Excitonic properties in (111)B-grown (In,Ga)As/GaAs piezoelectric multiple quantum wells

The excitonic properties in two (111)B-grown ${\mathrm{In}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{As}$ multiple quantum well $p-i-n$ diodes, with 7 and 14 quantum wells, respectively, are investigated by thermally detected optical absorption (TDOA) and by electroreflectance (ER) as a function of applied bias, the latter modifying the electric-field distribution in the heterostructure. The line shapes of the ER signals are analyzed by means of a multilayer model enabling the energies and the oscillator strengths of excitons to be deduced while the direct measurements of the energy positions of the TDOA peaks provide an accurate determination of the excitonic transition energies at zero-voltage applied bias. The excitonic characteristics are calculated by using a variational approach with a two-parameter trial function. The piezoelectric field in the strained ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ layers is determined by including the excitonic contribution. The theoretical oscillator strengths are compared to those obtained from ER experiments for several excitonic transitions; all the physical trends are well reproduced but it appears that a quantitative agreement cannot be found without taking into account the in-plane valence-band mixing. A study is also presented for the optimization of optoelectronic devices by means of a figure of merit that combines the oscillator strength of the fundamental excitonic transition and the ability for such devices to produce the largest energy shift for a 1-V additional applied bias.