A Two-Fluid Model for the Transition Shape in Transition-Edge Sensors

Superconducting microcalorimeters based on transition-edge sensors (TESs) are being successfully used in applications ranging from optical photon counting to gamma-ray and alpha particle spectroscopy. Practical instruments often require a complex optimization among speed, linearity and energy resolution. However, a?lack of understanding of the superconducting transition limits our ability to predict the behavior of a new TES design. Specifically, there is an unmet need for a model that predicts the current and temperature dependent resistance surface that describes the transition: R(I,T). This paper describes the predictions of a two-fluid model for the resistance of a TES based on a Ginzburg-Landau form of the critical current. We compare the predictions of the model for the logarithmic derivatives of resistance with temperature and current (α and β) to measurements of TESs used in x-ray and gamma spectrometers. The model shows excellent qualitative agreement that provides useful insight into the dependence of α and β on the current density and bias point of the TES.     

The Superconducting Transition in 4-D: Temperature, Current, Resistance and Heat Capacity

We measured the superconducting phase transition of a transition-edge sensor (TES) provided by SRON. Using newly developed techniques, we obtain thousands of impedance measurements to find sensitivity α _I , current dependence β _I , and heat capacity of the TES in the phase transition at various temperatures and bias currents. The resulting data illustrate the shape of the phase transition and probe the internal state of the device.      

Fabrication of Microstripline Wiring for Large Format Transition Edge Sensor Arrays

We have developed a process to integrate microstripline wiring with transition edge sensors (TES). The process includes additional layers for metal-etch stop and dielectric adhesion to enable recovery of parameters achieved in non-microstrip pixel designs. We report on device parameters in close-packed TES arrays achieved with the microstrip process including R _n , G, and T _c uniformity. Further, we investigate limits of this method of producing high-density, microstrip wiring including critical current to determine the ultimate scalability of TES arrays with two layers of wiring.     

Current distribution measurement in YBCO thin film for a superconducting fault current limiter

Current distribution in the superconducting film for a resistive fault current limiter is important, because it influences AC loss and a uniformity of S/N transition. The lateral current distribution of the film was reconstructed from the magnetic field distribution which is measured by multiple Hall probes. The following results were obtained. (1) Non-uniform current distribution in the superconducting film was observed when the current was less than 1.3 times of critical current (I_c). (2) The current in a superconducting film was uniform when the current was much higher than I_c. The current can be considered uniform when the film works as a fault current limiter, because the S/N transition starts about twice of I_c. (3) The validity of the measurement was verified by the comparison with the electric circuit simulation.     

Kilopixel X-ray Microcalorimeter Arrays for Astrophysics: Device Performance and Uniformity

We are developing kilopixel arrays of TES microcalorimeters to enable high-resolution x-ray imaging spectrometers for future x-ray observatories and laboratory astrophysics experiments. Our current array design was targeted as a prototype for the X-ray Microcalorimeter Spectrometer proposed for the International X-ray Observatory, which calls for a 40×40-pixel core array of 300?μm devices with 2.5?eV energy resolution (at 6?keV). Here we present device characterization of our 32×32 arrays, including x-ray spectral performance of individual pixels within the array. We present our results in light of the understanding that our Mo/Au TESs act as weak superconducting links, causing the TES critical current (I _c ) and transition shape to oscillate with applied magnetic field (B). We show I _c (B) measurements and discuss the uniformity of these measurements across the array, as well as implications regarding the uniformity of device noise and response. In addition, we are working to reduce pixel-to-pixel electrical and thermal crosstalk; we present recent test results from an array that has microstrip wiring and an angle-evaporated copper backside heatsinking layer, which provides copper coverage on the four sidewalls of the silicon wells beneath each pixel.     

Effect of On-Chip Magnetic Shielding for TES Microcalorimeters

We investigated the magnet field dependence of the X-ray pulse height and the critical current of a Ti/Au bilayer TES micro-calorimeter. The pulse height was strongly affected by the magnetic field intensity applied perpendicularly to the TES surface. We found that the critical current at zero temperature, I _c0, decreased by a factor of two by applying a magnet field of ∼10 μT. Our data are consistent with a TES sensitivity proportional to (I/I _c0)^−2/3, as predicted by the Ginzburg-Landau theory. This fact implies that the shape of the R–T curve of the TES is partly determined by the critical current of the superconductor. In order to make our TES microcalorimeters less sensitive to the external magnetic field, we fabricated devices equipped with on-chip magnetic shielding. One device has a turn-around style electrical lead made of Al, in which the return line is laid beneath the Ti/Au TES. Another device has a Nb layer deposited between a multi-layer membrane. We demonstrated that the devices were usable below 200 μT with small degradation of the pulse height and energy resolution.      

Can the Lateral Proximity Effect Be Used to Create the Superconducting Transition of a Micron-Sized TES?

Recent measurements of micron-sized Mo/Au bilayer TESs have demonstrated that the TES can behave like an S-S′-S weak link due to the lateral proximity effect from superconducting leads. In this regime the T _c is a function of bias current, and the effective T _c shifts from the bilayer T _c towards the lead T _c . We explore the idea that a micron-sized S-N-S weak link could provide a new method to engineer the TES T _c . This method would be particularly useful when small size requirements for a bilayer TES (such as for a hot-electron microbolometer) lead to undesirable shifts in the bilayer T _c . We present measurements of a variety of micron-sized normal Au ‘TES’ devices with Nb leads. We find no evidence of a superconducting transition in the Au film of these devices, in dramatic contrast to the strong lateral proximity effect seen in micron-sized Mo/Au bilayer devices. The absence of a transition in these devices is also in disagreement with theoretical predictions for S-N-S weak links. We hypothesize that a finite contact resistance between the Nb and Au may be weakening the effect. We conclude that the use of the lateral proximity effect to create a superconducting transition will be difficult given current fabrication procedures.     

A Study of the Paramagnetic to Ferromagnetic Transition in the Optimally Doped CMR Compound La0.65Ca0.35MnO3 and Its Dependence on Oxygen Mass

We present a study of the paramagnetic to ferromagnetic transition in the CMR compound La_0.65Ca_0.35MnO₃ and its dependence on magnetic field and oxygen mass. The transition is characterized by two temperatures, the thermodynamic transition temperature at T _c, obtained from specific heat and thermal expansion data, and the resistive transition obtained from the resistivity maximum. The resistive transition occurs well within the paramagnetic range. The magnetic susceptibility in the paramagnetic range is isotope dependent up to 400 K. The magnitude of the Curie-Weiss constant indicates the presence of small clusters of about 4–5 unit cells. The resistive transition occurs when the percolation limit for these clusters is reached.     

Critical current distributions in superconducting composites

The transition from the flux pinning state to the full flux flow state occurs over a range of current in composite superconductors. The critical current, therefore, does not have a single, unique value, there being a distribution of critical currents throughout the composite. This Paper describes a technique for deriving the critical current distribution from the resistive critical current transition. The analysis has been applied to Nb---Ti and Nb₃Sn composites of different types. The technique has been used to analyse good quality conductors, where the l_c is largely determined by the intrinsic fluxoid-microstructure interactions, At the other extreme, composites with irregular filaments in which the transport critical current is significantly less than the intrinsic critical current, have also been examined. The analysis shows that good conductors have narrow resistive transitions with average l_c values within 5–10% of a high sensitivity measurement of l_c. This difference broadens to ≈ 35% for a badly sausaged composite. A relationship between the n value of the resistive transition and the relative width of the l_c distribution is presented. A simple but accurate method of deriving the average l_c from the resistive transition is also presented.     

A Mo/Au Bilayer Transition Edge Sensor Modified with Normal Metal Structures

In this work, we explore a technical path to defining the normal-to-superconducting transition profile of a superconducting transition edge sensor (TES) using normal metal stripes on surface. The stripes modify the TES transition through the lateral proximity effect. We experimentally demonstrate that varying the width, thickness and spacing of the normal metal stripes alters the TES resistive transition profile as a function of temperature and current.     

Towards Ultra-Low-Noise MoAu Transition Edge Sensors

We report initial measurements on our first MoAu transition edge sensors (TESs). The TESs formed from a bilayer of 40?nm of Mo and 106?nm of Au showed transition temperatures of about 320?mK, higher than identical TESs with a MoCu bilayer which is consistent with a reduced electron transmission coefficient between the bilayer films. We report measurements of thermal conductance in the 200?nm thick silicon nitride SiN _x support structures at this temperature, TES dynamic behaviour and current noise measurements.     

Implications of Weak Link Effects on Thermal Characteristics of Transition-Edge Sensors

Weak link behavior in transition-edge sensor (TES) microcalorimeters creates the need for a more careful characterization of a device’s thermal characteristics through its transition. This is particularly true for small TESs where a small change in the bias current results in large changes in effective transition temperature. To correctly interpret measurements, especially complex impedance, it is crucial to know the temperature-dependent thermal conductance, G(T), and heat capacity, C(T), at each point through the transition. We present data illustrating these effects and discuss how we overcome the challenges that are present in accurately determining G and T from I–V curves. We also show how these weak link effects vary with TES size. Additionally, we use this improved understanding of G(T) to determine that, for these TES microcalorimeters, Kaptiza boundary resistance dominates the G of devices with absorbers while the electron-phonon coupling also needs to be considered when determining G for devices without absorbers     

An Approach to Use a Raw Single Crystal Whisker as Intrinsic Josephson Junctions Stack

We have developed a technique to observe the intrinsic Josephson effect in Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) single crystal whiskers. In this technique, a raw Bi-2212 single crystal whisker used as intrinsic Josephson junctions (IJJs) along the c-axis. The technique is simple, quick, and less-cost processing. First, a whisker made to stand on ac-plane and then two electrodes were made in ab-planes on either side. The standing whisker with this configuration worked as IJJs. The standing whisker (1.6 mm×40 μm×3 μm) showed the transition temperature of about 84 K. The critical current was about 15 mA at 8 K (critical current density ～23 A/cm²). We observed voltage gap of about 500 mV in current–voltage (I–V) characteristics. This corresponds to a few hundred of IJJs out of ～2,000 IJJs in the whisker thickness. Observations reflect that the technique can be further improved with the single crystal quality, shape of single crystal whisker, and annealing conditions.     

The Magnetically-Tuned Transition-Edge Sensor

We present the first measurements on the proposed magnetically-tuned superconducting transition-edge sensor and compare the modified resistive transition with the theoretical prediction (Sadleir et al., IEEE Trans App Supercond 23:2101405, 2013). A TES’s resistive transition is customarily characterized in terms of the unitless device parameters \(\alpha \) and \(\beta \) corresponding to the resistive response to changes in temperature and current respectively. We present a new relationship between measured IV quantities (sensor current \(I\) and voltage \(V\) ) and the parameters \(\alpha \) and \(\beta \) and use these relations to confirm we have stably biased a TES with negative \(\beta \) parameter with magnetic tuning. Motivated by access to this new unexplored parameter space, we investigate the conditions for bias stability of a TES taking into account both self and externally applied magnetic fields.     

Current-Temperature Diagram of Resistive States in Long Superconducting Niobium Filaments

By applying nanosecond current pulses to narrow superconducting Nb strips, we have observed the induced resistive states expected for quasi 1-D transport, namely localized phase-slip centres (PSC) and hot spots (HS). The current-controlled drive discriminates stable-in-time PSC structures near T _c from expanding HS at lower temperatures. HS-PSC exchange and return towards equilibrium are studied by using two-step current pulses. Remarkably, it appears that a hot spot never forms unless a PSC has first been nucleated. Then from a plot of the threshold currents I _c (T) and I _h (T), corresponding to PSC and HS, respectively, one can predict the response to current, temperature, or luminous excitation, as well as the effect of an applied magnetic field.     

Peculiarities of the current-voltage characteristics of a Josephson medium in a YBCO high-temperature superconductor

The influence of a weak magnetic field (H < 150 Oe) on the current-voltage (I-U) characteristic of a YBa₂Cu₃O_{7 ? x} (YBCO) high-temperature superconductor (HTSC) near the superconducting transition temperature has been studied. It is established that there exist narrow (<0.2 K) temperature regions where the I-U curve exhibits sharp bending for H < 30 Oe and the ohmic behavior changes to a quadratic dependence of the voltage on current in a region of several milliamperes. At higher temperatures, the I-U curve bending exhibits smearing. This behavior is observed at a temperature below that corresponding to a zero critical current. Above a certain current, the temperature and magnetic field exhibit equivalent effects on the I-U curve of YBCO. Experimental results are explained by a sharp decrease in the critical currents of intergranular Josephson junctions under the action of magnetic field and by the current-induced formation of uncoupled (with respect to the order parameter) superconducting grains. Characteristic currents for the transition of the intergranular Josephson medium into an incoherent state are determined and the first critical fields in YBCO are evaluated.     

A Study of the Paramagnetic to Ferromagnetic Transition in the Optimally Doped CMR Compound La0.65Ca0.35MnO3 and Its Dependence on Oxygen Mass

We present a study of the paramagnetic to ferromagnetic transition in the CMR compound La_0.65Ca_0.35MnO₃ and its dependence on magnetic field and oxygen mass. The transition is characterized by two temperatures, the thermodynamic transition temperature at T _c, obtained from specific heat and thermal expansion data, and the resistive transition obtained from the resistivity maximum. The resistive transition occurs well within the paramagnetic range. The magnetic susceptibility in the paramagnetic range is isotope dependent up to 400 K. The magnitude of the Curie-Weiss constant indicates the presence of small clusters of about 4–5 unit cells. The resistive transition occurs when the percolation limit for these clusters is reached.     

Percolation and the resistive transition of the critical temperature Tc of Nb3Sn

The relationship between the distribution of the critical temperature, the percolation function, and the resistive transition of the critical temperature is explored for polycrystalline Nb₃Sn. In the neighborhood of the critical temperature, Nb₃Sn is assumed to be a random mixture of superconducting and normal grains. Percolation concepts are applied to a study of the resistivity. A general analysis is made showing that the onset and shape of the resistive transition for composite conductors are determined by the percolation function and the distribution of the critical temperature. An approximate form of the percolation function is determined based on a linear FEM analysis. Example resistive transitions are calculated for an assumed normal distribution of the critical temperature. An argument is presented that relates grain orientation and strain dependence in Nb₃Sn. It is noted that a dependence of the distribution of T_c with strain, in addition to the usual shift in T_c with strain, would be the result of a strain dependence that is a function of grain orientation. The analysis shows the extent to which the slope of the resistive transition is a measure of the distribution of the critical temperature, and therefore a measure of the grain orientation strain sensitivity. Finally, a method is described to determine the percolation function experimentally.     

Metallic contacts to nitrogen and boron doped diamond-like carbon films

Hydrogenated diamond-like carbon (DLC) was deposited using a radio-frequency plasma-enhanced chemical vapor deposition method. Electrical properties of Al, Au, Ti, and Zr contacts to nitrogen and boron doped DLC films have been studied, and mechanisms of the observed current-voltage (I-V) characteristics are investigated. Linear I-V characteristics were observed for Au, Ti, and Zr contacts to both nitrogen and boron doped DLC films. A band structure model for metal-DLC contact is proposed to explain the observed ohmic contacts. Fermi level shifting at the surface of DLC films produces an ohmic resistive layer instead of a Schottky barrier for metal-DLC contacts. Al contacts to both nitrogen and boron doped DLC films show nonlinear I-V characteristics, which are attributed to a dielectric layer of carbide (Al₄C₃) instead of a Schottky barrier suggested by other groups. Inert elements such as Au and Pt, and transition metals such as Ti, Zr and W, which form conductive carbides, are considered good contacting metals for electrical studies of DLC films.     

M-type potassium conductance controls the emergence of neural phase codes: a combined experimental and neuron modelling study

Rate and phase codes are believed to be important in neural information processing. Hippocampal place cells provide a good example where both coding schemes coexist during spatial information processing. Spike rate increases in the place field, whereas spike phase precesses relative to the ongoing theta oscillation. However, what intrinsic mechanism allows for a single neuron to generate spike output patterns that contain both neural codes is unknown. Using dynamic clamp, we simulate an in vivo-like subthreshold dynamics of place cells to in vitro CA1 pyramidal neurons to establish an in vitro model of spike phase precession. Using this in vitro model, we show that membrane potential oscillation (MPO) dynamics is important in the emergence of spike phase codes: blocking the slowly activating, non-inactivating K⁺ current (I_M), which is known to control subthreshold MPO, disrupts MPO and abolishes spike phase precession. We verify the importance of adaptive I_M in the generation of phase codes using both an adaptive integrate-and-fire and a Hodgkin–Huxley (HH) neuron model. Especially, using the HH model, we further show that it is the perisomatically located I_M with slow activation kinetics that is crucial for the generation of phase codes. These results suggest an important functional role of I_M in single neuron computation, where I_M serves as an intrinsic mechanism allowing for dual rate and phase coding in single neurons.