New expression for base transit time in an exponentially doped base bipolar transistor for all levels of injection

A new and compact formula for the base transit time, τ_b, of a modern high speed npn bipolar transistor with exponential base doping profile is derived. The present treatment includes doping dependence of mobility, bandgap narrowing effect, high injection effect and carrier velocity saturation at the base edge of the collector-base junction The derivation is not based on the charge control concept, but shows how current and charge depend on minority carrier concentration, which in turn are function of junction voltage. The expression is applicable for arbitrary injection before the onset of Kirk effect and it is simple and straight forward to give insight into device operation. The base transit time calculated analytically is compared with numerical results in order to demonstrate the validity of the assumptions made in deriving the expression.