Characterising heat transport in 2D dumbbell resonators

Abstract

When a free-standing membrane is actuated with photothermal method, the heat flux requires a certain time to diffuse through this membrane. This duration of time, called thermal time constant, is important for its application in sensors, nano-electromechanical systems, filters, etc. This report is devoted to exploring what plays a major role in the variation of experimentally measured thermal time constants, and to investigating the relationship between dumbbell dimensions (namely, two drum radius R1 for drum 1 and R2 for drum 2, half bridge width y0, bridge length x0) and thermal time constants.

First, dumbbell resonators of various dimensions were fabricated using exfoliated molybdenum disulfide flakes. Optomechanical experiments were conducted on these devices, involving two collocated (actuation and measurement located in the same drum) and two non-collocated (actuated at one drum and measured at the other) measurements for each device. Accordingly, four thermal time constants were extracted for each resonator through curve fitting. To understand temperature distribution and experimental variation, a COMSOL model and an analytical model were established, solving the heat equation with a harmonic laser actuation.

As a result, four thermal time constants for 16 devices were extracted. These experimental data were verified with a synergy of the two models. The primary contributors for large experimental data variation were the 2D material irregularities and laser locations. For collocated τ, it was almost unaffected by dumbbell dimensions, except for R1 which gave a parabolic curve. For non-collocated τ, it increased monotonously with x0, but a minimum was always observed when sweeping the other three parameters.

Such minimum occurred when x0 is around 25% of the drum radius. This minimum was attributed to a balance between the efficiency of heat transport across the bridge and the acceptable duration required to heat the bridge itself. Meanwhile, the COMSOL model and the analytical model disagreed on the relationship between non-collocated τ and y0, R1, R2. Moreover, the analytical model’s deviation from the COMSOL model increased with larger bridge width or thermal conductivity. This stemmed from errors in the assumed boundary conditions: the existence of the bridge altered the temperature distribution at the boundaries of drum 1, and in the analytical model the boundaries of the dumbbell are fixed while in the COMSOL model they are controlled by the substrate.