Optimum doping distribution for minimum base transit time

The problem of determining the necessary impurity distribution function which will minimize the minority carrier emitter-to-collector transit time is considered. The use of this optimum profile affords a possibility of improvement in the overall high-frequency performance of diodes and transistors. A simple one-dimensional geometry is assumed, and the drift and diffusion components of minority current are considered. The mobility is assumed independent of electric field and is approximated by
\mu =a_{0} - b_{0} \ln N(x)
. When optimum doping is used, the resulting electric field is found to be a monotonically decreasing function over the base region. When the ratio of impurity densities at the boundaries of the base region is 10
³
, the minority current is primarily drift over most of the base region and the base cutoff frequency is approximately 6.5 times higher than the value resulting when the base is uniformly doped.