Heat Exchange Between Electrons and Phonons in Nanosystems at Sub-Kelvin Temperatures

Abstract

Abstract. Ultra-sensitive nanoscopic detectors for electromagnetic radiation consist of thin metallic films deposited on dielectric membranes. The metallic films, of thickness d of the order of 10 nm, form the thermal sensing element (TSE), which absorbs the incident radiation and measures its power flux or the energies of individual photons. To achieve the sensitivity required for astronomical observations, the TSE works at temperatures of the order of 0.1 K. The dielectric membranes are used as support and for thermal insulation of the TSE and are of thickness L − d of the order of 100 nm (L being the total thickness of the system). In such conditions, the phonon gas in the detector assumes a quasi-two-dimensional distribution, whereas quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces leads to the formation of quasi twodimensional electronic sub-bands. The heat exchange between electrons and phonons has an important contribution to the performance of the device and is dominated by the interaction between the electrons and the antisymmetric acoustic phonons.High sensitivity electromagnetic radiation detectors for space applications are nanometer-size devices which work at sub-Kelvin temperatures [1,2]. Such a detector consists of a thermal sensing element (TSE) which is deposited on a supporting membrane. The TSE is formed of one or several metallic layers and has the role of absorbing and measuring the incident electromagnetic radiation. The supporting membrane is dielectric and provides the thermal insulation of the TSE from the bulk material [1][2][3][4]. To ensure the level of sensitivity required by the astrophysical observations, the thickness of the TSE should be of the order of 10 nm, the thickness of the supporting membrane is of the order of 100 nm, whereas the working temperature of the device may be about 100 mK [5,6]. The layers of materials that form the detector are shown schematically in Fig. 1.The TSE may consist of a normal metal strip coupled to a superconducting antenna [2,3,[5][6][7][8][9]. When the incident radiation is absorbed, its energy is dissipated into the normal metal strip. At the detector's working temperature, the electrons are weakly coupled to the lattice and therefore we can associate an effective temperature to each of these subsystems: T e will denote the temperature of the electrons and T ph will denote the temperature of the lattice (phonons).Being at different temperatures, a net heat power P flows between the electron system and the phonon system, due to the electron-phonon interaction. This interaction is described by the deformation potential Hamiltonian [10-12]