The effect of impurity concentration dependent static dielectric constant on band-gap narrowing in heavily doped silicon

Abstract

The influence of the impurity concentration dependent static dielectric constant on the band-gap narrowing in heavily doped silicon at room temperature is considered. By using phosphorus as an example, the existing expression for the static dielectric constant at low temperatures is recast into a form suitable for the application at room temperature. This is done by taking into account the contribution of non-ionized impurities at room temperature to the static dielectric constant behaviour. Applying the proposed expression for the static dielectric constant to the band-gap narrowing calculations, a good agreement with the widely used empirical expression of Del Alamo and Swanson is obtained.