ANALYTICAL MODELING OF BJT NEUTRAL BASE REGION UNDER VARIABLE INJECTION CONDITIONS

We present a set of closed form analytical solutions of the transport equation in the base of bipolar transistors. The presented 1D solution s hold for variable injection conditions, arbitrary doping profiles an d arbitrary intrinsic carrier concentrations along the base, allowing to consider bandgap narrowing effects and a variable composition base (e.g. Si1-xGex graded base). The above solutions lay on the commonly u sed assumption of zero majority carrier current in the neutral zone, a nd are valid up to the onset of the Kirk effect. Two solutions are ana lysed; the zero-order solution, found as a correction of the low injec tion case, and the first order solution, derived as a correction of th e zero-order case. The perturbative procedure can naturally be iterate d leading to an exact solution, which is used to assess the accuracy o f the proposed analytical solutions. The first-order solution shows th e best trade-off between accuracy and complexity. (C) 1997 Elsevier Sc ience Ltd.