Determination of the electron density in GaAs/AlxGa1−xAs heterostructures

An optimized self-consistent method for determination of the quantal electron density is presented. It is applied, in the zero-temperature case, to devices with either partial or full donor ionization. A Thomas-Fermi approximation for the T=0 limit is developed and shown to be appropriate for systematic studies of the two-dimensional electron density, ${\mathrm{\sigma }}_{\mathrm{-}}$. A suitable linear approximation is found that provides simple and accurate analytic expressions for ${\mathrm{\sigma }}_{\mathrm{-}}$ in terms of the physical parameters of the device.