Modeling temperature dynamic effects for high‐power light‐emitting diodes

Abstract

Temperature is a dynamic variable in most electronic devices. As the device operates, it generates heat, which translates in a temperature increase. Available models commonly disregard these variations due to the fact that they manifest at very large time scales. However, temperature dynamic effects have profound implications on the device model and on our common understanding. This paper discusses implications of considering the temperature variations on the current-voltage characteristic curves of power light-emitting diodes. The main theoretical results establish that the current equation has a memristive nature when temperature is assumed as a dynamical state variable. This hypothesis is then validated experimentally. K E Y W O R D SDC characteristic, hysteresis, memristor, power diode, power LED, thermo-electrical diode model | INTRODUCTIONStandard thermal analysis of power electronic circuits usually assumes static temperature conditions, that is, temperature evolution is considered a very slow process when compared to the operating frequencies. Under this simplifying assumption (and assuming one can neglect the transfer of heat through radiation and convection), the thermal analysis of a given circuit follows straightforward Ohm's law-like relations, where temperature increases linearly with the dissipated power with a slope equal to the thermal resistance of the device. 1 This simple relation is the basis of conventional heat sink (HS) selection procedures, where a series of multiple thermal resistances account for the heat conduction from the device's active region, where it is generated, to the environment, where it is dissipated.Temperature is also a parameter that influences the device's characteristics. Current-voltage relations in diodes and transistors involve temperature in multiple instances: (i) the thermal voltage k B T=q (where k B is the Boltzmann constant and q is the charge of the electron) increases linearly with temperature; (ii) carrier concentrations follow Fermi-Dirac distributions, which are strongly affected by temperature; and (iii) material properties such as thermal conductivity vary with temperature. 2 These temperature-dependent device's current-voltage relations are generally oversimplified and mistreated in the available literature. For instance, it is a common procedure to depict the temperature dependence of the diode current-voltage relation as a collection of curves obtained for different fixed temperature