Direct calculation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold">k</mml:mi><mml:mi>⋅</mml:mi><mml:mi mathvariant="bold">p</mml:mi></mml:math>parameters for wurtzite AlN, GaN, and InN

Abstract

Electronic band structure calculations have been performed for the wurtzite structures of AlN, GaN, and InN. In particular, the conventional $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ valence band parameters ${A}_{i} (i=1--7)$ have been computed from initial empirical pseudopotential calculations in two distinct ways. A Monte Carlo fitting of the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ band structure to the pseudopotential data was used to produce one set. Another set was obtained directly from the formulas for the ${A}_{i}$ in terms of the momentum matrix elements and energy eigenvalues at the center of the Brillouin zone. Both methods of calculating the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ parameters produce band structures in excellent agreement with the original empirical band calculations near the center of the Brillouin zone. The advantage of the direct method is that it produces a unique set of $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ parameters, in contrast to a fitting procedure in which a range of equally valid parameter sets can exist.