A Closed-Form Solution for the Low-Current Collector Transit Time in Group IV and Group III-V HBTs

In certain types of heterojunction bipolar transistors (HBTs), the carrier transit time associated with the base-collector (BC) space-charge region constitutes a significant contribution to the total transit time. In many compact models, the low-current BC transit time is lumped in with the total low-current transit time and often assumed to be constant-dependent only on the collector width and material saturation velocity. This assumption, however, is insufficient for modeling high-voltage Si-based HBTs as well as for III-V HBTs, where the negative differential mobility (NDM) effect can become relevant in high-speed low-power circuits. This paper presents a closed-form solution for the low-current collector transit time based on a novel accurate analytical velocity-field formulation, covering both group IV and group III-V semiconductor materials. The new solution includes the NDM effect and is suitable for implementation in compact models, and its relevance and accuracy are demonstrated for both TCAD simulated and measured data.