Electron-phonon heat exchange in layered nano-systems

Abstract

We analyze the heat power $P$ between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes in a temperature range in which the phonon gas has a quasi two-dimensional distribution. The quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces lead to the formation of quasi two-dimensional electronic sub-bands. The electron-phonon coupling is treated in the deformation potential model and, if we denote by $T_e$ the electrons temperature and by $T_{ph}$ the phonons temperature, we find that $P\equiv P^{(0)}(T_e)-P^{(1)}(T_e,T_{ph})$; $P^{(0)}$ is the power "emitted" by the electron system to the phonons and $P^{(1)}$ is the power "absorbed" by the electrons from the phonons. Due to the quantization of the electronic states, $P$ vs $(d,T_e)$ and $P$ vs $(d,T_{ph})$ show very strong oscillations with $d$, forming sharp crests almost parallel to the temperature axes. In the valleys between the crests, $P\propto T_e^{3.5}-T_{ph}^{3.5}$. From valley to crest, $P$ increases by more than one order of magnitude and on the crests $P$ does not have a simple power law dependence on temperature. The strong modulation of $P$ with the thickness of the film may provide a way to control the electron-phonon heat power and the power dissipation in thin metallic films. Eventually the same mechanism may be used to detect small variations of $d$ or surface contamination. On the other hand, the surface imperfections of the metallic films may make it difficult to observe the oscillations of $P$ with $d$ and eventually due to averaging the effects the heat flow would have a more smooth dependence on the thickness in real experiments.

18 pages, 17 figures

References in corpus (7)

• Electron-phonon heat transfer in monolayer and bilayer graphene
• Micrometre-scale refrigerators
• Heat transport in ultra-thin dielectric membranes and bridges
• Influence of Phonon dimensionality on Electron Energy Relaxation
• Electron-phonon coupling and longitudinal mechanical-mode cooling in a metallic nanowire
• Non-equilibrium and proximity effects in superconductor-normal metal junctions
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Cited by in corpus (2)

• Crossover in the electron-phonon heat exchange in layered nanostructures
• Cold-electron bolometer, as a 1 cm wavelength photon counter