An analytic model for minority-carrier transport in heavily doped regions of silicon devices

A simple analytic description of the minority-carrier current injected into typical diffused (or ion-implanted) heavily doped regions of silicon bipolar devices is derived. The effects of energy-bandgap narrowing, majority-carrier degeneracy, Auger recombination, a doping-density gradient, and surface recombination are accounted for tractably by using key approximations. Numerical solutions of the minority-carrier continuity equation support the model and facilitate the evaluation of the model parameters, which follow directly from the doping-density profile. The accuracy of the model is within the bounds of uncertainty emanating from present equivocal characterizations of bandgap narrowing and of Auger carrier lifetimes.