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

The current density and temperature distribution in a bi-polar power transistor operating in the switching mode under transient conditions has been computed as a function of circuit environment. A modeling was done of the turnoff of the transistor in a circuit containing resistive and inductive elements. Of particular interest was the study of the local current and temperature distribution achieved in the transistor during turnoff in a circuit with a large inductance; in the process of shutoff this inductance maintains the transistor collector current at a high value as the collector junction undergoes avalanche multiplication due to the high voltage induced across this junction by the inductive load. The length of time that the transistor remains in the high-current high-voltage mode during the turnoff transient determines the extent of current crowding and local heating in the device. The method of computation was to solve numerically the electrical carrier flow as well as Poisson´s and the heat-flow equations in a two-dimensional model of an n⁺-p-n-n⁺transistor structure, as a function of time. The electrical boundary conditions on the emitter, base, and collector contacts were determined by considering the transistors interaction with its electric circuit environment. This interaction was calculated at each step in time, in an iterative fashion, as the transistor was turned off by extracting current from its base lead. The study permits the evaluation of a given bipolar transistor design with respect to current crowding, heating, and impact ionization in switching circuits containing inductive loads.