Carrier Density near the Semiconductor‐Insulator Interface. Local Density Approximation for Non‐Isotropic Effective Mass

For bent bands in a semiconductor near the interface to an insulator, a modified local density approximation is described which takes into account the influence of the interface barrier in the potential. Simple expressions are obtained for the electron and hole densities in a multi‐valley semiconductor with non‐isotropic parabolic bands. Due to the interface barrier the densities decrease to zero towards the interface. The characteristic length for this decrease is determined by the effective mass tensor and by the orientation of the interface. Results of self‐consistent density calculations are reported.