Simultaneous measurement of thermal conductivity and specific heat in quasi-two-dimensional membranes using the 3{\omega} method

TL;DR

This paper presents a method for simultaneously measuring thermal conductivity and specific heat in suspended quasi-two-dimensional membranes using the 3ω technique, with a detailed model and experimental validation.

Contribution

The authors develop a new approach to measure both thermal properties simultaneously in atomically thin membranes using a 3ω method with a one-dimensional thermal impedance model.

Findings

Successfully measured thermal conductivity and specific heat of silicon nitride.

The thermal impedance response acts as a low-pass filter, enabling property extraction.

Results agree with literature values for silicon nitride.

Abstract

Toward measuring the thermal properties of exfoliated atomically thin materials, we demonstrate simultaneous measurements of the thermal conductivity and specific heat in suspended membranes. We use the 3{\omega} technique applied to quasi-two-dimensional silicon nitride membranes having a metal line heater patterned on the surface to both deliver heat and directly measure the thermal impedance of the membrane at the heating frequency, Z(2{\omega}). We derive an expression for the complex thermal impedance as a function of frequency, approximating the actual rectangular membranes with a one dimensional model. The derivation accounts for potential parasitic heat loss mechanisms including conduction along the heater line, and by the gas load in an imperfect vacuum. Qualitatively, the thermal impedance response resembles a low-pass filter, owing to the combination of the total thermal resistance and total specific heat. Fitting Z(2{\omega}) to measurements across a few decades in frequency, we extract values of the thermal conductivity and specific heat of silicon nitride in agreement with literature values. We also study the dependence on the heating current, and compare to measurements of the thermal conductivity at zero frequency.