Multiharmonics Method Characterizing In-Plane Thermal Conductivity and TBR of Semiconductor Nanofilm on Substrate: Theoretical Analysis

The in-plane thermal conductivity of semiconductor nanofilm is difficult to be tested due to suspension problem. The thermal boundary resistance (TBR) plays a key role in semiconductor nanoscale structures and nanoscale thermal experiments. By applying alternating current and direct current currents simultaneously on the semiconducting nanofilm on highly insulated substrate, multiharmonics including 1ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\upomega $$\end{document}, 2ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\upomega $$\end{document} and 3ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\upomega $$\end{document} signals originating from the self-heating of nanofilm are measured. The thermal boundary resistance is introduced into the heat diffusion equation in in-plane direction. The expression of temperature oscillation and theoretical analysis of heat transport process show that the in-plane thermal conductivity and TBR can be decoupled from the multiharmonics in frequency domain. Thermal analysis justifies the multiharmonics method according to the effect of in-plane thermal conductivity, TBR between nanofilm and insulated substrate, resistance coefficient of semiconductor nanofilm on temperature oscillation at low frequency. Results show the multiharmonic method sensitivity variations depending on the TBR, the in-plane thermal conductivity, and the electric current frequency.