Limitations in Cooling Electrons using Normal-Metal-Superconductor Tunnel Junctions

Abstract

We demonstrate both theoretically and experimentally two limiting factors in cooling electrons using biased tunnel junctions to extract heat from a normal metal into a superconductor. Firstly, when the injection rate of electrons exceeds the internal relaxation rate in the metal to be cooled, the electrons do no more obey the Fermi-Dirac distribution, and the concept of temperature cannot be applied as such. Secondly, at low bath temperatures, states within the gap induce anomalous heating and yield a theoretical limit of the achievable minimum temperature.

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

“…In this configuration, a reduction of the electron temperature from 300 to about 100 mK was obtained. Later on, other experimental evidence of electron cooling in SINIS metallic structures was reported ͑Fisher et Leoni et al, 1999Leoni et al, , 2003Vystavkin et al, 1999;Arutyunov et al, 2000;Luukanen et al, 2000;Pekola, Anghel, et al, 2000;Tarasov et al, 2003;Clark et al, 2004;Pekola, Heikkilä, et al, 2004͒. In these experiments NIS junc- FIG. 26.…”

“…͑5͒ or ͑3͒ where the collision integrals and self-energies for inelastic scattering can be neglected. As a result, the shape of the electron distribution functions inside the wire at a finite bias voltage eV տ k B T may strongly deviate from a Fermi dis- Ti 300-800 500-800 1.3ϫ 10 9 Manninen et al, 1999 tribution ͑Heslinga and Klapwijk, 1993;Pothier et al, 1997b;Pierre et al, 2001;Heikkilä et al, 2003;Giazotto et al, 2004b;Pekola, Heikkilä, et al, 2004͒. The nonequilibrium shape shows up in most of the observable properties of the system, including the I-V characteristics, the current noise, or the supercurrent.…”

“…͑42͒: ͑a͒ No inelastic scattering, I coll =0, T = 0.1T c , and depairing strength ⌫ =10 −4 ⌬ inside the superconductors. The voltage runs from zero to V =3⌬ / e in steps of ⌬ / ͑2e͒ and spans three regimes: ͑i͒ anomalous heating regime ͑eV =0-⌬, solid lines, widening with an increasing V͒ discussed in the article by Pekola, Heikkilä, et al ͑2004͒, ͑ii͒ cooling regime ͑eV = 1.5⌬ and 2⌬, dashed lines, narrowing with an increasing V͒ and the strong nonequilibrium heating regime ͑eV = 2.5⌬ and 3⌬, dotted lines, widening with an increasing V͒. ͑b͒ Distribution at eV = 2.5⌬ for different strengths of the electron-electron interaction, parametrized by K e-e from Eq.…”

“…When the wire terminates in a point contact with resistance R T , the resistance R D in Eq. ͑16͒ should be replaced with the total resistance R D + R T ͑Pekola, Heikkilä, et al, 2004͒. Typically the energy scale characterizing the deviation from ͑quasi͒equilibrium is E * = eV.…”

A Theoretical Study of a Novel Single-Electron Refrigerator Fabricated from Semiconductor Materials

“…A single-electron refrigerator (SER) is an interesting single-electron device that refrigerates by extracting and injecting a single electron. [1][2][3][4][5][6][7][8][9] The SER reported in the literature consists of a normalmetal/insulator/superconductor tunnel junction based on a single-electron box 10) It refrigerates a metal dot by single-electron tunneling to and from the superconductor electrode under an ac bias. There are mainly two principal physical points in the refrigeration process.…”