Self-consistent calculations of the two-dimensional electron density in modulation-doped superlattices

Abstract

We present calculations of the two-dimensional densities of electrons, $N_s$, confined in the quantum wells in modulation-doped GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As multi-quantum-well structures. Input parameters are the quantum-well width, the width of the undoped spacer, and the aluminum concentration. Doping levels and the thickness of the doped layers are assumed to be large enough to pin the Fermi level. The calculations, done for 0 K, were based on numerical self-consistent solutions of the Poisson and Schrödinger equations. The calculated values of $N_s$ are compared with the experimental results found in the literature and in most cases the agreement is excellent. The present calculations also permit predictions concerning the persistent photoconductivity effect.