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 ¡xm tall, and either 50 or 85 ¡im wide. Measurements on the 85 ßm wide microbridges are made using both steady-state electrical resistance thermometry (SSERT) and optical time-domain thermoreflectance (TDTR). A thermal conductivity of 77 Wm^' K~' 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 patlis 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.

Bulk-like Intrinsic Phonon Thermal Conductivity of Micrometer-Thick AlN Films

“…This phenomenon is not due to boundary scattering, but instead due to phonon-defect scattering from a reduction in crystalline quality. This is consistent with our measurements of a reduction in the thermal conductivity of the 6 μm film at 80 K. These results demonstrate an opposite trend than the thermal conductivity measurements of alloy semiconductor materials conducted using TDTR and frequency domain thermoreflectance (FDTR) with heater length scales less than the thermal phonon mean free paths; the measured thermal conductivities at these heater length scales are reduced relative to bulk in these prior reports. ,− Our results are in agreement with the theories of Zeng and Chen, Wilson and Cahill, and Regner et al, in that a heater length scale-dependent thermal conductivity in nonalloy single crystals is not expected.…”

Ion irradiation of the native oxide/silicon surface increases the thermal boundary conductance across aluminum/silicon interfaces

“…Finally, recent works [52,60,61] that have observed both radial and frequency dependence in thermal conductivity measurements of silicon using TDTR or related techniques have theorized that these effects are driven by nonlocal heat conduction around the interface of a metal film and silicon substrate [44]. This nonlocal effect can affect our measurements of both thermal conductivity in the silicon and the measured thermal boundary conductance, as the gradient of energy could be a by-product of our TDTR experimental parameters.…”

An electrical probe of the phonon mean-free path spectrum

“…Thus we can plot data points collected on devices with different heater and thermometer widths on the same graph. Earlier literature 21 30 31 has examined the heater size dependence of the effective thermal conductivity. Although those papers reported on the order of 30–50% change to the effective thermal conductivity, this was for a spot-size ranging from 1 micron to 10 micron.…”