Analytical model for base transit time of a bipolar transistor with Gaussian-doped base

Abstract

The present analysis for base transit time τ b of a modern high-speed npn bipolar transistor is done for Gaussian-doped base considering doping dependence of mobility, bandgap narrowing effect and carrier velocity saturation effect at base–collector junction. First the minority carrier current density and electron density equations incorporating all the effects are analytically solved. The collector current density J c and base stored charge Q b are then separately expressed as a function of the injected electron density n(0) in the base in order to find base transit time. The modeling of J c, Q b and τ b are essential for the design of high-speed bipolar transistor. The equations are applicable for low level of injection. The base transit time calculated analytically is compared with numerical results in order to demonstrate the validity of the assumptions made in deriving the equations. The closed form equations 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.