Abstract
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 considering doping dependence of mobility, bandgap narrowing effect, high injection effect and carrier velocity saturation at the base edge of the collector–base junction. The collector current density, J c , and minority carrier stored charge, Q b , in the base are separately expressed as a function of the injected electron density n o in the base in order to find an empirical expression for τ b . The modelling of J c , Q b and τ b is essential for the design of high-speed bipolar transistor. The expressions are applicable for arbitrary injection before the onset of the Kirk effect and they are simple and straight forward to give insight into device operation. The base transit time calculated analytically is compared with simulation results in order to demonstrate the validity of the assumptions made in deriving the expression. The closed form expressions for collector current density and base transit time offer a physical insight into device operation and are a useful tool in device design and optimization.
Published Version
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