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Steady-state and transient electron transport within the wide energy gap compound semiconductors gallium nitride and zinc oxide: an updated and critical review

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Abstract

The wide energy gap compound semiconductors, gallium nitride and zinc oxide, are widely recognized as promising materials for novel electronic and optoelectronic device applications. As informed device design requires a firm grasp of the material properties of the underlying electronic materials, the electron transport that occurs within these wide energy gap compound semiconductors has been the focus of considerable study over the years. In an effort to provide some perspective on this rapidly evolving field, in this paper we review analyzes of the electron transport within the wide energy gap compound semiconductors, gallium nitride and zinc oxide. In particular, we discuss the evolution of the field, compare and contrast results determined by different researchers, and survey the current literature. In order to narrow the scope of this review, we will primarily focus on the electron transport within bulk wurtzite gallium nitride, zinc-blende gallium nitride, and wurtzite zinc oxide. The electron transport that occurs within bulk 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 compound 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 featured. Steady-state and transient electron transport results are presented. We conclude our discussion by presenting some recent developments on the electron transport within these materials. The wurtzite gallium nitride and zinc-blende gallium arsenide results, being presented in a previous review article of ours (O’Leary et al. in J Mater Sci Mater Electron 17:87, 2006), are also presented herein for the sake of completeness.

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Notes

  1. The earliest recorded studies on GaN, reported in the 1920s and 1930s, were performed on small crystals and powders [23]. Unfortunately, these materials were of insufficient quality for device applications. Thus, GaN remained a material of widely recognized but unrealized potential for many years. It was only when modern deposition approaches, such as molecular beam epitaxy and metal-organic chemical vapor deposition, were employed for the preparation of GaN that this material approached the levels of quality demanded of devices. Thus, intense interest into the material properties of GaN only really began in earnest in the early-1990s. While initial reports on the material properties of ZnO were made in the 1920s and 1930s, it was only much later that the quality of the material became sufficiently high that a diverse range of device applications could be considered. Accordingly, interest in the material properties of ZnO began in earnest in the early-2000s. Interest in both of these materials, and the device applications thus engendered, continues today.

  2. This requires that the electron ensemble has settled on a new equilibrium state. By an equilibrium state, however, we are not necessarily referring to thermal equilibrium, thermal equilibrium only being achieved in the absence of an applied electric field.

  3. By electron drift velocity, we are referring to the average electron velocity, determined by statistically averaging over the entire electron ensemble.

  4. The Monte Carlo approach to simulating the electron transport within semiconductors has been employed by many authors. A Monte Carlo electron transport simulation resource, with code included, may be found at https://nanohub.org/resources/moca. Further information about the Monte Carlo approach, beyond the electron transport context, may also be found at http://www.codeproject.com/Articles/767997/Parallelised-Monte-Carlo-Algorithms-sharp and http://www.codeproject.com/Articles/32654/Monte-Carlo-Simulation?q=Monte+Carlo+code.

  5. The conduction band minima may be degenerate, i.e., the same conduction band energy minima may be achieved at multiple points throughout the conduction band band structure. Valley 1 corresponds to those conduction band minima that are at the lowest energy. Valleys 2 and 3 correspond to those conduction band minima at the second most and third most lowest energy minima, respectively.

  6. Albrecht et al. [82] generalize this relationship in order to include a second-order non-parabolocity coefficient that reduces to the traditional Kane model in the limit that this second-order non-parabolocity coefficient is set to zero.

  7. The longitudinal and transverse sound velocities are equal to

    $$\sqrt{\frac{C_{l}}{\rho }} \quad \hbox {and}\quad \sqrt{\frac{C_{t}}{\rho }},$$

    respectively, where \(C_{l}\) and \(C_{t}\) denote the respective elastic constants and \(\rho \) represents the density.

  8. Piezoelectric scattering is treated using the well established zinc-blende scattering rates, and thus, a suitably transformed piezoelectric constant, \(\hbox {e}_{14}\), must be selected. This may be achieved through the transformation suggested by Bykhovski et al. [149, 150]. The \(\hbox {e}_{14}\) value selected for wurtzite GaN is that suggested by Chin et al. [86]. The \(\hbox {e}_{14}\) values selected for zinc-blende GaN and wurtzite ZnO is that corresponding to wurtzite GaN.

  9. All inter-valley deformation potentials are set to \(10^{9}\) eV/cm, following the approach of Gelmont et al. [85].

  10. We follow the approach of Bhapkar and Shur [90], and set the inter-valley phonon energies equal to the optical phonon energy, a relationship which holds approximately for the case of GaAs [151].

  11. The band structures are specified according to the three lowest energy conduction band valley minima, each minima corresponding to a valley, their locations in the band structures, the degeneracy of each valley, the effective mass of the electrons at each valley minimum, and the non-parabolicity coefficient corresponding to each valley being specified.

  12. For the case of direct-gap semiconductors, the \(E_{o}\) energy gap corresponds with the regular energy gap, \(E_{g}\). For the case of indirect-gap semiconductors, however, the \(E_{o}\) energy gap exceeds \(E_{g}\).

  13. Interest in the material properties of ZnO was ignited later than that associated with GaN, primarily on account of material quality considerations, i.e., high-quality GaN was prepared earlier, and a lack of familiarity with means of effectively handling II–VI compound semiconductors, many GaN processing techniques being borrowed directly from the GaAs case.

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Acknowledgments

Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. The work performed at Rensselaer Polytechnic Institute was supported by the Army Research Laboratory under the auspices of the ARL MSME Alliance program.

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Authors and Affiliations

  1. School of Engineering, The University of British Columbia, 3333 University Way, Kelowna, BC, V1V 1V7, Canada

    Walid A. Hadi & Stephen K. O’Leary

  2. Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York, 12180-3590, USA

    Michael S. Shur

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Correspondence to Stephen K. O’Leary.

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This paper is dedicated to the memory of our friend, mentor, and co-author, Professor Lester F. Eastman, of Cornell University, who passed away in 2013.

Note to Reader Some of the results presented herein, and portions of the text, are borrowed from our previous review article; see O’Leary et al. [62]. This overlap in results and text is meant to make this particular review article as self-contained and complete as possible.

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Hadi, W.A., Shur, M.S. & O’Leary, S.K. Steady-state and transient electron transport within the wide energy gap compound semiconductors gallium nitride and zinc oxide: an updated and critical review. J Mater Sci: Mater Electron 25, 4675–4713 (2014). https://doi.org/10.1007/s10854-014-2226-2

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