Electromodulation spectroscopy of an array of modulation-doped GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum dots: Experiment and theory

A recent photoreflectance (PR) experiment on a GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As modulation-doped quantum-dot array shows that at 77 K the quasi-two-dimensional ‘‘2C-2H’’ interband transition develops a series of evenly spaced oscillations. Such features are due to the quantization of the energy levels related to the in-plane paraboliclike potential for such reduced-dimensional sytems, e.g., evenly spaced conduction and valence subbands. However, for the other dominant feature, i.e., ‘‘1C-1H’’/‘‘1C-1L,’’ no fine structure is observed since the first electron subband is occupied. We present a self-consistent field theory and numerical calculations for the intersubband absorption coefficient of an array of modulation-doped GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As quantum dots with lateral parabolic confining potentials for electrons and holes. Our numerical results for the derivative of the absorption coefficient have features which are quite similar to those observed in the PR experiment.