Doping Dependent Bandgap Narrowing in Silicon and Germanium

Abstract

AbstractA simple model for bandgap narrowing in doped silicon and germanium is developed. The model assumes that bandgap narrowing in doped semiconductors results primarily from electron—electron, electron—hole, electron—donor, and hole—donor interactions. Based on the suggestion of Hermanson and Phillips that in an impure crystal spatially dependent dielectric screening represents a measure of electron—hole, electron—donor, and hole—donor interactions, the model attempts to determine electron—donor, hole—donor, and electron—hole interactions by making use of the DYP (Dingle/Yakawa potential) modified by including spatially variable dielectric constant. The electron—hole interaction energy is estimated on the basis of many‐body techniques of Mahan and Abram et al. Physics justifying the use of modified DYP for calculating bandgap narrowing is discussed in some details. It is noted that the use of the DYP is valid for doping concentrations up to about 4 × 1020 cm−3. Calculated results are displayed in figures, which show good agreements with available experiments.