Analyzing thermal runaway in semiconductor devices using the constrained method of optimization

Thermal runaway is a major cause of failure of semiconductor devices in electronic systems. Analyzing the conditions for thermal runaway and its prevention is important to prevent this failure mechanism. In this paper, the Lagrange´s constrained method of optimization is applied to the problem of thermal runaway. Cases of thermal runaway in MOSFET,BJT and semiconductor ICs are discussed. A case of power generation and dissipation represented by a quadratic function in two-variables is taken as an example and the method of application is explained. The geometrical interpretation of the mathematical results is also discussed. Methods of prevention of thermal runaway in a few types of semiconductor components are given.