Thermal relaxation in metal films limited by diffuson lattice excitations of amorphous substrates

TL;DR

This study investigates how amorphous insulating substrates influence thermal relaxation in thin metal films at temperatures above 5 K, revealing a dominant role of diffuson lattice excitations over traditional electron-phonon mechanisms.

Contribution

It demonstrates that diffuson excitations govern thermal relaxation in metal films on amorphous substrates, challenging conventional electron-phonon coupling models.

Findings

Power scales as $T_e^2$, inconsistent with electron-phonon coupling.

Thermal conductivity depends linearly on temperature, indicating diffuson excitations.

Suspended samples show length-dependent thermal behavior consistent with diffuson-mediated heat transport.

Abstract

Here we examine the role of the amorphous insulating substrate in the thermal relaxation in thin NbN, InO$_x$, and Au/Ni films at temperatures above 5 K. The studied samples are made up of metal bridges on an amorphous insulating layer lying on or suspended above a crystalline substrate. Noise thermometry was used to measure the electron temperature $T_e$ of the films as a function of Joule power per unit of area $P_{2D}$. In all samples, we observe the dependence $P_{2D}\propto T_e^n$ with the exponent $n\simeq 2$, which is inconsistent with both electron-phonon coupling and Kapitza thermal resistance. In suspended samples, the functional dependence of $P_{2D}(T_e)$ on the length of the amorphous insulating layer is consistent with the linear $T$-dependence of the thermal conductivity, which is related to lattice excitations (diffusons) for the phonon mean free path smaller than the dominant phonon wavelength. Our findings are important for understanding the operation of devices embedded in amorphous dielectrics.