Dielectric response in p-type silicon: Screening and band-gap narrowing

Abstract

Some physical effects that arise due to large impurity concentrations in p-type semiconductors are discussed. This consists of a detailed analysis of the screening of static impurities and also band-gap narrowing in p-type silicon. A finite-temperature dielectric-response formalism is used together with a 6×6 Hamiltonian operator to describe the hole-energy eigenstates. A comparative study between our results and a Thomas-Fermi model generalized for the same valence-band structure is also presented. It is found that at high doping the Thomas-Fermi approximation overestimates the impurity screening except at very large distances where the Thomas-Fermi potential exhibits a greater long-range tail. Calculations of the band-gap narrowing in p-type silicon are performed using the same dielectric-response function and are shown to be in good agreement with experiment at both 20 and 300 K. © 1993 The American Physical Society.