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Electronic Transport In Mesoscopic Systems

Topological states of matter are characterized by topological invariants, which are physical quantities whose values are quantized and do not depend on the details of the system (such as its shape, size and impurities). Of these quantities, the easiest to probe is the electrical Hall conductance, and fractional values (in units of e2/h, where e is the electronic charge and h is the Planck constant) of this quantity attest to topologically ordered states, which carry quasiparticles with fractional charge and anyonic statistics. Another topological invariant is the thermal Hall conductance, which is harder to measure. For the quantized thermal Hall conductance, a fractional value in units of κ0 (κ0 = π2kB2/(3h), where kB is the Boltzmann constant) proves that the state of matter is non-Abelian. Such non-Abelian states lead to ground-state degeneracy and perform topological unitary transformations when braided, which can be useful for topological quantum computation. Here we report measurements of the thermal Hall conductance of several quantum Hall states in the first excited Landau level and find that the thermal Hall conductance of the 5/2 state is compatible with a half-integer value of 2.5κ0, demonstrating its non-Abelian nature.

Observation of half-integer thermal Hall conductance

The "textbook" phonon mean free path of heat carrying phonons in silicon at room temperature is ∼40  nm. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range ∼1-10  μm. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.

Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

Photothermal catalysis is an emerging sub-discipline of heterogeneous catalysis. It is distinct from both thermochemical catalysis driven by heat and photochemical catalysis powered by sunlight. Instead, photothermal catalysis exploits broad absorption of the solar spectrum to stimulate a combination of thermochemical and photochemical processes, which contribute synergistically to driving catalytic reactions. In particular, it is proving an effective and promising strategy for converting CO2 to synthetic fuels. This article provides a critical appraisal of the concepts and principles underpinning the theory and practice of photothermal CO2 catalysis. Ultimately, the goal is to gain an appreciation of the scientific, technological, economic, and environmental challenges inevitably confronted by those pursuing the development of photothermal CO2 refineries.

Principles of photothermal gas-phase heterogeneous CO2 catalysis

Photo-thermal catalysis has recently emerged as an alternative route to drive chemical reactions using light as an energy source. Through the synergistic combination of photo- and thermo-chemical contributions of sunlight, photo-thermal catalysis has the potential to enhance reaction rates and to change selectivity patterns, even under moderate operation conditions. This review provides the fundamentals of localized surface plasmon resonance (LSPR) that explain the photo-thermal effect in plasmonic structures, describes the different mechanistic pathways underlying photo-thermal catalysis, suggests methodologies to disentangle the reaction mechanisms and proposes material design strategies to improve photo-thermal performance. Ultimately, the goal is to pave the way for the wide implementation of this promising technology in the production of synthetic fuels and chemicals.

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Fundamentals and applications of photo-thermal catalysis.

Imaging temperature fields at the nanoscale is a central challenge in various areas of science and technology. Nanoscopic hotspots, such as those observed in integrated circuits or plasmonic nanostructures, can be used to modify the local properties of matter, govern physical processes, activate chemical reactions and trigger biological mechanisms in living organisms. The development of high-resolution thermometry techniques is essential for understanding local thermal non-equilibrium processes during the operation of numerous nanoscale devices. Here we present a technique to map temperature fields using a scanning thermal microscope. Our method permits the elimination of tip-sample contact-related artefacts, a major hurdle that so far has limited the use of scanning probe microscopy for nanoscale thermometry. We map local Peltier effects at the metal-semiconductor contacts to an indium arsenide nanowire and self-heating of a metal interconnect with 7 mK and sub-10 nm spatial temperature resolution.

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Temperature mapping of operating nanoscale devices by scanning probe thermometry.

A method for determining charge carrier concentration, mobility, and relaxation time in semiconducting nanowires is presented. The method is based on measuring both the electrical conductivity and the Seebeck coefficient of the nanowire. With knowledge on the bandstructure of the material, Fermi level and charge carrier concentration can be deduced from the Seebeck coefficient. The ratio of measured conductivity and inferred charge carrier concentration then leads to the mobility, and using the Fermi level dependence of mobility one can finally obtain the relaxation time. Using this approach we exemplarily analyze the characteristics of an n-type InAs nanowire.

Using the Seebeck coefficient to determine charge carrier concentration, mobility, and relaxation time in InAs nanowires

We have measured the thermopower and the thermal conductivity of individual silicon and indium arsenide nanowires (NWs). In this study, we evaluate a self-heating method to determine the thermal conductivity λ. Experimental validation of this method was performed on highly n-doped Si NWs with diameters ranging from 20 nm to 80 nm. The Si NWs exhibited electrical resistivity of \(\rho = (8\pm4)\, \hbox{m}\Upomega\,\hbox{cm}\) at room temperature and Seebeck coefficient of −(250 ± 100) μV/K. The thermal conductivity of Si NWs measured using the proposed method is very similar to previously reported values; e.g., for Si NWs with 50 nm diameter, λ = 23 W/(m K) was obtained. Using the same method, we investigated InAs NWs with diameter of 100 nm and resistivities of \(\rho = (25\pm5)\, \hbox{m}\Upomega\,\hbox{cm}\) at room temperature. Thermal conductivity of λ = 1.8 W/(m K) was obtained, which is about 20 to 30 times smaller than in bulk InAs. We analyzed the accuracy of the self-heating method by means of analytical and numerical solution of the one-dimensional (1-D) heat diffusion equation taking various loss channels into account. For our NWs suspended from the substrate with low-impedance contacts the relative error can be estimated to be ≤25%.

Measurement of Thermoelectric Properties of Single Semiconductor Nanowires

The most direct definition of a patterning process' resolution is the smallest half-pitch feature that is capable of transferring onto the substrate. Here, the authors demonstrate that thermal scanning probe lithography (t-SPL) is capable of fabricating dense line patterns in silicon and metal lift-off features at sub-20 nm feature size. The dense silicon lines were written at a half pitch of 18.3 nm to a depth of 5 nm into a 9 nm polyphthalaldehyde thermal imaging layer by t-SPL. For processing, the authors used a three-layer stack comprising an evaporated SiO2 hardmask, which is just 2–3 nm thick. The hardmask is used to amplify the pattern into a 50 nm thick polymeric transfer layer. The transfer layer subsequently serves as an etch mask for transfer into silicon to a depth of ≈65 nm. The line edge roughness (3σ) was evaluated to be less than 3 nm both in the transfer layer and in silicon. The authors also demonstrate that a similar three-layer stack can be used for metal lift-off of high resolution patterns. A device application is demonstrated by fabricating 50 nm half pitch dense nickel contacts to an InAs nanowire.

Sub-20 nm silicon patterning and metal lift-off using thermal scanning probe lithography

Frequency modulated Kelvin probe force microscopy (FM-KFM) is the method of choice for high resolution measurements of local surface potentials, yet on coarse topographic structures most researchers revert to amplitude modulated lift-mode techniques for better stability. This approach inevitably translates into lower lateral resolution and pronounced capacitive averaging of the locally measured contact potential difference. Furthermore, local changes in the strength of the electrostatic interaction between tip and surface easily lead to topography crosstalk seen in the surface potential. To take full advantage of the superior resolution of FM-KFM while maintaining robust topography feedback and minimal crosstalk, we introduce a novel FM-KFM controller based on a Kalman filter and direct demodulation of sidebands. We discuss the origin of sidebands in FM-KFM irrespective of the cantilever quality factor and how direct sideband demodulation enables robust amplitude modulated topography feedback. Finally, we demonstrate our single-scan FM-KFM technique on an active nanoelectronic device consisting of a 70 nm diameter InAs nanowire contacted by a pair of 120 nm thick electrodes.

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Philipp Mensch

Papers

Temperature mapping of operating nanoscale devices by scanning probe thermometry.

Using the Seebeck coefficient to determine charge carrier concentration, mobility, and relaxation time in InAs nanowires

Measurement of Thermoelectric Properties of Single Semiconductor Nanowires

Sub-20 nm silicon patterning and metal lift-off using thermal scanning probe lithography

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices