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. Real transistors are three-dimensional, however, 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. In this paper, a fast and accurate numerical technique is used to solve the partial differential equation. This makes feasible a three-dimensional small-signal analysis of transistors operating in the low-injection regime. Calculated h-parameters for a high-frequency, double-diffused, silicon transistor are in good agreement with experimental values.