Physics
N.B. This page is slightly outdated (and slightly broken due to recent software updates!) The physics in itself is correct, but my work has advanced somewhat! Please bear with me, I'll try to update it soon! - 15th April 2012
My PhD project focusses on Gallium Nitride (GaN). GaN is a desirable material for use in high power and high frequency applications, due to it's wide, direct band gap (3.4eV). It is currently the material used in blue laser-diodes, such as those currently used in Blu-Ray players. However, more recently, significant interest has been shown in the use of GaN based devices as a potential source of so-called "terahertz radiation", that is, the emission of electro-magnetic waves that have a frequency of 300 GHz to 3 THz. Through the use of empirical pseudo-potential models (EPM), the electronic band structure of GaN has been calculated (a diagram of which can be seen at Ioffe's semiconductor pages), and as such, it has been determined that there is the potential for negative effective mass states to occur in the material, both theoretically, and experimentally [1].
Monte Carlo simulations have been used for many years in the simulation of many semiconductors. For most materials, such as Silicon and Gallium Arsenide, the use of the popular parabolic and k.p band-structure approximations provide an excellent analytic approximations to the true band structure, and allow for relatively quick simulation run times. However, these approximations do not provide a satisfactory approximation to the band-structure of GaN around the Gamma point, missing vital features of the structure that have been postulated to cause negative effective mass transport in GaN, and ultimately, a retardation in average electron velocity at high fields. Therefore, to accurately simulate electron transport in GaN, full-band structure simulations have had to be used, which are computationally expensive to run due to the numerical integrations involved throughout the simulation.
The cosine band-structure, originally proposed by Ridley, Schaff and Eastman in 2005 [2] was suggested as an analytic model that would be able to accurately simulate the negative mass transport at higher energies. It takes the form
(1)
where EB is the width of the band, which is 2.7eV, k is the electron wave-vector (in reciprocal space), and c is the hexagonal lattice constant along the c-axis which is 5.186Å. It turns out that this is an excellent approximation to the band-structure of GaN around the Gamma point, as can be seen in a paper by Dyson and Ridley [2, fig 1.] It can be seen that this band-structure approximation contains the negative-mass states by simply looking at the velocity-k expression for the approximation,
(2)
It is easy to see that after the electrons attain an energy of EB/4, the electron velocity will decrease as the energy increases, suggesting that the "negative mass" states are accounted for in some form through the use of this approximation.
My PhD project focusses on GaN and the cosine band structure with the aim of creating a Monte Carlo code for GaN based devices. It is hoped that the use of the cosine band-structure approximation in Monte Carlo codes will be significantly faster than using a numerical full-band simulation, yet still provide accurate results. Using equation 1, some scattering rates using this new band-structure have been derived (including polar-optical phonon scattering, which has previously been derived [3]), and are currently being implemented into Monte Carlo codes designed to simulation electron transport in bulk GaN, and in future, devices. Preliminary results from the code for bulk GaN are promising, the current output of the bulk GaN code appears to be in excellent agreement of other full band models and also in close agreement with experimental data.
[1] A. Dyson, B.K. Ridley et. al, physica status solidi (c). 4, pp. 528-530, 2007. Link
[2] B.K. Ridley, W.J.Schaff and L.F. Eastman, J. Appl. Phys. 97, pp. 094503-094509, 2005. Link
[3] A. Dyson and B.K. Ridley, J. Appl. Phys. 104, pp. 113701-113709, 2008. Link