Electron Concentration Profiles in Modulation Doped Structures With Wide Quantum Well

Abstract

We calculate a concentration profile of Fermi electrons in modulation doped structures with a wide quantum well. The electron system with a sufficiently high density, such that the de Broglie wavelength of electrons is smaller than the potential well width, is considered. To calculate the spatial distribution of the electrons, we have formulated a hydrodynamic model with the consideration of electron-ion Coulomb interaction, screening effects, and exchange coupling. Within this model, we have obtained analytical solutions for the charge carrier concentration as a function of coordinates in the potential well. In quantum areas near the interfaces, we carried out quantum mechanical calculations for a screened exchange potential. The electron concentration profile is presented for modulation doped AlGaAs/GaAs/AlGaAs heterostructures.