Recombination Effects on Base Transit Time in Exponentially-Doped SiGe Heterojunction Bipolar Transistor (HBT): An Analytical Approach

In conventional models of base transit time in SiGe HBTs, the recombination in the base is usually neglected because the base is considered very thin to justify simplifications in the numerical calculation. Indeed, this assumption turns out not to be very valid at moderate injection levels, since carrier recombination could have important consequences for transistor performance. The paper presents an analytical model, which includes the recombination process in the exponentially doped base of SiGe HBTs operating under intermediate injection conditions. The inclusion of recombination makes the mathematical solution very complicated. In this work, an exponential approximation technique together with perturbation theory is applied, making it possible to solve the equations with a high degree of accuracy while reducing the mathematical complications. The model that is proposed clearly depicts that the recombination effects might play an important role in defining the base transit time of SiGe HBTs with a non-uniform doping profile. It also shows that any neglect of recombination could be seriously wrong, particularly in devices operating under an intermediate injection level. The insight obtained from the results of this study will lead to a deeper understanding of the behavior of SiGe HBT and its design and optimization for improved performance in various applications. A practical method developed herein is applied to the analysis of recombination effects with limited complication.