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The 6×6 effective mass Hamiltonian for semiconductor heterostructures grown on (11N)-oriented substrates is derived and is compared with the 4×4 model. The hole subbands of InGaAs/InP single quantum wells grown on (11N)-oriented substrates with N=∞ (that is, (001)], 0, 1 are calculated using the effective mass Hamiltonian as an example. The spin-orbit coupling affects the light-hole subband at k∥ = 0, but it affects all subbands at finite k∥ for all substrate orientations. In the 4×4 model (without spin-orbit coupling), the coupling between the heavy hole and the light hole is overestimated. At a critical uniaxial stress, the position of the first heavy hole and the first light hole as the highest energy level cross over. The separation between the first heavy hole and the first light hole is overestimated at the uniaxial stress below the critical value and is underestimated above the critical stress in the 4×4 model. The spin-orbit coupling greatly affects the valence band structures of the semiconductor heterostructures resulting in the modifications of the optical transitions anisotropy for structures grown on (11N)-oriented substrates.

physical review. b, condensed matter

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>6</mml:mn><mml:mo>×</mml:mo><mml:mn>6</mml:mn></mml:math>effective mass Hamiltonian for heterostructures grown on (11<i>N</i>)-oriented substrates

6×6effective mass Hamiltonian for heterostructures grown on (11N)-oriented substrates