Evanescent Wave Transport and Shot Noise in Graphene: Ballistic Regime and Effect of Disorder

We have investigated electrical transport and shot noise in graphene field effect devices. In large width over length ratio W/L graphene strips, we have measured shot noise at low frequency (f=600–850 MHz) in the temperature range of 4.2–30 K. We observe a minimum conductivity of $\frac{4e^{2}}{\pi h}$ and a finite and gate dependent Fano factor reaching the universal value of $\frac{1}{3}$ at the Dirac point, i.e. where the density of states vanishes. These findings are in good agreement with the theory describing that transport at the Dirac point should occur via evanescent waves in perfect graphene samples with large W/L. Moreover, we show and discuss how disorder and non-parallel leads affect both conductivity and shot noise.     

Comparing Transition-Edge Sensor Response Times in a Modified Contact Scheme with Different Support Beams

We present measurements of the thermal conductance, G, and effective time constants, \(\tau \) , of three transition-edge sensors (TESs) populated in arrays operated from 80–87 mK with T \(_\mathrm{C}\)   \(\sim \)  120 mK. Our TES arrays include several variations of thermal architecture enabling determination of the architecture that demonstrates the minimum noise equivalent power, the lowest \(\tau \) , and the trade-offs among designs. The three TESs we report here have identical Mo/Cu bilayer thermistors and wiring structures, while the thermal architectures are: (1) a TES with straight support beams of 1 mm length, (2) a TES with meander support beams of total length 2 mm and with two phonon-filter blocks per beam, and (3) a TES with meander support beams of total length 2 mm and with six phonon-filter blocks per beam. Our wiring scheme aims to lower the thermistor normal state resistance R \(_{N}\) and increase the sharpness of the transition \(\alpha =\)  dlogR/dlogT at the transition temperature T \(_\mathrm{C}\) . We find an upper limit of \(\alpha \) given by ( \(25\pm 10\) ), and G values of 200 fW/K for (1), 15 fW/K for (2), and 10 fW/K for (3). The value of \(\alpha \) can be improved by slightly increasing the length of our thermistors.     

Thermal Properties of Two Materials Commonly Used in Low Temperature Laboratories

We carried out measurements of thermal conductance and thermal contact resistance of two materials commonly used in low temperature laboratories such as an Electro-Magnetic Interference (EMI) Filter and Stycast 2850 FT epoxy. Both samples were attached on a heat sink made of oxygen-free high thermal conductivity (OFHC) copper and characterized at temperatures between 0.3 K and 4.5 K, using a ³He refrigerator mounted on a pumped ⁴He cryostat. For the EMI filter we applied a varied input power from 0.25 up to 50 μW to the heater which is soldered to its central pin, whereas for a thin layer of Stycast sandwiched between a copper strap and the heat sink we applied an input power from 10 up to 810 μW. The temperature dependences obtained in each case were $K=3\,{\cdot}\,10^{-5}T^{2.3}~[\frac{\mathrm{W}}{\mathrm{K}}]$ , and $R_{K}=8.4\,{\cdot}\,10^{-3}T^{1.7}\ [\frac{\mathrm{W}}{\mathrm{cm}^{2}\,\mathrm{K}}]$ respectively.     

Effect of the Substrate on Phonon Properties of Graphene Estimated by Raman Spectroscopy

Low-temperature Raman studies of supported graphene are presented. A linear temperature dependence of 2D peak linewidths was observed with the coefficients of 0.036 and 0.033 cm\(^{-1}\)/K for graphene on copper and glass substrates, respectively, while G peak linewidths remained unchanged throughout the whole temperature range. The different values observed for graphene on glass and copper substrates were explained in terms of the substrate effect on phonon–phonon and electron–phonon interaction properties of the material. The results of the present study can be used to consider substrate effects on phonon transport in graphene for nanoelectronic device engineering.     

Measurement on the Thermal Properties of Graphene Powder

We report on an in-plane thermal diffusivity study of suspended graphene powder (GP) measured by the transient electro-thermal (TET) technique. The GP with a density of 0.24 \(\hbox {g}\,\cdot \,\hbox {cm}^{-3}\) is made up of five–six-layer graphene. And the average size of graphene flakes used in our study is 0.98 \(\upmu \)m. The intrinsic thermal conductivity perpendicular to in-plane of GP is determined at 18.8 \(\hbox {W}\,\cdot \,(\hbox {m}\,\cdot \,\hbox {K})^{-1}\) using the thermal conductivity instrument, and the range of the in-plane thermal diffusivity of GP is identified from \(0.86\times 10^{-5 }\,\hbox {m}^{2 }\,\cdot \,\hbox {s}^{-1}\) to \(1.52\times 10^{-5 }\,\hbox {m}^{2}\,\cdot \,\hbox {s}^{-1}\) measured by the TET technique. Accordingly, the corresponding intrinsic thermal conductivity is 13.5 \(\hbox {W}\,\cdot \,(\hbox {m}\,\cdot \,\hbox {K})^{-1}\)–23.8 \(\hbox {W}\,\cdot \,(\hbox {m}\,\cdot \,\hbox {K})^{-1}\). It is obvious that the two methods used in the experimental research on the intrinsic thermal conductivity of GP in different directions are not only the same order of magnitude but also have a maximum difference of only 5 \(\hbox {W}\,\cdot \,(\hbox {m}\,\cdot \,\hbox {K})^{-1}\). The results of our experiments are about one order of magnitude lower than those reported for four–five-layer graphene. There are various porosities in the whole sample after the compaction steps in the preparation of the samples, which gives rise to a large thermal contact resistance. And widely uneven surface defects observed under an optical microscope for the studied GP lead to substantial phonon scattering. Those factors combine together to give the observed significant reduction in the thermal conductivity.     

Photon-Noise Limited Performance in Aluminum LEKIDs

We have measured noise in aluminum lumped element kinetic inductance detectors (LEKIDs) in dark conditions at different base temperatures and with optical illumination from a variable temperature blackbody source. LEKIDs are photon-sensitive superconducting resonators coupled to planar transmission lines. We convert variations in the raw in-phase ( \(e_I\) ) and quadrature ( \(e_Q\) ) signals from a fixed frequency source transmitted through a transmission line coupled to the LEKID into a measure of the fluctuation in the resonant frequency of the LEKID ( \(e_f\) ) using the measured electrical response of the resonator to a swept frequency source. We find that the noise of the LEKID in the dark has a constant frequency fluctuation level, \(e_f^0\) which is rolled off at a base temperature-dependent frequency corresponding to the quasiparticle lifetime in the device. Above this frequency, the noise is dominated by amplifier noise at a level a factor of 2–10 times lower than the low frequency white noise level depending on the quality factor of the resonator. The amplitude of this noise and the frequency cutoff agree well with the expected frequency flucution level from generation and recombination of thermal quasiparticles from a simple Mattis–Bardeen model. When we illuminate the device with a variable temperature blackbody source through a bandpass filter centered at a frequency of 150 GHz, we observe a reduction in the quasiparticle lifetime and an increase in the level of frequency fluctuation noise as the blackbody temperature is increased. This indicates that the quasiparticle number is dominated by optically generated quasiparticles and that the noise in the device is dominated by photon noise.     

Effective Thermal-Conductivity Measurement on Germanate Glass–Ceramics Employing the 3\omega Method at High Temperature

It can be noted that the germanate glass–ceramic is a functional material with excellent thermal stability which can be used in optical devices. The temperature-dependent effective thermal conductivities of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) glass–ceramics from 295.5 K to 780 K are determined using a \(3\omega \) method. One of the main advantages for the \(3\omega \) method is to diminish radiation errors effectively when the temperature is as high as 1000 K. Thermal conductivities of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) increase with a rise in temperature. Effective thermal conductivities of a sample increase from \(1.55~\hbox {W}\cdot \hbox {m}^{-1}\cdot \hbox {K}^{-1}\) at 295.5 K to \(7.64~\hbox {W}\cdot \,\hbox {m}^{-1}\cdot \hbox {K}^{-1}\) at 698.1 K. The effective thermal conductivity of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) glass–ceramic increases with a rise of temperature. This investigation can be used as a basis for the measurement of thermal properties of ceramic materials at higher temperature.     

Correlation on the Electrical and Thermal Conductivity for Binary Mg–Al and Mg–Zn Alloys

In this work, the electrical resistivity and thermal conductivity of both as-solution binary Mg–Al and Mg–Zn alloys were investigated from 298 K to 448 K, and the correlation between the corresponding electrical conductivity and thermal conductivity of the alloys was analyzed. The electrical resistivity of the Mg–Al and Mg–Zn alloys increased linearly with composition at 298 K, 348 K, 398 K, and 448 K, while the thermal conductivity of the alloys exponentially decreased with composition. Moreover, the electrical resistivity and thermal conductivity for both Mg–Al and Mg–Zn alloys varied linearly with temperature. On the basis of the Smith–Palmer equation, the thermal conductivity of both binary Mg alloys was found to be correlated quite well with the electrical conductivity in the temperature range from 298 K to 448 K. The corresponding Lorenz number is equal to $2.162\times 10^{-8} \,\hbox {V}^{2}\cdot \hbox {K}^{-2}$ 2.162 × 10 - 8 V 2 · K - 2 , and the lattice thermal conductivity is equal to $5.111 \,\hbox {W}\cdot \hbox {m}^{-1}\cdot \hbox {K}^{-1}$ 5.111 W · m - 1 · K - 1 . The possible mechanisms are also discussed.     

Quartz Tuning Forks as Cryogenic Vacuum Gauges

We report measurements of the mechanical \(Q\) of a 32.7 kHz quartz tuning fork as a function of pressure for helium and argon at T  \(=\)  300 K and for helium in the temperature range 7.0–0.7 K. In the low pressure ballistic regime, the damping due to the surrounding gas is inversely proportional to \(P\) , while for higher pressures, a hydrodynamic treatment accounts for most of the variation of \(Q\) with \(P\) . We have combined the ballistic and hydrodynamic models together with calculations of the thermal transpiration correction to correlate the tuning fork \(Q\) at low temperature with the pressure measured with a room temperature pressure gauge. The fork was found to be useful as an in situ pressure gauge for pressures above \(\sim \) 0.1 mTorr. A dissipation peak and frequency drop associated with the superfluid transition in the adsorbed helium film is also observed for \(T<1.4\)  K.     

Toward a Detector/Readout Architecture for the Background-Limited Far-IR/Submm Spectrograph (BLISS)

We have built and tested 32-element linear arrays of absorber-coupled transition-edge sensors (TESs) read out with a time-division SQUID multiplexer. This detector/readout architecture is designed for the background-limited far-IR/submm spectrograph (BLISS) which is a broadband (35–433  \(\upmu \) m), grating spectrometer consisting of six wavebands each with a modest resolution of R \(\sim \) 700. Since BLISS requires the effective noise equivalent power (NEP) of the TESs to equal 1  \(\times \)  10 \(^{-19}\)  W/Hz \(^{1/2}\) , our detectors consist of very long (1–2 mm), narrow (0.4 \(\upmu \) m), and thin (0.25 \(\upmu \) m) Si \(_{x}\) N \(_{y}\) support beams that reduce the thermal conductance G between the substrate and the optical absorber. The thermistors of our lowest noise TESs consist of iridium with \(T_{c}=130\) mK. We have measured the electrical properties of arrays of these Ir TESs with various meander and straight support beams and absorber shapes and found that G is \(\sim \) 30 fW/K (meander) and \(\sim \) 110 fW/K (straight), the electrical NEP is 2–3  \(\times \)  10 \(^{-19}\) W/Hz \(^{1/2}\) (meander and straight), and the response time \(\tau \) is 10–30 ms (meander) and 2–5 ms (straight). To reduce spurious or “dark” power from heating the arrays, we mounted the arrays into light-tight niobium boxes and added custom L/R and L/C low-pass chip filters into these boxes to intercept dark power from the bias and readout circuit. We found the average dark power equals 1.3 and 4.6 fW for the boxes with L/R and L/C chip filters, respectively. We have built arrays with \(T_{c}= 70\)  mK using molybdenum/copper bilayers and are working to lower the dark power by an order of magnitude so we can demonstrate NEP \(~=~1~\times \)  10 \(^{-19}\)  W/Hz \(^{1/2}\) with these arrays. PACS numbers: 85.25.Pb; 95.85.Gn; 95.85.Fm; 63.22. \(+\) m     

Development of Microwave Kinetic Inductance Detectors for a Detection of Phonons

We present a status of the development of microwave kinetic inductance detectors (MKIDs) for a detection of athermal phonons in a substrate. The energy deposited in the substrate is converted to athermal phonons. Athermal phonons arriving at the surface can break Cooper pairs in the MKIDs which are formed as a thin superconducting metal layer in the substrate surface. By counting the number of Cooper pairs broken and measuring the phonon arrival times, we can measure the amount of deposited energy and its position. MKIDs are suitable for the frequency-domain multiplexing readout, which enables us to readout hundreds of pixels simultaneously and, hence, to detect athermal phonons with a large detection efficiency. We fabricated MKIDs with a combination of aluminum and niobium on a silicon substrate, and then irradiated it with \(\alpha \) particles from an \(^{241}\) Am source. We detected phonons and made a rough estimation of the phonon propagation velocity of 1.1–1.3 km/s. We found that a thin insulator layer can block the phonon propagation from the substrate to the thin metal layer.     

Thermal-Conductivity Measurements of Aqueous Orthophosphoric Acid Solutions in the Temperature Range from (293 to 400) K and at Pressures up to 15 MPa

A new improved guarded parallel-plate thermal-conductivity cell for absolute measurements of corrosive (chemically aggressive) fluids under pressure has been developed. Using the new modified guarded parallel-plate apparatus the thermal conductivity of aqueous orthophosphoric acid solutions was measured over the temperature range from (293 to 400) K and pressures up to 15 MPa. Measurements were made for three compositions of \(\text {H}_{3}\text {PO}_{4}\) (8 mass%, 15 mass%, and 50 mass%) along three isobars of (0.101, 5, and 15) MPa. The combined expanded uncertainty of the thermal-conductivity \((\lambda )\) measurements at the 95 % confidence level with a coverage factor of \(k=2\) is estimated to be 2 %. The uncertainties of the temperature, pressure, and concentration measurements were 15 mK, 0.05 %, and 0.01 %, respectively. The temperature, concentration, and pressure dependences of the thermal conductivity of the solution were studied. The measured values of thermal conductivity were compared with the available reported data and the values calculated from various correlation and prediction models. A new wide-range correlation model (extended Jones–Dole type equation with pressure-dependent coefficients) for the \(\text {H}_{3}\text {PO}_{4}\) (aq) solution was developed using the present experimental data.     

Ab Initio Transport Coefficients of Gaseous Hydrogen

The spherical version of the hydrogen intermolecular potential ${\phi_{\rm P}}$ recently determined in ab initio calculations by Patkowski et al. was used to calculate the viscosity and thermal conductivity of hydrogen using a full quantum-mechanical formalism. Viscosities in the temperature range 203 K to 394 K were compared with recent high-accuracy (uncertainty of 0.084 %) measurements of May et al. The measured viscosities all fall in a range between 0.02 % and 0.06 % below the calculated viscosities. This close agreement supports the accuracy of ${\phi_{\rm P}}$ . Classical calculations of the viscosity with ${\phi_{\rm P}}$ fall in a range between 0.4 % and 1.3 % below the experimental values. In the lower temperature range 20 K to 300 K, other measurements typically lie above the theoretical values by a few percent. Above 400 K, measurements fall below the theoretical values by a fraction that increases with temperature, reaching ?4% at 2000 K. For normal hydrogen, the average fractional difference between the calculated thermal conductivity in the temperature range 21 K to 384 K and measurements reported in six publications is (0.1 ± 1.1) %. For para-hydrogen in the temperature range 20 K to 275 K, the average fractional difference between calculations and measurements reported in three publications is (?0.7 ± 1.2) %. At higher temperatures (600 K to 2000 K), measurements range between 4 % and 10 % below the calculated values.     

Characterization of Low Noise TES Detectors Fabricated by D-RIE Process for SAFARI Short-Wavelength Band

SRON is developing TES detectors based on a superconducting Ti/Au bilayer on a suspended SiN membrane for the short-wavelength band of the SAFARI instrument on SPICA mission. We have recently replaced the wet KOH etching of the Si substrate by deep reactive ion etching. The new process enables us to fabricate the detectors on the substrate and release the membrane at the very last step. Therefore the production of SAFARI large arrays (43 \(\,{\times }\,\) 43) on thin SiN membrane (250 nm) is feasible. It also makes it possible to realize narrow supporting SiN legs of \(\le \) 1 \(\upmu \) m, which are needed to meet SAFARI NEP requirements. Here we report the current–voltage characteristics, noise performance and impedance measurement of these devices. The measured results are then compared with the distributed leg model that takes into account the thermal fluctuation noise due to the SiN legs. We measured a dark NEP of \(\sim \) 0.7 aW/ \(\sqrt{\hbox {Hz}}\) , which is 1.6 times higher than the theoretically expected phonon noise.     

Accurate Simulations of ^{206}Pb Recoils in SuperCDMS

SuperCDMS is a direct detection search for WIMPs, currently operating a 9 kg array of germanium detectors in the Soudan Underground Laboratory. The detectors, known as iZIPs, are cylindrical in shape and each flat surface is instrumented with both ionization and phonon sensors. Charge and phonon information is collected for each event, and comparing the energy collected in the phonon sensors to the charge sensors gives excellent discrimination power between nuclear recoil and electron recoil events. Furthermore, this technology provides excellent discrimination between surface and bulk events. In order to show the surface event rejection capability of these detectors, two \(^{210}\) Pb sources were installed facing two of the detectors currently operating in the Soudan experimental run. The \(^{210}\) Pb decays to \(^{210}\) Bi, which in turn decays to \(^{210}\) Po. The \(^{210}\) Po decays by alpha emission, yielding a recoiling \(^{206}\) Pb ion with 103 keV kinetic energy and an alpha particle with 5.4 MeV kinetic energy. We used the non-standard Screened Nuclear Recoil Physics List (Mendenhall and Weller, Nucl. Instrum. Methods Phys. Res. B 227:420–430, 2005) in Geant4 (Agostinelli et al., Nucl. Instrum. Methods Phys. Res. Sect. A 506:250–303, 2003) to simulate all of the above decays and achieve excellent agreement with experiment. The focus of this paper is the simulation of the \(^{210}\) Po decay.     

A Microkelvin Magnetic Flux Noise Thermometer

Due to its non-driven nature, noise thermometry intrinsically is the method of choice when minimal heat input during the temperature measurement is required. Our noise thermometer, experimentally characterized for temperatures between 42  ${{\upmu }}$ K and 0.8 K, is a magnetic Johnson noise thermometer. The noise source is a cold-worked high purity copper cylinder, 5 mm in diameter and 20 mm long. The magnetic flux fluctuations generated by the electrons’ Brownian motion is measured inductively by two dc-SQUID magnetometers simultaneously. Cross-correlation of the two channels leads to reduction of parasitic noise by more than one order of magnitude which allows for measuring the tiny noise powers at microkelvin temperatures.     

Experimental Study of the Density and Viscosity of n-Heptane at Temperatures from 298 K to 470 K and Pressure upto 245 MPa

The density and viscosity of $n$ -heptane have been simultaneously measured over the temperature range from 298 K to 470 K and at pressures up to 245 MPa using the hydrostatic weighing and falling-body techniques, respectively. The expanded uncertainty of the density, pressure, temperature, and viscosity measurements at the 95 % confidence level with a coverage factor of $k= 2$ is estimated to be 0.15 % to 0.30 %, 0.05 %, 0.02 K, and 1.5 % to 2.0 % (depending on temperature and pressure ranges), respectively. The measured densities were used to develop a Tait-type equation of state for liquid $n$ -heptane. Theoretically based Arrhenius–Andrade and Vogel–Tamman–Fulcher type equations with pressure-dependent coefficients were used to describe the temperature and pressure dependences of the measured viscosities for liquid $n$ -heptane. The measured values of the density and viscosity were compared in detail with reported data and with the values calculated from a reference EOS and correlation models for the viscosity.     

112-Pixel Arrays of High-Efficiency STJ X-Ray Detectors

We are developing the next generation of high-resolution high-speed X-ray detectors based on superconducting tunnel junctions (STJs). They consist of 112-pixel arrays of 208  \(\mu \) m \(\times \) 208  \(\mu \) m Ta–Al– \({\text {AlO}}_x\) –Al–Ta tunnel junctions whose Ta absorber increases the detection efficiency compared to earlier Nb-based STJs. To read out these medium size detector arrays we have also developed a compact and scalable 32-channel preamplifier with an input voltage noise \(<\) 1 nV/ \(\surd \) Hz and a dc voltage bias for stable STJ operation between Fiske mode resonances. The pixels have a uniform response across the array, an energy resolution between 7.5 and 9.5 eV FWHM at 525 eV, and can be operated at several 1,000 counts/s per pixel.     

First-principles study of heat transport properties of graphene nanoribbons

We use density-functional theory and the nonequilibrium Green's function method as well as phonon dispersion calculations to study the thermal conductance of graphene nanoribbons with armchair and zigzag edges, with and without hydrogen passivation. We find that low-frequency phonon bands of the zigzag ribbons are more dispersive than those of the armchair ribbons and that this difference accounts for the anisotropy in the thermal conductance of graphene nanoribbons. Comparing our results with data on large-area graphene, edge effects are shown to contribute to thermal conductance, enhance the anisotropy in thermal conductance of graphene nanoribbons, and increase thermal conductance per unit width. The edges with and without hydrogen passivation modify the atomic structure and ultimately influence the phonon thermal transport differently for the two ribbon types.     

Photopyroelectric Calorimetry of \hbox {Fe}_{3}\hbox {O}_{4} Magnetic Nanofluids: Effect of Type of Surfactant and Magnetic Field

Five types of magnetic nanofluids, based on \(\hbox {Fe}_{3}\hbox {O}_{4}\) nanoparticles with water as the carrier liquid, were investigated by using the two photopyroelectric (PPE) detection configurations (back (BPPE) and front (FPPE)), together with the thermal-wave resonator cavity (TWRC) technique as the scanning procedure. The difference between the nanofluids was the type of surfactant: double layers of lauric (LA–LA), oleic (OA–OA), and miristic (MA–MA) acids and also double layers of lauric–miristic (LA–MA) and palmitic-oleic (PA–OA) fatty acids were used. In both detection configurations, the information was contained in the phase of the PPE signal. The thermal diffusivity of nanofluids was obtained in the BPPE configuration, from the scan of the phase of the signal as a function of the liquid’s thickness. Using the same scanning procedure in the FPPE configuration, the thermal effusivity was directly measured. The influence of a 0.12 kG magnetic field on the thermal effusivity and thermal diffusivity was also investigated. Because of different surfactants, the thermal effusivity of the investigated nanofluids ranges from \(1530\,\hbox {W}\cdot \hbox {s}^{1/2} \cdot \hbox { m}^{-2}\cdot \hbox { K}^{-1}\) to \(1790\,\hbox { W}\cdot \hbox {s}^{1/2}\cdot \hbox { m}^{-2}\cdot \hbox { K}^{-1}\) , and the thermal diffusivity, from \(14.54~\times ~10^{-8}\,\hbox { m}^{2}\cdot \hbox { s}^{-1}\) to \(14.79~\times ~10^{-8}\,\hbox { m}^{2}\cdot \hbox { s}^{-1}\) . The magnetic field has practically no influence on the thermal effusivity, and produces a maximum increase of the thermal diffusivity (LA–LA surfactant) of about 4 %.