Anisotropic longitudinal electron diffusion coefficient in wurtzite gallium nitride
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Anisotropic longitudinal electron diffusion coefficient in wurtzite gallium nitride Shulong Wang · Hongxia Liu · Jibin Fan · Fei Ma · Xiaoyi Lei
Received: 6 July 2012 / Accepted: 16 November 2012 / Published online: 4 December 2012 © Springer-Verlag Berlin Heidelberg 2012
Abstract The longitudinal electron diffusion coefficient (Dl ) of wurtzite (WZ) gallium nitride (GaN) is calculated by an ensemble Monte Carlo (EMC) method. By using the power spectral density associated with velocity fluctuation, the relationship between Dl and electric field strength, frequency, doping concentration and temperature is presented. The anisotropic Dl of GaN impacted by anisotropy of the electronic dispersion is also investigated. It has been found that the Dl in Γ –A direction (c-direction) is larger than that in Γ –M direction (basal plane) in most cases. For lower electric field, the Dl keeps constant at first, then decreases with increasing frequency. However, for higher electric field, the Dl firstly approaches a peak value, then decreases with increasing frequency. When the frequency is zero, the Dl decreases with the increasing electric field, and then increases until a peak value. Finally, it decreases with increasing electric field again. When the temperature increases, the Dl decreases in both directions for increasing scattering rate. A comparison between our calculated diffusion coefficient and the mobility under low electric field by Einstein equation is presented.
1 Introduction As a wide-band gap semiconductor and a promising candidate in semiconductor device, GaN material has shown potential application in millimeter-wave, solar cells, and optoelectronic devices, which have been researched widely in S. Wang () · H. Liu · J. Fan · F. Ma · X. Lei Key Laboratory of Ministry of Education for Wide Band-Gap Semiconductor Material and Devices, School of Microelectronics, Xidian University, Xi’an 710071, China e-mail: [email protected]
the past few years [1–6]. To make a clear description and an understanding of the working theory of the devices, the transport property of GaN has been researched a lot, which includes the experiments and theory simulations, especially the velocity-field relation [7–9] or electron mobility calculation [10–12]. In addition to the drift velocity, the diffusion coefficient is also an important parameter in the fundamental theoretical model of the material, which has not been paid much attention. The widely used diffusion coefficient is deduced from the Einstein equation by mobility. However, the Einstein equation can only hold at low electric field when the Boltzmann distribution is satisfied [13, 14]. Moreover, much work assumes an isotropic electronic structure of GaN [8, 10, 11]. Some researches are based on anisotropy of electronic dispersion of GaN [7, 9], which mainly concerns about the velocity-field relation. And recent experiments have shown the anisotropic transport characteristics of GaN [15, 16]. The anisotropic electron diffusion coefficient is still an unsolved question. And the
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