We present a quantitative theory of the electronic levels in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As 〈001〉 quantum wires (x≤0.35). For the ground state of thick wires (cross-section area ≳100×100 A${̊}^2$) our results support the infinite-well approximation in which the two quantization coordinates are decoupled. However, the excited states, and all confined states in thin wires (≲70×70 A${̊}^2$), are affected by additional reflections which can be identified from tables of the momentum wave-function coefficients presented in this study.

• Received 7 July 1986

DOI:https://doi.org/10.1103/PhysRevB.35.2463