Dynamic electrothermal simulation of integrated resistors at device level

This paper presents the dynamic electrothermal simulation of a rectangular resistor integrated on a semi-conductor substrate. Due to the temperature dependence of the electrical conductivity of the resistive sheet, self-heating provokes a coupling between the electrical and thermal problem and gives rise to nonlinear phenomena. We introduce a time stepping iterative method to perform the calculations. The electrical and thermal solvers are based on FEM and Green's functions techniques, respectively. An extensive dynamic analysis of the device will be presented. The results include heating and cooling curves, Nyquist plot (complex locus) of the thermal impedance, time constant spectrum and structure function. Comparisons with the linear case, i.e. a temperature independent resistor, are made and accompanied by analytical approximations if possible. One key observation is that the nonlinearity may easily be overlooked: its detection is only possible in particular characteristics.