Minority carrier transport equations in heavily doped silicon including band tail effects at thermal equilibrium

Minority carrier transport equations in heavily doped silicon with a non-parabolic density of states are proposed for the first time. The derivation is based on a minimum of assumptions and approximations without any artificial quantities like 'apparent bandgap narrowing' and 'effective mobility'. Two coupled first-order differential equations are obtained for the calculation of the minority carrier current. It is shown that the band tail has only little influence on the steady-state transport due to the small contribution of the charge carriers in the localised states, but it does affect the transient-state transport. It is predicted that the measured Auger coefficient is a decreasing function of doping due to band tail states.