Doping effects on the band structure in n- type silicon at 300 K

Abstract

Based on two screened donor potential models and taking into account the electron-electron interaction effect in the electron-donor interaction, the band-gap narrowing (BGN) in n-type doped silicon at 300 K is investigated. The BGN effect is expressed in terms of physical BGN ( ΔE g ), a change in density of conduction-band states ( Γ n ) and the change in effective electron (hole) mass ( γ n ( γ p )). In fact, electrical BGN is found to be given by ΔE g, elec. ∗ = ΔE g + Γ n γ n + Γ p + ΔE g, fd ≅ ΔE g + Γ n , where ΔE g, fd represents the Fermi-Dirac statistics effect. Our results of ΔE g and ΔE tg, elec. ∗ agree fairly with corresponding observed results, and the large values of Γ n ≅ ΔtE g, elec. ∗ − ΔE g obtained at high donor concentration are in good agreement with a qualitative discussion given by Marshak and Van Vliet. Finally, the present results for the effective intrinsic-carrier concentration n ie are compared with corresponding results observed by Tang.