BALLISTIC VERSUS DIFFUSIVE BASE TRANSPORT IN THE HIGH-FREQUENCY CHARACTERISTICS OF BIPOLAR-TRANSISTORS

The time-dependent Boltzmann equation is used to calculate the small-signal complex base transport factor-alpha(omega) for different ratios between the base width W and the scattering mean-free path l(sc). It is shown that the phase trajectory (Re-alpha, Im-alpha) has a universal character both in the diffusion limit (W much greater than l(sc)) and the ballistic limit (l(sc) much greater than W). In the latter limit, the trajectory is completely determined by the distribution function of minority carriers injected into the base. The complex trajectories are plotted for several model distributions, including the usual thermal distribution and taking into account the injection energy appropriate for a heterojunction bipolar transistor with a wide-gap emitter.