Performance Optimization of Cascaded Subband Degeneracy Cryogenic Refrigerator

The design for a cascaded solid-state refrigerator is introduced as an alternative to dilution refrigerators for eventual use in cryogenic cooling of quantum computers. The design achieves cooling through adiabatic subband degeneracy expansion in a closed-cycle electron heat-pump controlled by electrostatic gates – a cooling mechanism whose single-shot principle was first outlined by Rego and Kirceznow (1999). Whereas a single stage reduces temperature by at most the ratio of the degeneracies g₁ and g₂ of the “compressed” and “expanded” quantum well states, here a multi-stage, cascaded design is shown to reach lower temperatures. The optimal ratio of areas between successive hot and cold stages is equal to the square root of g₂/g₁. In a 1 K heat bath, a 1 cm², double degeneracy two-stage device can reach a base temperature of 0.68 K. Multi-stage refrigerators have base temperatures below 0.10 K, where electrons and phonons thermally decouple. Modeling the Joule heating and thermal conduction through gate wires, as well as electron-phonon coupling, the parasitic heat load at low temperatures can be determined. The thermodynamic coefficients of performance for this device are also derived.