Interplay between Raman shift and thermal expansion in graphene: temperature-dependent measurements and analysis of substrate corrections

TLDR: In this article, dedicated Raman scattering experiments were conducted for graphene monolayers deposited on silicon nitride substrates and over a broad temperature range extending over 150--800 K. The relation between those measurements for the $G$ band and the graphene TEC, which involves correcting the measured signal from the mismatch contribution of the substrate, was analyzed based on different theoretical candidates for $\ensuremath{\alpha}(T)$.

Abstract: Measurements and calculations have shown significant disagreement regarding the sign and temperature variations of the thermal expansion coefficient (TEC) of graphene $\ensuremath{\alpha}(T)$. Here we report dedicated Raman scattering experiments conducted for graphene monolayers deposited on silicon nitride substrates and over a broad temperature range extending over 150--800 K. The relation between those measurements for the $G$ band and the graphene TEC, which involves correcting the measured signal from the mismatch contribution of the substrate, is analyzed based on different theoretical candidates for $\ensuremath{\alpha}(T)$. Contrary to calculations in the quasiharmonic approximation, a many-body potential reparametrized for graphene correctly reproduces experimental data, suggesting that the TEC is more likely to be positive above room temperature.