Three-Dimensional Small-Signal Analysis of Bipolar Transistors

One-dimensional transistors are well-understood today; computer techniques for detailed large-signal and small-signal analyses are available. 1 A new charge-control model, 2 which is quite promising for use in circuit analysis programs, has been developed with the aid of insight obtained from the large-scale computer analyses. However, real transistors are three-dimensional and lateral effects are only understood qualitatively. Accurate modeling of lateral effects cannot be accomplished without quantitative analyses of three-dimensional transistors. Unfortunately, even the simplest analysis of lateral effects leads to a partial differential equation [namely (7)]. Except for certain very simple transistor geometrical configurations, an analytic solution to the partial differential equation is not possible, and up to now, numerical solutions have been at best difficult and expensive in computer time. In this paper, a fast and accurate numerical technique 3 ' 4 is used to S89 890 T H E BELL SYSTEM TECHNICAL JOURNAL, APRIL