Self-consistent energy levels in low-dimensionally delta -doped structures

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Abstract
We investigate the electronic states in low-dimensional semiconductor systems created by delta doping of donors by solving Schrodinger and Poisson equations self-consistently. The increase of the density of states near the population threshold leads to the existence of two physical solutions to the same boundary-value problem due to the electron-donor dipole charge potential. An empty and a filled state can be self-consistent for a depletion potential in the two-dimensional system for heavy carriers as well as in the one-dimensional and zero-dimensional systems, The bisolution behaviour for electrons in the GaAs wire persists up to approximately 37 K if level broadening is negligible. We find that the energy levels of the lowest subband are well described using simple variational functions. The carrier density does not vanish gradually as the doping density that compensates the fixed depletion charge is decreased, indicating that true bistability does not take place in these systems.