Abstract
The mathematical foundation for a linear lumped transistor model is developed from the nonlinear regional model proposed by Schilling. A one-dimensional model is described with simple analytic equations representing carrier density and electric field profiles and stored charge across the base and collector regions of a bipolar transistor. The regional boundaries are derived as simple functions of the device parameters, e.g., impurity profile, and operating conditions at its terminals. A one-to-one correspondence between these physical device parameters and lumped model elements is provided by the model. The linear regional model is demonstrated to be equivalent to its nonlinear counterpart, consequently to Gummel's charge control model.
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