Electronic refrigeration and thermometry in nanostructures at low temperatures

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1 Electronic refrigeration and thermometry in nanostructures at low temperatures Jukka Pekola Low Temperature Laboratory Aalto University, Finland Nanostructures Temperature Energy relaxation Thermometry Refrigeration Present topics of interest

2 What new can micro- and nanostructures provide at low temperatures? 1. New physical phenomena and versatile fabrication techniques lead to new electronic device concepts. - quantum mechanical effects - single-electron effects - superconductivity - non-equilibrium effects 2. Thermal properties are very different from those of macroscopic systems, especially at low temperature. Local refrigeration and thermometry become possible.

3 Technological basis: micro- and nanofabrication 1. Lithography and thin film deposition (structures in 2D) A. Kemppinen et al., Single-electron transistor 2. Etching (structures in 3D) A. Luukanen et al., Antenna Coupled Microbolometer

4 f(e) Temperature in an electronic device E = m hot intermediate cold E

5 Generic thermal model for an electronic thermometer

6 The energy distribution of electrons in a small metal conductor The distribution is determined by energy relaxation: Equilibrium Thermometer measures the temperature of the bath Quasi-equilibrium Thermometer measures the temperature of the electron system which can be different from that of the bath Non-equilibrium There is no well defined temperature measured by the thermometer Illustration: diffusive normal metal wire H. Pothier et al. 1997

7 Electron-phonon relaxation in metals at low T

8 Tunnelling and thermometry by tunnel junctions G + METAL METAL G - Symbols: Normal junction Superconducting junction

9 Tunnel barrier Examples of aluminium-oxide tunnel barriers

10 Basics of tunnel junctions E 1 2 Tunneling from occupied states to empty states Energy is conserved V

11 E Metal Insulator Metal (MIM or NIN) tunnel junction Now, density of states (DOS) is almost constant over the small energy interval: V If f 1 = f 2 = f, we may use Ohmic, no temperature dependence NOT A THERMOMETER!

12 Noise? Average current through a basic tunnel junction is not sensing T. How about fluctuations around the mean current? Equilibrium noise: I ave = 0 Tunnel junction behaves like a resistor S I SV Noise thermometry is possible, but it is seldom used as such in nanostructures.

13 Non-equilibrium: Shot noise thermometry (SNT) L. Spietz et al., Science 300, 1929 (2003); PhD thesis 2006; APL 89, (2006).

14 SNT quantitative analysis Idea: measure the crossover voltage between thermal noise and shot noise; not necessary to know the absolute calibration for noise measurement.

15 Single-electron tunneling and Coulomb blockade thermometry

16 Single-electron transistor (SET) R T1, C 1 ne R T2, C 2 Unit of charging energy: V/2 V g C g V/2

17 2 CONDUCTANCE di/dv CURRENT Coulomb Blockade Thermometry principal idea VOLTAGE IV curve I (e/2r T C ) V (e/c ) conductance With increasing temperature the IV curve of a SET transistor gets increasingly smeared VOLTAGE

18 Basic properties of a Coulomb blockade thermometer (CBT) An array of N tunnel junctions in weak Coulomb blockade, E C << k B T: primary thermometer secondary thermometer J.P. et al., PRL 73, 2903 (1994)

19 CBT (mk) CBT performance at low T Experiments against MCT at CNRS Grenoble and at PTB CBTs produced by VTT optical lithography process (2007) Thermal decoupling 3He MCT (mk) Solution: Larger islands and make a (known) correction. M. Meschke et al., J. Low Temp. Phys. 134, 1119 (2004); arxiv: (2010).

20 CBT in magnetic field T = 1.46 K B (T) Magnetic field has no observable influence on CBT J. Appl. Phys. 83, 5582 (1998) J. Low Temp. Phys. 128, 263 (2002) T = 1.46 K

21 Single junction thermometer (SJT) CBT SJT I I In both cases: V V PRL 101, (2008) V Nk e B T

22 Single Junction Thermometer for T > 77 K FABRICATED BY Yu. Pashkin, NEC

23 Single Junction Thermometer V 1/2 G/G T 0.94 V 1/ T=77 K T=42 K U BIAS (mv) Error of ~1% mainly due to background

24 NIS-tunnelling and thermometry 3 2 er T I/ ev/

25 V (mv) NIS-thermometry Probes electron temperature of N island (and not of S!) I = 3 pa I (na) mK 48mK 78mK 110mK 145mK 180mK 215mK 250mK 285mK 320mK 360mK 395mK 430mK V (mv) T (mk)

26 Outlook Electronic primary thermometers, SNT, CBT and SJT presented as prime examples, show great promise 1. as practical calibration-free on-chip thermometers over a wide temperature range 2. in realising the temperature scale, based on a fixed value of the Boltzmann constant, in the sub - 10 K regime Problems: Measurement of SNTs is not straightforward CBTs suffer from self-heating at the lowest temperatures

27 NANO-REFRIGERATION

28 Refrigeration on-chip Thermoelectric refrigeration Peltier refrigerators, Peltier 1834 Thermionic refrigeration, Mahan, 1994 Korotkov and Likharev, 1999 Quantum-dot refrigerator, Edwards et. al., 1993 Experiment: Prance et al., PRL 102, (2009).

29 Refrigeration by tunnelling

30 Energy current in a tunnel junction In order to find energy current (from conductor 1) one replaces e by E ev in the corresponding expression: Compare to: For a NIN junction, we obtain This means that the Joule power is divided evenly between 1 and 2.

31 NIS junction as a refrigerator Cooling power of a NIS junction: Optimum cooling power is reached at V /e: Optimum cooling power of a NIS junction at T S,T N << T C Efficiency (coefficient of performance) of a NIS junction refrigerator:

32 SINIS structure cooler junctions V c /2 S N N S -V c /2 S V/2 S -V/2 probe junctions Basic idea: - bias voltage V c modifies electron distribution f(e) on N island - probe junctions measure modified f(e)

33 Early experiments M. Leivo et al., 1996

34 Cooling of a superconductor (SIS IS cooler) Ti Al sample [T C (Ti) = 0.5 K, T C (Al) = 1.3 K] COOLING FROM NORMAL TO SUPERCONDUCTING STATE A. J. Manninen et al., Appl. Phys. Lett. 74, 3020 (1999).

35 Experimental status Nahum, Eiles, Martinis 1994 Demonstration of NIS cooling Leivo, Pekola, Averin 1996, Kuzmin 2003, Rajauria et al Cooling electrons 300 mk -> 100 mk by SINIS Manninen et al Cooling by SIS IS see also Chi and Clarke 1979 and Blamire et al. 1991, Tirelli et al Manninen et al. 1997, Luukanen et al Lattice refrigeration by SINIS Savin et al S Schottky Semic Schottky S cooling Clark et al. 2005, Miller et al x-ray detector refrigerated by SINIS Prance et al Electronic refrigeration of a 2DEG Kafanov et al RF-refrigeration Refrigeration of a bulk object For a review, see Rev. Mod. Phys. 78, 217 (2006). A. Clark et al., Appl. Phys. Lett. 86, (2005).

36 RF-refrigerator Question: can one cool the island of a single-electron box by gate?

37 Typical cooling cycle J. P., F. Giazotto, O.-P. Saira, PRL 98, (2007) Influence of photon assisted tunneling: N. Kopnin et al., PRB 77, (2008)

38 RF-refrigerator - experiment S. Kafanov et al., PRL

39 Hybrid single-electron turnstile (SINIS)

40 DC properties of the cooler Source-drain voltage cools the island, measured current yields temperature

41 [K] Results of the RF experiments DC current provides thermometry for RF cooling G - G + ev A G - / G + = e -ev/kt [e] [e]

42 Curiosity experiments and (till now) Gedanken experiments Quantum of thermal conductance Brownian refrigerator Temperature fluctuations

43 Quantized conductance Electrons: Electrical conductance in a ballistic contact: Thermal conductance: G Q and s Q related by Wiedemann-Franz law More generally: Expression of G Q is expected to hold for carriers obeying arbitrary statistics, in particular for electrons, phonons, photons (Pendry 1983, Greiner et al. 1997, Rego and Kirczenow 1999, Blencowe and Vitelli 1999).

44 Example of quantized thermal conductance: phonons in a nanobridge K. Schwab et al., Nature 404, 974 (2000) C. Yung, D. Schmidt and A. Cleland, Appl. Phys. Lett (2002)

45 Electromagnetic transfer of heat (photons) Electron system G n Electrical environment Lattice Schmidt et al., PRL 93, (2004) Meschke et al., Nature 444, 187 (2006) Ojanen et al., PRB 76, (2007), PRL 100, (2008) D. Segal, PRL 100, (2008)

46 Heat transported between two resistors Radiative contribution to net heat flow between electrons of 1 and 2: Impedance matching: Linearized expression for small temperature difference T = T e1 T e2 :

47 Classical or quantum heat transport? w w w C w C Classical Quantum

48 Classical or quantum heat transport? Classical: Johnson, Nyquist 1928 Quantum limited:

49 e1 Demonstration of photonic heat x R 2 x x R 1 x 10 µm L J C J F conduction Tunable impedance matching using DC-SQUIDs Thermal model T (mk) Gen n F (a.u.) T 0 = 167mK 157mK 118mK 105mK 75mK 60mK M. Meschke, W. Guichard and J.P., Nature 444, 187 (2006)

50 SAMPLE A in a loop ( matched ) [SAMPLE B without loop ( not matched )] 2nd experiment

51 Heat transport in different set-ups Loop geometry (Sample A) R T 1 r ~ 1 R T 2 ~ ~ Linear geometry (Sample B) R T 1 r << 1 R T 2 ~ ~ C C for small temperature difference in the present experiment

52 Results in the two sample geometries Heat transported by residual quasiparticles at T > 0.3 K and by photons (in the loop sample) at T < 0.3 K A. Timofeev et al., PRL 2009 Quasiparticles

53 Brownian refrigerator

54 Heat flows from hot to cold by photon radiation This happens between two resistors The situation is identical if we replace one resistor by an ordinary tunnel junction R, T R N N R T, T N

55 Harmonic vs stochastic drive in refrigeration R, T R R, T R R, T R N R T, T N,S S Sinusoidal bias Refrigerates N if frequency and amplitude are not too high N S N S R T, T N,S R T, T N,S Stochastic drive Refrigerates N if spectrum is suitable Brownian refrigerator?

56 COOLING POWER OF N (fw) Brownian refrigerator R, T R N S R T, T N,S J.P. and F. Hekking, PRL 98, (2007)

57 Preliminary experiment on the Brownian refrigerator A. Timofeev et al., unpublished

58 Temperature fluctuations

59 Temperature fluctuations

60 Classical temperature fluctuations Assume that all T i are equal, and equal to the average of T (equilibrium fluctuations) (fluctuation-dissipation theorem) (balance equation) (Fourier transform into noise spectra)

61 Classical temperature fluctuations

62 Example system: electrons in the phonon bath electrons phonon bath In this grain at T = 100 mk, = (10 mk) 2. S T f / f C Cut-off frequency f c determined by electronphonon relaxation rate, it varies in the range 10 khz 10 MHz: suitable for a measurement.

63 I p [¹ A] Preliminary measurements Experimental setup Resonance: Quality factor: Optimal bias point: 2 0 I p V p [mv] Magnitude response: Phase response:

64 CBT results for an array Uniform array, E C << k B T: G/G T V (mv)

65 CBT sensors Low T High T 1 mm Long arrays suppress efficiently the errors due to co-tunnelling and finite impedance of the electromagnetic environment. Parallel arrays lower the sensor impedance to a convenient value. Another configuration is a 2D array, employed by T. Bergsten et al., APL 78, 1264 (2001).

66 NIS-thermometry This method is self-calibrating and can be considered (almost) primary

67 On-Chip Cooling/small junctions Cooling of electrons from 0.3 K to 0.1 K (M.M. Leivo, J.P. Pekola, and D.V: Averin, Appl. Phys. Lett. 68, 1996 (1996).) Cooling of lattice from 0.2 K to 0.1 K (A. Luukanen, M.M. Leivo, J.K. Suoknuuti, A.J. Manninen, and J.P. Pekola, JLTP, 120, 281 (2000).)

68 Schottky barrier coolers with superconductor and heavily doped silicon U th I th I 60mm I 30mm A. M. Savin et al., Appl. Phys. Lett. 79, 1471 (2001).

69 I T /mk I / ma Schottky barrier coolers results , X3F2, cooler 20x mk 163 mk 255 mk 424 mk 631 mk V / mv 812 mk 940 mk 1060 mk 1340 mk V Thermometry by S-Sm-S Schottky barrier I V / mv Cooling results

70 2nd experiment N S N SAMPLE B ( mismatched )

71 Results in the two sample geometries BLUE LINE: Directly cooled resistor RED LINE: Remote resistor