Correlating Microscale Thermal Conductivity of Heavily-Doped Silicon With Simultaneous Measurements of Stress

The functioning and performance of today’s integrated circuits and sensors are highly affected by the thermal properties of microscale silicon structures. Due to the well known size effect, the thermal properties of microscale silicon structures are not the same as those of the bulk silicon. Furthermore, stress/strain inside microscale silicon structures can significantly affect their thermal properties. This article presents the first thermal conductivity measurements of a microscale silicon structure under applied compressive stress at 350 K. Atomic force microscope (AFM) cantilevers made of doped single-crystal silicon were used as samples. A resistance temperature detector (RTD) heater attached to another RTD sensor was used as the heating module, which was mounted onto a nanoindentation test platform. This integrated system applied compressive load to the cantilever in the longitudinal direction while supplying heat. The thermal conductivity of the cantilevers was calculated using steady state heat conduction equation. The result shows that the measured thermal conductivity varies from $110 W/(m·K)$ to $140 W/(m·K)$ as compressive strain varies from 0.1% to 0.3%. Thermal conductivity is shown to increase with increase in compressive strain. These results match with the published simulation values. The measured thermal conductivity and stress values vary in the similar manner as a function of applied strain.