Solution of the Boltzmann equation for the electron Hall mobility in Ga 1-xN xAs

M. P. Vaughan*, B. K. Ridley

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review


The ladder method for solving the linearized Boltzmann equation is developed to deal with a non-parabolic conduction band. This is applied to find the low field Hall mobility of electrons in bulk GaN xAs 1-x using the band-anticrossing (BAC) model, which predicts highly non-parabolic energy dispersion relations. Polar optical, acoustic phonon, piezoelectric, ionized impurity, neutral impurity and nitrogen scattering are incorporated. In finding an exact solution to the linearized Boltzmann equation, we avoid the unrealistic assumption of a relaxation time for inelastic scattering via polar optical phonons. Nitrogen scattering is found to limit the electron mobility to values of the order 1000 cm 2V -1s -1, in accordance with relaxation time approximation calculations but still an order of magnitude higher than measured values for dilute nitrides. We conclude that the non-parabolicity of the conduction band alone can not account for these low mobilities. In recent years, there has been growing interest in the use of dilute nitrides for optoelectronic applications. Since the early 90s, fabrication techniques have been developed 1,2,3,4 that allow the incorporation of nitrogen in dilute concentrations into III-V semiconductors. This leads to a large reduction of the energy gap with N content 5, making the dilute nitrides attractive candidate materials for long wavelength semiconductor lasers for telecommunications 6 and efficient solar cells operating in the infrared 7. Although considerable attention has been given to theoretical models of the band-structure in dilute nitrides 8,9,10,11, until recently there has been very little development in the theory of carrier transport 12,13. Studies that have been carried out 12 suggest that there may be intrinsic limits on electron mobility, which will be an important consideration for device applications. These calculations, however, have only addressed nitrogen scattering in isolation, based on a relaxation time approximation for the mobility. The effect of the high degree of non-parabolicity in the energy dispersion relations predicted by the band-anticrossing (BAC) model 11 has not been addressed. Furthermore, the incorporation of polar optical scattering, which limits the room temperature mobility in most semiconductors, can not be treated using a relaxation time approximation due to the highly inelastic nature of the interaction. Hence, we have developed the ladder method 14,15 for solving the Boltzmann equation to deal with a non-parabolic conduction band. Using the BAC model to calculate the modified effective mass and density of states, we have calculated the low field Hall mobilities for bulk GaN xAs 1-x.

Original languageEnglish
Article number123
Pages (from-to)790-798
Number of pages9
JournalProceedings of SPIE
Volume5840 PART II
Publication statusPublished - 2005


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