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Journal Article•DOI•

Electron transport within the wurtzite and zinc-blende phases of gallium nitride and indium nitride

Poppy Siddiqua1, Stephen K. O’Leary1•
University of British Columbia1
11 Jan 2018-Journal of Materials Science: Materials in Electronics (Springer US)-Vol. 29, Iss: 5, pp 3511-3567
TL;DR: In this paper, a review of electron transport in wide energy gap semiconductors is presented, focusing on the electron transport that occurs within the wurtzite and zinc-blende phases of gallium nitride and indium oxide.
Abstract: Wide energy gap semiconductors are broadly recognized as promising materials for novel electronic and opto-electronic device applications. As informed device design requires a firm grasp on the material properties of the underlying electronic materials, the electron transport that occurs within the wide energy gap semiconductors has been the focus of considerable study over the years. In an effort to provide some perspective on this rapidly evolving and burgeoning field of research, we review analyzes of the electron transport within some wide energy gap semiconductors of current interest in this paper. In order to narrow the scope of this review, we will primarily focus on the electron transport that occurs within the wurtzite and zinc-blende phases of gallium nitride and indium nitride in this review, these materials being of great current interest to the wide energy gap semiconductor community; indium nitride, while not a wide energy gap semiconductor in of itself, is included as it is often alloyed with other wide energy gap semiconductors, the resultant alloy often being a wide energy gap semiconductor itself. The electron transport that occurs within zinc-blende gallium arsenide will also be considered, albeit primarily for bench-marking purposes. Most of our discussion will focus on results obtained from our ensemble semi-classical three-valley Monte Carlo simulations of the electron transport within these materials, our results conforming with state-of-the-art wide energy gap semiconductor orthodoxy. A brief tutorial on the Monte Carlo electron transport simulation approach, this approach being used to generate the results presented herein, will also be provided. Steady-state and transient electron transport results are presented. The evolution of the field, a survey of the current literature, and some applications for the results presented herein, will also be featured. We conclude our review by presenting some recent developments on the electron transport within these materials. This review is the latest in a series of reviews that have been published on the electron transport processes that occur within the class of wide energy semiconductor materials. The results and references have been updated to include the latest developments in this rapidly evolving field of study.

Summary (2 min read)

Jump to: [Introduction: The Controversial Nature of Transfer Factor] – [The Peptide Fragment of TF] – [The RNA Component of TF] – [How Specific is TF Activity?] – [How Transfer Factor Challenges the Standard Model of Immunological Activation] – [Is TF Part of a Eukaryotic CRISPR-Cas-Like System?] – [New Tests of TF] and [Conclusion: A Few Notes on the History and Philosophy of Discovery]

Introduction: The Controversial Nature of Transfer Factor

  • Most immunologists have never heard of transfer factor (TF) despite the fact that it may be – emphasis on “may” — one of the most important discoveries ever made in immunology.
  • The thesis of this review is that TF research was abandoned prematurely.
  • Each clone is therefore predetermined to produce a single, unique T cell receptor, B cell receptor or antibody sequence.
  • Only in the best cases did investigators employ partially purified materials and it was not until the early 1980s that the specific molecular nature of TF began to emerge (Wilson and Fudenberg, 1983).
  • TF was universally characterized as having a molecular weight greater than 3000 daltons and less than 12,000.

The Peptide Fragment of TF

  • It is important to note that some TF researchers have argued that the peptide contained in TF preparations is not derived from the antigen.
  • Borkowsky and Lawrence (1981), Petersen, et al. (1983), and Kirkpatrick (1988) each immunized animals with an antigen, isolated the TF fraction, and then used various methods to adsorb the active ingredients of the TF fraction.
  • Before passing on to the characterization of the RNA component of TF, it is worth considering what the peptide component might be if it is not derived from antigen.
  • Another possibility is that the peptide is (like the protamine in the Hoerr beta galactosidase experiment summarized above) only present to stabilize the RNA component against RNAases.

The RNA Component of TF

  • Because the RNA component of TF is also uncharacterized, many of the questions just raised about the peptide component remain unresolved for the RNA component.
  • Fudenberg (Wilson and Fudenberg, 1981; Wilson, Paddock & Fudenberg, 1981; Wilson, Paddock & Fudenberg, 1982; Wilson and Fudenberg, 1983) proposed a model of TF consisting of a peptide conjugated to a diribonucleotide.
  • Rifkind (Rifkind, et al., 1976; 1977) reported that treating TF isolates with RNAase resulted in release of a peptide or RNP that lost TF activity, suggesting that RNA was a critical component of specific TF.
  • Another possibility is that the peptide binds specifically to double-stranded RNAs.

How Specific is TF Activity?

  • TF research has, since its inception, focused largely on two problems besides the physicochemical nature of TF.
  • The other involved fourteen patients treated for AIDS-related cryptosporidiosis, which yielded very significantly positive results (McMeeking, et al., 1990).
  • Friedman (1973) showed that TF induced by Shigella lipopolysaccharides produced immunity completely distinguishable from that induced against sheep red blood cells or Salmonella vaccine.
  • Also, Kirkpatrick (1993) demonstrated that murine TF raised against ovalbumin, cytochrome c, ferritin, horse radish peroxidase, and a random copolymer of glutamic acid, lysine and alanine each induced immunity in recipients that was not cross-reactive with the other antigens.

How Transfer Factor Challenges the Standard Model of Immunological Activation

  • Assuming TF exists and has the kinds of properties that investigators have associated with it, then the consequences for immunological theory are potentially revolutionary.
  • And secondly, there should be no set of naïve clones that could be programmed (or reprogrammed) by whatever message TF carries.
  • This possibility has been overlooked because it is at odds with current immunological dogma, which states that there are no such uncommitted cells.
  • Finally, experiments involving tadpoles, which have only about 10,000 total lymphocytes, have failed to identify any antigen against which a specific antibody response cannot be induced (Du Pasquier, 1976).

Is TF Part of a Eukaryotic CRISPR-Cas-Like System?

  • Basten and Edwards (1976) reported, for example, that TF isolates from mice contain fragments of I-region gene products, which is to say, hypervariable region sequences.
  • Might the RNA component in TF therefore be hypervariable region-encoding (HRE) RNAs.
  • Reasons for rejecting the Dogma’s prohibition of reverse translation have been addressed by several investigators (RootBernstein, 1983; Nakashima and Fox, 1986; Nashimoto, 2001) and essentially amount to the fact that the prohibition against reverse translation is based on lack of evidence.

New Tests of TF

  • For the many reasons discussed above, I believe that it is well worth exploring whether TF exists and has the properties ascribed to it by previous investigators.
  • In order to do so, new approaches are required.
  • If such data are forthcoming, an obvious follow-up would be to search for a CRISPR-Cas-like mechanism within TCR and BCR capable of generating hypervariable regions for these proteins.
  • Moreover, the sequence relationship, if any, between the peptide and the RNA components of TF will easily become apparent by using such a well-defined antigen.
  • Most importantly, technologies developed since 1990 make it possible to identify and track the production of TF by the immune system.

Conclusion: A Few Notes on the History and Philosophy of Discovery

  • In concluding, it is worth placing TF research within a more general framework of the history and philosophy of biomedical discovery.
  • To begin with, while skepticism is one of the most important of scientific tools, I believe that the authors should doubt most those results that best fit their preconceptions and take most seriously those that challenge them.
  • TF certainly challenges many aspects of modern immunology and molecular biology.
  • On the other hand, its effects have been reported so often by so many diverse groups that to ignore its possible existence seems obtuse.
  • Precisely for this reason, the authors must take it most seriously and most rigorously test TF.

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Content maybe subject to copyright    Report

ELECTRON TRANSPORT WITHIN THE WURTZITE AND ZINC-BLENDE PHASES OF
GALLIUM NITRIDE AND INDIUM NITRIDE
by
Poppy Siddiqua
M.Sc., North South University, 2011
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
in
THE COLLEGE OF GRADUATE STUDIES
(Electrical Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA
(Okanagan)
March 2019
© Poppy Siddiqua, 2019
ii
The following individuals certify that they have read, and recommend to the College of Graduate
Studies for acceptance, a thesis/dissertation entitled:
ELECTRON TRANSPORT WITHIN THE WURTZITE AND ZINC-BLENDE PHASES OF
GALLIUM NITRIDE AND INDIUM NITRIDE
submitted by Poppy Siddiqua in partial fulfillment of the requirements of
the degree of Doctor of Philosophy
Dr. Stephen K. O’Leary, School of Engineering
Supervisor
Dr. Jonathan Holzman, School of Engineering
Supervisory Committee Member
Dr. Murray Neuman, Irving K. Barber School of Arts and Sciences
Supervisory Committee Member
Dr. Jake Bobowski, Irving K. Barber School of Arts and Sciences
University Examiner
Dr. Jayshri Sabarinathan, Department of Electrical and Computer Engineering, The
University of Western Ontario
External Examiner
iii
Abstract
Wide energy gap semiconductors are broadly recognized as promising materials for novel
electronic and opto-electronic device applications. As informed device design requires a firm
grasp on the material properties of the underlying electronic materials, the electron transport that
occurs within the wide energy gap semiconductors has been the focus of considerable study over
the years. We review analyses of the electron transport within some wide energy gap
semiconductors of current interest. In this thesis, I primarily focus on the electron transport that
occurs within the wurtzite and zinc-blende phases of gallium nitride and indium nitride, these
materials being of great current interest to the wide energy gap semiconductor community; indium
nitride, while not a wide energy gap semiconductor of itself, is included as it is often alloyed with
other wide energy gap semiconductors. The electron transport that occurs within zinc-blende
gallium arsenide has also been considered. Most of the discussion focus on the steady-state and
transient electron transport results obtained from the ensemble semi-classical three-valley Monte
Carlo simulations of the electron transport within these materials.The evolution of the field, a
survey of the current literature, and some applications for the results will also be featured. Based
on this analysis, we have drawn the following conclusions. First, it is found that all of the velocity-
field characteristics corresponding to the materials under investigation in this analysis exhibit
peaks, regions of negative differential mobility, and regions of high-field saturation. Wurtzite
Indium nitride, with its small electron effective mass, exhibits the highest peak electron drift
velocity. The transient overshoot observed for the case of wurtzite Indium nitride is also found to
be the most pronounced of all of the materials considered in this analysis. This suggests that the
wurtzite phase of Indium nitride and its zinc-blende counterpart may offer great potential for future
electron device applications.
iv
Lay Summary
The study of electron transport within semiconductors has a long and rich tradition. In this thesis,
I present recently acquired electron transport results, corresponding to the wurtzite and zinc-
blende phases of gallium nitride and indium nitride, materials that have attracted a considerable
following in recent years. Both steady-state and transient electron transport results are featured,
these being obtained from ensemble Monte Carlo simulations. The zinc-blende phase results
represent some of the first detailed examinations into the nature of the electron transport within
these materials. Other results, such as those corresponding to the wurtzite phases, and those
corresponding to gallium arsenide, are added in for benchmarking purposes. Projections for
device performance, based on these results, are offered. In addition to a presentation of results,
the evolution of the field, a survey of the current literature, and some applications for the results
presented herein, will also be featured.
v
Preface
At the outset, I would like to make it clear that while others have certainly contributed to
the overall body of work presented within the scope of this thesis, the majority of the work was
performed by me and by me alone. In addition to learning about the background required for the
work, my work really began with a tabulation of the material and band structural parameters
corresponding to the wurtzite and zinc-blende phases of gallium nitride and indium nitride. Given
the changes that have been occurring in the understanding of these materials, this was not a
completely straightforward matter. I then sequentially went through each material, performing both
steady-state and transient electron transport simulations for each material under the range of
conditions considered in this thesis. I then used a routine in order to extract the relevant electron
transport properties associated with each simulation. From these raw results, figures were
generated and critical comparisons were made.
As a consequence of this body of work, six journal papers, four conference proceedings,
and one book chapter were published; further details are discussed in Appendix A. The majority
of these publications focused on the nature of the electron transport within the wurtzite and zinc-
blende phases of gallium nitride and indium nitride, results corresponding to the nature of the
electron transport within zinc oxide also being published during the course of my studies. With
editorial corrections from my academic advisor, Dr. Stephen K. O’Leary, I wrote the text
associated with each manuscript. I also produced the figures associated with each manuscript.
So the majority of the content related to these publications was authored by me. Copyright
permissions have been sought and acquired from the respective publishers.
In terms of my co-authors, they have been involved with Monte Carlo simulations of
semiconductor materials for many years. Their role in these publications that I have published,
however, was more as supporting authors rather than as principal ones. Dr. Michael S. Shur of
Citations
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The Monte Carlo method for semiconductor device simulation

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R.W. Kelsall1•
University of Leeds1
03 Apr 1995
TL;DR: If the authority ascribed to Monte Carlo models of devices at 1/spl mu/m feature size is to be maintained, modelling of the fundamental physics must be further improved, and the device model must be made more realistic.
Abstract: There can be little doubt that the Monte Carlo method for semiconductor device simulation has enormous power as a research tool. It represents a detailed physical model of the semiconductor material(s), and provides a high degree of insight into the microscopic transport processes. However, if the authority ascribed to Monte Carlo models of devices at 1/spl mu/m feature size is to be maintained for devices below O.1/spl mu/m, modelling of the fundamental physics must be further improved. And if the Monte Carlo method is to be successful as a semiconductor device design tool, the device model must be made more realistic. Success in the industrial sector depends on this, but also on achieving fast run-times optimisation - where the scope and need for ingenuity is now greatest.

436 citations

Book•
Properties of group-IV, III-V and II-VI semiconductors

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定雄 安達
01 Jan 2005
TL;DR: In this article, the authors present an overview of the properties of optical dispersion in terms of properties such as: 1.1 Ionicity. 2.2 Specific Heat. 3.4 Microhardness. 4.5 Sound Velocity.
Abstract: Series Preface. Preface. Acknowledgements. 1 Structural Properties. 1.1 Ionicity. 1.2 Elemental Isotopic Abundance and Molecular Weight. 1.3 Crystal Structure and Space Group. 1.4 Lattice Constant and Its Related Parameters. 1.5 Structural Phase Transition. 1.6 Cleavage Plane. 2 Thermal Properties. 2.1 Melting Point and Its Related Parameters. 2.2 Specific Heat. 2.3 Debye Temperature. 2.4 Thermal Expansion Coefficient. 2.5 Thermal Conductivity and Diffusivity. 3 Elastic Properties. 3.1 Elastic Constant. 3.2 Third-Order Elastic Constant. 3.3 Young's Modulus, Poisson's Ratio and Similar. 3.4 Microhardness. 3.5 Sound Velocity. 4 Lattice Dynamic Properties. 4.1 Phonon Dispersion Relation. 4.2 Phonon Frequency. 4.3 Mode Gruneisen Parameter. 4.4 Phonon Deformation Potential. 5 Collective Effects and Some Response Characteristics. 5.1 Piezoelectric and Electromechanical Constants. 5.2 Frohlich Coupling Constant. 6 Energy-Band Structure: Energy-Band Gaps. 6.1 Basic Properties. 6.2 E0-Gap Region. 6.3 Higher-Lying Direct Gap. 6.4 Lowest Indirect Gap. 6.5 Conduction-Valley Energy Separation. 6.6 Direct-Indirect-Gap Transition Pressure. 7 Energy-Band Structure: Effective Masses. 7.1 Electron Effective Mass: G Valley. 7.2 Electron Effective Mass: Satellite Valley. 7.3 Hole Effective Mass. 8 Deformation Potentials. 8.1 Intravalley Deformation Potential: G Point. 8.2 Intravalley Deformation Potential: High-Symmetry Points. 8.3 Intervalley Deformation Potential. 9 Electron Affinity and Schottky Barrier Height. 9.1 Electron Affinity. 9.2 Schottky Barrier Height. 10 Optical Properties. 10.1 Summary of Optical Dispersion Relations. 10.2 The Reststrahlen Region. 10.3 At or Near The Fundamental Absorption Edge. 10.4 The Interband Transition Region. 10.5 Free-Carrier Absorption and Related Phenomena. 11 Elastooptic, Electrooptic and Nonlinear Optical Properties 11.1 Elastooptic Effect. 11.2 Linear Electrooptic Constant. 11.3 Quadratic Electrooptic Constant. 11.4 Franz-Keldysh Effect. 11.5 Nonlinear Optical Constant. 12 Carrier Transport Properties. 12.1 Low-Field Mobility: Electrons. 12.2 Low-Field Mobility: Holes. 12.3 High-Field Transport: Electrons. 12.4 High-Field Transport: Holes. 12.5 Minority-Carrier Transport: Electrons in p-Type Materials. 12.6 Minority-Carrier Transport: Holes in n-Type Materials. 12.7 Impact Ionization Coefficient. Index.

258 citations

Journal Article•
Narrow band gap group III-Nitride alloys

[...]

Wladek Walukiewicz1•
Lawrence Berkeley National Laboratory1
01 Aug 2004-Lawrence Berkeley National Laboratory
TL;DR: In this paper, it was shown that InN with the energy gap of 0:7 eV exhibits classical characteristics of a narrow gap semiconductor with strongly nonparabolic conduction band and an energy dependent electron e ective mass.
Abstract: Available online at www.sciencedirect.com Physica E 20 (2004) 300 – 307 www.elsevier.com/locate/physe Narrow band gap group III-nitride alloys Wladek Walukiewicz ∗ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Abstract Recent results on the properties of narrow gap group III-nitrides and their alloys are reviewed. It is shown that InN with the energy gap of 0:7 eV exhibits classical characteristics of a narrow gap semiconductor with strongly nonparabolic conduction band and an energy dependent electron e ective mass. With the new discovery, the direct band gaps of the group III-nitride alloys span an extremely wide energy range from near infrared in InN to deep ultraviolet in AlN o ering possibilities for new device applications of these materials. We also discuss properties of dilute group III-N–V alloys in which incorporation of a small amount of nitrogen results in a dramatic band gap reduction. All the unusual properties of the alloys are well described by a band anticrossing model that considers an interaction between localized nitrogen states and the extended states of the conduction band. ? 2003 Elsevier B.V. All rights reserved. PACS: 72.80.Ey; 78.66.Fd; 71.20.Nr; 78.40.Fy; 71.10.Fd Keywords: InN; Group III-nitrides; Nonparabolic bands; Bowing parameters; Dilute nitrides; Band anticrossing; Electron e ective mass; Highly mismatched alloys 1. Introduction Wide gap group III-nitrides and their alloys are now one of the most extensively studied classes of semi- conductor materials. The interest in these materials has been generated by a successful implementation of the Ga-rich In x Ga 1−x N alloys for short wavelength light emitters and a variety of electronic devices [1]. Until recently, all group III-nitrides were qualiyed as wide gap semiconductors since it was commonly accepted that even InN, the narrowest gap member of the nitride family had a relatively wide gap of 1:9 eV [2,3]. This gap was determined from optical absorption studies of polycrystalline thin ylms. In a surprising recent dis- covery it has been shown that InN has a gap of only Tel.: +1-510-486-5329; fax: +1-510-486-5530. E-mail address: w walukiewicz@lbl.gov (W. Walukiewicz). 0:7 eV [4,5]. This expanded the range of the direct band gaps covered by the group III-nitride alloys into a near infrared region. It has been demonstrated more than 10 years ago that alloying of standard III–V compounds with small amounts of group III-nitrides leads to a dra- matic reduction of the band gap of the resulting IIIN x V 1−x alloys [6]. Thus it has been shown that the gap of In y Ga 1−y N x As 1−x can be reduced by several hundreds of meV bringing the band gap of these alloys into the mid-infrared region [6]. Sig- niycant, N-induced band gap reductions have been also reported in other group IIIN x V 1−x materials (see, for example, Ref. [7]) including narrow gap InN x Sb 1−x alloys [8]. The group IIIN x V 1−x materials belong to a much broader class of highly mismatched alloys (HMA) in which metallic (electronegative) atoms are partially replaced by more electronegative 1386-9477/$ - see front matter ? 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2003.08.023

29 citations

Posted Content•
Control of surface and bulk crystalline quality in single crystal diamond grown by chemical vapour deposition

[...]

Ian Friel, S L Clewes, H K Dhillon, N. Perkins, Daniel J. Twitchen, Geoffrey Alan Scarsbrook 
07 Sep 2009-arXiv: Materials Science
TL;DR: In this article, an inductively coupled plasma (ICP) etching using an Ar/Cl gas mixture is demonstrated to remove sub-surface damage of mechanically processed surfaces, whilst maintaining macroscopic planarity and low roughness on a microscopic scale.
Abstract: In order to improve the performance of existing technologies based on single crystal diamond grown by chemical vapour deposition (CVD), and to open up new technologies in fields such as quantum computing or solid state and semiconductor disc lasers, control over surface and bulk crystalline quality is of great importance. Inductively coupled plasma (ICP) etching using an Ar/Cl gas mixture is demonstrated to remove sub-surface damage of mechanically processed surfaces, whilst maintaining macroscopic planarity and low roughness on a microscopic scale. Dislocations in high quality single crystal CVD diamond are shown to be reduced by using substrates with a combination of low surface damage and low densities of extended defects. Substrates engineered such that only a minority of defects intersect the epitaxial surface are also shown to lead to a reduction in dislocation density. Anisotropy in the birefringence of single crystal CVD diamond due to the preferential direction of dislocation propagation is reported. Ultra low birefringence plates (< 10-5) are now available for intra-cavity heat spreaders in solid state disc lasers, and the application is no longer limited by depolarisation losses. Birefringence of less than 5*10-7 along a direction perpendicular to the CVD growth direction has been demonstrated in exceptionally high quality samples.

9 citations

Journal Article•
Wide bandgap III-Nitride semiconductors : opportunities for future optoelectronics

[...]

Yoon-Soo Park
01 Jan 2001-Opto-electronics Review
TL;DR: The development of violet-blue-green light emitting Diodes (LEDs) and laser diodes based on wide band gap III-nitride semiconductors has attracted a plethora of activity in semiconductor science and technology as discussed by the authors.
Abstract: The world at the end of the 20th Century has become blue. Indeed, this past decade has witnessed a blue rush towards the development of violet-blue-green light emitting diodes (LEDs) and laser diodes (LDs) based on wide band gap III-nitride semiconductors. And the hard work has culminated with, first, the demonstration of commercial high brightness blue and green LEDs and of commercial violet LDs, at the very end of this decade. Thanks to their extraordinary properties, these semiconductor materials have generated a plethora of activity in semiconductor science and technology. Novel approaches are explored daily to improve the current optoelectronics state-of- the-art. Such improvements will extend the usage and the efficiency of new light sources (e.g. white LEDs), support the rising information technology age (e.g. high density optical data storage), and enhance the environmental awareness capabilities of humans (ultraviolet and visible photon detectors and sensors). Such opportunities and many others will be reviewed in this presentation.

9 citations

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Frequently Asked Questions (16)
Q1. How does the electron drift velocity change with the applied electric field strength?

For applied electric fields58strengths in excess of 140 kV/cm, the electron drift velocity decreases in response to further increases in the applied electric field strength, i.e., a region of negative differential mobility is observed, the electron drift velocity eventually saturating at about 1.4 × 107 cm/s for sufficiently high applied electric field strengths. 

For applied electric fields strengths in excess of 4 kV/cm, the electron drift velocity decreases in response to further increases in the applied electric field strength, i.e., a region of negative differential mobility is observed, the electron drift velocity eventually saturating at about 1.0 × 107 cm/s for sufficiently high applied electric field strengths. 

In this paper, steady-state and transient electron transport results, corresponding to the wurtzite and zinc-blende phases of GaN and InN, were presented, these results being obtained from Monte Carlo simulations of electron transport within these materials. 

In general, scattering processes within semiconductors can be classified into three basic types: (1) phonon scattering, (2) defect scattering, i.e., related to lattice dislocations, and (3) carrier scattering [95]. 

The motion of these electrons, which in large measure determines the performance of such a device, is the fundamental issue at stake in the study of electron transport. 

The authors note that initially, the electron drift velocity monotonically increases with the applied electric field strength, reaching a maximum of about 3.3 × 107 cm/s when the applied electric field strength is around 50 kV/cm. 

The large non-parabolicity of the lowest energy conduction band valley is the principal factor responsible for this effect [157]. 

For the identification of papers focused only on the zinc-blende phases of these materials, the search terms “gallium nitride zinc blende” and “indium nitride zinc blende” were employed. 

For the case of zinc-blende GaAs, the peak electron drift velocity, 1.6 × 107 cm/s , occursat a much lower applied electric field strength than that for the other compound semiconductors considered in this analysis, i.e., only 4 kV/cm. 

the velocity-field characteristics associated with the wide energy gap compound semiconductors, GaN and InN, are less sensitive to variations in the doping concentration than those associated with zinc-blende GaAs; in fact, for the case of 1019 cm-3 doping, the peak in the velocity-field characteristic associated with zincblende GaAs completely disappears, the velocity-field characteristic associated with zinc-blende GaAs monotonically increasing with the applied electric field strength until saturation is achieved for this particular case. 

Understanding how the electron ensemble evolves in response to the application of an electric field, in essence, represents the fundamental issue at stake when the electron transport within a semiconductor is studied [95]. 

As with the cases of wurtzite and zinc-blende GaN and InN, a linear regime of electron transport is observed for the case of zinc-blende GaAs, the low-field electron drift mobility, μ, corresponding to the velocity-field characteristic depicted in Figure 3.13, being about 5400 cm2/V.s. 

The three-valley model used to represent the conduction band electron band structure associated with bulk wurtzite GaN for the Monte Carlo simulations of the electron transport within this material. 

The electron effective mass plays an important role in defining the low-field electron drift mobility, the higher this mass the lower the corresponding low-field electron drift mobility. 

As with the cases of wurtzite and zinc-blende GaN, and wurtzite InN, a linear regime of electron transport is observed for the case of zinc-blende InN, the low-field electron drift mobility, corresponding to the velocity-field characteristic depicted in Figure 3.10, being about 4400 cm2/V.s. 

As with the cases of wurtzite and zinc-blende GaN, a linear regime of electron transport is observed for the case of wurtzite InN, the low-field electron drift mobility, 𝜇, corresponding to the velocity-field characteristic depicted in Figure 3.7, being about 8700 cm2/V.s .