In this paper, we present an exactly solvable small-signal model to analyze transport in the base region of a bipolar transistor. Both graded-base and uniform-base structures are considered. The solutions describe both ballistic and diffusive transport under specific, simplifying conditions. Moreover, these results are in excellent agreement with a numerical solution of the Boltzmann equation. This model predicts a number of interesting features of the current-gain factor α(f) in the quasi-ballistic regime and explains the importance of scattering, however small, on the base transport properties of electrons. Finally, we use this model to interpret some recent experiments on short-base transport.
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