Optical and electrical energy gaps of the n-type impure silicon at 300 K

The band-gap narrowing ΔE_{g, opt} and ΔE_{g, elec} (or ΔE_{g, eff}) for optical and electrical energy gaps of the n-type impure silicon at 300 K, are investigated based on simplified models of heavily doped semiconductors. It is suggested that, for $\text{4 × 10}{}^{19}\text{cm}{}^{-3}\text{? n}{}_0\text{? 3 × 10}{}^{20}\text{cm-3}\text{, ΔE}{}_{\mathrm{g,\; elec}}\text{(or ΔE}{}_{\mathrm{g,\; eff}}\text{)}$ is significantly larger than ΔE_{g, opt}, in good agreement with observed results. This difference is caused especially by the effect of the polaron.