 3.7, I-V data plotted in Figure 3.6 is re-
plotted to show the conductance versus voltage characteristics of the freestanding

gold/nanodiamond/ gold sample. The data, plotted on a logarithmic scale, shows a linear

30

Current (A)

Conductance (S)

6.00E-04 7

l
40013—04 —

2.00E-04 -'

 

-100 a .' ,, », i -60 -40 -20 0 20 40 60 80 100
-2.00E-04
I
-4.00E-04 4
l
-6.00E-O4
Voltage (V)

Figure 3.6 Representative I-V plot for freestanding nanodiamond structure

  

 

1.001305 7
1.00E-06 -
1
1005-07 i
1.00E-08 *4 ._ - ___ mm, __ -1
10 20 30 40 50 6O 70 80 90 100
Voltage (V)

Figure 3.7 Conductance versus voltage plot for freestanding nanodiamond

31

trend from about 55 to 100 volts. This is consistent with a conductance exponentially
related to voltage, characteristic of Poole’s Law. As noted in equation [2.05], Poole’s

Law results in ﬁeld-activated conductivity repeated here for convenience as:

a = 000 + ooeaE [3.01]
or for conductance and voltage:

G = GOO + GoeaV [3.02]
The exponential region of the ﬁeld-activated conductance of Figure 3.7 indicates
a = 1.0 x 10‘5 cmN and 00: 1.79 x 10'13 ((2 cm)‘, in good agreement with previous

reports of Poole’s Law in polycrystalline diamond ﬁlms [14]. Prior to ﬁeld activation,

the conductance G00 is approximately 1.5 x 10'8 S. Given the contact radius of 2 mm
and ﬁlm thickness of approximately 1 pm, this corresponds to a conductivity 000 of

approximately 1.0 x 10'11 (0 cm)‘. Thus it appears that the gold provides ohmic
contacts to a ﬁlm that exhibits ﬁeld-activated conductivity according to Poole’s Law.

l-V measurements were also performed on a freestanding ultrananocrystalline
diamond sample using the same sample conﬁguration shown in Figure 3.2 and HP4145B
measurement setup shown in Figure 3.4. A representative plot of I-V data collected from
the ultrananodiamond/washer sample is shown in Figure 3.8 for a diamond ﬁlm
approximately 1.57 pm thick. Although the data shows a non-linear relationship similar
to that of Figure 3.6, there appears to be no discemable evidence of Poole’s Law when
plotted on a logarithmic scale.

The ﬂexible nanodiamond ﬁlm wrapped around the stainless steel tube (Figure

3.3) also used a HP4145B measurement apparatus similar to that of Figure 3.4. The

32

 

1.50E-06 .

Current (A)

 

-1 .50E-06 ~
Voltage (V)

Figure 3.8 Representative I-V plot for freestanding ultrananodiamond

zirconium/nanodiamond/silicon sample was replaced with the stainless steel sample and
SMU] and SMU2 were connected to Electrode 2 and Electrode 1, respectively. A
representative I-V plot created using data taken with HP4145B is shown in Figure 3.9.
Although the plot is nonlinear, Poole-Frenkel lowering of Coulombic trapping potentials
attributed to the I-V behavior of the gold/nanodiamond/gold sample and evident in Figure
3.7, is not apparent in the data collected from this sample. Also, the data lacks the same
degree of symmetry across the y—axis, which can be attributed to the difference in contact
materials. Electrode 1 is made of carbon paint and Electrode 2 is a stainless steel
pressure contact. Finally, it is noted that the current in Figure 3.9 is much less that in
Figure 3.6. These observations combine to indicate a lack of good ohmic contacts.

Therefore, a large amount of voltage is lost to the high resistance of this contact and

33

electric ﬁelds present in the diamond are too small to induce Poole’s Law. One may

speculate that the stainless steel pressure contact is the likely cause of this.

1.50E-07 -

1.00E-07 '

 

......
_.-:.--v o
‘0 U.
, .
.

.
o,’
.1'
’U
C.
,1
,l
I”
I”
I

Current (A)

 

-l .00E-07 -

-l .50E-07 '
Voltage (V)

Figure 3.9 Representative I-V plot for nanodiamond wrapped tube structure

3.7 I-V measurement setup — Tektronix 577 curve tracer

Due to the current limitations of the HP414SB discussed in the proceeding
section, a Tektronix 577 curve tracer with Tektronix 177 test ﬁxture was used to source
voltages and currents beyond those capable of the HP4145B. The Tektronix curve tracer
and test ﬁxture is speciﬁcally designed to measure the DC characteristics of
semiconductor devices. The Tektronix 577 curve tracer has no digital interface or storage

and is limited to only manual control. The measurement data must be visually read off of

34

the built-in CRT monitor; therefore, accuracy is not as high compared with digital
models. The device does not posses any graphical analysis tools and is unable to perform
arithmetic calculations unlike the HP4145B. However, despite the lack of ﬁrnctionality,
the advantage of the Tektronix for this study comes from its power output capability
which can reach a maximum of 100 Watts with an absolute maximum voltage of 1600 V.
After using the HP4145B to the extent of its power handling capabilities, the
Tektronix 577 curve tracer with Tektronix 177 test ﬁxture was connected to the probe
station and, subsequently, connected to the sample contacts. Data was then collected in
10-20 volt steps beyond the 100 volt maximum imposed by the HP4145B. To test the
limits of the device, the voltage across the diodes were increased and data was collected
until breakdown, a phenomena discussed in the subsequent chapters. Due to the lack of
an auto-range feature, the display was constantly adjusted to display a meaningful
reading that could be easily read of the CRT and recorded. The measurement apparatus
is similar to Figure 3.4 except the HP4145 is replaced with the Tektronix curve tracer and

a computer system is not present in the measurement setup.
3.8 Transmission spectroscopy

Several times throughout the course of this study, thickness measurement of a
diamond-ﬁlm was desired and transmission spectroscopy was the chosen tool. The

transmission spectroscopy setup included: a Bausch & Lomb monochromator, Bausch &

Lomb light source, lenses, Newport 818-IR optical power sensor and Newport 835

35

 

 

optical power meter. The Bausch & Lomb light source fed the monochromator with its
Tungsten ﬁlament quartz bulb. Inserting an appropriate ﬁlter between the light source
and monochromator eliminated higher order wavelengths and allowed a monochromatic
beam of light to pass through the diamond-ﬁlm sample. Transmitted light power was
detected and measured using the optical power sensor and optical power meter,
respectively. A lens was inserted before the sample at a distance from the sample where
the light beam spot was sufﬁciently small for an accurate thickness measurement. A
second lens was inserted after the sample at a speciﬁc distance from the sensor to
recollect refracted light and tighten the light beam down to a sufﬁciently small dot on the
optical power sensor. The wavelength of the transmitted light was varied from 700 nm to
1050 nm and the transmitted power was recorded at every 10 nm step. The sample was
then removed and the same experiment was completed again providing transmission
power versus wavelength for air. The transmission spectroscopy measurement setup is
shown in Figure 3.10.

After the data was collected, the wavelength was converted to wavenumber and
the optical transmission of the diamond sample, relative to air, was plotted versus
wavenumber. An example relative transmission versus wavenumber plot is shown in
Figure 3.11. The diamond-ﬁlm thickness can be determined from the transmission and
reﬂection theory of dielectrics. For details, the reader is referred to the Macleod text
book for an in depth explanation of transmission and reﬂection through multiple
mediums with multiple refraction indexes [31]. However, for this study, the resulting

formula for dielectric thickness of an air-dielectric-air arrangement simpliﬁes to:

l
t:
2nAVWV

 

[3.03]

36

Newport 818-IR
Optical Power Sensor

 
 
  
  
 
     
   

Transmission (%)

Dark Box

 
   
 

_i Filter
l

 

Baucsh&Lomb

'- -- Bausch& F Light Source
-. ........ 3.33:5: ”’15 . . 5355353 Lomb Mono- :‘W’:
chromator i‘ a c

 

 

 

 

 

 

 

Shielded

Cable l:l El El [:1 Newport 835

Optical Power Meter
‘—_—

 

 

 

9000 10000

1 1000 12000 13000 14000 15000
Wavenumber (cm-1)

Figure 3.1 1 Example plot of relative transmission vs. wavelength

37

where n is the index of refraction for the material (2.38 was used for diamond) and WN is
the wavenumber. The change in wavenumber, AWN , is determined by plotting the
relative transmission versus wavenumber and choosing two consecutive “peaks” in the
transmission plot. The difference in wavenumber between these two peaks is the
AWNpresent in equation [3.03]. With the 700 nm to 1350 nm wavelength range used in
this work, the plots created were limited to only two peaks and, therefore, one choice in

choosing consecutive peaks.

38

Chapter 4

Experimental Results of Zirconium/Nanodiamond Diodes on Silicon

4.1 Introduction

This chapter reports on the observed and measured characteristics of the
fabricated diamond-based Schottky barrier diodes on silicon. Key parameters of a diode
include rectiﬁcation ratio and breakdown voltage, both of which are presented here. In
the process of performing higher power forward bias measurements on some of the
diodes, an unexpected change was induced that resulted in a permanent and repeatable
behavioral change. The characteristics of both “initial-state” and the changed diodes are
reported in this chapter. While this chapter primarily presents the experimental data,

most of the subsequent diode modeling and analysis is discussed in the following chapter.

4.2 I-V characteristics of initial-state diodes vs. thickness at 300K

All diodes described in this chapter were formed on a diamond ﬁlm coated silicon
wafer created by Booth and denoted as F B-23 [28]. The diamond-based Schottky barrier
diodes exhibited consistent and predictable I-V behavior across the entire silicon wafer.
Diodes with lower diamond ﬁlm thickness exhibited higher rectiﬁcation ratios than the

diodes with thicker diamond ﬁlms. Transmission spectroscopy was used to verify an

39

increase in diamond ﬁlm thickness moving away from the outer edge of the ﬁlm towards
the center of the wafer where its thickest region was located. Thus, for a given wafer,
higher rectiﬁcation ratio diodes were located near the wafer’s edge. Natural color fringes
on the diamond surface were used as a visual reference for thickness variation across the
wafer. Fringes were identiﬁed by numbering them sequentially from the wafers edge. A
relative change in diamond ﬁlm thickness of about 0.13 um between any two consecutive
color ﬁinges was measured using transmission spectroscopy.

After completion of the current-voltage measurements reported in the later
sections of this chapter, the silicon was etched away and diamond-ﬁlm thickness was
measured optically for Fringe 5 as described in section 3.8. The remaining ﬁinge
thicknesses were approximated by subtracting multiples of 0.13 um from the Fringe 5

thickness. The thickness values for the ﬁve ﬁinges referred to in this chapter are shown

 

 

 

 

 

 

in Table 4.1.
Fringe Fringe Thickness (pm)
1 0.249
2 0.379
3 0.509
4 0.639
5 0.769

 

 

 

 

Table 4.1 Diamond thickness values for the ﬁve ﬁinges

As described in chapter 3, using an HP4145B semiconductor parameter analyzer,

40

current measurements were taken between 0 and 100 volts for both forward and reverse
bias at a temperature of 300 K. The I-V plot of a typical Schottky barrier diode found
along Fringe 1 is shown in Figure 4.1. The plateau at the peak of the curve in the forward

bias region represents the limit of the HP4145B output current restricted to 20 mA.

20015-02 -#

15013-02 l

E ;

e '

95 1.001302 -<
5

 

Voltage (V)

Figure 4.1 I-V plot of typical Schottky banier diode located on Fringe 1

The rectiﬁcation ratio is deﬁned as the ratio of forward bias current to reverse bias

current at a given and identical absolute value of forward and reverse bias voltage, or:

1F (VF)

1R (VR)

where IVFI = IVRI' A large rectiﬁcation ratio is always desired for diode applications.

Rectiﬁcation Ratio = [4.01]

 

 

For this study, Fringe 1 diodes were found to have the highest rectiﬁcation ratios

41

on the wafer. Fringe 1 represents the diodes located in the thinnest region of the diamond
coated silicon wafer. Speciﬁcally, the highest rectiﬁcation ratio was for device (10, 1)
where the forward bias current at 80 volts was 19.7 mA and the reverse bias current at
-80 volts was 1.78 [1A, leading to a rectiﬁcation ratio of 1.107 x 104. Other Fringe 1
diodes measured had rectiﬁcation ratios within 01-03 x 104 of the largest.

Further diodes were chosen randomly across the entire nanodiamond/silicon
wafer on each color fringe and I-V characteristics were measured. For consistency in
thickness variation, only diodes located in or near a purple color ﬁinge were studied.
Figure 4.2 and Figure 4.3 shows the forward bias and reverse bias I-V data, respectively,
on a logarithmic scale for typical diodes located on all 5 fringes of the wafer sample. The
plateau at the top of both “Fringe 1” and “Fringe 2” plot lines are the result from the
HP414SB’s current limiter safety circuit capped at 20 mA. The resolution of the HP4145
and probe station appears to be around 100 pA in this series of measurements.

A composite I-V plot of Figure 4.2 and 4.3 is shown in Figure 4.4. The reverse
bias current varies slightly with respect to fringe while the forward bias current varies
more severely with respect to fringe. For example, the current at 78 volts for the ﬁinge
area diodes under forward bias varies by more than 3 orders of magnitude, from about 18
mA to about 7 uA. In contrast, the current at 78 volts for the ﬁinge area diodes under
reverse bias varies by less than one order of magnitude, from about 2 [1A to about 0.5 [1A.
This observation would indicate a consistent metal to semiconductor Schottky barrier
formation for all diodes regardless of thickness, which is discussed in detail in the

following chapter.

42

Current (A)

Current (A)

l .OOE-Ol
l .00E—02
l .00E-O3

l .00E-04 ~

1.00E-05

l .00E-08 ,

1.00E-06 9
l .00E-07 ‘

1.00E-09 -

1.00E— l 0
ll

1.00E-l l

1.00E-12

l .00E-05 ':

1.00E-06 ;
1.005-07 ,
1.00E-08 ‘
1005-09

1005-10 7

ll
0
1005-11 “/5

0

    
  
 

‘—o— Fringe l I
- ‘—a— Fringe 2 .
—s— Fringe 3 ‘
‘—)(— Fringe 4

3O 40 50

Voltage (V)

Figure 4.2 I-V plot of fringe area diodes in forward bias

I-B— Fringe l 1
-9- Fringe 2
+ Fringe 3

‘-e— Fringe 4 I

—-X- Fringe 5

40

50
Voltage (V)

Figure 4.3 I-V plot of ﬁinge area diodes in reverse bias

43

 

Current (A)

1.00E-01
1.00E-02 1

1.00E-03 -

  
  

1.00E-04
1.00E-05 ‘
1.00E-06 9

1005-07 j

 

ﬁﬁ—rﬁ .. . v————-——— — _.. 'v — — — 77W—— ~- ovu—~——— — I T - - —— -

20 30 40 50 60 70 80 90 100
Voltage (V)

Figure 4.4 I-V plot of fringe area diodes in both forward and reverse bias

Rectiﬁcation ratios calculated for the initial-state diodes with respect to fringe

location are shown in Figure 4.5. Examination of the data shows that the rectiﬁcation

ratio reaches a maximum of about 200 for the thickest diodes (Fringe 5) and 11,000 for

the thinnest diodes (Fringe 1). In contrast, when gold is used instead of zirconium, the

rectiﬁcation ratios are on the order of unity and 200 for the thickest and thinnest,

respectively. This shows that the diode behavior is dependent on the work function of the

metal. In fact, as noted in Chapter 3, if the diamond is sufﬁciently thick, gold acts as an

ohmic contact for these ﬁlms. Evidence for surface conductivity along the top surface of

the diamond ﬁlm was also investigated. When the SMUl and SMU2 probes are

connected to two zirconium top surface contacts, the resulting I-V characteristics are that

of back-to-back diodes. This indicates the lack of any appreciable surface conductivity.

44

 

In summary, one may conclude, that the observed diode action is at the metal-diamond
interface and that the lower the work ﬁmction, the better the rectiﬁcation ratio.
Furthermore, both reverse bias and forward bias IV characteristics were also
measured with the curve tracer allowing the rectiﬁcation ratios to be determined beyond
the 20 mA limitation of the HP4145. The rectiﬁcation ratios of these devices continued
to increase with bias until they reached a maximum rectiﬁcation of about 1.0-2.0 x 104,
near that of the calculated Fringe 1 maximum. At the point of maximum rectiﬁcation, the

current abruptly increased resulting from a breakdown in the diode’s physical structure.

This phenomenon is further discussed in a later section.

r005+05~
1.005+04 ’ , . 5 . _
3 ,, y 5 5 l - . ‘ A
23100303 '55
.2 ' ’ 5 a ‘ ‘ -
c 1.005+02 ; ,, " , a ‘ . - ‘
.2 , , ‘ .
‘5 5 5 ‘ a
(4% ” r 5 a ‘
“a 1.005+01 ~ . a ‘ , ‘ :— —.---
8 - ” 5 5 . ‘ +Frrnge 1 j
x 2 ‘ 8‘ ‘ arcé§ '“S- t”! ‘2; 5 1 ‘ ‘ A I_B—Fringe 2]
1.005+00 ] .1 . FM’ ‘ ' ‘ "°“" ,—¢-Fringc3l
1 —x—Fringe4'
. . j!- Fringe, .51
1005-01 . ~ - - .- - - , , . . .2222. 222-, ‘
10 20 30 40 50 60 70 80 90 100
Voltage (V)

Figure 4.5 Rectiﬁcation ratios calculated for initial-state diodes vs. fringe

45

 

4.3 l-V characteristics of initial-state diodes vs. thickness and temperature

The I-V characteristics of diamond ﬁlm Schottky barrier diodes were investigated
for varying diamond ﬁlm thickness and varying temperature. The same fringes discussed
in the previous section were used in this experiment for consistency in thickness
variation. Using a Signatone S-lO60 QuieTemp System hot chuck and Fluke 80T-150U
Temperature Probe, I-V data was collected at 5 more temperatures from diodes on all 5
fringes. The temperature was varied from 300 K to 425 K with I—V data collected every
25 K. At every 25 K step, I—V data was collected from —100 to 100 volts for diodes on
every fringe. The forward bias and reverse bias I-V plots for a typical Fringe l diode

versus temperature are shown in Figure 4.6 and Figure 4.7, respectively.

1.00E-Ol

     

1.005-02 ~
l
1.005-03 ‘
1 .005-04

1.00E—05

Current (A)

1.00E-06

1.00E-07

10 20 30 40 50 60 70
Voltage (V)

Figure 4.6 I-V plot of a Fringe l diode under forward bias versus temperature

46

 

1.00E-O3

 

Current (A)

 

1.005-09 - -- 7 22. . v - . ,
10 20 30 40 50 60 70 8O 90 100

Voltage (V)

Figure 4.7 I-V plot of a Fringe 1 diode under reverse bias versus temperature

It should be noted that even though the I-V data collected in the previous section
has a resolution of about 100 pA, the data collected for this particular experiment has a
resolution of about 1 nA. The measurement apparatus was used for each experiment but
data was collected on different days. The particular reason behind the variation was not
determined and any attempt to eliminate this difference in resolution failed. Therefore,
the I-V curves present in the ﬁgures of this section become increasingly noisy as the
current approaches 1 nA. However, despite the low-current noise, the general trends in
the data are readily apparent to the reader.

As shown in Figure 4.7, only the data collected between 10 and 70 volts is

displayed in the ﬁgure. The reason for displaying data in this particular range deals with

47

 

the current limitations of the HP4145B. The Fringe 1 diode reaches this maximum
allowed current at 73 volts operating at a temperature of 425 K. The rest of the I-V
curves run into this maximum current at slightly larger voltages. As a result, the data was
deemed not relevant and was omitted from the ﬁgure. To maintain consistency in the
following forward bias ﬁgures for the remaining ﬁinge diodes, data from the same
voltage range is used in all ﬁgures.

The forward bias and reverse bias I-V plots for a typical Fringe 2 diode versus
temperature are shown in Figure 4.8 and Figure 4.9, respectively.

The forward bias and reverse bias I-V plots for a typical Fringe 3 diode versus
temperature are shown in Figure 4.10 and Figure 4.11, respectﬁilly. As shown in Figure
4.10, the 300 K and 325 K I-V curves show a different trend in data at low voltages
compared to the other temperatures in the ﬁgure, or in previous ﬁgures. The reason for
this behavior is due to corrupted data collected during the original experimental
undertaking. The I-V data displayed for the 300 K and 325 K temperatures is data re-
collected after the sample wafer was exposed to the complete range of temperatures used
for the experiment. The corrupted data was not discovered until after the device had been
subjected to tests at all ﬁve temperatures. Therefore, the 300 K and 325 K I-V curves
show an increase in current at low voltages as a result of a physical change in the diodes
themselves brought upon by the temperatures they were exposed to. Note that this
change is limited to the impact on current at lower voltages. The trend in data above 30
volts is consistent with the data shown in previous ﬁgures and ﬁgures to come. It’s
reasonable to assume the original data at 300 K and 325 K collected below 30 volts

would have followed the same trend.

48

 

1.00E-02

l .00E-O3

   
 
 
  
 

l .00E-04 -‘
l .OOE-OS -

1.00E-06 3

Current (A)

1.005-07
1.00E-08
100509 I
100540 ,2 -7 2, , ,, ,2

10 20 30 40 50 60 70

Voltage (V)

Figure 4.8 I-V plot of a Fringe 2 diode under forward bias versus temperature

 

 

 

 

 

 

1.00E-03 7‘
1.00E'04 Ii ’,,--:==: ::: m

l __=, _____ ........

1.00E-05 I ““‘M
A l ‘___.-“"-‘--"-.-" H_A::;::,;-_:::=3°:I";A"
$ ]_00E-06 71‘ -4“ -“:::’:;:;;::::::: .....
5 1.00E-07 . ' +300K

‘ +325 K‘
1.00E-08 - ‘ +35°Kl

. ‘ -a—375K]

.: y rue—400K]
1.00E—09 :2'. g ~e—425 KJ
1.005-10 ~ - , , ~ , .

10 20 30 40 50 60 70 80 90 100

Voltage (V)

Figure 4.9 I-V plot of a Fringe 2 diode under reverse bias versus temperature

49

1.00E-03

l .00E-04 ‘

 

10 20 30 40 50 60 70
Voltage (V)

Figure 4.10 I-V plot of a Fringe 3 diode under forward bias versus temperature
1.00E-03

1 .00E-04

 

1.00E-05

1.00E-06

 

100510 I - , . . , . , , ., , 2‘
10 20 30 40 50 60 7o 80 90 100
Voltage (V)

Figure 4.11 I-V plot of a Fringe 3 diode under reverse bias versus temperature

50

Figure 4.11 also has one curve (300 K) with a similar difference in data trends as
Figure 4.10; however, the explanation for this behavior is not the same. As shown, the
300 K I-V curve does not follow the same data trend at voltages below 30 volts as the
other I-V curves in the ﬁgure, although, all data was collected at the same point in time.
The change in the 300 K I-V curve appears to be more dramatic, not gradually changing
like the I-V curves from the previous ﬁgure. The explanation for the discrepancy is not
as apparent but most likely can be attributed to a momentary glitch in the HP414SB
machine during the measurement process. Further instances of these random but rare
“glitches” were experienced and the data gathered within this small voltage range is not
representative of the diode’s true behavior.

The forward bias and reverse bias I-V plots for a typical Fringe 4 diode versus
temperature are shown in Figure 4.12 and Figure 4.13, respectfully. The same difference
in low-voltage data curve trends at 300 K and 325 K of Figure 4.10 is present in Figure
4.12. As with the Fringe 3 diode, the original data collected for the 300 K and 325 K
temperatures was corrupted for this diode. Again, the data displayed in the ﬁgure for the
300 K and 325 K I-V curves is data re-collected after the diodes were exposed to all
temperatures used in this experiment. The result is an increase in current at voltages less
than about 30 volts. As shown in Figure 4.13, the same discrepancy in Figure 4.11 also
appears in this ﬁgure concerning the 300 K I-V curve. Again, the explanation determined
for the “jump” in current around 30 volts is a random glitch in the HP414SB during the
measuring process.

The forward bias and reverse bias I-V plots for a typical Fringe 5 diode versus

temperature are shown in Figure 4.14 and Figure 4.15, respectfully.

51

Current (A)

Current (A)

1005-04 7

    

1.00E-05 ~

1.00E-06 ‘

30 40 50 60
Voltage (V)

Figure 4.12 I-V plot of a Fringe 4 diode under forward bias versus temperature

1 .00E-03 >
1 .00E-04 .
l .00E-05 ‘

l
1.00E-06 5

70

 

1.005-07 .
1.00E—08 -
1,005-09
1.005-10 I‘

1.00E-ll 7' ,

Voltage (V)

Figure 4.13 I—V plot of a Fringe 4 diode under reverse bias versus temperature

52

 

l .00E-04

l .00E-05

l .00E-06

1.00E-07

Current (A)

1 0013-09 ., 1‘

l .00E- 1 O

 

1005.11 12 . __-.. 22 g
10 20 30 40 50 60 70

Voltage (V)

Figure 4.14 I-V plot of a Fringe 5 diode under forward bias versus temperature

1.00E—03

1.005-04 ..

4
, , --
4‘ . -.F”

"0

1005-05 ~ ,

    
 

l

 

 

A 1.00E-06
35. ‘92:; I
2:, 1005-07
5 .‘°' 300 K
l.00E-08 _ “-15- 325 K .
. r. ;+350K-
1.005-09 ...‘uv'fr 5-9- 375 K
1 111-. 1
III 5 |+400 Kl
1.005-10 4." . [€325,152
1.005.” I- ~ , ,2 - - , , ~ . 2 - ~ 2 .
10 20 30 40 50 60 70 80 90 100
Voltage (V)

Figure 4.15 I-V plot of a Fringe 5 diode under reverse bias versus temperature

53

I-V plots of both Fringe l and Fringe 5 diodes comparing the two temperature
extremes are shown in Figures 4.16 and 4.17, respectively. The change in temperature
has a larger impact on the diode while in reverse bias than forward bias. Using 70 volts
as an example, the reverse bias current in both ﬁgures increase by over two orders of
magnitude from 300 K to 425 K while the forward bias current for diode 1 and diode 5

increase by one order of magnitude or less.

1005-01 a
l
1.005-02 »;

1.00E-03 I

 

1 0013-04 ~

100505 J

Current (A)

-4
......
------------
.....
.....

l .00E-06 '

 

] ' ‘4“ i—rs— 300 K Reverse Bias
1.00E-07 ..6" ,IN‘I

, + 300 K Forward Bias ‘
I f -6- 425 K Reverse Bias |
1-005-03 . ,_ , ..-,r_v' " je— 425 K Forward Bias

‘
.

 

._4

1005.09 ‘ ~- use . 22 2,2,- ,2
10 20 30 40 50 60 70 80 90 100
Voltage (V)

 

 

2 _ ___. Y‘ _ 2,2 222,2- 2

Figure 4.16 I-V plot of Fringe 1 diode for both temperature extremes

After the reverse bias curves break away from their respective forward bias
curves, these current-temperature relationships hold fairly steady up to the maximum
voltage used in this experiment. Using Figure 4.16 as an example, at approximately 40
volts, the reverse bias curves have split off from the forward bias curves and they

maintain two orders of magnitude current difference up to 100 volts. This observation

54

can be made with both forward bias and reverse bias I-V curves in both ﬁgures.

     

 

1.00E-03
1.00E-04 'I . - ,.o;:::==== ====
1005-05 4
g 1.00E-06 .
E .
Q) .
g .
U 1.00E-07 ,_
1.00E-08 ' r _
: -JK- 300 K Forward Bias :
1 . . 19 Vi ‘ +425 K Reverse Bias
MOE-09 ., «VII? l-x— 425 K Forward Bias .1
1.00E-10 ~ - 222 . , 7% . gﬂr—‘m‘ ~ 7 - ‘r”*—‘f————“” 22,
10 20 30 40 50 60 70 80 90 100
Voltage (V)

Fringe 4.17 I-V plot of Fringe 5 diode for both temperature extremes

4.4 Reverse breakdown voltage vs. thickness for initial-state diodes

Using a Tektronix 577 Curve Tracer with a Tektronix 177 test ﬁxture, the reverse
bias breakdown voltage was measured for diodes with varying thickness. Unlike the case
of the HP4145B where the data was logged automatically by a computer, this data was
taken manually by setting the voltage to a particular value and reading the current from
the Curve Tracer screen. Reverse bias I-V curves for diodes from all 5 fringes are shown
in Figure 4.18. The last data point shown for each I-V curve is the last recorded before

the current began to increase almost vertically. Shown in Figure 4.18 for 4 out of the 5 I-

55

 

 

V curves, as the diodes approach their respective breakdown voltage, the current begins
to increase exponentially. The breakdown voltages along with calculated electric ﬁelds

are recorded in Table 4.2.

 

1.005-04 -i
l o "
l ., ,
I ./
I
100505 l
i
310013-06 l
a
0)
t: .
:r '2 222 2_
0 1005—07 g+Fringel
I l-A-Fringe2]
l-e-Fringe3l
l .
1.00E-08 ,. [*Fr’ng“.
9.3559365]
II
[00509 - - , 222.__ -w—n——»A-»r——-—-———————.———~—_—-—4——— ——.— -
0 50 100 150 200 250 300 350

Voltage (V)

Figure 4.18 Reverse bias breakdown curves for diodes of varying thickness

 

 

 

 

 

 

Fringe Reverse Breakdown Voltage (V) Electric Field (106 V/cm)
1 225 9.04
2 255 6.73
3 270 5.31
4 280 4.38
5 300 3.90

 

 

 

 

 

Table 4.2 Observed breakdown voltages and electric ﬁelds for the ﬁinge diodes

56

4.51nitiation of a change in initial-state diode characteristics

On select diodes, a Tektronix 577 Curve Tracer with a Tektronix 177 Test Fixture
was used to push the diodes in forward bias beyond the 20 mA current limit imposed by
the HP4145B. On all devices subjected to this treatment, when the power reached a
critical value, an abrupt change in I-V characteristics was observed. The change
exhibited itself as a dramatic drop in forward voltage for a given forward bias current.
The initial impression of the high power induced change was that of a thermal breakdown
short circuit in forward bias. However, upon closer examination, it was observed that the
devices were still highly rectifying, but with a much lower forward voltage drop.

Identiﬁcation of the physical basis of the change was beyond the scope of this
thesis. One may speculate that the high power levels caused a temperature increase
which in turn caused a change in carbon atom conﬁguration, from a highly resistive
diamond state to a highly conductive carbon conﬁguration. In any case, the
nomenclature of “phase-change” diodes is used in this thesis.

Initial-state diodes from Fringe 1, Fringe 2, Fringe 3 and Fringe 5 were tested and
subsequently modiﬁed. Fringe l diodes reached 32-60 mA at 80-90 volts before they
reached thermal breakdown. Fringe 2 drew the highest power of 5.58 Watts with a
maximum current of 45 mA at 124 volts. Fringe 3 and Fringe 5 diodes reached currents

of 33 mA at 120 volts and 20-30 mA at 130-140 volts, respectively. The absorbed power

ranged from about 4 to 5.58 Watts, corresponding to power densities of over 2 kW / cmz.

57

4.6 l-V characteristics of phase-change diodes vs. thickness at 300K

The resulting “phase-change” led to improved I-V characteristics. The “phase-
change” diodes delivered much larger currents at smaller voltages while often increasing
their rectiﬁcation ratio. A maximum rectiﬁcation ratio of 1.69 x 105 was measured
at .+_ 10 V. Due to the large increase in current, I-V data was collected from only -10 to 10
volts to avoid reaching another thermal breakdown and destroying the diode. The curve
tracer was used to induce this permanent change in several devices to verify repeatability.
The I-V plot of an example phase-change diode is shown in Figure 4.19.

The forward bias and reverse bias I-V plots for the phase-change diodes versus
fringe are shown in Figures 4.20 and 4.21, respectively. In the previous section, the
dominating variable for I-V behavior of the initial-state diodes was shown to be the
thickness of the diamond ﬁlm. Sampling diodes from different ﬁinges resulted in a
consistent change in I-V characteristics; however, this is not the case for the phase-
change diodes as evident by the I-V data presented in the ﬁgures. Data from multiple
diodes ﬁ'om the same fringe are displayed in each ﬁgure to demonstrate this fact. Figure
4.20 includes three Fringe 5 diodes with differing forward bias I-V curves where the
same fringe has diodes with both the largest forward bias current and the smallest. In this
same ﬁgure, a Fringe 1 diode has an almost overlapping I-V curve with the highest
Fringe 5 curve, which is not consistent with the initial-state diode’s I-V behavior.

The reverse bias data in Figure 4.21 demonstrates the same lack of dependence on
ﬁlm thickness. The three Fringe 5 diodes occupy the top three I-V curves while Fringe 3

has the lowest with the Fringe 1 diode curves residing in between. Again, this does not

58

Current (A)

Current (A)

l .OOE-Ol

l.OOE-02 .
1.00E-03 '.
1.005-04 ;
1.0013-05 j
1.00E-06 7
1.005-07 ;

l .00E-08 ' H

..
...-
..........
..........
...............
_,..--- ........
..-- ......
.-“ ZZZ

.-
‘
a' ::::
‘ '
0"

1.00E-09 ';"

l.OOE-lO -

LOOE-Ol

1.001302 ~
1.00E-03 .
1.00E-O4 .
1.00305 5
l.00E-O6 }
1.005-07 ;

1.00E-08 "

l .OOE-O9

Figure 4.20 I-V plot of phase-change diodes under forward bias versus fringe

Voltage (V)

ooooooo
..-ao-gqn. _.
.‘O.---.. - .......
.--¢---.:::::-,---------oo--
o...
...............
.---
oooooo
.........
c
-.-o
.--
0"
-O
.o
c
o

. - -_- - - . ,
p-e- Forward Bias
_: Reverse Bias

Figure 4.19 I-V plot of a phase-change Schottky barrier diode

 

l 2 3 4 5
Voltage (V)

59

10

-.l‘
-------------
.....

--.o
--.oo-’ _-
o --—
.- .---

 

l+ Fringe 3 Device
i-X- Fringe 5 Device
+ Fringe 5 Device

Psi-Fringe 1 Dare“. 2
i-B- Fringe 1 Device

"efﬁng: 5. Renee .

--
-----------

10

 

1 .OOE-O6

 

 

E
E
Q)
l:

3 _. -_'.-- . .-..-- _ ___ _.-____-w l

U 5 1,29." ;+Fringe 1 Devicei

1.00E-08 l 53.." l-B—Fringe 1 Devicel

: . ‘

l y," —X- Fringe 3 Devrce

‘ ,f' :+ Fringe 5 Device

u" j-9-- Fringe 5 Device

'—+- Fringe 5 Device

 

1.00E-O9 v— ~ 77 -,_ - «AH -— .__._. ~17 #-—-——-« — - -. — —» —
O l 2 3 4 5 6 7 8 9 10
Voltage (V)

Figure 4.21 I-V plot of phase-change diodes under reverse bias versus fringe

conform to the behavior of a device where ﬁlm thickness is the dominating variable.
From previous data, we would expect to see a more consistent change in I-V behavior
from fringe to fringe. Therefore, thickness may still be a variable in I-V behavior for
these phase-change devices, but the difference in device-to-device behavior is the
dominating variable.

Rectiﬁcation ratios calculated as a function of voltage for phase-change diodes
from Fringe 1, 2, 3 and 5 are shown in Figure 4.22. Multiple phase-change diodes from
Fringe 1 and Fringe 5 were studied but only data from diodes with the highest
rectiﬁcation ratios were plotted in this Figure. Rectiﬁcation ratios as a function of

voltage for all Fringe 1 and Fringe 5 diodes are plotted in Figure 4.23. Figure 4.23

60

1.00E+06 ~

 

LO0E+05 . N
31.00304 - ......................
3. 5. ---------
E 1.005+03 3
t: i
.9 l
*5 1.00E+02 1
E
8 1.00E+Ol 0! L0-Fringel
a: , I r-X-FringeZ
1 L-9-Fringe 3
1.001—:+00 ?-_e-— Fringe 5
1005-01 ¥ . . . .. . ‘_ _____
0 l 2 3 4 5 6 7 8 9 10

Voltage (V)

Figure 4.22 Rectiﬁcation ratios calculated for phase-change diodes vs. fn'nge

 

 

 

1.00E+06
1.00E+05 -«.
E: LO0E+04 J "Lb"..- "czﬁzzﬁ‘ﬁzzzﬁz .........................................
‘0’ ,1," 4:4“ """"""""""""""""""""""""""""""""
5 1001—303 1 ----
g l ."
g 1.0013+02 1 _1 In,”
5.3 2.; +Fr1ngel.
‘3 1005+01 H .-B_Fri"gel
‘3‘ ' lu j—A—angeS‘

‘ -; i-e-FringeS'
1.005+00 l '-J|§f_l:ringﬁe75
1305-0] . _ ._ . .___ . . __. ,_ _ . __ _ .__._______,_-.

0 l 2 3 4 5 6 7 8 9 10

Voltage (V)

Figure 4.23 Rectiﬁcation ratios calculated for phase-change diodes vs. ﬁinge

61

 

provides another example of the lack in consistency between I-V characteristics ﬁ'om

device to device, where both devices are located on the same ﬁinge.

4.7 I-V characteristics of phase-change diodes vs. thickness and temperature

To identify the temperature dependence, the phase-change diodes were exposed to
the same temperatures as the initial-state diodes. At every 25 K step in temperature, I-V
data was collected from the diodes from -10.0 to 10.0 V along with a detailed
measurement from 0.1 to 0.7 V. Only diodes from Fringe l, Fringe 2 and Fringe 5 were
used in this study. Forward bias and reverse bias I-V plots of a Fringe 1 diode versus

temperature are shown in Figures 4.24 and 4.25, respectively.

I .00E-02 i
J

l.OOE-O3 '

Current (A)

10013-04 5'

 

Voltage (V)

Figure 4.24 I-V plot of Fringe 1 phase-change diode in forward bias vs. temp

62

From 1 to 10 V, where bulk series effects dominate forward bias current, Figure
4.24 shows a slight monotonic increase of forward bias current with increasing
temperature. The temperature variation is substantially less than for initial-state diodes.
However, the variation in current with respect to temperature in Figure 4.25 is
pronounced. As was the case for initial-state diodes, there is over two orders of
magnitude increase in reverse bias current from 300 K to 425 K. As will be discussed in
chapter 5, the reverse bias I-V characteristics are dominated by the metal-semiconductor

banier for initial-state diodes, but this is not the case for phase-change diodes.

l .00E-04

 

 

 

Current (A)

 

 

1,005-09 L --.— .. , - .- ._ . .--_ .. Wm _ _ -» —-.
1 2 3 4 5 6 7 8 9 10
Voltage (V)

Figure 4.25 I-V plot of Fringe 1 phase-change diode in reverse bias vs. temp

More forward bias temperature dependence is seen in Figure 4.26, for an I-V plot

of a Fringe 1 phase-change diode, over a voltage range of 0.1 to 0.7 volts. In this voltage

63

region, diode barrier affects dominate the current, particularly up to about 0.4 volts.

Initially, a considerable distance separates all curves from each other; however, as the

voltage increases beyond 0.4 volts, the curves begin to pinch together as bulk series

effects come into play. Referring to Figure 4.24, the curves remain pinched together for

the extent of the measured voltage range.

I-V plots for a Fringe 2 diode in forward and reverse bias with varying

temperature are shown in Figure 4.27 and Figure 4.28, respectively. Figure 4.29 shows a

detailed I—V plot for the diode under forward bias from 0.1 to 0.7 volts. The same trends

in forward data appear for the Fringe 2 diode as the Fringe 1 diode, although, there is

slightly more temperature dependence from 1 to 10 volts.

Current (A)

l .00E-04

1.00E-05

 

1.00E-06
1005-07 ," .ﬁ"
1 ,, "
"’1
1.00E-08 l- -7 _- , _ _
0.1 0.2 0.3 0.4
Voltage (V)

 

-B-300K

+325K
+350K
—x—37SK
+400K“
:425K]

0.5

 

0.6 0.7

Figure 4.26 I-V plot of Fringe 1 phase-change diode in forward bias vs. temp

64

1.00E-02

Current (A)

l 2 3 4 5 6 7 8 9
Voltage (V)

Figure 4.27 Plot of Fringe 2 phase-change diode in forward bias vs. temp

1.00E-O3

Current (A)

+400K;

1.00E-07 ~ - ,

1 2 3 4 5 6 7 8 9
Voltage (V)

Figure 4.28 I-V plot of Fringe 2 phase-change diode in reverse bias vs. temp

65

 

 

10

l .00E-03

Current (A)

:-e—300K
'-A—325K
-B-3SOK
E l—x—375K
.‘ fit-400K

1
I

 

 

10013-07 —- -- — . ________ ._ .
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Voltage(V)

 

Figure 4.29 I-V plot of Fringe 2 phase-change diode in forward bias vs. temp

Forward bias and reverse bias I-V plots for the ﬁnal phase-change diode tested,
Fringe 5, are shown in Figures 4.30 and 4.31, respectively. Figure 4.32 shows a detailed
plot of the diode under forward bias from 0.1 to 0.7 volts. Again, the data trends of the
Fringe 5 diode resemble that of both Fringe 1 and Fringe 2; however, Fringe 1 and Fringe
2 are much closer in current values. Both Fringe l and Fringe 2 current values fall within
the range of 10'4 to 10'2 amps while Fringe 5 falls within 10'5 to just over 10'4 amps.

There is a slight discrepancy with Figure 4.32. The 300 K I-V curve does not
follow the same pattern as the other I-V curves from this ﬁgure and other diode ﬁgures.

The exact reason for this odd behavior has not been determined.

66

 

Current (A)

Current (A)

1.00E-03

 

1.00E-04
1.00E-05 ‘
1.00E-06 . . .--- _ - . .. . ---_...-____.- . . _ ,. a-
l 2 3 4 5 6 7 8 9 10
Voltage (V)
Figure 4.30 I-V plot of Fringe 5 phase-change diode in forward bias vs. temp
1.00E-O4

 

 

ALLAA AAAAAAA A AAAAAA AAA
AAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAA -‘I‘--'--‘x--“‘- Y)

 

A

A AAAAAA I- --u

l _

1.00E-06 W

AAAAAAAAAA
A
AA‘

 

 

 

l.OOE-08 —x— 375 K1
+ 400 K
-9- 425 K
1.00E-09 - . - . - - - . a . ,, . ‘
l 2 3 4 S 6 7 8 9 10

Voltage (V)

Figure 4.31 I-V plot of Fringe 5 phase-change diode in reverse bias vs. temp

67

1.00E-04

10013-05 ; - - -
3 - - - .-. .-. .-. :.=.=A=+:‘:€:£‘t£:-: a -. 1. .
- - = 3 3 :Asxvgu‘“ i £0§930101v1 - ‘ 1.?
1‘ - -L=‘=‘:‘:”grex-knboioi‘oioxgﬁoﬁ’x‘d" ° .......... “ “ “if. : : :
l ,;:=,;:L~'“ --_=g'_-,'.'.'-_'i':-f'_-..‘_-g ----
A l ' :A‘: 5‘35 - ‘ ' - = = = = 7*:JT’ ;‘,'.;.-...‘ A - A
< I "’:’&C\ '—=====-‘ ;:;__--
:: 0 ‘3‘ ' = = = = ‘ '
v = ‘ - 1“
g 1.00E-06 -5555‘ A‘-’-‘¢J'
L‘ r 5 ‘ - ‘ ‘ ’ ’4 I _ .
5 5 ,=="" " +3001<[
,r rte-325K;
. . ‘ ‘ —B— 350 K)
‘ 1
1.001507 . ‘ §+375 K:
1+ 400 K;
g .
:—e—- 425 K 1
1.00E-08 " -- . __ __
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Voltage (V)

Figure 4.32 I—V plot of Fringe 5 phase-change diode in forward bias vs. temp

It should also be mentioned that the reverse breakdown voltage of these phase-

change diodes was tested but not to the same degree as the initial-state diodes. Of the

few diodes tested, the reverse breakdown voltage fell around 120 volts, roughly half the

breakdown voltage of the equivalent initial-state diodes.

68

Chapter 5

Analysis and Discussion

5.1 Introduction

This chapter presents an analysis and discussion of the results shown in chapter 4.
A general DC model proposed for the nanocrystalline diamond based Schottky barrier
diodes and discussion of ﬁeld-activated conductivity according to Poole’s Law observed
in these devices is presented in the ﬁrst two sections. Electric ﬁeld dependency in
forward biased structures along with temperature dependence in both forward and reverse
bias is considered in the next three sections. Finally, a DC model for the phase-change
diodes through characterization of these devices is investigated in the last section of this

chapter.

5.2 General model

As shown in chapter 4, the nanocrystalline diamond ﬁlms are highly resistive at
low to moderate electric ﬁelds. Application of a sufﬁciently high voltage across the
diamond ﬁlm results in a ﬁeld—activated conductivity modeled by Poole’s Law where the
relationship follows from equation [2.04]. Thus, the current—voltage characteristics of a

two terminal structure with one rectifying contact can be modeled by a voltage variable

69

resistor in series with a diode as shown in Figure 5.1.

   

p-type Silicon Zirconium

Figure 5.1 General model for two-terminal rectifying structure

Consider, as a conceptual example, where the current-voltage characteristics of
the resistive ﬁlm and rectifying junction are as shown in Figure 5.2 with the dashed line
representing the I-V characteristics of the junction and the solid line representing the I-V
characteristics of the diamond ﬁlm with ﬁeld-activated conductivity. Since the two
model elements are in series, the voltage will be divided between the two. Given the I-V
characteristics shown in Figure 5.2, for forward bias voltage, the current will be limited
by the high resistance of the diamond ﬁlm. For reverse bias current, at low voltages the
current will be limited by the diamond ﬁlm but at high voltages the current will be
limited by the rectifying junction. The resulting ﬁlm limited forward-bias current (solid
line) and junction limited reverse-bias current (dashed line) for the two-terminal
rectifying structure is shown in Figure 5.3. In fact, this conceptual illustration is
qualitatively comparable with the experimental data, as shown in Figure 5.4. It is this
general approach that is used in analyzing the rectifying structures described in chapter 4,
where the structures may be analyzed as a voltage variable resistance in series with a

Schottky rectifying junction.

70

 

 

 

I
10-4
I
I
10'6 I
,— I
3 10'8 |
‘a’ -100 -50
0)
5 50 100
L)
-10-8
-10'6
-10-4
Voltage (V)

Figure 5.2 IV plot of rectifying junction (dashed) and ﬁeld-activation (solid)

    
  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Forward Bias - Film Limited
10-4
Fwd and Rev Bias - Film Limited
3 _
E 10-6 __ __ .. — —
E T
0
Reverse Bias - Junction Limited
10-8
0 50 100

Voltage (V)

Figure 5.3 I-V plot of two-terminal rectifying structure with series resistance

71

Current (A)

1.00E-02

1.00E-03 ‘

1.00E-04 ‘

1.00E-05 ‘

1.00E-06 ‘

1.00E-07

1.00E-08 '

l .OOE-O9

1.008-10

I:

n
.. _ . ..,_ _La_.,,_

20 3O 4O 50

60

Voltage (V)

 

' -A— Ra/erse Current 7
-8— Forward Current

80 90 100

Figure 5.4 I-V plot of diamond based Schottky banier diode

5.3 Poole’s Law

F ieId-activated conductivity in our polycrystalline diamond ﬁlm follows Poole’s

Law as described in Chapter 2 and experimentally observed in Chapters 3 and 4. This

section considers the physical origin of this phenomenon in order to further investigate

the implications of these ﬁndings. Under moderate electric ﬁelds, current density follows

thermionic emission and is proportional to exp(—q(p,- / kT) where 0),- is the potential banier

of the trapped carrier. Application of a high electric ﬁeld results in a reduction of the

potential barrier by an amount:

72

Agp=qu/kT [5.01]
where E is electric ﬁeld and s is the distance between Coulombic centers [32]. If the
distance traveled by the carrier aﬁer emission is proportional to s, meaning the carrier is
immediately recaptured at the next available Coulombic potential, then the current

density is proportional to [32]:

J cc 3 exp(:gi)[exp(%) —- exp[ 3(qu H [5.02]

 

or at large E:

J at sexp[:q—¢i)exp(£S—) [5.03]
kT 2kT

However, if the distance that the carrier travels after emission is proportional to E, then

the current density is proportional to [32]:

J oc Eexp(;%ﬁ]exp(%] [5.04]

or in terms of conductivity:
0' = 00 exp(—Z§g—) = 00 exp(aE) [5.05]

2kT

where 00 is proportional to:

00 cc exp(%ﬂ) [5.06]
and:

a = qs/ZkT [5.07]

Equation [5.05] is deﬁned as Poole’s Law. Therefore, the total conductivity of the

sample including the ohmic conductivity, 0'00 , becomes:

73

 

0' = 000 + 0'0 exp(aE) [5.08]
Equation [5.08] is the most convenient form of Poole’s Law and was used in the analysis

of the ﬁeld-activated conductivity present in the nanocrystalline diamond layer of the

Schottky barrier diodes.

5.4 Field-activated conductivity in forward-biased rectifying structures

Current-voltage data collected from the diamond-based Schottky barrier diodes
under forward bias, presented in section 4.2, is used to investigate the ﬁeld-activated
conductivity according to Poole’s Law in these structures. Calculating conductivity and
electric ﬁeld and plotting the data on a semi-log scale displays an exponential
relationship at high ﬁelds indicative of Poole’s Law. Due to the magnitude of the electric
ﬁelds approached in this study, it is believed that electrons reaching saturation velocity
introduced non-linearity into the data curves around 1.5 MV/cm. Therefore, Poole’s Law
was investigated in the linear portions of the data curves before the data became non-
linear at higher electric ﬁelds. Data from thicker ﬁlms retained this linear portion of the
data curve for more of the voltage range as opposed to thinner ﬁlms whose linear
portions are much smaller. Electrons in the thinner ﬁlms would reach saturation velocity
at lower voltages due to the higher electric ﬁelds for a given voltage. A plot of
conductivity versus electric ﬁeld for all ﬁve fringe thicknesses is shown in Figure 5.5 and

the Poole’s Law variables calculated from the data curves are shown in Table 5.1. The

ohmic conductivity, 0'00 , was found to be approximately 1-10 x 10'13 (0 cm)'1 where

74

accuracy was reduced by the current limitation of the measuring apparatus.

Conductivity (9 cm)

1.13-10 -
l.E-Il l

l ,.‘
1.13-12 11,50,34

1.5-13 '--»

I.E-03 -
1.5-04
1.13-05 1'
1.5-06 «
1.13-07
1.13-08 ~

LIE-09 -

I

 

 

0.0E+00 5 .OE+05

 

I .OE+06

1.5E+06

u

H

“

FIB-Fringe 1
:-0-Fringe2§
'—&-Fringe3§
j—x—Fringe4f
1+Frin8e5

 

2.0E+06
Electric Field (V/cm)

2.5 E+06

3.5E+06

r

3.0E+06

Figure 5.5 Conductivity vs. electric ﬁeld plot versus ﬁ'inge thickness

 

 

 

 

 

 

 

 

 

 

 

Fringe Thickness (um) 11(105 cm/V) 0'0[10'14(Qcm)'1] 000[10'12(Qcm)'1]
1 .249 0.781 0.737 ~ 1-10
2 .379 0.969 1.468 ~ 1-10
3 .509 1.200 0.993 ~ 1-10
4 .639 1.321 0.933 ~ 140
5 .769 1.331 1.598 ~ 1-10

 

Table 5.1 Calculated Poole’s Law variables for the ﬁve fringe thicknesses

75

 

 

Ideally, the Poole’s Law expression characterizing the ﬁeld-activated conductivity
for each of the ﬁve ﬁlm thicknesses would be equal, having no dependence on thickness.
In other words, the equation variables a, 0'0 , and 0'00 would be the same for each ﬁlm
thickness which is what would be expected for a homogeneous diamond ﬁlm. Although
the variables are within a factor of two in this study, there is a systematic increase in a
with increasing ﬁlm thickness. The relationship between diamond thickness and slope, a,

can be seen in the table and is more apparent in Figure 5.6.

1.4 -
1.3-
1.2 -

1.1 ~

-5
01(10 cm/V)

0.9 ;
0.8 «
0.7 i

0.6- .- — .-- -3- _-,_L ,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Thickness (um)

Figure 5.6 Plot of a versus diamond thickness

As shown in Figure 5.6, the Poole slope, a, increases and eventually plateaus as
diamond thickness increases. This would suggest the structure of the ﬁlm is not

completely homogeneous with depth, but varies in the initial stages of growth,

76

inﬂuencing the ﬁeld-activated conductivity. As thickness increases, this difference in
diamond structure becomes less noticeable and a eventually stabilizes. However, despite
this effect, all ﬁve values calculated for a speciﬁc variable in the Poole’s Law expression,
and shown in Table 5.1, are in relatively close proximity of each other for each of the
three variables. Moreover, the Poole slopes are within the ranges previously reported for

thin diamond ﬁlms [14].

5.5 Temperature dependence of forward-biased rectifying structures

I-V data collected from the Schottky diodes while exposed to six different
temperatures ranging from 300 K to 425 K, presented in section 4.3, was used to further
investigate the temperature dependence of the ﬁeld-activated conductivity in the context
of Poole’s Law. Plots of conductivity versus electric ﬁeld for Fringe 1 through Fringe 5,
each with six separate temperature plot lines, were created. Two example conductivity
versus electric ﬁeld plots are shown in Figure 5 .7 and Figure 5.8 for Fringe 1 and Fringe

5, respectively. For each temperature plot line the Poole’s Law variables, a and 00 , were

calculated. Again, due to non-linearity at higher electric ﬁelds, the data range used to

calculate a and 00 was limited to the smaller linear region in the middle of the plot lines.

All computed values of a and 00 for each ﬁinge and temperature are shown in Table 5.2

and Table 5.3, respectively.

77

 

-1

LOB-05 ,

l .0E—06

I .0E-07 -

l.0E-08

l.0E-09 ~

Conductivity (Q cm)

 

LOB-12 ‘ 7 ~~~77 ~ 7 r7 -, , 7 7~
0.0E+00 5.0E+05 l.0E+06 1.5E.+06 2.0E+06 2.5E+06 3.0E+06 3.5E+06
Electric Field (V/cm)

Figure 5.7 Conductivity vs. electric ﬁeld plot for Fringe 1 diode
LOB-06
l.0E-07 -
1013-08 4
l.0E-09

l.0E-IO 7

Conductivity ((2 cm)

 

l.0E-l3 -

0.0E+00 2.0E+05 4.0E+05 6.0E+05 8.0E+05 I.0E+O6 I.2E+06 1.4E+O6
Electric Field (V/cm)

Figure 5.8 Conductivity vs. electric ﬁeld plot for Fringe 5 diode

78

 

 

 

 

 

 

 

 

 

 

 

 

a (10-5 cm/V) Fringe 1 Fringe 2 Fringe 3 Fringe 4 Fringe 5
300 K 0.711 0.902 0.965 1.043 1.141
325 K 0.694 0.943 0.940 1.013 1.207
350 K 0.698 0.942 1.031 1.090 1.183
375 K 0.667 0.897 0.926 1.063 1.146
400 K 0.661 0.833 0.838 0.990 1.055
425 K 0.609 0.782 0.808 0.843 0.964

 

 

 

Table 5.2 The Poole slope, a, calculated for each ﬁinge and temperature

 

 

 

 

 

 

 

 

 

 

 

 

 

‘70 ((2 cm)-1 Fringe 1 Fringe 2 Fringe 3 Fringe 4 Fringe 5
300 K 2.36x10‘14 2.97x10'14 5.71x10‘14 6.22x10'l4 5.86x10'l4
325 K 5.36x10‘14 3.70x10'14 1.20x10'l3 1.40x10‘l3 6.59x10‘l4
350 K 9.58x10‘14 7.34x10'14 1.12x10'13 1.51x10'l3 1.56x10‘13
375 K 2.55x10'13 2.15x10'l3 4.97x10'l3 3.76x10‘l3 4.18x10'13
400 K 2.73x10'13 5.93x10'13 1.37x10'12 9.86x10'13 1.12x10'12
425 K 1.49x10'12 1.83x10‘12 3.80x10'12 4.60x10‘l3 3.95x10'12

 

 

Table 5.3 The Poole conductivity, 0'0 , calculated for each fringe and temperature

The separation, s, between Coulombic centers can be determined using Equation
[5.07] which provides the relation between a and s. Due to the inverse temperature
dependence of s, plotting a versus inverse temperature for all ﬁve diamond thicknesses
and determining the slope of the linear line provided the average separation distance, s,

for a particular fringe thickness. The values of a used in the plot are shown in Table 5.2.

79

An example plot of a versus inverse temperature is shown in Figure 5.9 for Fringe 1. The
method of least squares regression was used to ﬁt an appropriate linear trend line to the
data. The slope from this line for Fringe 1 along with the slopes calculated for Fringes 2-

5 are presented in Table 5.4.

7.40E-06
7.20E-06 -
7.00E-O6 :

A 6.-801306f
E
d

 

66013-06 -
6.40E-06 7
6.20E-06 3
C]
6.00E-06 - -- - ---—--——— —--‘--—— —- i- H“ m- ......
0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034

Inverse Temperature (l/K)

Figure 5.9 Plot of a versus inverse temperature for Fringe 1

The potential barrier, (0,, is proportional to 00 as described in equation [5.06]. The
potential barrier was determined by plotting the natural log 00 versus inverse temperature.
An example plot of natural log 00 versus inverse temperature is shown in Figure 5.10 for
Fringe l. The values of 00 used in the plot are shown in Table 5.3. The method of least

squares regression was used to ﬁt an appropriate linear trend line to the data. The slope

of this line provided the potential barrier, 02,-, for a given thickness. The slope from this

80

line for Fringe 1 along with the slopes calculated for Fringes 2-5 are presented in Table

5.4. Ideally, for a ﬁlm that is homogeneous with thickness, the potential barrier should

not be dependent on thickness. Although the values are different, they are all reasonably

close in value ranging from 0.330 to 0.375 V, within range of previously reported [17].

-27
-27.5 1
-28 '

-28.5 3|

-29.5

ln(o'0)

-30 .
-30.5 f
-31 f

-3l.5 1

-32. , .,_ ,_.. . _
0.0022 0.0024 0.0026

_ .—_,—-_ _- .__ .-.r _ __ __ _,
1

0.0028 0.003 0.0032 0.0034
Inverse Temperature (I/K)

Figure 5.10 Natural log of 00 versus inverse temperature for Fringe 1

 

 

 

 

 

 

 

 

Fringe s (nm) 0),- (V)
1 1.55 0.330
2 2.24 0.368
3 2.76 0.366
4 2.42 0.346
5 3.28 0.375

 

 

 

Table 5.4 Separation, s, and barrier height, 02,-, calculated for each fringe thickness

81

Looking at Table 5.4, a trend of increasing 5 with increasing fringe thickness is
apparent. Diamond growth by a CVD process is Columnar, with larger grains surviving
at the expense of smaller grains as the thickness increases. Thus, the diamond grains, or
crystallites, increase in size as diamond is grown. The separation size, s, was found to be
smallest in the thinner ﬁlms which is appropriate because at this thickness the crystallites
have not had a chance to grow very large. Therefore, the Coulombic potentials arising
from defects associated with grain boundaries are at a relatively high concentration
giving a small value of 3. Taking s to be equal to N”, where N is the concentration of
Coulombic potentials, for Fringe 1 N equals 2.69 x 1020 cm'3, or approximately one
center per 658 carbon atoms since the atomic density of diamond at 300 K is 1.77 x 1023
atoms/cm3. The opposite can be said for the thicker ﬁlms where the crystallites are larger
leading to a larger separation in grain boundaries and a larger value of s. For Fringe 5,
the density is 2.83 x 1019 cm'3, or one Coulombic center per 6,254 atoms. The N and s
values are within proximity of other reported values for polycrystalline diamond [15,16].

As can be seen in Figure 5.9 and 5.10, the data does not ﬁt the regression line
perfectly; therefore, error is present in the slope values. The error in the slope of the least

squares regression line was computed for both s and 0),. An 80% conﬁdence interval was

found for both variables of Fringe 1 such that separation, s, has a range of 1.55 i 0.37 nm

and potential barrier, 01,-, has a range of 0.330 t 0.042 V. The error range of s does not

span values calculated in Table 5.4 giving more evidence to a legitimate relationship

between s and thickness. The error range of 01,- does overlap all calculated (p,- values
which may challenge the appearance of a dependency of 0),. Note, however, that the

extracted barrier height does monotonically increase with ﬁlm thickness. This suggests a

82

large effective barrier height on thicker ﬁlms with a smaller Coulombic defect density.
This may result from an effective lowering of barrier height due to increased overlap of

potentials with higher N values.

5.6 Temperature dependence of reverse-biased rectifying structures

As stated in section 5.2, the general model of the rectifying device can be divided
into two sub-devices in series. Under forward bias and high electric ﬁeld, the current is
limited by the diamond ﬁlm exhibiting ﬁeld-activated conductivity. Under reverse bias
and high electric ﬁeld, the current is limited by the Schottky junction formed between the
zirconium contact and nanodiamond ﬁlm. In this case, we are able to characterize the
Schottky junction by extracting the potential barrier height, 023 , from the reverse I-V data
collected from the devices shown in Chapter 4.

Using the Schottky diode equation stated as Equation [2.11] in Chapter 2, the
temperature dependence of the barrier height can be investigated. Under a large reverse
bias voltage, the exponential term dependent on applied voltage reduces to zero leaving

the saturation current, 15, as the dominating contributor to the current through the device.

The saturation current is deﬁned in Equation [2.12] and has a strong exponential
dependence on the banier height, (03, and temperature. I-V data collected at -100 V (the

Image Force Effect was ignored in this analysis) was used to produce a plot of natural log

IS versus inverse temperature resulting in a linear relationship. The method of least

squares regression was used to ﬁt an appropriate linear trend line from which the banier

83

height could be extracted. An example plot of natural log Is versus inverse temperature

for Fringe 1 is shown in Figure 5.11. The extracted barrier height, (03 , from this slope

and the barrier heights for the rest of the fringes are shown in Table 5.5. The values are

within range of previously reported for thin submicrocrystalline diamond [33].

-7-

-9 .
-10 i

-11 i

In(Is )

-12 i

-13 : . . - .. -. ,- «WWW- _,L,._..._--_ _- .. . *
0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034

Inverse Temperature (1/K)

Figure 5.1] Natural log of Is versus inverse temperature for Fringe 1

 

 

 

 

 

 

Fringe 013 (V)
1 0.427
2 0.455
3 0.473
4 0.482
5 0.470

 

 

 

 

Table 5.5 Table of (03 calculated for each diamond fringe thickness

84

As shown in Table 5.5, there is an apparent relationship between barrier height
and fringe thickness. As thickness increases, (pg increases until it reaches a maximum
around 047-048 V. A plot of 023 versus ﬁinge thickness is shown in Figure 5.12. This
increasing barrier height trend is believed to be attributed to the polycrystalline diamond
structure within the ﬁlm. As mentioned previously, as the diamond ﬁlm grows in
thickness, the individual crystallites grow in height and width changing trap location and
density. It’s reasonable to assume that a Schottky junction formed on the surface of the
ﬁlm at different thicknesses and subsequently different distances between grain
boundaries will result in the formation of different effective potential barriers. Since the
banier height appears to level off at larger thicknesses, the barrier formation within the

diamond eventually stabilizes as the ﬁlm grows.

0.49
0.48
0.47 1

0.46 '*

(153 (V)

0.45 7
0.44 3
0.43 .

0.42 - - — -
0.2 0.3 0.4 0.5 0.6 0.7 0.8

Fringe Thickness (um)

Figure 5.12 Barrier height, (PB, versus fringe thickness

85

In the general Schottky diode case, the thermionic emission theory is sufﬁcient
for explaining the current transport process from metal to semiconductor. The equation
for current ﬂow in a Schottky diode according to thermionic emission, previously stated

in [2.11] and [2.12] and repeated here as one equation for convenience, is:

1: AA "72 exp[-—————— “”3 ] exp[q—Va) 1 [5.09]
kT nkT
and Richardson’s constant, A *, is equal to:
A“ = 47117;;1"‘k2 /h3 [5.10]

The thermionic emission theory is for high-mobility, single-crystalline semiconductors.
When a semiconductor does not fall into this category, other theories on current transport
in a Schottky junction exist such as the diffusion theory for low-mobility semiconductors
and the thermionic-diffusion theory which is a synthesis of the previous two [34]. Just as
in the thermionic emission case, the current ﬂow according to these two theories has a

strong dependence on applied voltage, Va , and the banier height, 023. The current

equation for an n-type sample according to the diffusion theory is deﬁned as:

2 1/2
kT a, kT n—kT

 

where A is cross sectional area, D,, is diffusitivity, NC is the conduction band effective
density of states, Vb,- is built-in potential, N D is donor density, and as is permittivity. The

current equation for an n-type sample according to the thermionic emission-diffusion

theory is deﬁned as:

 

In — -A——qLVC—R——exp[:q—¢5—) exp(an)—1 [5.12]
1+ UR /UD kT nkT

86

where UR is the thermal velocity and DD is the diffusion velocity through the sample.
Based on the thermionic theory and potential barrier, (03 , solved for the ﬁve

fringes, the Richardson constant should be easily extracted from the data. However, the
Richardson constant calculated for the devices fabricated in this study was several orders
of magnitude below a realistic value. Therefore, the thermionic theory is not sufﬁcient in
explaining the transport process within the nanodiamond ﬁlm. This is a reasonable
conclusion considering the thermionic emission theory is used to describe the transport
process in high-mobility, single crystalline ﬁlms which is not the case for the
nanocrystalline diamond ﬁlms used in this study. However, investigating further into the
other transport processes discussed previously requires a more detailed investigation and
is beyond the scope of this study. Despite the shortcomings of the thermionic emission

theory for these ﬁlms, the alternative theories also have a principal temperature

dependence for the saturation current proportional to exp(—qgoB / kT) . Thus, the

extracted values of 023 are valid in any case.

5.7 Modeling of phase-change rectifying structures

As previously mentioned in Chapter 4, the phase-change diodes are believed to be
the result of a thermal breakdown in the diamond layer from high voltage/current
combinations subjected to the original initial-state diodes. It is speculated that high
power levels caused a temperature increase which in turn caused a change in carbon atom

conﬁguration, from a highly resistive diamond state to a conductive carbon conﬁguration.

87

A ﬁlament of conducting carbon between the top zirconium contact and the silicon
substrate. where the zirconium/carbon-ﬁlament forms a Schottky barrier with the silicon,
is thought to exist within the diamond layer directly below the zirconium contact.
However, the ﬁlament is believed to occupy only a fraction of the area where the
majority of the carbon between the zirconium and silicon substrate still remains in the
highly resistive diamond state. A proposed DC model for the phase-change diode
structure is shown in Figure 5.13. There may be additional transitional materials between

the conductive carbon ﬁlament and the original diamond.

 

 

 

  

Diamond ''''''''''''' Carbon ............. Diamond

 

 

 

 

Silicon Substrate

 

 

 

Figure 5.13 DC model of the phase-change diode

Using the I-V data collected from the Fringe 1 phase-change diode, presented in
Chapter 4, several characteristics can be extracted to help explain the reverse-bias and
forward-bias behavior. The forward-bias I-V behavior resembles a typical Schottky

diode; however, the reverse bias I-V characteristics show an unexpected linear

88

relationship. This linear relationship would suggest that the reverse bias current is not
primarily originating from the reverse biased Schottky banier junction but is traveling
through a leakage path in the surrounding diamond or other transitional material. Due to
the low voltage, any ﬁeld-activated conductivity is negligible. Therefore, the leakage
path behaves as an ohmic resistance. A current-voltage plot of the reverse bias data
collected from the Fringe l phase-change diode at 300 K is shown in Figure 5.14. The
leakage current for the phase-change diode as shown in this ﬁgure is higher than the
leakage current for the original diode in Figure 4.7. This implies that either the
surrounding diamond was also affected by the thermal breakdown or that there is some

other transitional material between the conducting ﬁlament and the diamond.

8.0E-08 ~
7.0E-08 -
6.0E-08
5.0E-08 ~

4013-08 4‘

Current (A)

3013-08 7

2.0E-08

l.0E-08 ’

l

 

0,013+00 -- -- - . —-- - - -- —- - --- —- .
O l 2 3 4 5 6 7 8 9 10

Voltage (V)

Figure 5.14 Reverse bias I-V plot of Fringe 1 phase change diode at 300 K

89

The resistance of the leakage path has temperature dependence. Resistances for
the Fringe 1 phase change diode at each temperature are shown in Table 5.6. Activation
energy for the leakage path can be found by plotting natural log of the resistance versus
inverse temperature. The plot is shown in Figure 5.15 where the slope of the line,

acquired through the method of least squares, gives activation energy equal to 0.480 eV.

 

 

 

 

 

 

 

Temperature (K) Leakage Path Resistance (M9)
300 138.0
325 59.2
350 21.0
375 5.25
400 1.49
425 0.765

 

 

 

 

Table 5.6 Fringe 1 phase-change diode resistances under reverse bias

The Fringe 1 saturation current, 13, can be extracted from the forward I-V plot in

Figure 4.26 for the ﬁrst three temperatures, 300-350 K, by extrapolating the linear region
to zero volts. This was not possible for the other temperatures due to lack of a sufﬁcient
linear region in the plot line. The saturation currents are shown in Table 5.7. The
ideality factor, n, can also be determined through the slope of these same three linear
regions using the following equation derived ﬁom the Schottky current equation:

n=_4_ V1-V2

[5.13]
kT 111(11/12)

where (V1, 11) and (V2, 12) are two points on the linear portion of the plot line. The n

90

values are also shown in Table 5.7.

20 ,
19 1%
18 -1
17 ~-
16

15 9

14

 

ln(Resistance)

13 f
12
111

10 — -- .- -— --—-- ______. — —.-—-—---—-— -—-—- *-

0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034
Inverse Temperature (l/K)

Figure 5.15 Natural log resistance vs. inverse temp for Fringe 1 phase-change diode

 

Temperature (K) Is (nA) n

 

 

 

300 2.0 1.88
325 4.0 1.69
350 15.0 1.67

 

 

 

 

 

Table 5.7 Is and n values for Fringe 1 phase-change diode

The temperature dependence of the saturation currents presented in Table 5.7 can
be used to estimate the barrier height of the Schottky junction. Plotting the natural log of

IS versus inverse temperature and using the method of least squares regression to ﬁt a

91

linear line provides the slope from which the barrier height can be extracted. However,
since there are only three data points, the computed barrier height should be taken only as

an estimation. The natural log of Is versus inverse temperature plot for Fringe 1 is shown
in Figure 5.16. The banier height extracted from the slope of this line was found to be

0.306 V.

-29.5 .

~30.5 ‘

ln(Is )

-3l.5 ‘

-32 . . _ .. .. , __.- .. _ - .__.._., _ __
0.0028 0.0029 0.003 0.0031 0.0032 0.0033 0.0034

Inverse Temperature (l/K)

Figure 5.16 Natural log [5 vs. inverse temp for Fringe l phase-change diode

At higher voltages, a small parasitic resistance, Rs, in series with the diode limits

the current through the diode. To take these effects into account, the Schottky diode

equation must be modiﬁed to include the voltage drop due to this resistance which is

deﬁned as:

92

1 = I,[exp(1W—;—T”§l] — 1] [5.14]
n

Solving the equation in terms of RS yields the following:

RS =l[V—ﬂ[ln—I—]:l [5.15]
I q Is

The resistance, RS, was calculated for voltages from 5-10 V and was fairly constant

throughout this range. The resistance calculated for the temperatures 300-350 K are

shown in Table 5.8. The change in Rs may be considered to be within experimental error.
However, the monotonic decrease of R, with increasing temperature (see Table 5.8) is

noted to be characteristic of semiconducting material, such as graphite or moderately

doped silicon, rather than metallic.

 

Temperature (K) Rs (k9)

 

 

 

300 2.35
325 2.25
350 2.05

 

 

 

 

Table 5.8 RS values versus temperature for Fringe 1 phase-change diode

The research of phase-change diodes in this study is rather preliminary, only
seven such diodes were subjected to experiment and the phase change was induced with
varying amounts of power from device to device. Other phase-change diodes were not
measured as extensively as the diode corresponding to Figures 5.14, 5.15, 5.16 and
Tables 5.6, 5.7, and 5.8. However, some characteristics of the diodes were investigated

as a partial analysis and used as a comparison to the Fringe 1 phase-change diode values

93

reported earlier.

Not all diodes showed the same linear behavior (from an ohmic resistance) under
reverse bias, so the model proposed in Figure 5.13 may only be valid for some of the
phase-change diodes, which includes diodes from Fringe 1, Fringe 2, and Fringe 3 but
excluding all three Fringe 5 diodes reported in this study. Figure 5.17 shows the linear
relationship in the reverse bias I-V data for Fringe 1 and Fringe 3 diodes at 300 K. Both
Fringe 1 and Fringe 3 diodes have resistance values at a temperature of 300 K in close
proximity to the 300 K resistance value in Table 5.6. The Fringe 2 diode with
temperature dependence data up to 350 K has resistance values around half of those in
Table 5.6; however an activation energy was unable to be extracted because the device
had inconsistent reverse-bias behavior at certain temperatures resulting in a non-linear
log (13) versus inverse temperature plot. A linear I-V plot of Fringe 2 phase-change diode
versus temperature is shown in Figure 5.18.

Both saturation current, 13, and n values were extracted from the Fringe 2 forward
bias data and were in proximity to those obtained for Fringe 1. A barrier height of
0.274 V was calculated using these values; however, this value is based on only two
temperature data points. Although this value should also be taken only as an estimation
due to lack of data points, interestingly enough, it is in proximity to the 0.306 V barrier
height calculated earlier for Fringe 1. Using these same [5 and n values to determine the
diode series resistance, Rs, provided resistance values in close proximity to those in Table

5.8.

94

1.25-07 -

Current (A)

    

 

1.013-07 '
8.05-08 "
v.2"
6.0E-08 '
405-08 -
, ,5 O, === 4:51.221 68‘...
. - 1 , I-B-Fringe 1 Device
1 . 4"": 7X- Fringe 3 Device
005+00 5' ._ WW
0 l 2 3 8 9 10

5
Voltage (V)

Figure 5.17 I-V reverse bias plot of phase-change diodes showing linearity at 300 K

  
 

1.25-04 -.
+300K'
1
1.0504 ‘9'325K ,.
+350K
+375K
8.0E-05 .7
3:
5 605-05
1:
3
U
405-05
---“"““-..-.::::;;::==52
ZOE-05 c ' “..----‘“:1::,,,=;555§§§E§§§§??;?"° 333
0.0E+OO — _ -_ __WT _ ___ __ g _
1 2 3 4 5 6 7 8 9 10

Voltage (V)

Figure 5.18 I-V reverse bias plot of Fringe 2 diode vs. temperature showing linearity

95

Chapter 6

Conclusion and Recommendations for Future Research

6.1 Introduction

This chapter presents a brief overview of the accomplishments made from this

research with discussion on possible improvement through future research.

6.2 Two-terminal nanodiamond based structures

This thesis has investigated the electrical properties of two-terminal structures
with nanocrystalline diamond ﬁlms of thickness ranging from approximately a quarter-
micrometer to one micrometer. Several electrode types were investigated including
indium, gold, zirconium, titanium, graphite paint, and pressure contacts to metals. Also,
several sample conﬁgurations were considered. Freestanding 1 pm thick nanodiamond
ﬁlms with gold contacts on each side provided symmetric current-voltage relations.
These behaved as voltage-variable resistors through the ﬁeld-activated conductivity
according to Poole’s law exhibited in the nanodiamond ﬁlms. Also, ﬂexible diamond
ﬁlm wrapped around a stainless steel tube with carbon paint acting as one electrode and
the tube acting as another was studied. Ultimately, a silicon-nanodiamond-zirconium

conﬁguration was fabricated from which over a hundred Schottky banier diodes were

96

fabricated with varying diamond ﬁlm thickness. The Schottky junction formed between
the zirconium contact and diamond ﬁlm where the silicon behaves as the ohmic contact.

Much of the data presented in the thesis was collected from these Schottky devices.

6.3 Nanocrystalline diamond based Schottky barrier diode results

Undoped nanocrystalline diamond based Schottky banier diodes exhibiting
rectiﬁcation ratios up to 1.1 x 104 at i 80 V were fabricated and studied in this research.
Investigation into the DC current-voltage characteristics of these devices versus
temperature and diamond ﬁlm thickness was presented. Devices were fabricated with
diamond ﬁlm thickness from about 250 — 770 nm and tested at temperatures from 300 —
425 K. A voltage variable resistor in series with a Schottky barrier diode was developed
as a DC model where the forward bias current was limited by the ﬁeld-activated
conductivity in the diamond ﬁlm and the reverse bias current was limited by the Schottky
junction. Following this proposed model, device characterization was completed and
presented in Chapter 5. Field-activated conductivity according to Poole’s Law was
observed in the diamond ﬁlm at all temperatures and thicknesses from which a separation

distance, s, and barrier height of a trapped carrier, 01,-, was extracted from the data.

Barrier height, saturation current, and reverse breakdown voltage for the Schottky

junction were extracted from the reverse-bias data.

97

6.4 Phase-change material Schottky barrier diodes

Under very high forward bias voltages, the nanocrystalline diamond based
Schottky diodes, or initial-state diodes, mentioned in the previous section would
experience a sharp increase in current resulting in a permanent change in current-voltage
characteristics. These current-voltage characteristics were investigated under the same
testing conditions mentioned above where rectiﬁcation ratios as high as 1.69 x 105 at
i 10 V were observed. This “phase-change” is speculated to be a physical change in the
diamond ﬁlm where a conductive carbon ﬁlament, formed directly below the zirconium
contact, is believed to form a Schottky barrier junction with the silicon substrate. A DC
model was proposed for these devices where the forward bias current is limited by the
Schottky junction and the reverse bias current is limited by the surrounding diamond or
other transitional material, behaving as an ohmic resistance. Device characterization then
followed in Chapter 5 where an estimation of barrier height, forward bias and reverse
bias resistance, reverse bias activation energy, saturation current, and ideality factor was

found.

6.5 Recommendations for future research

The goal of this research was investigation into the fabrication of ﬂexible

diamond based electronics. As mentioned above, a freestanding diamond ﬁlm structure

with top and bottom electrodes along with a stainless steel tube with diamond wrapped

98

around were investigated. Obviously, much more research needs to be conducted into
this area. Voltage-variable resistors were created from these structures, but more
advanced electronic devices such as Schottky barrier diodes need to be researched and
developed. Structural problems due to post-metallization diamond ﬁlm cracking,
unintentional contact removal upon back-etching, and loss of rectiﬁcation prevented the
development of a ﬂexible Schottky barrier diode when silicon was removed from diodes
created in this thesis. One possibility would be to take the same zirconium-
nanodiamond-silicon sample conﬁguration and etch away most of the silicon leaving a
very thin layer capable of being ﬂexed to the same degree as the diamond ﬁlm, hopefully
retaining the diode’s rectiﬁcation. However, as for the mechanical problems, more
investigation needs to be done to identify a possible solution.

Also, recommended future work into the nanocrystalline diamond based Schottky
barrier diodes would include research into thinner diamond ﬁlms and boron doped
diamond. It is of interest to determine the ultimate thinness of a grown diamond ﬁlm that
would be possible for creating a Schottky barrier diode especially when this research
showed an improvement in rectiﬁcation ratio as thickness decreased. Also, doped
diamond would be the next logical step in these devices potentially showing an
improvement in rectiﬁcation ratio since the ﬁeld-activated conductivity would no longer
be a limitation to the amount of current through these devices. Future research into other
metals for Schottky contacts, other types of polycrystalline diamond ﬁlm, and AC
analysis would also be of interest, too.

Finally, only a few of the phase-change diodes were created and studied

throughout this research providing limited data. Although data was limited and

99

subsequent analysis was not performed extensively on these phase-change diodes, some
device characterization was possible leaving the reader with at least a general impression
of these unexpected devices. Further investigation into the phase-change state including
the physics behind the formation, material analysis of the presumed carbon-
ﬁlament/diamond structure, and detailed device characterization is necessary beginning
with a more controlled setup to instigate the phase-change. Though this was beyond the

scope of this thesis, it would most surely be of interest in future research.

100

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30
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60
65
70
75
80
85
90
95
100
105
l 10

115 .

120
125
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135
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APPENDIX

HP414SB I-V Measurement Software

' Set up program for MS-DOS HP-IB I/O Library
’ For use independent of the PC instrument bus system

DEFSEG

DATA &H32CD, &HO0CB

DIM GETDS%(2)

READ GETDS%(0): READ GETDS%(1)
ADDR% = VARPTR(GETDS%(0))
CALL ADDR%

CLEAR, &HFC00

1= &HFC00

' PCIB.DIR$ represents the directory where the library ﬁles
' are located
' PCIB is an environment variable which should be set from MS-DOS
' i.e. A:> SET PCIB=A:\LIB
' If there is insufﬁcient environment space a direct assignment
' can be made here, i.e
' PCIB.DIR$ = "A:\LIB"
' Using the environment variable is the preferred method

PCIB.DIR$ = ENVIRON$("PCIB")
IS = PCIB.DIR$ + "\IBHPIB.LIB"
BLOAD I$, &HFC00

CALL 10%)

PCIB.SEG = 1%

' Deﬁne entry points for setup routines
DEF SEG = PCIB.SEG

IOABORT = 3

IOCLEAR = 6

IOCONTROL = 9

IODMA = 12

IOENTER = 15

IOENTERA = 18

IOENTERAB = 21

101

205 IOENTERB = 24
210 IOENTERS = 27
215 IOEOI = 30

220 IOEOL = 33

222 IOFASTOUT = 36
225 IOGETTERM = 39
230 IOLLOCKOUT = 42
235 IOLOCAL = 45
240 IOMATCH = 48
245 IOOUTPUT = 51
250 IOOUTPUTA = 54
255 IOOUTPUTAB = 57
260 IOOUTPUTB = 60
265 IOOUTPUTS = 63
270 IOPEN = 66

275 IOPPOLL = 69
280 IOPPOLLC = 72
285 IOPPOLLU = 75
290 IOREMOTE = 78
295 IORESET = 81

300 IOSEND = 84

305 IOSPOLL = 87
310 IOSTATUS = 90
315 IOTIMEOUT = 93
320 IOTRIGGER = 96
325 DEFERR = 99
330 '

335 ' Establish error variables and ON ERROR branching

340 '

345 PCIB.BRRS = STRING$(64, 32): PCIB.BRR = 0
350 PCIB.NAME$ = STRING$(16, 32): PCIB.GLBERR = 0
355 CALL DEF.ERR(PCIB.ERR, PCIB.BRR$, PCIB.NAME$, PCIB.GLBERR)

360 PCIB.BASERR = 255
365 ON ERROR GOTO 395

370
375 GOTO 460
380 '

385 ' Error handling routine

390 '

395 IF ERR = PCIB.BASERR THEN GOTO 410
400 PRINT "BASIC error #"; ERR; " occurred in line "; ERL

405 STOP

410 TMPERR = PCIB.BRR

415 IF TMPERR = 0 THEN TMPERR = PCIB.GLBERR
420 PRINT "HPIB error #"; TMPERR; " detected at line "; ERL

425 PRINT "Error: "; PCIB.BRR$

102

430 STOP

435 '

440 ' COMMON declarations are needed if your program is going to chain

445 ' to other programs. When chaining, be sure to call DEF .ERR as

450 ' well upon entering the chained-to program

455 '

460 COMMON PCIB.DIR$, PCIB.SEG

465 COMMON DEFERR, PCIB.BASERR, PCIB.BRR, PCIB.BRRS, PCIB.NAME$,
PCIB.GLBERR

470 COMMON IOABORT, IOCLEAR, IOCONTROL, IOENTER, IOENTERA,
IOENTERS, IOEOI, IOEOL, IOGETTERM, IOLLOCKOUT, IOLOCAL, IOMATCH,
IOOUTPUT, IOOUTPUTA, IOOUTPUTS

475 COMMON IOPPOLL, IOPPOLLC, IOPPOLLU, IOREMOTE, IORESET,
IOSEND, IOSPOLL, IOSTATUS, IOTIMEOUT, IOTRIGGER, IODMA, IOPEN,
IOENTERB, IOENTERAB, IOOUTPUTB, IOOUTPUTAB, IOFASTOUT

480 '

485 FALSE = 0

490 TRUE = NOT FALSE

495 NOERR = 0

500 EUNKNOWN = 100001!

505 ESEL = 100002!

510 ERANGE = 100003!

515 ETIME = 100004!

520 ECTRL = 100005!

525 EPASS = 100006!

530 ENUM = 100007!

535 EADDR = 100008!

540 COMMON FALSE, TRUE, NOERR, EUNKNOWN, ESEL, ERANGE, ETIME,
ECTRL, EPASS, ENUM, EADDR

545 '

550 ' End Program Set-up

555 ' User program can begin anywhere past this point
1000'*****************************************************

1010 ' Connect to HP4145B, Begin Remote control
1020'*****************************************************
1030 OPTION BASE 1

1040 INF O$ = SPACE$(13)

1050 DINFO = 20

1060 CODES$ = SPACE$(50)

1070 ISC = 7: PARA =17

1080 HP4145B = ISC * 100 + PARA

1090 CALL IORESET(ISC)

1100 IF PCIB.BRR <> NOERR THEN ERROR PCIB.BASERR
1110 TIMEOUT = 5

1120 CALL IOTIMEOUT(ISC, TIMEOUT)

1130 IF PCIB.BRR <> NOERR THEN ERROR PCIB.BASERR

103

1140 CALL IOCLEAR(ISC)
l 150 IF PCIB.BRR <> NOERR THEN ERROR PCIB.BASERR
1160 CALL IOREMOTE(ISC) '

4000 '********************* 3 terminal MOS measurement
***********************

4010 CLS : LOCATE 5, 15

4020 PRINT "This program will perform a 2 terminal measurement!"
4030 CLS : LOCATE 6, 15

4040 PRINT "Perform the following connections before beginning measurementsz"
4050 PRINT ""

4060 LOCATE 8, 20

4070 PRINT "- Connect the + end to SMUI "

4080 LOCATE 9, 20

4090 PRINT "- Connect the - end to SMU2"

4120 LOCATE 15, 15

4130 PRINT "Once ﬁnished choose one of the options below"

4140 LOCATE 16, 20

4150 PRINT " B - To Begin taking measurements"

4180 LOCATE 17, 20

4190 PRINT " Q - To QUIT program "

4200 INPUT " ENTER LETTER OF YOUR CHOICE: "; BS

4210 IF 85 = "B" OR B$ = "b" THEN CLS : GOTO 4300

4230 IF B$ = "Q" OR B$ = "q" THEN GOTO 9000

4240 GOTO 4200

4300 '********************* HP41453B Setup ***********************
4310 INPUT "Give ﬁlename where data will be stored "; FPUT$
4320 FPUTS = FPUT$ + ".DAT"

4330 INPUT "Start (V): "; SVD

4340 INPUT "End (V): "; EVD

4350 INPUT "Voltage step (V): "; VDSTEP

4390 NDAT = (ABS(EVD - SVD) / VDSTEP) + 1

4400 GOSUB 8000 'Initialize data ﬁle

4410 CLS

4420 PRINT ""

4430 PRINT ""

4440 PRINT "#1.!****************************************************"
4450 PRINT " Setting Up HP4145B - Measurements will begin shortly"

4460 Pm "*II!****************************************************"
4470 PRINT ""

4480 '****** Setting up 41453 ******

4490 CODESS = "1T1 CA1 DRO BC": GOSUB 8500

4500 CODESS = "DE CH1,'VN','IN',3,3": GOSUB 8500

4510 CODESS = "CH2,'VP','IP',1,1": GOSUB 8500

4520 CODES$ = "CH3;CH4;": GOSUB 8500

4540

CODESS = "VS1;VS2;VM1;VM2": GOSUB 8500

104

4550

C0DES$ = "SS VRI." + STR$(SVD) + + STR$(EVD) + +

STR$(VDSTEP) + ",.1": GOSUB 8500

4570
8500
4580
4590
4600
4610
4620
4630
4640
4650
4660
4670
4680
4700
4710
4720
4730
4740
4760
4770
4780

CODESS = "SM DMl XN 'VP',1," + STR$(SVD) + "," + STR$(EVD): GOSUB

CODESS = "YA 'IP',1,0,.1": GOSUB 8500

CODESS = "MD MEI": GOSUB 8500

INPUT "Press F once HP4145B has ﬁnished taking measurements"; F $
IF F$ = "F" OR F$ = "t" THEN CLS : GOTO 4630

GOTO 4600

PRINT ""

PRMT "********IIIill*******1!13***********************"

PRINT " Transferring and Saving Data to Computer "
PRINT "**********III*******************************"
PRINT ""
CODES$ = "DO 'IP'": GOSUB 8500
FOR N = 1 TO NDAT
GOSUB 8700 'GET DATA
OPEN FPUT$ FOR APPEND AS #1
VDrain = SVD + (VDSTEP * N) - VDSTEP
PRINT VDrain; INFO$
PRINT #1, VDrain, MID$(INFO$, 2, 12)
CLOSE (1)
NEXT N

4800 GOTO 8800

8000 '****************** INITIALIZE DATA FILE ********************
8010 OPEN FPUT$ FOR APPEND AS #1

8020 PRINT #1, "O/OIHIIIII*IIUII*********************************************** "
8030 '** PRINT #1,"% SAMPLE: "; SAMPLES

8040 PRINT #1, "IV measurement using HP414SB and probe station"

8130 CLOSE (1)

8140 RETURN

8300 '****************** CLOSE DATA FILE ********************

8310 OPEN FPUTS FOR APPEND AS #1

8320 CLOSE (1)

8330 RETURN

8500 '******************** Talk to HP4145B **************************
8510 LENGTH = LEN(CODES$)

8520 CALL IOOUTPUTS(HP414SB, CODESS, LENGTH)

8530 IF PCIB.BRR <> NOERR THEN ERROR PCIB.BASERR

8540 RETURN

8700 '******************** LiStCn t0 HP4145B ************************
8710 CALL IOENTERS(HP4145B, INFOS, DINFO, ACINFO)

8720 IF PCIB.BRR <> NOERR THEN ERROR PCIB.BASERR

8730 RETURN

8800 '********************* DATA READ DONE ************************

105

8810 GOSUB 8300
8820 Pm'r 1111

8830 PRINT "an**********************n

8840 PRINT " Data Transfer Complete "

8850 PRIN'T "#31!*********************III"

8860 PRINT ""

8870 INPUT "Press W once you have ﬁnished viewing data from HP4145B"; H$
8880 GOTO 1000

9000 END

106

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