Raman Thermometry and Thermal Modeling of Highly Doped Silicon-on-Insulator Joule Heated MEMS Bridges Under Varying Gas Pressures

This paper reports on experimental and numerical investigations of electrically powered MEMS structures operated under different gas pressure and electrical power conditions. The structures studied are boron-doped single crystal silicon-on-insulator (SOI) microbridges that are heated by an electrical current. The microbridges are 85 μm wide, 125 μm tall and 5.5 mm long and lie 2 μm above the substrate. The impact of the narrow gap in the gas phase thermal transport is evaluated by operating the devices under various nitrogen gas pressure conditions, ranging from 625 Torr to ∼1 mTorr — spanning the continuum to noncontinuum gas heat transfer regimes. Raman thermometry is used to obtain spatially-resolved temperature measurements along the length of the device under the various operating conditions. The large dopant concentration (∼4 × 10¹⁹ cm⁻³) within the active silicon layer is found to affect the Raman spectrum used for thermometry via Fano-type interactions, resulting in an asymmetric Raman line shape. With large Raman peak asymmetries, use of the Raman line width as the temperature metric is less reliable as it shows decreased sensitivity to temperature. However, the asymmetry itself, when considered as a fitting parameter, was found to be a reliable indicator of sample temperature. The measured device temperatures are compared to finite element simulations of the structures. Noncontinuum gas phase heat transfer effects are incorporated into the continuum simulations via temperature discontinuities at the solid-gas interface, provided by a model developed from noncontinuum simulation results. Additionally, the impact of the large dopant concentrations is incorporated into the thermal models via a modified thermal conductivity model which considers impurity scattering effects on thermal transport. The simulation and experimental results show reasonable agreement.