A small-signal calculation for one-dimensional transistors

A computation method to obtain an exact small-signal solution of a one-dimensional transistor model for high-frequency operation is presented under the assumption of negligible bulk recombination effect. Basis for the small-signal calculation is 1) a dc solution at the operating point under consideration, 2) trial potentials (electrostatic potential and quasi-Fermi potentials for electrons and holes, respectively), and 3) frequency. A scheme for iterative computation can be constructed in a manner similar to that for dc steady state given by Gummel. Discussions are made on conservation of the total currents, terminal currents relationship, as on a simplified method to obtain terminal characteristics. Some computation results will be demonstrated for potentials, carrier densities, current densities, and the current transfer factor. In the Appendix the relation between the exact solution and low-frequency treatment will be discussed.