Heat capacity of a thin membrane at very low temperature

TL;DR

This paper analyzes how the heat capacity of a thin membrane varies with thickness and temperature, revealing a universal ratio and a minimum, with implications for optimizing microbolometer support membranes.

Contribution

It provides a theoretical calculation of heat capacity dependence on thickness and temperature, identifying a universal ratio and a minimum point, useful for device optimization.

Findings

Heat capacity has a minimum at a specific thickness for each temperature.

The ratio of heat capacity to its minimum is a universal function of thickness ratio.

Minimal heat capacity scales with temperature squared.

Abstract

We calculate the dependence of heat capacity of a free standing thin membrane on its thickness and temperature. A remarkable fact is that for a given temperature there exists a minimum in the dependence of the heat capacity on the thickness. The ratio of the heat capacity to its minimal value for a given temperature is a universal function of the ratio of the thickness to its value corresponding to the minimum. The minimal value of the heat capacitance for given temperature is proportional to the temperature squared. Our analysis can be used, in particular, for optimizing support membranes for microbolometers.