Envelope-function formalism for valence bands in wurtzite quantum wells

A theoretical treatment of the valence-band spectrum of wurtzite-type materials is developed starting from the Rashba-Sheka-Pikus (RSP) 6×6 matrix Hamiltonian for coupled ${\mathrm{\Gamma }}_9$, ${\mathrm{\Gamma }}_7$, and ${\mathrm{\Gamma }}_7$ levels. A unitary transformation is applied in order to diagonalize the RSP Hamiltonian to two 3×3 blocks and the results are compared with those obtained for cubic structures [C. Y.-P. Chao and S. L. Chuang, Phys. Rev. B 46, 4110 (1992)]. Using the diagonalized form of the Hamiltonian, a solution for hole states in wurtzite quantum wells (QW’s) is constructed and explicit expressions for the QW valence subband edges are obtained. We suggest that parameters of the RSP Hamiltonian for würtzite structures can be deduced from experimental observations of the energy separation between edges of the hole subbands in QW’s. © 1996 The American Physical Society.