Band nonparabolicities in lattice-mismatch-strained bulk semiconductor layers

Analytic expressions for band nonparabolicities and effective masses are derived for lattice-mismatch-strained bulk semiconductor layers. We have investigated both a full 6×6 valence-band Hamiltonian and an 8×8 model. In the latter, the interactions between the singlet conduction band and the triplet valence bands were treated exactly, with the effects of higher bands calculated to order ${\mathit{k}}^2$. To our knowledge, the present work constitutes the first explicit calculation of strain and k⋅p matrix elements using a basis consistent with the formalism of Luttinger and Kohn [Phys. Rev. 97, 869 (1955)] throughout. The present results should prove to be valuable in determining strained-layer heterostructure band alignments using excitation spectroscopy and in applications requiring highly accurate estimates of confinement energies in narrow quantum-well structures (such as those used in long-wavelength infrared detection).