In this joint research activity we propose to develop ultralow temperature nanorefrigerators in which devices can be cooled to milliKelvin and sub-milliKelvin temperatures by nanoelectronic means. We will investigate nanoscale hybrid refrigerators as well as quantum dot based nano-coolers and develop the necessary filtering and thermalization methods to obtain ultralow temperatures in nano-samples. This will make use of innovative ideas, materials and optimized geometries.
Promising micro- and nanoelectronics applications include low temperature devices with unprecedented properties and functionalities as compared to conventional devices operating at room temperature. One of the main challenges of present-day cryogenics is to develop small, low-temperature refrigeration systems that provide targeted microscale cooling.
Hybrid nanostructures combining Superconductors (S) and Normal metals (N) offer a promising possibility in nanocooling. Owing to energy-selective electron tunneling, an N-I-S tunnel junction voltage-biased below the gap features a quasiparticle cooling effect: only electrons with an energy exceeding the gap are effectively removed from N. As a consequence, the normal metal electrons are cooled. Two tunnel junctions arranged in a symmetric S-I-N-I-S configuration routinely give a reduction of the electron temperature from 300 mK to below 100 mK. Innovative materials choices seem appropriate to improve cooler performance, but this still needs to be explored explicitly. Such coolers could provide a platform for experiments on actual quantum devices under ultra-low temperature conditions, which can hardly be reached by other means. In order to ensure a galvanic isolation of the detector from to the cooler, a membrane technology appears necessary.
The feasibility of unexplored nanocooling methods needs to be investigated. For instance, the discrete energy spectrum in semiconductor QDs can be exploited for quantum cooling at ultra-low temperatures. If a two-dimensional electron gas is coupled to two electrodes via QDs, electrons can be transmitted through the sample by resonant tunneling. The QDs quantized energy levels can be adjusted so that the transfer from the gas to one electrode depletes the electron states above the Fermi energy. Similarly, the tunneling from the other electrode to the gas can fill states below the Fermi energy. The quasiparticle distribution function in the electron gas then sharpens, leading to electron cooling.
In order to go beyond the present limitations, an important objective is to fulfill the stringent filtering and thermalization requirements in order to reach low effective electron temperatures in nanodevices. This development will be very beneficial for nanoelectronics in general. Further, to reach microKelvin temperatures in samples regardless of the cooling method (nano-refrigerators in JRA2, demagnetization for nanosamples JRA1) will require even more efficient filtering and thermalization methods, which we aim to develop here.
Normally, the electronic temperature in a nano-device exceeds that of the cryostat bath, because of the insufficient thermal contact and the external noise which produces parasitic heating and photon-assisted tunneling. It is then not uncommon to have saturation of the effective electron temperature in the range of 100 mK. A thermalization down to 10 mK has been achieved in a very few places. Achieving a thermalization well below 10 mK of a nano-sample requires good thermal contact of the leads, suppression of noise background heating to about 10⁻²⁰ W level in a typical nano-device and suppression of the out-of-equilibrium photons at the level of -200 dB.
We will build a strategy to filter and thermalize the nano-samples to the various microKelvin coolers developed in this network so that their electronic bath temperature would be as close as possible to the corresponding refrigerator temperature. We will investigate sintered silver heat exchangers mounted in the mixing chamber or in a separate 3He cell. Each electronic wire connecting to the nano-sample would be attached to an electrically isolated sintered silver heat exchanger in order to overcome insufficient thermal contact through insulators and/or large Kapitza resistances at low temperatures (see also JRA1, task 1).
We will further develop existing ex-chip filtering techniques including lossy coaxes or striplines, discrete cryogenic low pass filters, copper powder and silver epoxy filters for reaching microKelvin electron temperatures in nano-samples. In particular, we will develop lossy filters made by lithography of resistive films. Compared to present designs, the filtering efficiency will be optimized through extensive rf propagation simulation, the miniaturization and the connectivity will be improved.
We will combine this ex-chip approach with on-chip filtering techniques. In particular, we are going to use SQUID-arrays as filters, which are known to suppress excess quasi-particle tunneling in superconducting Single Electron Transistors (SET) due to efficient noise filtering. Other on-chip filtering techniques are to be developed and perfected.
An electron temperature down to below 50 mK can be achieved with state-of-the-art S-I-N-I-S nano-coolers, starting from a base temperature of 300 mK.
In this task, we make use of the filtering developed in Task 1, and test different strategies to realize an electronic nano-cooler to reach sub-mK electron temperatures starting at the 10 mK base cryostat temperature. The following routes will be pursued:
Normal metal — superconductor tunnel junctions-based optimized coolers
A low critical temperature Tc is needed in order to enhance the efficiency of superconducting coolers at very low temperature, since the energy-selective tunneling is most efficient at a temperature approximately one third of the critical temperature. We will develop nano-coolers based on Ti (Tc = 0.4 K) and possibly other materials. The main difficulty will be to achieve a barrier quality comparable to what is routinely obtained with Al-based oxide barriers.
We will also develop strategies for trapping energetic quasi-particles in the superconductor, for instance by using ferromagnetic traps. Such a trap brings the interest of little proximity effect even in the case of a transparent interface between the superconductor and the normal metal. The problem of the inverse proximity effect (creation of quasi-particle states in the superconductor) will be taken into account.
The thermal relaxation channels in superconductors and normal metals not due to electron-phonon interaction will be investigated. There is evidence that in a superconductor, owing to sub-gap states possibly originating at magnetic impurities, recombination of quasiparticles occurs at a much faster rate than expected from the electron-phonon interaction. This study will contribute to define an improved geometry for the nano-coolers.
Quantum dot cooler
Since a QD transmissivity can be tuned by adjusting gate voltages, a QD refrigerator can operate in different ways without modification. It can be tuned to provide larger cooling power at a certain bath temperature by lowering the barrier height, as well as being tuned to reach the lowest electronic temperature. With a GaAs/AlxGa1-xAs heterostructure, the prediction is to cool 1 μm³ volume down to below 100 μK from a lattice temperature of 10 mK, i.e. a reduction in the electron temperature of more than two orders of magnitude.
We will fabricate and test such a device. The determination of both the temperature and the quasiparticle distribution function in the cooled electron gas will be based on the line shape (conductance as a function of gate voltage) of resonant tunneling through the discrete states of an additional QD. Under suitable conditions, the line shape width should provide an absolute thermometer at ultra-low temperatures.
Cooled platforms for radiation detectors were initially demonstrated in two experiments. These experiments were, however, each one of the kind, and no consistent technology was achieved to produce such micro-cooler platforms routinely. Thermally isolating low-stress silicon nitride membranes has in the meantime become widely available thanks to the need of such windows in TEM microscopy. Thus they can form a strong basis for a new development.
We will develop a technique to fabricate a 300 mK to 50 mK cooler with a sufficient heat lift to serve as a cryogenic measuring platform for such objects as bolometers, calorimeters and superconducting nano-devices including quantum bits. This platform will enable the cooling of nano-samples while keeping them galvanically isolated from the refrigerator.
N-I-S micro-refrigerators with a large cooling power (about 1 nW at 50 mK) will be fabricated on silicon nitride membranes. In order to combine the required large junctions area with the well-controlled angle deposition technique, we will make use of mechanical masks made of a lithographically patterned membrane. During the deposition, they will be separated from the substrate by calibrated spacers of 20-50 μm.
We will integrate a quantum detector on the cooled membrane and demonstrate the compatibility of the N-I-S nano-refrigeration with the quantum detector operation. Two aspects will be tested: the efficiency of refrigeration of galvanically isolated structures and the immunity of those structures to electromagnetic noise intrinsic to the refrigerator.
We will fabricate superconducting Single Electron Transistors (SET) on the refrigerator plate. Such devices can be constructed that demonstrate both the 1e and 2e periodicity. As this behaviour is most sensitive to temperature, the SETs will be used as a nano-fabricated thermometer, able to test rather directly the temperature of the working surface. Using the same devices, we will explore the interaction of the SET under test with the operation of the refrigerator.