Thermal conductance of IC interconnects embedded in dielectrics

Accurate prediction of temperatures in metal wiring for integrated circuits is essential to the evaluation of electromigration reliability for high-frequency applications and electrical overload as well as for wafer-level die testing. Accurate prediction requires knowledge of the thermal conductivity of the surrounding dielectric and the heating effect of applied currents. Both quasi-analytical and numerical models for line heating as a function of applied current are presented for the case of lines fully embedded in a dielectric. Heat loss and current density at the melting point are projected as a function of linewidth, line thickness, underlying insulator thickness and insulator thermal conductivity. As intuitively expected, these projections indicate the allowed current density decreases with increasing linewidth, line thickness and insulator thickness, and also decreases as thermal conductivity decreases. Furthermore, the models are found to match heat loss measurements for isolated lines in SiO₂ and return a value of 1.07 W/m-°K for the thermal conductivity of the oxide