Generalization of thek⋅papproach for strained layered semiconductor structures grown on high-index-planes

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Abstract
We present a generalized theoretical description of the 8×8 k⋅p approach for determining the band structure of layered semiconductor structures for any growth direction, including strain and piezoelectric effects. The definition of heavy, light, and splitoff hole states is extended to arbitrary growth directions in analogy to the conventional (001) case, by choosing an adapted set of basis functions. The choice of this basis allows a qualitative understanding of the in-plane band structure and of the optical properties of strained and unstrained structures. Besides, we solve the k⋅p Hamiltonian by means of an efficient real-space method allowing us to deal with arbitrary confining potentials. The theory is applied to unstrained, compressively strained, and tensilely strained quantum wells. We find that confinement energies, warping, and in-plane effective masses strongly depend on the direction of confinement and on strain. Piezoelectric effects further affect the dispersion for all growth directions other than (001) and (011). We also find that the optical transition strength depends on the in-plane light polarization for growth directions other than (001) and (111). © 1996 The American Physical Society.