Nonparabolic coupled Poisson-Schrödinger solutions for quantized electron accumulation layers: Band bending, charge profile, and subbands at InN surfaces

Abstract

The one-electron potential, carrier concentration profile, quantized subband state energies, and parallel dispersion relations are calculated for an accumulation layer at a semiconductor surface by solving Poisson’s equation within a modified Thomas-Fermi approximation and numerically solving the Schrödinger equation for the resulting potential well. A nonparabolic conduction band, described within the Kane $\mathbf{k}\cdot \mathbf{p}$ approximation, is incorporated in the model. Example calculations are performed for a typical clean InN surface and for a variety of surface state densities and bulk carrier concentrations. Agreement is found between the model calculations and experimental measurements of the subband energies and dispersions at $c$-plane InN surfaces from electron tunneling spectroscopy and angle resolved photoemission spectroscopy.