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We theoretically study the heat flux between electrons and phonons in a thin metallic film embedded in a suspended dielectric slab (called a \textit{membrane}, in accordance with the established nomenclature), forming a layered structure. The thickness of the membrane is much smaller than the other two dimensions and, in the considered temperature range, is comparable to the dominant phonon wavelength. The thickness of the metallic layer is an order of magnitude smaller than the thickness of the membrane. While the dependence of the heat exchange on the thicknesses of the film and of the membrane has been studied before, it is not yet known how this depends on the position of the film inside the membrane. Here we show that the position strongly influences the heat exchange. If we denote by $T_e$ the effective temperature of the electrons in the metal and by $T_{ph}$ the effective temperature of the phonons (assumed to be uniform in the entire system), then we may write in general the heat power as $P \equiv P^{(0)}(T_e) - P^{(0)}(T_{ph})$, where $P^{(0)}(T) \equiv P_s^{(0)}(T) + P_a^{(0)}(T)$, with $P_s^{(0)}(T)$ and $P_a^{(0)}(T)$ being the contributions of the symmetric and antisymmetric Lamb modes, respectively. In the low-temperature limit, we may write $P_s^{(0)}(T) \equiv C_s T^4$ and $P_a^{(0)}(T) \equiv C_a T^{3.5}$, where $C_s$ is independent of the position of the film inside the membrane, whereas $C_a$ increases with the distance between the mid-plane of the film and the mid-plane of the membrane, being zero when the film is at the center of the membrane. Our examples show that by changing the position of the film inside the membrane one may change the electron-phonon heat power by orders of magnitude, depending on the dimensions and the temperature range., Comment: 14 pages, 4 figures

We suggest a new type of an ultrasensitive detector of electromagnetic fields exploiting the giant thermoelectric effect recently found in superconductor/ferromagnet hybrid structures. Compared to other types of superconducting detectors where the detected signal is based on variations of the detector impedance, the thermoelectric detector has the advantage of requiring no external driving fields. This becomes especially relevant in multi-pixel detectors where the number of bias lines and the heating induced by them becomes an issue. We propose different material combinations to implement the detector and provide a detailed analysis of its sensitivity and speed. In particular, we perform to our knowledge the first proper noise analysis that includes the cross correlation between heat and charge current noise and thereby describes also thermoelectric detectors with a large thermoelectric figure of merit., Comment: 7 pages + appendix; 7 figures

Thermomagnetic avalanches in superconducting films propagating extremely fast while forming unpredictable patterns, represent a serious threat for the performance of devices based on such materials. It is shown here that a normal-metal frame surrounding a selected region inside the film area can provide efficient protection from the avalanches during their propagation stage. Protective behavior is confirmed by magneto-optical imaging experiments on NbN films equipped with Cu and Al frames, and also by performing numerical simulations. Experimentally, it is found that while conventional flux creep is not affected by the frames, the dendritic avalanches are partially or fully screened by them. The level of screening depends on the ratio of the sheet conductance of the metal and the superconductor in the resistive state, and for ratios much larger than unity the screening is very efficient., Comment: 5 pages, 5 figures

Experimental evidence of wave properties of dendritic flux avalanches in superconducting films is reported. Using magneto-optical imaging the propagation of dendrites across boundaries between a bare NbN film and areas coated by a Cu-layer was visualized, and it was found that the propagation is refracted in full quantitative agreement with Snell's law. For the studied film of 170 nm thickness and a 0.9 mkm thick metal layer, the refractive index was close to n=1.4. The origin of the refraction is believed to be caused by the dendrites propagating as an electromagnetic shock wave, similar to damped modes considered previously for normal metals. The analogy is justified by the large dissipation during the avalanches raising the local temperature significantly. Additional time-resolved measurements of voltage pulses generated by segments of the dendrites traversing an electrode confirm the consistency of the adapted physical picture., Comment: 4 pages, 4 figures

We introduce a microwave bolometer aimed at high-quantum-efficiency detection of wave packet energy within the framework of circuit quantum electrodynamics, the ultimate goal being single microwave photon detection. We measure the differential thermal conductance between the detector and its heat bath, obtaining values as low as 5 fW/K at 50 mK. This is one tenth of the thermal conductance quantum and corresponds to a theoretical lower bound on noise-equivalent-power of order $10^{-20}$ $W/\sqrt{\mbox{Hz}}$ at 50 mK. By measuring the differential thermal conductance of the same bolometer design in qualitatively different environments and materials, we determine that electron--photon coupling dominates the thermalization of our nanobolometer.

We report the development of superconducting tantalum nitride (TaN$_{x} $) normal metal-insulator-superconductor (NIS) tunnel junctions. For the insulating barrier, we used both AlO$_{x}$ and TaO$_{x}$ (Cu-AlO$_{x}$-Al-TaN$_{x} $ and Cu-TaO$_{x}$-TaN$_{x} $), with both devices exhibiting temperature dependent current-voltage characteristics which follow the simple one-particle tunneling model. The superconducting gap follows a BCS type temperature dependence, rendering these devices suitable for sensitive thermometry and bolometry from the superconducting transition temperature $T_{\text{C}}$ of the TaN$_{x} $ film at $\sim 5$ K down to $\sim$ 0.5 K. Numerical simulations were also performed to predict how junction parameters should be tuned to achieve electronic cooling at temperatures above 1 K., Comment: Appl. Phys. Lett. in press

In this paper we present a new measurement setup, where a transitionedge sensor detector array is used to detect X-rays in particle induced X-ray emission measurements with a 2 MeV proton beam. Transition-edge sensors offer orders of magnitude improvement in energy resolution compared to conventional silicon or germanium detectors, making it possible to recognize spectral lines in materials analysis that have previously been impossible to resolve, and to get chemical information from the elements. Our sensors are cooled to the operation temperature (65 mK) with a cryogen-free adiabatic demagnetization refrigerator, which houses a specially designed X-ray snout that has a vacuum tight window to couple in the radiation. For the best pixel, the measured instrumental energy resolution was 3.06 eV full width at half maximum at 5.9 keV.We discuss the current status of the project, benefits of transition-edge sensors when used in particle induced X-ray emission spectroscopy, and the results from the first measurements., Comment: 6 pages, 3 figure, LTD-15 proceedings

We have successfully fabricated micron-scale Cu-AlO$_{x} $-Al-NbN normal metal-insulator-superconductor (NIS) tunnel junction devices, using pulsed laser deposition (PLD) for NbN film growth, and electron-beam lithography and shadow evaporation for the final device fabrication. The subgap conductance of these devices exhibit a strong temperature dependence, rendering them suitable for thermometry from $\sim$ 0.1 K all the way up to the superconducting transition temperature of the NbN layer, which was here $\sim 11$ K, but could be extended up to $\sim 16$ K in our PLD chamber. Our data fits well to the single particle NIS tunnel junction theory, with an observed proximised superconducting gap value $\sim $ 1 meV for a 40 nm thick Al overlayer. Although this high value of the superconducting energy gap is promising for potential electronic NIS cooling applications as well, the high value of the tunneling resistance inhibits electronic cooling in the present devices. Such opaque barriers are, however, ideal for thermometry purposes as self-induced thermal effects are thus minimized.

Thermo-magnetic instability (TMI) in superconductors is known to destroy the critical state via magnetic flux avalanches, and hence it deteriorates the ability of the superconductors to shield external magnetic field. In this work, we quantify to what extent the shielding current is affected by TMI. We recover the critical state in one half of a thermo-magnetically unstable NbN film by coating it with a thin layer of Cu. Suppression of the instability in the metal coated part is confirmed by the results of a direct real time magneto-optical imaging. A pattern of discontinuity lines in the observed flux distribution indicates that only one quarter of the shielding current flows through the whole sample, including the unstable uncoated part, while three quarters flow in loops within the stable Cu-coated part., Comment: 5 pages, 5 figures

We have successfully fabricated Cu/AlOx-Al/Nb normal-metal/insulator/superconductor tunnel junction devices with a high value of the superconducting gap (up to $\sim 1$ mV), using electron-beam lithography and angle evaporation techniques in the sub-micron scale. The subgap conductance of these junctions shows the expected strong temperature dependence, rendering them suitable for thermometry all the way from 100 mK to 6 K. In addition, some direct electronic cooling of the normal metal was also seen at bias values near the gap edge. The device performance was strongly influenced by the details of the Al layer geometry, with lateral spilling of the aluminium giving rise to strong extra subgap features, and the thickness of Al layer affecting the proximised superconducting gap value of the superconducting Al/Nb bilayer., Comment: 5 pages 3 figures

The so-called excess noise limits the energy resolution of transition-edge sensor (TES) detectors, and its physical origin has been unclear, with many competing models proposed. Here we present the noise and impedance data analysis of a rectangular X-ray Ti/Au TES fabricated at SRON. To account for all the major features in the impedance and noise data simultaneously, we have used a thermal model consisting of three blocks of heat capacities, whereas a two-block model is clearly insufficient. The implication is that, for these detectors, the excess noise is simply thermal fluctuation noise of the internal parts of the device. Equations for the impedance and noise for a three-block model are also given., Comment: 6 pages, 5 figures

We have investigated the effect of a difference in the tunnelling resistances of the individual normal metal-insulator-superconductor (NIS) tunnel junctions in a double junction SINIS device, with particular emphasis on the impact on the conductance, cooling and thermometric performance. By solving the electrical and thermal equations of the junctions in a self-consistent way, we find that asymmetry gives rise to many new features, such as appearance of an excess sub-gap current, improved cooling performance, exhibition of negative differential resistance, and improved temperature range of thermometric sensitivity. Experiments were also carried out to complement some of the numerical results. In addition, we studied theoretically and experimentally the effect of a finite series resistance, which also causes an excess current in the subgap region, and a suppression of the conductance maxima at the gap edge. Experimental results agree well with the theoretical predictions., Comment: 14 pages

We have studied the origin of excess noise in superconducting transition-edge sensors (TES) with several different detector designs. We show that most of the observed noise and complex impedance features can be explained by a thermal model consisting of three bodies. We suggest that one of the thermal blocks and the corresponding thermal fluctuation noise arises due to the high-frequency thermal decoupling of the normal and superconducting phase regions inside the TES film. Our results are also consistent with the prediction that in thin bilayer proximitized superconductors, the jump in heat capacity at the critical temperature is smaller than the universal BCS theory result., Comment: 11 pages 14 figures

We have calculated the temperature profiles for phonon heat transport in a suspended membrane with a radially symmetric heat source in the two extreme cases of either fully ballistic or fully diffusive transport. Theoretical results confirm that it is possible to distinguish these two transport mechanisms from the radial temperature profiles alone. Models are also compared to experimental data measured with 40 nm thick, free standing silicon nitride membranes below 1 K by using tunnel junction (SINIS) thermometers. The measured temperature profile is qualitatively in agreement with the ballistic model., Comment: 7 pages, 3 figures Revised version, accepted for publication in the Chinese Journal of Physics

We demonstrate a local strain sensing method for nanostructures based on metallic Al tunnel junctions with AlOx barriers. The junctions were fabricated on top of a thin silicon nitride membrane, which was actuated with an AFM tip attached to a stiff cantilever. A large relative change in the tunneling resistance in response to the applied strain (gauge factor) was observed, up to a value 37. This facilitates local static strain variation measurements down to ~10^{-7}., Comment: 4 pages, 3 figures

We have investigated electronic cooling of suspended nanowires with SINIS tunnel junction coolers. The suspended samples consist of a free standing nanowire suspended by four narrow ($\sim$ 200 nm) bridges. We have compared two different cooler designs for cooling the suspended nanowire. We demonstrate that cooling of the nanowire is possible with a proper SINIS cooler design.

We demonstrate electronic cooling of 1D phonon modes in suspended nanowires for the first time, using normal metal--insulator--superconductor (NIS) tunnel junctions. Simultaneous cooling of both electrons and phonons to a common temperature was achieved. In comparison with non-suspended devices, better cooling performance is achieved in the whole operating range of bath temperatures between 0.1-0.7 K. The observed low-temperature thermal transport characteristics are consistent with scattering of ballistic phonons at the nanowire-bulk contact as being the mechanism limiting thermal transport. At the lowest bath temperature of the experiment $\sim$ 100 mK, both phonons and electrons in the beam were cooled down to 42 mK, which is below the refrigerator bath temperature.

We have investigated theoretically the effects of the charging energy to the normal metal--insulator--superconductor (NIS) tunnel junction used as a thermometer. We demonstrate by numerical calculations how the charging effects modify NIS thermometry, and how the voltage--to--temperature response and the responsivity $|dV/dT|$ of a current biased thermometer are affected. In addition, we show that the responsivity of the thermometer can be modulated with an additional gate electrode. The maximum responsivity is achieved when the Coulomb blockade is maximal, i.e. with a closed gate., Comment: 12 pages, 7 figures

At low temperatures, phonon scattering can become so weak that phonon transport becomes ballistic. We calculate the ballistic phonon conductance G for membranes using elasticity theory, considering the transition from three to two dimensions. We discuss the temperature and thickness dependence and especially concentrate on the issue of material parameters. For all membrane thicknesses, the best conductors have, counter-intuitively, the lowest speed of sound., Comment: 4 pages, 4 figures, proceedings to phonons 2007 conference

We studied experimentally the role of phonon dimensionality on electron-phonon (e-p) interaction in thin copper wires evaporated either on suspended silicon nitride membranes or on bulk substrates, at sub-Kelvin temperatures. The power emitted from electrons to phonons was measured using sensitive normal metal-insulator-superconductor (NIS) tunnel junction thermometers. Membrane thicknesses ranging from 30 nm to 750 nm were used to clearly see the onset of the effects of two-dimensional (2D) phonon system. We observed for the first time that a 2D phonon spectrum clearly changes the temperature dependence and strength of the e-p scattering rate, with the interaction becoming stronger at the lowest temperatures below $\sim$ 0.5 K for the 30 nm membranes., Comment: Phys. Rev. Lett. in press

We propose a mechanism responsible for the abrupt vanishing of the dendritic flux instability found in many superconducting films when an increasing magnetic field is applied. The onset of flux avalanches and the subsequent reentrance of stability in NbN films was investigated using magneto-optical imaging, and the threshold fields were measured as functions of critical current density, $j_c$. The results are explained with excellent quantitative agreement by a thermomagnetic model published recently, Phys. Rev. B73, 014512 (2006), showing that the reentrant stability is a direct consequence of a monotonously decreasing $j_c$ versus field.

We calculate the operating parameters of a transition edge sensor that is mounted on a thin dielectric membrane with the assumption that the phononic heat transport in the membrane is ballistic. Our treatment uses the correct phonon modes from elasticity theory (Lamb-modes), and spans the transition from 3D to 2D behavior. The phonon cooling power and conductance have a global minimum as function of membrane thickness, which leads to an optimal value for the membrane thickness with respect to noise equivalent power at a fixed operating temperature. The energy resolution of a calorimeter will not be affected strongly, but, somewhat counterintuitively, the effective time constant can be reduced by decreasing the membrane thickness in the 2D limit., Comment: 4 pages, 3 figures

We have observed that submicron sized Al--AlO{$_x$}--Al tunnel junctions can be stabilized completely by annealing them in vacuum at temperatures between $350^{\circ}$C and $450^{\circ}$C. In addition, low temperature characterization of the samples after the annealing treatment showed a marked improvement of the tunneling characteristics due to disappearance of unwanted resonances in the current. Charging energy, tunneling resistance, barrier thickness and height all increase after the treatment. The superconducting gap is not affected, but supercurrent is reduced in accordance with the increase of tunneling resistance., Comment: 4 pages, 3 figures

We have studied thermal gradients in thin Cu and AlMn wires, both experimentally and theoretically. In the experiments, the wires were Joule heated non-uniformly at sub-Kelvin temperatures, and the resulting temperature gradients were measured using normal metal-insulator-superconducting tunnel junctions. The data clearly shows that even in reasonably well conducting thin wires with a short ($\sim 10 \mu$m) non-heated portion, significant temperature differences can form. In most cases, the measurements agree well with a model which includes electron-phonon interaction and electronic thermal conductivity by the Wiedemann-Franz law., Comment: J. Low Temp. Phys. in press

We have used normal metal-insulator-superconductor tunnel junctions as thermometers at sub-Kelvin temperatures to study the electron-phonon (e-p) interaction in thin Aluminum films doped with Manganese, as a function of Manganese concentration. Mn in Al is known to be a Kondo impurity with extremely high Kondo temperature $T_K \sim$ 500 K, thus our results probe the e-p coupling in the fully spin compensated, unitary limit. The temperature dependence of the e-p interaction is consistent with the existing theory for disordered metals, however full theory including the Kondo effect has not been worked out yet. The strength of the interaction decreases with increasing Manganese concentration, providing a means to improve sensitivity of detectors and efficiency of solid state coolers.

We have used normal metal-insulator-superconductor (NIS) tunnel junction pairs, known as SINIS structures, for ultrasensitive thermometry at sub-Kelvin temperatures. With the help of these thermometers, we have developed an ac-technique to measure the electron-phonon (e-p) scattering rate directly, without any other material or geometry dependent parameters, based on overheating the electron gas. The technique is based on Joule heating the electrons in the frequency range DC-10 MHz, and measuring the electron temperature in DC. Because of the nonlinearity of the electron-phonon coupling with respect to temperature, even the DC response will be affected, when the heating frequency reaches the natural cut-off determined by the e-p scattering rate. Results on thin Cu films show a $T^{4}$ behavior for the scattering rate, in agreement with indirect measurement of similar samples and numerical modeling of the non-linear response., Comment: to appear in Phys. Stat. Solidi (2005)

We have studied the electron-phonon (e-p) interaction in thin Cu and Au films at sub-Kelvin temperatures with the help of the hot electron effect, using symmetric normal metal-insulator-superconductor tunnel junction pairs as thermometers. By Joule heating the electron gas and measuring the electron and the lattice temperatures simultaneously, we show that the electron-phonon scattering rate follows a $T^{4}$ temperature dependence in both metals. The result is in accordance with the theory of e-p scattering in disordered films with vibrating boudaries and impurities, in contrast to the $T^{3}$-law expected for pure samples, and $T^{2}$-law for static disorder., Comment: to appear in Phys. Stat. Solidi (2005)

We have used symmetric normal metal-insulator-superconductor (NIS) tunnel junction pairs, known as SINIS structures, for ultrasensitive thermometry in the temperature range 50 - 700 mK. By Joule heating the electron gas and measuring the electron temperature, we show that the electron-phonon (e-p) scattering rate in the simplest noble metal disordered thin films (Cu,Au) follows a $T^4$ temperature dependence, leading to a stronger decoupling of the electron gas from the lattice at the lowest temperatures. This power law is indicative e-p coupling mediated by vibrating disorder, in contrast to the previously observed $T^3$ and $T^2$ laws., Comment: 5 pages 4 figures

We present a numerical method to model electric field sensitive scanning probe microscopy measurements which allows for a tip of arbtrary shape and invokes image charges to exactly account for a sample dielectric overlayer. The method is applied to calculate the spatial resolution of a subsurface charge accumulation imaging system, achieving reasonable agreement with experiment., Comment: 5 pages, 3 figures

We have applied a scanning probe method, Subsurface Charge Accumulation (SCA) imaging, to resolve the local structure of the interior of a semiconductor two-dimensional electron system (2DES) in a tunneling geometry. Near magnetic fields corresponding to integer Landau level filling, submicron scale spatial structure in the out-of-phase component of the tunneling signal becomes visible. In the images presented here, the structure repeats itself when the filling factor is changed from nu=6 to nu=7. Therefore, we believe the images reflect small modulations in the 2DES density caused by the disorder in the sample., Comment: 2 pages, 2 color figures, submitted to LT23 proceedings

We have applied a novel scanned probe method to directly resolve the interior structure of a GaAs/AlGaAs two-dimensional electron system in a tunneling geometry. We find that the application of a perpendicular magnetic field can induce surprising density modulations that are not static as a function of the field. Near six and four filled Landau levels, stripe-like structures emerge with a characteristic wave length ~2 microns. Present theories do not account for ordered density modulations on this length scale., Comment: 5 pages, 4 figures. To appear in Phys. Rev. B

We report experiments on the energy structure of antidot-bound states. By measuring resonant tunneling line widths as function of temperature, we determine the coupling to the remote global gate voltage and find that the effects of interelectron interaction dominate. Within a simple model, we also determine the energy spacing of the antidot bound states, self consistent edge electric field, and edge excitation drift velocity., Comment: 4 pages, RevTex, 5 Postscript figures