Micro & nano-cooling: electronic cooling and thermometry based on superconducting tunnel junctions

Micro & nano-cooling: electronic cooling and thermometry based on superconducting tunnel junctions Hervé Courtois Néel Institute, CNRS and Université Joseph Fourier, Grenoble, France with L. Pascal, H. Nguyen, S. Rajauria, P. Gandit, T. Fournier, F. Hekking, B. Pannetier, C. Winkelmann

Summary Introduction The tunnel effect: a refresher Electron cooling and thermometry based on tunneling Electron and phonon cooling in a S-I-N-I-S junction Applications Conclusion

Introduction

Electronic cooling and thermometry Electronic cooling from 300 mk down to 100 mk. Electronic temperature directly measured. J. Pekola, T.T. Heikkila, A. M. Savin, J.T. Flyktman, F. Giazotto, F.W.J. Hekking, Phys. Rev. Lett. 92, 056804 (2004): Helsinki.

Applications Cooling of : - sensors (bolometers) - active devices (qbits, ) Only the small electronic sensor is cooled. A.M. Clark, N. A. Miller, A. Williams, S. T. Ruggiero, G. C. Hilton, L. R. Vale, J. A. Beall, K. D. Irwin, and J. N. Ullom, Appl. Phys. Lett. 84, 625 (2005): NIST Boulder.

Pre-requisite

Electronic temperature Non-zero temperature: the energy distribution function f(e) gives the probability for an e - state at the energy E to be occupied. At thermal equilibrium, f is the Fermi-Dirac function: f( E) = 1 1+ exp E E F k B T T > 0 T = 0 f(e) 1 0 4k B T E F At zero temperature, it reduces to a step function.

Tunneling of electrons Potential profile a the junction between two metals: U 0 =E F +W 1: Metal A 2: Vacuum 3: Metal B E=E F T exp( 2αd) α = 2mW Order of magnitude: T = exp( 10 10 d) T is non negligible for d of the order of the Å.

A superconductor DOS spectra Modified Density of States (DOS) at the Fermi Level From BCS theory: N S ( E) = 0 if E E F < Δ N S E ( ) = N N E DOS (a.u.) if E E F > Δ ( E E F ) 2 Δ 2 The energy gap is : (T=0) = 1.76k B T c (E-E F )/

The tunnel current expression Tunneling is an elastic process. From Fermi golden rule: I + N A ( E ev)n B E [ ]de ( ) f A ( E ev) f B ( E) ev E de A tunnel current occurs because of an electron states occupancy difference. E F A B N A (E) N B (E)

Electron thermometry in a S-I-N junction

Charge current in a N-I-S tunnel junction E T = 0.07 T c ev 2Δ I t N I S T = 0.49 T c Only electrons above the gap can tunnel. IV step rounded by temperature. I T = 1 er n + N S E [ ]de ( ) f S ( E ev) f N ( E)

Charge current in a N-I-S tunnel junction E T = 0.07 T c ev 2Δ I t N I S T = 0.49 T c The energy gap induces an energy-selective tunneling. Charge current (antisymmetric in bias): I T = 1 er n + N S E [ ]de ( ) f S ( E ev) f N ( E) slope α T in log scale

A N-I-S junction as a thermometer (1) I = 1 er N + N S E ( )[ f N ( E ev) f S ( E) ] de DOS 6 5 4 3 2 N S Consider T S small, T N to be measured, ev < Δ E f N (E ev) f S E Sub-gap current: ei = 1 R N + N S E ( ) exp E ev k B T ( ) exp E ev k B T de = ei 0 exp ev k B T 2 ev f N 1 f S 0-8 -4 0 4 8 Energy (mev)

A N-I-S junction as a thermometer (2) I = I 0 exp ev k B T The sub-gap current depends strongly on V and T. dv dt = k B e ln I I 0 0.5 µv / mk M. Nahum and J. Martinis, Appl. Phys. Lett. 63, 3075 (1993).

Application of N-I-S junction thermometry V SNS i SINIS v SINIS I SNS L = 1.5 µm, w = 0.17 µm, t = 30 nm S S I N S I S R N = 10 Ω : D = 100 cm 2 /s, l e = 22 nm Thouless energy ε c = 28 mk = 2.4 µev 0.5 µm

The SINIS thermometer calibration I(V) of the double N-I-S junction at thermal equilibrium. Calibration at a fixed current bias: no saturation down to 40 mk. v SINIS (mv) Hypothesis of quasi-equilibrium in the N metal: T e can be defined.

I(V) and electron temperature The electron thermometer correlates to switching. thermal origin of the hysteresis. T e up to 0.6 K! H. Courtois, M. Meschke, J. T. Peltonen, and J. P. Pekola, PRL 101, 067002 (2008): Grenoble-Helsinki. S S I N S I S

Electron cooling in a S-I-N-I-S junction

Charge current in a N-I-S tunnel junction E T = 0.07 T c ev 2Δ I t N I S T = 0.49 T c Only electrons above the gap can tunnel. IV step rounded by temperature. I T = 1 er n + N S E [ ]de ( ) f S ( E ev) f N ( E)

Heat current in a N-I-S tunnel junction E 0.06 T = 0.49 T c P cool 0.04 ev 2Δ PeR n /Δ 2 0.02 I t N I S 0 T = 0.07 T c Heat current (symmetric in bias): P cool ( V) = 1 e 2 R n + I T V + P cool is deposited in S. ( E ev)n S E -1-0.5 0 0.5 1 ev/δ [ ]de ( ) f N ( E ev) f S ( E)

Bias-dependent, optimum Cooling power P max = Δ2 e 2 0.59 k B T N R Δ T 3 / 2 2πk B T S Δ exp Δ k B T S reached at T N <<T C V Δ e k B T Max cooling power at: T T C 3

The S-I-N-I-S geometry Two cooling junctions in series: double cooling power + good thermal insulation of cooled metal. P cool P cool Cooler junctions S I cooler N S I thermometer (small) S S Thermometer junctions Plus two thermometer junctions for independent probing.

Electronic cooling and thermometry Cooling from 300 mk down to 100 mk can be achieved in a S-I-N-I-S geometry. Above the gap: qp injection and heating J. Pekola, T.T. Heikkila, A. M. Savin, J.T. Flyktman, F. Giazotto, F.W.J. Hekking, Phys. Rev. Lett. 92, 056804 (2004): Helsinki.

Limitations Basics of of electronic refrigeration Superconductor T bath Out-of-eq. q.p. at E > IT V I T V + P cool Photons I A V P cool Normal metal T e Phonons T ph < T bath Our objective: Understand the mechanisms coupling the cooled e- to the thermal baths. F. Giazotto, T. T. Heikkila, A. Luukanen, A. M. Savin and J. P. Pekola, Rev. Mod. Phys. 78, 217 (2006): Helsinki.

Phonon cooling vs electron cooling

The S-I-N-I-S samples Probe: metal strongly thermalized, no cooling. Probe 10µm 1µm Cooler: weakly coupled to pads, strong cooling, R t about 1 kω. No electron thermometer. S I N = Cu I Cooler I S = Al Nanofab, Institut Néel, CNRS & UJF Al-AlO x -Cu tunnel junctions: high stability and good reproducibility. Al behaves as a perfect BCS superconductor.

The differential conductance T base = 320 mk Cooler High resolution measurement (log scale) di/dv (norm.) 1 0.1 Probe 10 1 Probe follows isothermal prediction at T base. ei V + 0.01 ( ) = G T N S ( E) f S ( E) f N ( E + ev) [ ]de 0.001 0.1 0.01 Cooler behaves differently -2-1.5-1 -0.5 0 0.5 1 1.5 2 V/(2)Δ

Extraction of the electron temperature 0.1 I (µa) 0.01 0.001 Cooler Theory T = 320 mk T = 103 mk Inelastic scattering strong enough to define an electron temperature. Superposition of exp. data with theoretical I-V Exp. 300 T base T (mk) 0.0001 0 0.1 0.2 0.3 0.4 V (mv) 200 100 T e Determination of the biasdependent electron temperature 0-0.4-0.2 0 0.2 0.4 V (mv)

P cool ( V) = 1 er N The thermal model Power flow from N electrons to the S electrodes remaining at bath temperature + ( E ev)n S E [ ]de ( ) f S ( E) f N ( E + ev) S, T bath N electrons, T e S, T bath Electron - phonon coupling P e ph = ΣU( T 5 5 ph T ) e Kapitza thermal coupling N phonons, T ph = T bath P K = KA T bath 4 4 ( T ph ) Hyp.: N phonons are strongly thermalized Substrate phonons, T bath

Hypothesis of phonon thermalized to the bath Here T ph = T base 1 P cool = ΣU( T 5 5 e T ) bath 0.8 0.6 T e T bath 5 = 1 1 ΣU P 5 T bath (T/T 0 ) 5 0.4 0.2 Fitted Σ varies from 0.8 to 1.2 nw.µm -3.K -5! Need to consider that phonon temperature T ph varies. 0 0 50 100 150 P/T 0 5

P cool ( V) = 1 er n The thermal model Power flow from N electrons to the S electrodes remaining at bath temperature + ( E ev)n S E [ ]de ( ) f S ( E) f N ( E+ ev) S, T bath N electrons, T e S, T bath Electron - phonon coupling P e ph = ΣU( T 5 5 ph T ) e N phonons, T ph N phonons can be cooled Kapitza thermal coupling P K = KA T bath ( 4 4 T ) ph Substrate phonons, T bath

The phonon temperature 600 Two free fit parameters: Σ = 2 nw.µm -3.K -5 500 KA = 66 pw.k -4 400 Determination of both electron (T e ) and phonon (T ph ) temperature. T (mk) 300 200 100 T e T base T ph Phonons cool down by about 50 mk. 0 0 0.1 0.2 0.3 0.4 0.5 0.6 V (mv) S. Rajauria, P. S. Luo, T. Fournier, F. W. J. Hekking, H. Courtois, and B. Pannetier, Phys. Rev. Lett. 99, 047004 (2007): Grenoble.

The differential conductance (again) Cooler Consistency check: Fit of the cooler differential conductance. di/dv (norm.) 1 0.1 Probe 10 1 0.01 0.1 0.001 0.01-2 -1.5-1 -0.5 0 0.5 1 1.5 2 V/(2)Δ

Other approaches

Quantum dot cooling (1) Device = Drain QD «metal» - QD Source QD discrete energy spectrum open gaps, which acts as an energy filter, like the superconductor energy gap.

Quantum dot cooling (2) Electronic cooling visible in the current peak assymetry. Cooling from 280 to 190 mk. J. R. Prance, C. G. Smith, J. P. Griffiths, S. J. Chorley, D. Anderson, G. A. C. Jones, I. Farrer and D. A. Ritchie, PRL 102, 106641 (2009): Cambridge.

Applications

Applications (1) Heat current of about 10 pw/µm 2 (= 1 W/m 2 ). Need for highly-transparent and large junctions for a large cooling power: UV litho. and etching. AlMn is a normal metal with a natural barrier similar to Al. A.M. Clark, N. A. Miller, A. Williams, S. T. Ruggiero, G. C. Hilton, L. R. Vale, J. A. Beall, K. D. Irwin, and J. N. Ullom, Appl. Phys. Lett. 84, 625 (2005): NIST Boulder.

Applications (2) Relevant for on chip cooling of detectors, quantum devices Membrane technology provides a thermal decoupling to the bath.

Applications (3) A NTD bolometer is cooled from 320 mk down to 225 mk.

Cooling efficiency Dissipated power (by the bias source) in the superconductor : I.V Cooling power in the normal metal : P cool I( Δ ev) At the optimum bias, thermal qp overcome the gap : Δ ev k B T e Efficiency η = P cool I.V Δ ev Δ T e Δ = 1.76 k B T c ; T c = 1.3 K; T e = 0.1 K η = 4 % Rather low efficiency at low temperature, Energy dissipation in the superconductor is a major issue.

Conclusion Why cooling several kilograms while a nanogram (the detector) is enough? Electron and phonon cooling in N-I-S nanojunctions : out of equilibrium effects. Applications based on membrane technology, or use the cooled eletrons population as the sensor. Thanks to: MICROKELVIN ITN Q-NET