Mathematical modeling of thermal runaway in semiconductor laser operation

A mathematical model describing the coupling of electrical, optical and the rmal effects in semiconductor lasers is introduced. Through a systematic as ymptotic expansion, the governing system of differential equations is reduc ed to a single second-order boundary value problem. This highly nonlinear e quation describes the time-independent maximum temperature in the boundary layer adjacent to the mirror facet. The solution of the problem is a multi- valued function of current. The graph of the maximum steady-state temperatu re as a function of current gives a fold-shaped response curve, which indic ates that no bounded steady state exists beyond a critical value of current . For certain device parameters and initial conditions, thermal runaway occ urs. A mechanism for the sudden mode of semiconductor laser failure is desc ribed in terms of thermal runaway. (C) 2000 American Institute of Physics. [S0021-8979(00)04812-X].