Carrier densities and emitter efficiency in degenerate materials with position-dependent band structure

Abstract

We consider the electron and hole densities in degenerate and nondegenerate materials with a band structure that is position-dependent and/or having a nonparabolic density of states function. For nondegenerate materials it is shown that the pn-product deviates from its classical value n i 2 for two reasons which generally occur conjunctively. First a modifying factor exp ( ΔE g / kT) occurs due to the real change in bandgap. Secondly, a factor exp [( Γ n + Γ p )/ kT] is found stemming from the modified density of states or apparent change in band gap. These effects can be separated by studing the temperature dependence. Next we calculate the minority carrier current and the emitter efficiency and current gain. It is shown that β ψ will be degraded by the increased pn-product and will be further affected by the degeneracy of the emitter material, the direction of the change depending on the doping profiles.