Electron-phonon heat exchange in quasi-two-dimensional nanolayers

摘要

We study the heat power P transferred between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes. The temperature range is typically below 1K , such that the wavelengths of the excited phonon modes in the system is large enough so that the picture of a quasi-two-dimensional phonon gas is applicable. Moreover, due to the quantization of the components of the electron wavevectors perpendicular to the metal film's surface, the electrons spectrum forms also quasi two-dimensional sub-bands, as in a quantum well (QW). We describe in detail the contribution to the electron-phonon energy exchange of different electron scattering channels, as well as of different types of phonon modes. We find that heat flux oscillates strongly with thickness of the film d while having a much smoother variation with temperature (T-e for the electrons temperature and T-ph for the phonons temperature), so that one obtains a ridge-like landscape in the two coordinates, (d, T-e) or (d, T-ph), with crests and valleys aligned roughly parallel to the temperature axis. For the valley regions we find P proportional to T-e(3.5) - T-ph3.5. From valley to crest, P increases by more than one order of magnitude and on the crests P cannot be represented by a simple power law. The strong dependence of P on d is indicative of the formation of the QW state and can be useful in controlling the heat transfer between electrons and crystal lattice in nano-electronic devices. Nevertheless, due to the small value of the Fermi wavelength in metals, the surface imperfections of the metallic films can reduce the magnitude of the oscillations of P vs. d, so this effect might be easier to observe experimentally in doped semiconductors.