Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges

Abstract

Accurate thermal conductivity values are essential for the successful modeling, design, and thermal management of microelectromechanical systems (MEMS) and devices. However, the experimental technique best suited to measure the thermal conductivity of these systems, as well as the thermal conductivity itself, varies with the device materials, fabrication processes, geometry, and operating conditions. In this study, the thermal conductivities of boron doped single-crystal silicon microbridges fabricated using silicon-on-insulator (SOI) wafers are measured over the temperature range from 80 to 350 K. The microbridges are 4.6 mm long, 125 μm tall, and either 50 or 85 μm wide. Measurements on the 85 μm wide microbridges are made using both steady-state electrical resistance thermometry (SSERT) and optical time-domain thermoreflectance (TDTR). A thermal conductivity of 77 Wm−1 K−1 is measured for both microbridge widths at room temperature, where the results of both experimental techniques agree. However, increasing discrepancies between the thermal conductivities measured by each technique are found with decreasing temperatures below 300 K. The reduction in thermal conductivity measured by TDTR is primarily attributed to a ballistic thermal resistance contributed by phonons with mean free paths larger than the TDTR pump beam diameter. Boltzmann transport equation (BTE) modeling under the relaxation time approximation (RTA) is used to investigate the discrepancies and emphasizes the role of different interaction volumes in explaining the underprediction of TDTR measurements.