Mathematical Analysis of Bipolar Transistors

The mathematical theory of bipolar transistor operation is founded upon conclusions drawn primarily from one-dimensional models for this semiconductor device. These models are of varying complexity. The simple models offer the advantage of computational ease and, thereby, represent practical engineering tools. Other, more complex models require extensive computer time; these models are more applicable to research investigations into problems relating to the theory of transistor operation. Using statistical methods of analysis it is shown that many elementary models for transistor operation provide satisfactory agreement with experiment. A similar degree of agreement is seldom (if ever) obtained for the current gain or switching speed. It is suggested that this current gain problem arises from emitter region mechanisms for which there is only limited understanding. Additionally, it is suggested that this same problem has important implications in the theory of I2L logic structures.