Thermal Characterization of Si BEOL Microelectronic Structures

Resistor reliability rules are defined by certain electrical parameters that depend on operating temperature. As shown by Black’s Equation, a temperature change of 5°C can lead to a 30% reduction in expected lifetime [1]. The temperature rise of a resistor depends on its dimensions and thermal properties as well as those of surrounding materials that separate the resistor from the heat sink. In this study, a modified approximate model based on Schafft’s equation is developed to estimate the operating temperature and assess the reliability of BEOL microresistor structures. The additional contribution of the substrate thermal resistance is added to the model and validated through a combined approach of experimental thermal mapping and numerical modeling. The developed analytical and numerical model are validated with the experimental temperature maps and could then be used for parametrization to aid the BEOL design process.