Direct calculation of k•p parameters for wurtzite AlN, GaN, and InN

Electronic band structure calculations have been performed for the wurtzite structures of AlN, GaN, and InN. In particular, the conventional k . 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 k 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 k . 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 k . p parameters, in contrast to a fitting procedure in which a range of equally valid parameter sets can exist.