Doping profile and Ge-dose optimization for silicon-germanium heterojunction bipolar transistors

The speed of silicon-germanium (SiGe) heterojunction bipolar transistors (HBTs) has been dramatically increased. It is known that the speed of HBTs is dominated by the base transit time, which could be influenced by the doping profile in the base region and the Ge concentration. In this study, the design of the doping profile and Ge-dose concentration for SiGe HBTs are mathematically formulated and solved by a technique of geometric programming (GP). The solution calculated by the GP method is guaranteed to be a global optimal. The accuracy of the adopted numerical optimization technique is first confirmed by comparing with two-dimensional device simulation. The result of this study shows that a 23% Ge fraction may maximize the current gain; furthermore, a 12.5% Ge may maximize the cut-off frequency for the explored device, where a 254 GHz cut-off frequency is achieved.