Two-dimensional carrier flow in a transistor structure under nonisothermal conditions

A two-dimensional mathematical model is developed to predict the internal behavior of power transistors operating under steady-state conditions. This model includes the internal self-heating effects in power transistors and is applicable to predict the transistor behavior under high-current and high-voltage operating conditions. The complete set of partial differential equations governing the bipolar semiconductor device behavior under nonisothermal conditions is solved by numerical techniques without assuming internal junctions and other conventional approximations. Input parameters for this model are the dimension of the device, doping profile, mobility expressions, generation-recombination model, and the boundary conditions for external contacts. Computer results of the analysis of a typical power transistor design are presented for specified operating conditions. The current density, electrostatic potential, carrier charge density, and temperature distribution plots within the transistor structure illustrate the combined effect of the electrothermal interaction, base conductivity modulation, current crowding, base pushout, space charge layer widening, and current spreading phenomena in power transistors.