Analytical expressions of base transit time for SiGe HBTs with retrograde base profiles

Abstract

We present a regional base transit time ( τ b) model which results in a set of closed-form analytical expressions for an exponentially-doped retrograde base of a SiGe-base HBT with a linearly graded Ge profile. This model considers the retarding built-in electric field due to the retrograde region, heavy doping effects, the effect of velocity saturation at the collector-base junction, the effects of the doping dependency and the electric-field dependency of the electron diffusivity, and the electric field induced by the Ge concentration gradient. The impact of these different effects on τ b is assessed. Our model results show that the retarding field due to the retrograde region in the base does not increase τ b as much as Gao et al. reported, especially when a high Ge grading exists and the retrograde region is small compared to the total basewidth. For a high Ge grading across the base, the effect of the electric-field dependency of the electron diffusivity on τ b becomes very pronounced and must be considered in the model. We also show that this model results in Kroemer’s analytical expression for the special case of a uniformly-doped base. Our results agree well with the published simulation data of Patton et al. for their 75-GHz SiGe-base HBT.