Empirical determination of the energy band gap narrowing in p⁺ silicon heavily doped with boron

In the analysis of highly doped silicon, energy band gap narrowing (BGN) and degeneracy effects may be accounted for separately, as a net BGN in conjunction with Fermi-Dirac statistics, or lumped together in an apparent BGN used with Boltzmann statistics. This paper presents an experimental study of silicon highly doped with boron, with the aim of evaluating the applicability of previously reported BGN models. Different boron diffusions covering a broad range of dopant densities were prepared, and their characteristic recombination current parameters J₀ were measured using a contactless photoconductance technique. The BGN was subsequently extracted by matching theoretical simulations of carrier transport and recombination in each of the boron diffused regions and the measured J₀ values. An evaluation of two different minority carrier mobility models indicates that their impact on the extraction of the BGN is relatively small. After considering possible uncertainties, it can be concluded that the BGN is slightly larger in p⁺ silicon than in n⁺ silicon, in qualitative agreement with theoretical predictions by Schenk. Nevertheless, in quantitative terms that theoretical model is found to slightly underestimate the BGN in p⁺ silicon. With the two different parameterizations derived in this paper for the BGN in p⁺ silicon, both statistical approaches, Boltzmann and Fermi-Dirac, provide a good agreement with the experimental data.