Normal-metal Tunnel Junctions Research Articles

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 universal behaviour of the long array.

Full capacitance matrix of coupled quantum dot arrays: Static and dynamical effects

We numerically calculated the full capacitance matrices for both one-dimensional (1D) and two-dimensional (2D) quantum-dot arrays. We found it is necessary to use the full capacitance matrix in modeling coupled quantum dot arrays due to weaker screening in these systems in comparison with arrays of normal metal tunnel junctions. The static soliton potential distributions in both 1D and 2D arrays are well approximated by the unscreened (1/r) Coulomb potential, instead of the exponential fall-off expected from the often used nearest neighbor approximation. The Coulomb potential approximation also provides a simple expression for the full inverse capacitance matrix of uniform quantum dot arrays. In terms of dynamics, we compare the current-voltage (I-V) characteristics of voltage biased 1D arrays using either the full capacitance matrix or its nearest neighbor approximation. The I-V curves show clear differences and the differences become more pronounced when larger arrays are considered.

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.

On inversion of normal metal tunnelling data

A short summary of the theoretical and experimental status of elastic tunnelling between normal metals is given. Methods for the determination of the electron-phonon interaction function, alpha 2F( omega ), from the conductance. sigma ( omega ), of a normal metal tunnel junction are presented and their performance is discussed. A complete list of sum rules applicable to the inversion procedures is given for the first time. Elimination of the thermal smearing of the conductance data with the help of the fast Fourier transform algorithm and the regularization method is described. The possibility of the existence of 'interference' between the elastic and inelastic parts of the tunnelling current is discussed for conductivity data of Pb and Sn.

Tunnel junction used as thermometer for ions detection

We propose the use of a superconductor — normal metal tunnel junction as thermometer for the energy measurement on MeV ions, using a metallic bolometer. The direct measurement of electronic temperature leads to a small time constant even at very low temperature in contrast with systems where the time constant is limited by electronphonon interaction. Experiments with heat pulses obtained by LED and optical fibre confirm the calculated time constants. Sensitivity calculations using the measured data gives an energy resolution better than 1/1000 for 1MeV ions with a time constant of 50 µs.

Influence of the environment on the Coulomb blockade in submicrometer normal-metal tunnel junctions.

Submicrometer normal-metal tunnel junctions were fabricated with thin-film leads of either about 2 k\ensuremath{\Omega}/\ensuremath{\mu}m or about 30 k\ensuremath{\Omega}/\ensuremath{\mu}m. The current-voltage (I-V) characteristics at millikelvin temperatures displayed a much sharper Coulomb blockade for the high-resistance leads than for the low-resistance leads. The zero-bias differential resistance increased as the temperature was lowered, flattening off at the lowest temperatures. A heuristic model based on the quantum Langevin equation is developed, which explains these effects qualitatively in terms of the Nyquist noise generated in the leads; in this model, the flattening of the zero-bias resistance arises from zero-point fluctuations. The data are also compared with a more accurate phase-correlation model that treats the junction and the circuit coupled to it as a single quantum circuit. This model accounts for the observed I-V characteristics quite accurately except near zero bias where it overestimates the dynamic resistance by roughly 50% at the lowest temperatures. This model, however, does not account for the flattening of the zero-bias resistance at the lowest temperatures. It is suggested that the addition of quantum fluctuations in the junction to the phase-correlation theory may account for this discrepancy.

Gate-controlled conductance oscillations in small one-dimensional electron cavities

The low-temperature, low-bias regime of electron transport through narrow channels in semiconductor heterostructures interrupted by a finite number of potential barriers at zero magnetic field, is investigated with a simple model of resonant tunneling of noninteracting electrons in a single one-dimensional subband. By using a generalized wave impedance concept, we calculate the transmission coefficient for electrons passing through such devices, thus providing a satisfactory explanation for the periodic conductance oscillations observed in recent experiments. We also show that the oscillatory behaviour in the current of arrays of submicrometer normal-metal tunnel junctions may be understood as the formation of miniband structures in such coupled electron systems. Our results call into question the dominance of charging effects in small electron resonator devices.

Fabrication and properties of superconductor–insulator–normal metal tunnel junctions

This article first describes the preparation and properties of small area (∼1 μm2)Pb/Bi/In-oxide–Ag junctions made by evaporation through metal masks. These junctions have successfully been used in a 230 GHz receiver. We then describe the preparation and properties of two slightly different types of Nb/Al-based superconductor–insulator–normal conductor (SIN) junctions applying a ‘‘trilayer technique’’ similar to that used in the fabrication of Nb–Al-oxide–Nb superconductor–insulator–superconductor junctions. For one type of the Nb/Al-based SIN junctions the base layer consists of Nb, for the other type, the base layer is made of Al. In practical applications these devices will operate at temperatures where the Al is in the normal state. Junctions with areas down to about 0.5 μm2 have been made.

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.

Influence of defect site transitions on discrete resistance fluctuations in normal-metal tunnel junctions.

Influence of defect site transitions on discrete resistance fluctuations in normal-metal tunnel junctions.

Apparent critical currents and rf steps in a second-order proximity-induced Josephson effect.

Numerical {ital I}({ital V}) results for superconductor--insulator--normal-metal ({ital S}-{ital I}-{ital N}) tunnel junctions suggest that a unified treatment of the weak excess currents (pair-field susceptibility) and proximity-induced Josephson-effect (PJE) phenomena (apparent critical currents, rf steps, and Fraunhofer-like {ital I}{sub {ital c}}({ital B})) is provided by the Geshkenbein-Sokol time-dependent Ginzburg-Landau theory of second-order Josephson effects in {ital S}-{ital I}-{ital N} tunnel junctions. The numerical results and other considerations speak against a recent suggestion that a phase-slip center in the superconducting tip may play a role in PJE point-contact experiments. These considerations confirm the utility of proximity Josephson-effect experiments to probe unconventional superconductivity in materials such as UBE{sub 13}, as first pointed out by Han {ital et} {ital al}.

Giant discrete resistance fluctuations observed in normal-metal tunnel junctions.

Giant discrete resistance fluctuations are reported in large (50\ifmmode\times\else\texttimes\fi{}50 \ensuremath{\mu}${\mathrm{m}}^{2}$) tunnel junctions of Au-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$-Au over the temperature range 4--140 K, with applied dc bias voltages of 0--2 V. The fluctuations are believed to result from single electrons trapped on defect sites within the insulating barrier of the tunnel junction. The temperature and bias-voltage dependence of the characteristic switching lifetimes of these fluctuations have been measured, and departures from previously reported behavior are observed.

Quantum fluctuations and coulomb blockade in small tunnel junctions

We describe an experiment in which we attached high- and low-resistance thin film leads to normal metal tunnel junctions with capacitances of order 10-15 F. At 20 mK we observed a pronounced Coulomb blockade in the former case, and a very smeared blockade in the latter case. We outline a model which indicates that the low temperature behavior of the junctions is dominated by quantum fluctuations in the external circuit. The predictions of the model are in fairly good agreement with the observed current-voltage characteristics.

Correlated single-electron tunneling via mesoscopic metal particles: Effects of the energy quantization

The existing theory of correlated single-electron tunneling in the double normalmetal tunnel junction is extended to the case of an ultrasmall central electrode of the structure. It is shown that the form of theI–V curve of such a system depends on the energy relaxation rate in this electrode. For realistic values of the relaxation rate, the large-scale shape of the dcI–V curve, which is associated with Coulomb correlations, is close to that following from the earlier theory. However, theI–V curve should also exhibit small-scale singularities reflecting the structure of the energy spectrum of the central electrode.

Unbinding of charge-anticharge pairs in two-dimensional arrays of small tunnel junctions.

We describe the behavior of charges in two-dimensional arrays of normal-metal tunnel junctions with very small capacitance. A Kosterlitz-Thouless-Berezinskii phase transition with unbinding of charge-anticharge pairs occurs at a transition temperature of about Tc = e2/8πCkB, with C the junction capacitance. We calculate the influence of tunneling conductance; Tc is reduced with increasing conductance and no transition occurs for junction conductance above (14 kΩ)–1. In the superconducting state a similar transition occurs at a 4 times higher Tc. We present the first experimental results on the conductive transition of an array in the normal and superconducting states.

Coulomb fingerprints on the I–V curves of the normal tunnel junctions

Small deviations of the I–V curves of normal-metal tunnel junctions from the Ohm law due to the Coulomb interaction of tunneling electrons are analyzed. The electrodynamical properties of the junction itself and properties of its electrodynamic environment manifest themselves in these deviations. Several practical conclusions are made that can be of importance for the interpretation of experimental results.

Charge fluctuations in small-capacitance junctions.

The current-voltage characteristics of submicron normal-metal tunnel junctions at millikelvin temperatures are observed to exhibit a sharp Coulomb blockade with high-resistance thin-film leads, but to be heavily smeared for low-resistance leads. As the temperature is lowered, the zero-bias differential resistance tends asymptotically to a limit that is greater for junctions with high-resistance leads. Both observations are explained in terms of a model in which quantum fluctuations in the external circuit enhance the low-temperature tunneling rate. The predictions are in reasonable agreement with the data.

Electron-electron scattering and phase fluctuations in superconducting films.

The effects of weak disorder on superconducting aluminum films are studied over temperatures 0.4${T}_{c}$\ensuremath{\le}T\ensuremath{\le}0.98${T}_{c}$ and resistances per square of 1.7\ensuremath{\le}${R}_{\ensuremath{\square}}$\ensuremath{\le}22 \ensuremath{\Omega}. The primary effects of disorder are found to be disorder-enhanced electron-electron scattering and thermal phase, or supercurrent fluctuations, both of which cause pair-breaking effects. This conclusion is drawn from measurement of the low-voltage resistance of low-resistance superconductor--insulator--normal-metal (SIN) tunnel junctions with aluminum as the S electrode. The effective pair-breaking rates from both processes, evaluated at ${T}_{c}$, increases linearly with ${R}_{\ensuremath{\square}}$, in semiquantitative agreement with model calculations. The electron-electron scattering rate decreases very rapidly as T decreases below ${T}_{c}$, in agreement with theory. The pair-breaking rate from phase fluctuations decreases roughly linearly with decreasing temperature. Although distinct effects, phase fluctuations, and electron-electron scattering share a common origin in electron-density fluctuations, which are enhanced by disorder. A microscopic theory of disordered superconductors incorporating both electron-electron scattering and thermal phase fluctuations is needed.

Experimental study of the effect of a supercurrent on high-resistance superconductor-insulator- normal-metal tunnel junctions.

We have measured the low-voltage resistance of superconductor--insulator--normal-metal tunnel junctions as a function of supercurrent in the superconducting film. The superconducting films were Sn and Al. The junctions had sufficiently high resistances that nonequilibrium effects associated with a charge imbalance in the superconductor were negligible. We find that the supercurrent reduces the resistance as expected from the dirty-limit theory of superconductivity. We conclude that the theory accurately predicts the pair-breaking effects of supercurrents in films despite inevitable nonuniformities in film thickness and supercurrent density that occur in wide films.

Theory of the effect of supercurrents on the low-voltage resistance of superconductor-insulator-normal-metal tunnel junctions.

The theory of charge imbalance in tunnel junctions is adapted to describe the low-voltage resistance R/sub j/(T) of low-resistance superconductor--insulator--normal-metal (SIN) tunnel junctions. R/sub j/ is shown to be very sensitive to the pair-breaking effect of supercurrents. Numerical calculations for hypothetical SIN junctions illustrate how one can obtain information about the magnitude and temperature dependence of electron scattering rates, coherence factors, and the density of superconducting electrons from measurements of R/sub j/ in the presence of supercurrents either applied directly with a current supply or induced with a magnetic field applied parallel to the superconducting film. Such measurements should yield information similar to that obtained from other nonequilibrium techniques like NMR and ultrasonic attenuation.