We present a theoretical analysis of the effects of compressive uniaxial stress on the electronic structure of GaAs-${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum wells grown along the [001] axis. Strain interactions are incorporated by use of known deformation potentials of the bulk semiconductors, and, therefore, our analysis contains no adjustable parameters. We consider the cases where the external uniaxial stress X is parallel (X ∥ [001]) and perpendicular (X ∥ [100]) to the [001] growth axis of the quantum well. Our results indicate that, unlike the bulk case, the strain-induced energy shifts depend sensitively on whether the compressive stress is applied along the [001] or [100] axis. These differences are a direct consequence of the mixing of the bulk heavy-hole and light-hole states by the strain interactions and by the quantum-well potential. For X ∥ [100], the strain-induced energy shifts associated with the heavy- and light-hole quantum-well states are strong nonlinear functions of the magnitude of the applied compressive stress due to the admixing by the strain Hamiltonian of the corresponding bulk states. However, for X ∥ [001], a strong nonlinear behavior is only predicted for the light quantum-well states due to the mixing between the bulk light and spin split-off states. The strain-induced energy shifts are dependent on the GaAs quantum-well thickness. The results of our analysis are in excellent agreement with experimental measurements of strain-induced energy shifts in quantum wells.

• Received 3 April 1987

DOI:https://doi.org/10.1103/PhysRevB.36.2942