Electron Distribution in Non-uniformly Doped NPN Transistors

In this paper the analytical expressions of minority carrier distribution for Exponential and Gaussian doped base within the n-p-n bipolar transistors are obtained. The derivation of model equations starts by first considering low level of minority carrier injection within the base. A minority carrier profile is obtained by solving electric field equation and current equations for holes and electrons at equilibrium. Next a first order differential equation is obtained for minority carrier distribution. The solution of the differential equation gives the minority carrier profile. In this paper characteristics of the derived equations of minority carrier distribution are studied with the variation of different parameters with reliability. The analytical model is justified by using a simple TCAD simulation.