Theory of electron effective mass and mobility in dilute nitride alloys

Unexpectedly large values have been determined for the electron relative effective mass, m_c^* in GaN_xAs _1-x, which show a non-monotonic variation with x. We show that a quantitative understanding of this variation can be obtained by combining the experimentally motivated band-anti-crossing (BAC) model with detailed calculations of the electronic structure of nitrogen cluster states. The unexpectedly large mass values observed are due to interactions and hybridisation between the conduction band edge (CBE) E_- and nitrogen cluster states close to the band edge. These cluster states will also strongly influence the carrier mobility. We have previously established a fundamental connection between the composition-dependence of the CBE energy and the n-type carrier scattering cross-section in dilute alloys, with the scattering rate in the BAC model proportional to dE_-/dx², the square of the variation of the conduction band edge energy with alloy composition, x. The mobility estimated in GaN_xAs_1-x using the two-level BAC model is of the right magnitude (∼1000 cm²/Vs) but still larger than typical experimental values. We show that the inclusion of N cluster states further limits the calculated mobility, giving values comparable to experiment. Hydrostatic pressure causes the CBE to shift upwards relative to the N-related cluster states, so that the degree of hybridisation between the CBE and N cluster states will then vary with pressure. We predict this leads to a non-monotonic variation of m_c^* and mobility with hydrostatic pressure in GaN_xAs_1-x, with m_c ^* initially decreasing by ∼50% at certain alloy compositions, strongly contrary to the behaviour observed in conventional III-V alloys.