Thermal Dynamical Identification of Light-Emitting Diodes by Step-Based Realization and Convex Optimization

A new method for modeling the thermal response of semiconductor devices such as light-emitting diodes (LEDs) from temperature measurements is presented. The method uses a realization-theoretic approach to identification combined with convex optimization methods. Linear matrix inequalities are constructed to guarantee that the identified discrete-time model has strictly real eigenvalues between 0 and 1, so that, when converted to continuous time, the model will have strictly real time constants. Additional optional time-domain constraints are developed to guarantee a predetermined steady-state value, guarantee no undershoot or overshoot in the transient response, and/or guarantee a positive time-constant spectrum. The method is applied to the thermal response of a high-power LED. Temperature measurements of the semiconductor device are used to model the time constants of the thermal response and characterize the relative contribution of each time constant to temperature increase. Experiments indicate how the proposed method can be used to detect thermal defects. It is shown that models with five time constants can model the thermal effects of the LEDs used with high accuracy. The proposed method is applicable to larger order systems with multiple simultaneous temperature measurements.