Absorption spectroscopy on Ga0.47In0.53As/Al0.48In0.52As multi-quantum-well heterostructures. II. Subband structure.

The subband structure of ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As/${\mathrm{Al}}_{0.48}$${\mathrm{In}}_{0.52}$As multi-quantum-well heterostructures (MQWH's) lattice matched to InP, grown by molecular-beam epitaxy, was determined by absorption and magnetoabsorption experiments for well widths ranging from 2.3 to 13.8 nm. A comparison to theoretical models (parabolic single-band and coupled six-band envelope-function approximations) reveals the necessity of taking the nonparabolicity of the conduction band as well as of all the valence subbands into account. The equal values for the reduced effective mass and the electron effective mass, obtained by Shubnikov\char21{}de Haas and cyclotron-resonance experiments, show that the highest valence-subband mass is much larger than the theoretical assumption from decoupled valence subbands. In view of the complete subband structure the best theoretical description is given by using a conduction-band offset \ensuremath{\Delta}${E}_{c}$=500 meV as determined by capacitance-voltage measurements in the literature. For this value the calculated subband transition energies are about 10% higher than the experimental results.