Hot electron effects in metallic single electron components

Thermalisation of single electron devices is of considerable current interest because of its fundamental and practical consequences. We present experimental evidence of the effect of electrode volume and its shape on thermal equilibration of small metallic islands for single electron tunnelling. Heat transport between the conduction electrons and the lattice in a metal is commonly accepted to obey the ∝Te5-T0/5 law at low electron and lattice temperatures,Te andT0, respectively. We have investigated the power law and found that it obeys the ∝T5 law only for the smallest islands, and in the majority of the cases considered, it rather follows a law ∝Tp, wherep<5. The thermal coupling can be i…

Direct measurements of electron thermalization in Coulomb blockade nanothermometers at millikelvin temperatures

Abstract We investigate electron thermalization of tunnel junction arrays installed in a powerful dilution refrigerator whose mixing chamber can produce lattice temperatures down to 3 mK. The on-chip Coulomb blockade thermometers (CBT) against other thermometers at the mixing chamber provide direct information on the thermal equilibrium between the electronic system and the refrigerator. We can detect and discriminate between the heat load delivered through the wiring and that produced by the bias current of the CBT-measurement. The basic heat leak limits the minimum of the electronic temperature to slightly below 20 mK.

Heat capacity of small superconducting disks

Abstract The superconducting state of small samples in a magnetic field is strongly dependent on the sample dimensions and geometry. We have initiated measurements of heat capacity of small superconducting disks. Our method, extensively used in many of our related experiments, is to measure the thermal time constant as a function of temperature of disks on a thin silicon nitride membrane. Theoretical results on heat capacity of the disks based on the Ginzburg–Landau theory will be presented.

Solid State Analogue of a Double Slit Interferometer

In a conventional optical double slit interferometer Fig. 1a light emerges from a source at a point O’, passes through two slits A and B and forms an interference pattern at a point O. If the source provides monochromatic radiation the coherence between optical paths O’AO and O’BO is preserved at all reasonable scales. The intensity of the interference pattern at a given point O can be altered by changing the distance ∣O’AO∣ - ∣O’BO∣.

Fabrication and characterization of chromium based single-electron transistors with evaporated chromium oxide barrier tunnel junctions

We fabricated chromium based single-electron transistors comprising small-area Cr/CrOx/Cr tunnel junctions with an evaporated chromium oxide barrier. The transistors are fabricated using e-beam lithography with a bilayer resist and two-angle shadow evaporation. We describe the fabrication process and discuss the device characteristics.

LONG TERM CHARGE RELAXATION IN SILICON SINGLE ELECTRON TRANSISTORS

Production of zero energy radioactive beams through extraction across superfluid helium surface

A radioactive Ra-223 source was immersed in superfluid helium at 1.2-1.7 K. Electric fields transported recoiled Rn-219 ions in the form of snowballs to the surface and further extracted them across the surface. The ions were focussed onto an aluminium foil and alpha particle spectra were taken with a surface barrier spectrometer. This enabled us to determine the efficiency for each process unambiguously. The pulsed second sound wave proved effective in enhancing the extraction of positive ions from the surface. Thus we offer a novel method for study of impurities in superfluid helium and propose this method for production of zero energy nuclear beams for use at radioactive ion beam facilit…

Coulomb blockade thermometer: Tests and instrumentation

Coulomb blockade thermometry (CBT) provides a simple method for absolute thermometry in every day laboratory use at cryogenic temperatures. CBT has been found insensitive to even high magnetic fields. We review the principles and the operation of CBT and the fabrication of the sensors, and present new data on radiation hardness and stability of the sensors. We describe the instrumentation of CBT in detail. We have developed two signal conditioning units for CBT measurements. One is a modified alternating current resistance bridge, a versatile laboratory instrument operating with a PC computer, and the other one is a simple stand-alone instrument for direct temperature reading. Test results …

Coulomb blockade thermometry

One dimensional arrays of normal metal tunnel junctions have been found to exhibit properties which are very suitable for primary and secondary thermometry in a lithographically adjustable temperature range which extends over about two decades. The thermometer is remarkably insensitive to nonuniformities in the actual pattern and to even strong magnetic fields. We also discuss the behaviour of this device at very low temperatures where the hot electron effect due to poor electron phonon coupling ultimately takes over and at very high temperatures where the finite tunnel barrier effects appear. Short arrays, and especially single tunnel junctions show interesting deviations from the universa…

Fabrication and characterization of small tunnel junctions through a thin dielectric membrane

We show that a small tapered hole through a thin silicon nitride membrane provides a mask for tunnel junction structures. Our experiments imply, unlike in the conventional planar electron beam lithography, that tunnel junctions are well voltage biased in this structure with vanishingly small on-chip impedance. Our technique allows fabrication of double junctions, and even multijunction linear arrays, with small metallic islands in between.

Single electron transistor fabricated on heavily doped silicon-on-insulator substrate

Experiments on side-gated silicon single electron transistors (SET) fabricated on a heavily doped thin silicon-on-insulator substrate are reported. Some of the devices showed single-island-like and some multi-island-like behaviour, but the properties of individual samples changed with time. Single-electron gate modulation was observable up to T=100 K, at least. A slow response of SET current to a large change in gate voltage was observed, but the process speeded up under illumination.

Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection

An efficient two-stage algorithm is presented for the synthesis of high-frequency-carrier diffractive elements. First, an on-axis phase-only stripe-geometry element with an unconstrained profile along each stripe is designed by an iterative Fourier transform algorithm. In the second stage, a steep linear phase term is added, and the profile is hard-clipped along each stripe. The result is a binary, pulse-frequency-modulated element suitable, e.g. , for a resonance-domain realization, which permits the elimination of the twin image. Experimental results are provided by direct-write electron-beam lithography and optical lithography, using both fully and partially coherent illumination.

One dimensional arrays and solitary tunnel junctions in the weak coulomb blockade regime: CBT thermometry

In this article we review the use of the tunnel junction arrays for primary thermometry. In addition to our basic experimental and theoretical results we stress the insensitivity of this method to the fluctuating background charges, to nonidealities in the array and to magnetic field. Important new results of this article are the low temperature corrections to the half width and depth of the measured conductance dip beyond the linear approximation. We also point ou that short arrays, single tunnel junctions in particular, show interesting deviations from the universal behaviour of the long arrays.

Control of single-electron tunneling by surface acoustic waves.

IV-Curves of tunnel junction arrays at lowered temperature by numerical simulation

We have numerically investigated the effect of lowered T on the performance of the Coulomb blockade thermometer, which has been demostrated to yield primary thermometry in the high T limit where thermal excitations compete with the Coulomb blockade. The thermometer is formed by an array of tunnel junctions whose differentiated IV—curve is used to determine the temperature. The IV—curves were calculated by computer simulations and we have obtained corrections to the analytic high T behaviour due to the lowered temperature.

Efficient Peltier refrigeration by a pair of normal metal/ insulator/superconductor junctions

We suggest and demonstrate in experiment that two normal metal /insulator/ superconductor (NIS) tunnel junctions combined in series to form a symmetric SINIS structure can operate as an efficient Peltier refrigerator. Specifically, it is shown that the SINIS structure with normal-state junction resistances 1.0 and 1.1 k$\Omega$ is capable of reaching a temperature of about 100 mK starting from 300 mK. We estimate the corresponding cooling power to be 1.5 pW per total junction area of 0.8 $\mu$m$^2$ at $T= 300$ mK.

Properties of native ultrathin aluminium oxide tunnel barriers

We have investigated planar metal–insulator–metal tunnel junctions with aluminium oxide as the dielectricum. These oxide barriers were grown on an aluminium electrode in pure oxygen at room temperature till saturation. By applying the Simmons model we derived discrete widths of the tunnelling barrier, separated by Δs ≈ 0.38 nm. This corresponds to the addition of single layers of oxygen atoms. The minimum thickness of s0 ≈ 0.54 nm is then due to a double layer of oxygen. We found a strong and systematic dependence of the barrier height on the barrier thickness. Breakdown fields up to 5 GV m−1 were reached. They decreased strongly with increasing barrier thickness. Electrical breakdown could…

Electron-phonon heat transport in degenerate Si at low temperatures

The thermal conductance between electrons and phonons in a solid state system becomes comparatively weak at sub‐Kelvin temperatures. In this work five batches of thin heavily doped silicon‐on‐insulator samples with the electron concentration in the range of 2.0–16 × 1019 cm–3 were studied. Below 1 K all the samples were in the dirty limit of the thermal electron‐phonon coupling, where the thermal phonon wavelength exceeds the electron mean free path. The heat flow between electrons and phonons is proportional to (T6e–T6ph), where Te (Tph) is the electron (phonon) temperature. The constant of proportionality of the heat flow strongly depends on the electron concentration and its magnitude is…

Arrays of normal metal tunnel junctions in weak Coulomb blockade regime

Universal features of I–V characteristics of one‐dimensional arrays of normal metal tunnel junctions have been tested against inhomogenities in the junction parameters, number of junctions in the array, and magnetic field. We find that the differential conductance versus bias voltage obeys the analytic form to within 1% if the fabrication errors are smaller than 10% in junction areas, and if the array has more than ten junctions. Furthermore, the universal relation is insensitive to magnetic field at least up to 8 T.

Background charge fluctuations in SET-transistors

We have studied fluctuations of background charges in single electron tunnelling (SET) transistors. Changes in the charge distribution of the substrate and other dielectric materials near the transistor cause uncontrolled changes in its conductivity. We have observed big differences in the type and frequency of the conductivity fluctuations between different samples, but no systematic dependence on the substrate material has been found. To obtain information about the location of the source of the charge noise, we performed coincidence measurements on two separate SET transistors which were made very near to each other. The results suggest that the conductivity fluctuations are caused by ch…

Refrigeration of a dielectric membrane by superconductor/insulator/normalmetal/insulator/superconductor tunneling

We have applied tunneling of electrons between a normal metal and a superconductor to refrigerate a thin dielectric membrane attached to the normal electrode of a superconductor/ insulator/normal-metal/insulator/superconductor (SINIS) structure. Starting from T≈200 mK, a decrease in temperature of several mK was observed, measured by a separate thermometer on the membrane. It should be straightforward to improve the refrigerator performance to the level of the recently demonstrated SINIS electron cooling method, such that the drop in the lattice temperature would be more than an order of magnitude larger.

Numerical investigation of one‐dimensional tunnel junction arrays at temperatures above the Coulomb blockade regime

Arrays of tunnel junctions provide simple thermometric parameters in the limit where thermal excitations dominate over charging effects. We present numerical simulations for calculating the current versus voltage characteristics of an arbitrary one‐dimensional array at arbitrary temperatures on the premise of the ‘‘orthodox theory.’’ The purpose of the computer simulations is to investigate the suitability of tunnel junction arrays for thermometry at low temperatures when the analytical formulas do not hold and, specifically, to see the effect of background charges in this regime.

Transport and extraction of radioactive ions stopped in superfluid helium

A new approach to convert a high energy beam to a low energy one, which is essential for the next generation radioactive ion beam facilities, has been proposed and tested at Jyvaskyla, Finland. An open Ra-223 alpha-decay-recoil source has been used to produce radioactive ions in superfluid helium. The alpha spectra demonstrate that the recoiling Rn-219 ions have been extracted out of liquid helium. This first observation of the extraction of heavy positive ions across the superfluid helium surface was possible thanks to the high sensitivity of radioactivity detection. An efficiency of 36% was obtained for the ion extraction out of liquid helium. (C) 2003 Elsevier Science B.V. All rights res…

Efficient electronic cooling in heavily doped silicon by quasiparticle tunneling

Cooling of electrons in a heavily doped silicon by quasiparticle tunneling using a superconductor–semiconductor–superconductor double-Schottky-junction structure is demonstrated at low temperatures. In this work, we use Al as the superconductor and thin silicon-on-insulator (SOI) film as the semiconductor. The electron–phonon coupling is measured for the SOI film and the low value of the coupling is shown to be the origin of the observed significant cooling effect.

Silicon Single Electron Transistors with Single and Multi Dot Characteristics

AbstractSilicon single electron transistors (SET) with side gate have been fabricated on a heavily doped silicon-on-insulator (SOI) substrate. Samples demonstrate two types of characteristics: some of them demonstrate multiple dot behavior and one demonstrates single dot behavior in a wide temperature range. SETs demonstrate oscillations of drain-source current and changes in the width of the Coulomb blockade region with change of gate voltage at least up to 100 K. At temperature below 20 K long-term oscillations (relaxation) of source-drain current after switching the gate voltage has been observed in both multiple dot and single dot samples. Illumination affects both the characteristics o…

Interference of nonequilibrium quasiparticles in a superconductor

Abstract We have observed an interference of nonequilibrium quasiparticles, injected from a copper electrode into an aluminium loop through a tunnel barrier. At temperatures below 1K the tunnel current at fixed voltage bias is periodically modulated by external magnetic field. The amplitude of the modulation reaches maximum at a bias slightly below the gap energy, and decreases with the further increase of the bias voltage. For a given voltage bias the amplitude of the current oscillations decreases with increase of the temperature and the loop circumference.

Microrefrigeration by NIS tunnel junctions

By using a normal metal-insulator-superconductor (NIS) tunnel junction one can manipulate the Fermi-Dirac distribution of the electrons in the normal electrode. If the junction is biased close to the superconducting gap, Δ, only “hot electrons” above Fermi level can tunnel from the normal electrode to the superconductor. Thus, due to the decoupling of the conduction electrons from the lattice at low temperatures, there exists a possibility to decrease the electronic temperature by this method. Because of the symmetry with bias voltage, two NIS tunnel junctions in series can form an efficient microrefrigerator. Temperature can be measured with two additional junctions by considering the vari…

Electron–phonon coupling in degenerate silicon-on-insulator film probed using superconducting Schottky junctions

Abstract Energy flow rate in degenerate n-type silicon-on-insulator (SOI) film is studied at low temperatures. The electrons are heated above the lattice temperature by electric field and the electron temperature is measured via semiconductor–superconductor quasiparticle tunneling. The energy flow rate in the system is found to be proportional to T 5 , indicating that electron–phonon relaxation rate and electron–phonon phase breaking rate are proportional to T 3 . The electron–phonon system in the SOI film is in the “dirty limit” where the electron mean free path is smaller than the inverse of the thermal phonon wave vector.

A computer controlled patterning system for scanning probe microscopes

Abstract A pattern generator system for lithography based on scanning force microscopes has been developed. Patterns to be miniaturized onto a chip can be scanned or drawn by any common graphical program. The pattern file is used to control a voltage simultaneously with the microscope probe scanning the surface of the substrate. The voltage can be used in numerous different ways to manipulate the substrate, depending on the lithographic method preferred. We have demonstrated the system by adding this voltage to the z -piezo voltage of the scanner, in order to make the probe plow the pattern into a film spinned on the sample. To maintain linearity in zooming in and rotating the scanning dire…

Characterisation of Cooper pair boxes for quantum computing

We have measured and characterised superconducting single Cooper pair boxes (SCB) using superconducting single electron transistor (SET) fabricated on the same chip as an electrometer. The electrometer is sensitive to the potential changes of the SCB island and thus measures the number of excess Cooper pairs on the island. The boxes were of the Al/AlOx/Al Josephson junction type. The SCB and SET were characterised separately and the box storage performance for Cooper pairs was analysed by observing the changes in the SCB island potential while sweeping the gate voltage.

Fabrication of Nb-based superconducting single electron transistor

Abstract We have fabricated Nb/(Al-)AlOx/Nb junctions with a single electron transistor (SET) geometry using conventional e-beam lithographic technique. It was possible to reach a clearly defined superconducting gap of 0.75 meV as measured in the current vs. voltage (I–V) characteristic curve, which corresponds to Tc of 4.6 K . The Josephson coupling energy was comparable to the charging energy, EJ≈Ec=30– 40 μeV .

EU dissemination of the provisional ultra-low-temperature scale, PLTS-2000

Following the introduction of the provisional low-temperature scale from 0.9 mK to 1K, PLTS-2000, there is a need for primary and secondary thermometers and fixed points, which can disseminate the scale to users. This paper reports on the progress, within the EU collaborative project ‘ULT Dissemination’, in the development and evaluation of several devices with associated instrumentation. Principal among them are a current-sensing noise thermometer, a CMN thermometer adapted for industrial use, a Coulomb blockade thermometer, a second-sound thermometer, a 3He melting pressure thermometer for a direct realisation of the PLTS-2000. A superconductive reference device has also been developed, a…

Unconventional behavior of superconducting nanostructures

Abstract Various aluminium nanostructures have been studied experimentally. Unusual nonmonotonous dependence of the critical current on external magnetic field has been observed. Pronounced nonlocal interaction has been found to decay exponentially on a scale of the superconducting coherence length ξ(T).

Experiments on tunnelling in small normal-metal junctions influenced by dissipative environment: Critical comparison to the theories of quantum fluctuations

We report on experiments of charging in small normal metal tunnel junctions attached to well-defined resistive impedances. Our experiments are in very good agreement with the phase-correlation (PC) theory but not with the simplified voltage fluctuation (VF) model. The strong tunnelling corrections to the PC theory make the agreement with our results even better in the case of junctions with low resistance.

Coulomb blockade in one-dimensional arrays of high-conductance tunnel junctions

Properties of one-dimensional (1D) arrays of low Ohmic tunnel junctions (i.e. junctions with resistances comparable to, or less than, the quantum resistance $R_{\rm q}\equiv h/e^2\approx 25.8$ k$\Omega$) have been studied experimentally and theoretically. Our experimental data demonstrate that -- in agreement with previous results on single- and double-junction systems -- Coulomb blockade effects survive even in the strong tunneling regime and are still clearly visible for junction resistances as low as 1 k$\Omega$. We have developed a quasiclassical theory of electron transport in junction arrays in the strong tunneling regime. Good agreement between the predictions of this theory and the …

Transition-edge microcalorimeters for X-ray space applications

Abstract In an European Space Agency funded research project, our goal is to develop microbolometer technology for X-ray and far-infrared detection for ESA's future scientific missions. We report results on the X-ray calorimeter, which is based on the superconducting transition of the Ti/Au thermometer strip at about 200 mK. Incident X-rays heat up a Bi absorber, deposited on top of the 400 μm ×400 μm thermometer. The temperature rise of the absorber is measured as a change of the thermometer current with a SQUID operating at 1 K.

Integrated SINIS refrigerators for efficient cooling of cryogenic detectors

In this paper we report recent results obtained with large area superconductor-insulator-normal metal-insulator-superconductor tunnel junction coolers. With the devices we have successfully demonstrated electronic cooling from 260 mK to 80 mK with a cooling power of 20 pW at 80 mK. At present, we are focusing on obtaining similar performance in cooling cryogenic detectors. Additionally, we present recent results of successful operation of a metalsemiconductor structure with a Schottky barrier acting as the tunnel barrier and the possibility to use this kind of structures for on-chip cooling.

ELECTRON-PHONON COUPLING IN HEAVILY DOPED SILICON

The coupling constant in electron-phonon interaction is a very important issue in nanoscale applications. We have measured this constant in heavily doped silicon. Electron-phonon interaction is proportional to T6 and the coupling constant is found to be 1.5 × 108 W/K5m³, which is about one tenth of the value in normal metals.

Trapping of quasiparticles of a nonequilibrium superconductor

We have performed experiments where hot electrons are extracted from a normal metal into a superconductor through a tunnel junction. We have measured the cooling performance of such NIS junctions, especially in the cases where another normal metal electrode, a quasiparticle trap, is attached to the superconductor at different distances from the junction in direct metal-to-metal contact or through an oxide barrier. The direct contact at a submicron distance allows superior thermalization of the superconductor. We have analyzed theoretically the heat transport in this system. From both experiment and theory, it appears that NIS junctions can be used as refrigerators at low temperatures only w…

Turnstile behaviour of the Cooper-pair pump

We have experimentally studied the behaviour of the so-called Cooper pair pump (CPP) with three Josephson junctions, in the limit of small Josephson coupling EJ &lt; EC. These experiments show that the CPP can be operated as a traditional turnstile device yielding a gate-induced current 2ef in the direction of the bias voltage, by applying an RF-signal with frequency f to the two gates in phase, while residing at the degeneracy node of the gate plane. Accuracy of the CPP during this kind of operation was about 3% and the fundamental Landau-Zener limit was observed to lie above 20 MHz. We have also measured the current pumped through the array by rotating around the degeneracy node in the ga…

Application of superconductor-semiconductor Schottky barrier for electron cooling

Abstract Electronic cooling in superconductor–semiconductor–superconductor structures at sub kelvin temperatures has been demonstrated. Effect of the carrier concentration in the semiconductor on performance of the micro-cooler has been investigated.

Nonlocality in superconducting microstructures

We discuss experimental evidence of nonlocality in electron transport of small structures. It is shown that for superconductors reasonable agreement with experiment can be achieved by assuming exponential decay of the nonlocal interaction ∝ exp(—Lξ), where L is the distance between the interacting points and ξ is the correlation length. ξ is associated with the Ginzburg - Landau coherence length ξGL.

Electron-phonon heat transport and electronic thermal conductivity in heavily doped silicon-on-insulator film

Electron–phonon interaction and electronic thermal conductivity have been investigated in heavily doped silicon at subKelvin temperatures. The heat flow between electron and phonon systems is found to be proportional to T6. Utilization of a superconductor–semiconductor–superconductor thermometer enables a precise measurement of electron and substrate temperatures. The electronic thermal conductivity is consistent with the Wiedemann–Franz law. Peer reviewed

Decoherence in circuits of small Josephson junctions

We discuss dephasing by the dissipative electromagnetic environment and by measurement in circuits consisting of small Josephson junctions. We present quantitative estimates and determine in which case the circuit might qualify as a quantum bit. Specifically, we analyse a three junction Cooper pair pump and propose a measurement to determine the decoherence time $\tau_\phi$.

Superconducting transition of single-crystal tin microstructures

Single-crystal superconducting microstructures have been fabricated. The resistances of tin whiskers were measured in a multiprobe configuration. Contacts were made of copper, gold, or niobium films using e-beam lithography followed by a lift-off process. Structures with normal metal probes showed unusual behavior: below the critical temperature of bulk tin, the resistance decreases in distinct steps and does not reach zero even when cooled down to 1 K. The origin of these phenomena is not clear but is likely related to a proximity effect.

Proximity-induced Josephson-quasiparticle process in a single-electron transistor

We have performed the first experiments in a superconductor - normal metal - superconductor single electron transistor in which there is an extra superconducting strip partially overlapping the normal metal island in good metal-to-metal contact. Superconducting proximity effect gives rise to current peaks at voltages below the quasiparticle threshold. We interpret these peaks in terms of the Josephson-quasiparticle process and discuss their connection with the proximity induced energy gap in the normal metal island.

Performance of cryogenic microbolometers and calorimeters with on-chip coolers

Astronomical observations of cosmic sources in the far-infrared and X-ray bands require extreme sensitivity. The most sensitive detectors are cryogenic bolometers and calorimeters operating typically at about 100 mK. The last stage of cooling (from 300 mK to 100 mK) often poses significant difficulties in space-borne experiments, both in system complexity and reliability. We address the possibility of using refrigeration based on normal metal/insulator/superconductor (NIS) tunnel junctions as the last stage cooler for cryogenic thermal detectors. We compare two possible schemes: the direct cooling of the electron gas of the detector with the aid of NIS tunnel junctions and the indirect cool…

Thermometry by Arrays of Tunnel Junctions

We show that arrays of tunnel junctions between normal metal electrodes exhibit features suitable for primary thermometry in an experimentally adjustable temperature range where thermal and charging effects compete. $I\ensuremath{-}V$ and $\frac{\mathrm{dI}}{\mathrm{dV}}$ vs $V$ have been calculated for two junctions including a universal analytic high temperature result. Experimentally the width of the conductance minimum in this regime scales with $T$ and $N$, the number of junctions, and its value (per junction) agrees with the calculated one to within 3% for large $N$. The height of this feature is inversely proportional to $T$.

Wide-range thermometer based on the temperature-dependent conductance of planar tunnel junctions

The effect of the Fermi–Dirac distribution on the current through standard planar tunnel junctions is a suitable basis for thermometry in a wide temperature range. In particular, it extends the range spanned by Coulomb-blockade thermometers up to room temperature.

Effect of the electromagnetic environment on arrays of small normal metal tunnel junctions: Numerical and experimental investigation

We present results of a set of experiments to investigate the effect of dissipative external electromagnetic environment on tunneling in linear arrays of junctions in the weak tunneling regime. The influence of this resistance decreases as the number of junctions in the chain increases and ultimately becomes negligible. Further, there is a value of external impedance, typically \~5 k$\Omega$, at which the half-width of the zero-voltage dip in the conductance curve shows a maximum. Some new analytical formulae, based on the phase-correlation theory, along with numerical results will be presented.

Primary thermometry with nanoscale tunnel junctions

We have found current-voltage (I-V) and conductance (dI/dV) characteristics of arrays of nanoscale tunnel junctions between normal metal electrodes to exhibit suitable features for primary thermometry. The current through a uniform array depends on the ratio of the thermal energy kBT and the electrostatic charging energy E c of the islands between the junctions and is completely blocked by Coulomb repulsion at T = 0 and at small voltages eV/2 ≤ Ec. In the opposite limit, kBT ≫ Ec, the width of the conductance minimum scales linearly and universally with T and N, the number of tunnel junctions, and qualifies as a primary thermometer. The zero bias drop in the conductance is proportional to T…

Observation of thermally excited charge transport modes in a superconducting single-electron transistor

Experiments on a superconducting single-electron transistor are reported. A new structure in the current-voltage characteristics at subgap voltages was observed when temperature was not too low as compared to the superconducting transition temperature Tc of the sample. The strength of the anomalies increases exponentially with temperature. The dominating features arise from matching of singularities in the density of states on two sides of a tunnel junction, and from the Josephson-quasiparticle cycle. Thermal excitations are essential for the former process, and they also make the latter process possible at low voltages.

Fluctuation-Limited Noise in a Superconducting Transition-Edge Sensor

In order to investigate the origin of the until now unaccounted excess noise and to minimize the uncontrollable phenomena at the transition in x-ray microcalorimeters we have developed superconducting transition-edge sensors into an edgeless geometry, the so-called Corbino disk, with superconducting contacts in the center and at the outer perimeter. The measured rms current noise and its spectral density can be modeled as resistance noise resulting from fluctuations near the equilibrium superconductor-normal metal boundary. Peer reviewed

Properties of the Phonon Gas in Ultrathin Membranes at Low Temperature

We analyze heat conduction by phonons in ultrathin membranes by constructing a new theoreticalframework which implies a crossover from a bulk three-dimensional phonon distribution into a quasi-two-dimensional distribution when the temperature is lowered. We calculate the corresponding changesin the relevant thermodynamic quantities. At the end we make a comparison to experimental data.[S0031-9007(98)07273-1]

Heat Capacity of Mesoscopic Superconducting Disks

We study the heat capacity of isolated giant vortex states, which are good angular momentum ($L$) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small magnetic fields the $L$=0 state qualitatively behaves like the bulk sample characterized by a discontinuity in heat capacity at $T_c$. As the field is increased the discontinuity slowly turns into a continuous change which is a finite size effect. The higher $L$ states show a continuous change in heat capacity at $T_c$ at all fields. We also show that for these higher $L$ states, the behavior of the peak position with change in field is related to the paramagnetic Meissner effect (irreversible) and can …

Solid-State Analog of an Optical Interferometer

To some extend one may treat a metal ring with two probes as a solid-state analog of an optical interferometer. One node can be considered as a beam splitter (bi-prism, for example), and the electric current at the other node as an equivalent to a light intensity of an interference pattern formed at a screen. In optics, to obtain a stationary pattern one should use a monochromatic source of radiation, as afterwards in a conventional passive media (i.e. air) the phase of the radiation is preserved. On the contrary, in solids the phase of a conducting electron wavefunction is randomly altered due to inelastic collisions (mainly phonons at high temperatures). Hence, to satisfy the condition of…

Arrays of Josephson junctions in an environment with vanishing impedance

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhomogeneity in the array and non-ideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.

Response time of a thermometer based on normal metal–insulator–superconductor (NIS) tunnel junctions

Abstract We have measured the thermal response of a superconductor–normal metal–superconductor (SINIS) tunnel junction structure at substrate temperature ∼60 mK by directly heating the electron system in the normal metal island. In our structure, we find the response time is determined by the electron–phonon coupling in the electron temperature range 300– 600 mK . By using AC heating, the cut-off frequency caused by this response time has been measured, showing that SINIS structures operate as a thermometer up to a few MHz in this temperature range.

European Dissemination of the Ultra-low Temperature Scale, PLTS-2000

The first phase of the EU collaborative project on sub‐kelvin thermometry, ‘ULT Dissemination’, is nearing completion, leading to the development of several thermometers and devices, and the instrumentation needed to disseminate the new Provisional Low Temperature Scale, PLTS‐2000, to users. Principal among these are a current‐sensing noise thermometer (CSNT), a CMN thermometer adapted for industrial use, a Coulomb blockade thermometer, a second‐sound acoustic thermometer and a superconductive reference device SRD‐1000. Several partners have set up 3He melting‐pressure thermometers to realise the PLTS‐2000, and will check it using Pt‐NMR, CMN and other thermometers. The scale, which was for…

Coulomb blockade-based nanothermometry in strong magnetic fields

We have performed experiments to test for the susceptibility to strong magnetic fields of electron tunneling in normal metal -based nanostructures for Coulomb blockade primary thermometry. We have confirmed that, to within our accuracy of about ±1%, the single electron charging -induced zero bias differential resistance maximum is unaffected by the field up to 23 T at temperatures of 0.4–4.2 K. We discuss the simple theoretical basis of this immunity. We also report on the practical limitation at low temperatures imposed by superconductivity of aluminium in small magnetic fields.

Cooling of a superconductor by quasiparticle tunneling

We have extended the cryogenic cooling method based on tunneling between a superconductor and another metal to the case when both metals are superconducting but when their energy gaps are different; earlier, this method was applied between a superconductor and a normal metal. The electron system of a titanium strip with the superconducting transition temperature Tc2=0.51 K has been cooled from 1.02Tc2 to below 0.7Tc2 by this method, using aluminum as the other superconductor.

NIS chip refrigeration

A normal-metal/insulator/superconductor (NIS) tunnel junction can be applied to cool electrons by biasing the junction suitably with external voltage. Two NIS junctions in series can form an efficient microrefrigerator because of the symmetry with bias voltage. Our SINIS microrefrigerator has been capable of reaching electronic temperatures of about 100 mK starting from 300 mK. To achieve appreciable refrigeration of the underlying lattice, the microrefrigerator must be thermally decoupled from the bulk substrate. We have demonstrated experimentally the reduction of lattice temperature by 23 mK at 180 mK by extending the normal electrode on a thin dielectric membrane with four suspended bri…

Economical device for measuring thickness of a thin polymer film

An inexpensive device (about $2K) for thickness measurements of thin (<1 μm) polymer films has been constructed. The homogeneous film is placed on a bulk substrate and three semiconductor lasers of different wavelengths are used to measure the reflectances at normal incidence. The thickness can be deduced with typically 4–8 nm uncertainty.

Adiabatic transport of Cooper pairs in arrays of Josephson junctions

We have developed a quantitative theory of Cooper pair pumping in gated one-dimensional arrays of Josephson junctions. The pumping accuracy is limited by quantum tunneling of Cooper pairs out of the propagating potential well and by direct supercurrent flow through the array. Both corrections decrease exponentially with the number N of junctions in the array, but give a serious limitation of accuracy for any practical array. The supercurrent at resonant gate voltages decreases with N only as sin(v/N)/N, where v is the Josephson phase difference across the array.

Feasibility of Coulomb blockade thermometry in metrology

Abstract Coulomb blockade thermometer (CBT) is a simple, magnetic-field-independent primary thermometer for everyday use at cryogenic temperatures. Its properties are well understood by now. The absolute accuracy at present is about ±0.5%. Recently, we have started studying the possibility of using CBT in metrological applications. We have especially in mind the future extension of the international temperature scale below 0.65 K, which is the lower end of ITS-90. Experiments with arrays containing more than 100 tunnel junctions in series are in progress in order to decrease the effects of electromagnetic environment and of co-tunnelling even below the present level.

Pumping of single electrons with a traveling wave

Abstract We describe the operation and performance of a one-dimensional chain of small metallic islands whose potentials are modulated in a wave-like manner. The sinusoidal voltages, applied to the gate electrodes, carry individual charges coherently through the array. In practice, the wave-like potential is induced on the gates by a surface acoustic wave (SAW) traveling on a piezoelectric substrate. The resulting transfer of charges should produce a DC current I = ± ef through the chain, where f is the frequency of the wave and the sign ofthe current depends on the value of the common DC bias of the islands as well as on the direction of the wave propagation. We observe, however, a much sm…

Electron-phonon heat transport in arrays of Al islands with submicrometer-sized tunnel junctions.

We present experimental evidence of the effect of electrode volume and its shape on thermalization of small metallic islands for single electron tunneling. We have investigated the power law and the magnitude of the thermal transport and found that it obeys the common ${T}^{5}$ law for electron-phonon coupling only for the smallest islands studied, and in other cases considered, with cooling fins attached to the islands, the coupling per unit volume is weaker and it rather follows a law $\ensuremath{\propto}{T}^{p}$, where $pl5$. We attribute this to local hot electrons adjacent to the tunnel junctions.

Microrefrigeration by quasiparticle tunnelling in NIS and SIS junctions

Abstract A solid-state refrigeration method at sub-kelvin temperatures has been developed. It is based on quasiparticle tunnelling between a superconductor and a normal metal, or, between two dissimilar superconducting metals. The refrigerator is fabricated by combining nanolithography and micromachining methods. This technique has been demonstrated in both electron cooling from 0.3 to 0.1 K and in refrigeration of a dielectric platform. We describe a new fabrication method of tunnel junctions in a shadow evaporation configuration using a mechanical mask of silicon nitride.

Characterisation of Cooper Pair Boxes for Quantum Bits

We have fabricated and measured single Cooper pair boxes (SCB) using superconducting single electron transistors (SET) as electrometers. The box storage performance for Cooper pairs was measured by observing the changes in the SCB island potential. We are also fabricating niobium structures, which are expected to have less problems with quasiparticle contamination than similar aluminium based devices because of the high critical temperature. The use of niobium may also reduce decoherence and thereby increase the time available for quantum logic operations.

Influence of magnetic field on cooling by normal-insulator–superconductor junctions

Cooling by normal-insulator–superconductor junctions in external magnetic field has been studied experimentally. For all orientations of magnetic field the cooling performance correlates with the magnetic field dependent superconducting energy gap Δ(H). In perpendicular orientation of magnetic field with respect to the sample plane, additional degradation of the cooling power originates from scattering of nonequilibrium quasiparticles in the superconductor on magnetic vortices. The effect is hysteretic and its magnitude depends on the shape of the superconducting probes.

Electronic cooling and hot electron effects in heavily doped silicon-on-insulator film

The influence of carrier concentration in silicon-on-insulator film on the thermal characteristics of semiconductor and performance of the superconductor-semiconductor-superconductor micro-coolers have been investigated at sub kelvin temperatures. The overheating of the lattice in heavily doped silicon film must be taken into account in the analysis of electron-phonon coupling experiment and operation of the cooler device. The heat flow between electrons and phonons in heavily doped silicon films is found to be proportional to T6, which is in accordance with theoretical prediction for dirty limit. Increasing the doping level in the semiconductor considerably increases both the efficiency of…

Resonant Tunneling through a Macroscopic Charge State in a Superconducting Single Electron Transistor

We predict theoretically and observe in experiment that the differential conductance of a superconducting single electron transistor exhibits a peak which is a complete analog, in a macroscopic system, of a standard resonant tunneling peak associated with tunneling through a single quantum state. In particular, in a symmetric transistor, the peak height is universal and equal to ${e}^{2}/2\ensuremath{\pi}\ensuremath{\Elzxh}$. Away from the resonance we clearly observe the cotunneling current which, in contrast to the normal-metal transistor, varies linearly with the bias voltage.

Measuring charge based quantum bits by a superconducting single-electron transistor

Single-electron transistors have been proposed to be used as a read-out device for Cooper pair charge qubits. Here we show that a coupled superconducting transistor at a threshold voltage is much more effective in measuring the state of a qubit than a normal-metal transistor at the same voltage range. The effect of the superconducting gap is to completely block the current through the transistor when the qubit is in the logical state 1, compared to the mere diminishment of the current in the normal-metal case. The time evolution of the system is solved when the measuring device is driven out of equilibrium and the setting is analysed numerically for parameters accessible by lithographic alu…

Thermal characteristics of silicon nitride membranes at sub-Kelvin temperatures

We have performed calorimetric measurements on 200 nm thin silicon nitride membranes at temperatures from 0.07 to 1 K. Besides full windows, membranes cut into a thermally isolating suspended bridge geometry were investigated. Based on dc and ac measurements employing normal-metal/insulator/superconductor (NIS) tunnel junctions both as a thermometer and a heater, we report on heat transport and thermal relaxation in silicon nitride films. The bridge structure improves thermal isolation and, consequently, energy sensitivity by two orders of magnitude over those of the full membrane with the same size, and makes such a structure very attractive for bolometric and microrefrigeration applicatio…

Charging in Solitary, Voltage Biased Tunnel Junctions.

Nano-lithography by electron exposure using an Atomic Force Microscope

Abstract We have used a conductive Atomic Force Microscope (AFM) tip to expose a very thin resist film. An exposing current of low energy electrons was induced from the tip to the substrate by applying a small bias voltage. Uniform resist films as thin as 10 nm were fabricated using the Langmuir–Blodgett technique. To orient the defined pattern and to make electrical connections a special larger scale alignment structure was first defined by conventional electron beam lithography, either directly in the Langmuir–Blodgett resist film or in a separate first lift-off process with a thicker resist. The results from the one resist process gave conducting 50 nm lines with a 60 A thick vacuum depo…

Extraction of radioactive positive ions across the surface of superfluid helium: A new method to produce cold radioactive nuclear beams

Alpha-decay recoils 219Rn were stopped in superfluid helium and positive ions were extracted by electric field into the vapour phase. This first quantitative observation of extraction was successfully conducted using highly sensitive radioactivity detection. The efficiency for extraction across the liquid surface was 23 ± 4% at 1.60 K, the release time was 90 ± 10 ms at 1.50 K and the barrier for positive ions through a free superfluid-helium surface was 19.4 ± 4.5 K. The pulsed second sound proved to be effective in enhancing the extraction.

Nano-lithography using a resist, patterned by electron exposure in an AFM configuration

We have used a metallised force microscope tip to apply a voltage and thereby expose a very thin resist film. It is possible to image the film surface before, during and after the exposure, without interference with the process. Uniform resist films as thin as 10 nm are fabricated using the Langmuir-Blodgett technique. To orient the defined pattern and to make electrical connections a special larger scale alignment structure is first defined by conventional electron beam lithography, either directly in the Langmuir-Blodgett resist film or in a complete first process with a separate resist system. The results from the one resist process gave conducting 50 nm lines in a 60 A thick aluminium f…

Microrefrigeration by normal-metal/ insulator/superconductor tunnel junctions

Abstract A normal-metal/insulator/superconductor (NIS) tunnel junction can be applied to cool electrons by biasing the junction suitably with external voltage. Because of the symmetry with bias voltage, two NIS junctions in series can form an efficient microrefrigerator. So far our SINIS microrefrigerator has been capable of reaching electronic temperatures of about 100 mK starting from 300 mK. To achieve appreciable refrigeration of the underlying lattice, microrefrigerator must be thermally decoupled from the bulk substrate. We have demonstrated experimentally the reduction of lattice temperature of a few mK at 200 mK by extending the normal electrode on a thin dielectric membrane. Method…

Sub-kelvin current amplifier using DC-SQUID

Abstract We have set up a system where a low-noise DC-SQUID is used as a current amplifier. The SQUID output is read using a wide band electronics unit based on the noise cancellation scheme. The SQUID has been installed in a compact Nanoway PDR50 dilution refrigerator, and superconducting transitions of Ti/Au thermometer strips for X-ray calorimeter applications have been measured. We can operate at 100 mK using a SQUID with Pd shunt resistors. Noise and bandwidth results of the setup are presented.