Monte Carlo Simulation of Hall Effect in n-Type GaN
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ECE Department, University of Minnesota, Minneapolis, MN 55455
;School of ECE, Georgia Institute of Technology, Atlanta, GA 30332
Cite this article as: MRS Internet J. Nitride Semicond. Res. 4S1, G6.6 (1999)
ABSTRACT Results of Monte Carlo simulations of electron transport for wurtzite phase GaN in crossed, weak electric and magnetic fields are presented. It is found that the Hall factor, rH = !-HaWalldrift, decreases monotonically as the temperature increases from 77K to 400K. The low temperature value of the Hall factor increases significantly with increasing doping concentration. The Monte Carlo simulations take into account the electron-lattice interaction through polar optical phonon scattering, deformation potential acoustic phonon scattering (treated as an inelastic process), and piezoelectric acoustic phonon scattering. Impurity scattering due to ionized and neutral donors is also included, with the latter found to be important at low temperature due to the relatively large donor binding energy which implies considerable carrier freeze-out already at liquid nitrogen temperature. The temperature dependences of the electron concentration, drift mobility, and Hall factor are calculated for donor concentrations equal to 5 x 1016 cm- 3 , 1017 cm- 3,and 5 x 1017 cm-3. The Monte Carlo simulations are compared to classical analytical results obtained using the relaxation-time approximation, which is found to be adequate at low temperatures and sufficiently low carrier concentrations so that inelastic scattering effects due to optical phonons and degeneracy effects are negligible. The influence of dislocations on the Hall factor is discussed briefly.
INTRODUCTION Electronic characterization of epitaxially grown GaN relies on temperature dependent Hall measurements to accurately determine carrier concentration and mobility. Analysis of measured Hall data has already led to the examination of several effects unique to GaN Hall measurements. Specifically, the variation of the electron Hall mobility in the presence of a highly conducting layer at the interface between the substrate and the epitaxial GaN crystal has been resolved1 , and the dependence of the Hall measurement on the orientation of the current with respect to threading dislocations has recently been explained 2. Also, the low temperature behavior of measured electron mobilities in heavily doped GaN has been found to be consistent with transport associated with band-tailing and impurity-band states 3 . Exceptions aside, interpretations of GaN Hall data often make the assumption that !1 HaIl = 9drift, independent of temperature 4 '5 . One consequence of assuming a unity Hall factor is that total donor concentrations and donor activation energies extracted from electrical measurements are difficult to analyze with confidence. G 6.6 Mat. Res. Soc. Symp. Proc. Vol. 537 c 1999 Materials Research Society
We present new calculations of the Hall factor, rH, for n-type wurtzite GaN that predict a monotonic decrease with increasing temperature for fixed donor c
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