The Boltzmann transport equation for phonons is recast directly in terms of the heat-flux by means of iteration followed by truncation at the second order in the spherical harmonic expansion of the distribution function. This procedure displays the heat-flux in an explicitly coordinate-invariant form, and leads to a natural decomposition into two components, namely the solenoidal component in addition to the usual irrotational component. The solenoidal heat-flux is explicitly shown to arise by applying the heat-flux equation to a right-circular cylinder. These findings are important in the context of phonon resonators that utilize the strong quasi-ballistic thermal transport reported recently in silicon membranes at room temperature.
For a thermal conductivity that is spatially uniform and independent of temperature, Fourier's law of heat transfer predicts a curl-free heat-flux. In the quasi-ballistic phonon transport regime, where the Fourier law breaks down, it has been proven starting from the Boltzmann transport equation that the constitutive relation for the heat-flux contains a solenoidal (circulatory) term with zero divergence and non-zero curl. In this paper we show how to reduce the effective thermal conductivity of a material with dimensions on the same scale as the phonon mean-free path, by exploiting the soleno…
In this article, we show how relativistic alpha stable processes can be used to explain quasi-ballistic heat conduction in semiconductors. This is a method that can fit experimental results of ultrafast laser heating in alloys. It also provides a connection to a rich literature on Feynman-Kac formalism and random processes that transition from a stable Lévy process on short time and length scales to the Brownian motion at larger scales. This transition was captured by a heuristic truncated Lévy distribution in earlier papers. The rigorous Feynman-Kac approach is used to derive sharp bounds for…
Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here we show that in viscous flows interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit $G_{\rm ball}$. The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum-mechanical ballistic transport at $T=0$ but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodyn…
The influence of ballistic channels superimposed on tunneling conduction channels in magnetic tunnel junctions has been studied in a manganese oxide based tunneling device. Inversion of magnetoresistance has been observed in magnetic tunnel junctions with pinhole nanocontacts over a broad temperature range. The tunnel magnetoresistance undergoes a change of sign at higher bias and temperature. This phenomenon is attributed to the parallel conduction channels consisting of spin conserved ballistic transport through the pinhole contact where the transmission probability is close to unity and spi…
Future of silicon-based microelectronics relies on solving the heat dissipation problem. A solution may lie in a nanoscale phenomenon known as ballistic heat conduction, which implies heat conduction without heating the conductor. But, attempts to demonstrate this phenomenon experimentally are controversial and scarce whereas its mechanism in confined nanostructures is yet to be fully understood. Here, we experimentally demonstrate quasi-ballistic heat conduction in silicon nanowires (NWs). We show that the ballisticity is strongest in short NWs at low temperatures but weakens as the NW length…
Previous studies have predicted the failure of Fourier's law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by this phenomenon. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two (three) dimensional s…
It is well-known that in the disordered harmonic chain, heat conduction is subballistic and the thermal conductivity ($κ$) scales asymptotically as $\lim_{L\rightarrow\infty}κ\propto L^{0.5}$ where $L$ is the chain length. However, using the nonequilibrium Green's function (NEGF) method and analytical modeling, we show that there exists a critical crossover length scale ($L_{C}$) below which ballistic heat conduction ($κ\propto L$) can coexist with mass disorder. This ballistic-to-subballistic heat conduction crossover is connected to the exponential attenuation of the phonon transmittance fun…
Rational design of artificial lattices yields effects unavailable in simple solids, and vertical superlattices of multilayer semiconductors are already used in optical sensors and emitters. Manufacturing lateral superlattices remains a much bigger challenge, with new opportunities offered by the use of moire patterns in van der Waals heterostructures of graphene and hexagonal crystals such as boron nitride (h-BN). Experiments to date have elucidated the novel electronic structure of highly aligned graphene/h-BN heterostructures, where miniband edges and saddle points in the electronic dispersi…
The general isotropic constitutive equations of heat conduction with second sound and ballistic propagation in isotropic materials is given using Non-Equilibrium Thermodynamics with Internal Variables (NET-IV). The consequences of Onsager reciprocity between thermodynamic fluxes and forces and positive definiteness of the entropy production is considered. The relation to theories of Extended Thermodynamics is discussed in detail.
We propose to use l_0/(l_0+L) for the energy transmission covering both ballistic and diffusive regimes, where l_0 is mean free path and L is system length. This formula is applied to heat conduction in carbon nanotubes (CNTs). Calculations of thermal conduction show: (1) Thermal conductance at room temperature is proportional to the diameter of CNTs for single-walled CNTs (SWCNTs) and to the square of diameter for multi-walled CNTs (MWCNTs). (2) Interfaces play an important role in thermal conduction in CNTs due to the symmetry of CNTs vibrational modes. (3) When the phonon mean free path is …
Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a thermo-mechanical model in which the generalized heat equation - the so-called Maxwell-Cattaneo-Vernotte equation - is coupled to thermal expansion. At the same time, the other one uses internal variables. For the first one, we developed a numerical solution and tested on the heat pulse experiment performed by McNelly et al.~on NaF samples. For the second one…
We explore ballistic regime quantum transport characteristics of oxide-embedded crossing and kinked silicon nanowires (NWs) within a large-scale empirical pseudopotential electronic structure framework, coupled to the Kubo-Greenwood transport analysis. A real-space wave function study is undertaken and the outcomes are interpreted together with the findings of ballistic transport calculations. This reveals that ballistic transport edge lies tens to hundreds of millielectron volts above the lowest unoccupied molecular orbital, with a substantial number of localized states appearing in between, …
Long-distance propagation of heat carriers is essential for efficient heat dissipation in microelectronics. However, in dielectric nanomaterials, the primary heat carriers - phonons - can propagate ballistically only for hundreds of nanometres, which limits their heat conduction efficiency. Theory predicts that surface phonon-polaritons (SPhPs) can overcome this limitation and conduct heat without dissipation for hundreds of micrometres. In this work, we experimentally demonstrate such long-distance heat transport by SPhPs. Using the 3$ω$ technique, we measure the in-plane thermal conductivity…
We will study the competitive effect between the transport of a quantum dot adsorbed to a ballistic channel and laterally coupled to a single-walled carbon nanotube (SWNT). We will use the tight-binding approach to analytically write the SWNT Green function and the quantum dot will be solved by the atomic method for U very large. We will present curves of the electronic density of states for some different sizes of nanotubes. The results for the conductance curves will be presented as a function of Ef and for different values of n and hopping between the nanotube and the quantum dot.
The minimization of electronics makes heat dissipation of related devices an increasing challenge. When the size of materials is smaller than the phonon mean free paths, phonons transport without internal scatterings and laws of diffusive thermal conduction fail, resulting in significant reduction in the effective thermal conductivity. This work reports, for the first time, the temperature dependent thermal conductivity of doped epitaxial 6H-SiC and monocrystalline porous 6H-SiC below room temperature probed by time-domain thermoreflectance. Strong quasi-ballistic thermal transport was observe…
In a mesoscopic conductor electric resistance is detected even if the device is defect-free. We engineer and study a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induce a current through the channel and find ohmic conduction, even for a ballistic channel. An analysis of in-situ density distributions shows that in the ballistic case the chemical potential drop occurs at the entrance and exit of the channel, revealing the presence of contact resistance. In contras…
A ballistic strip of graphene (width W>> length L) connecting two normal metal contacts is known to have a minimum conductivity of 4e^{2}/pi h at the Dirac point of charge neutrality. We calculate what happens if one of the two contacts becomes superconducting. While the ballistic conductance away from the Dirac point is increased by Andreev reflection at the normal-superconductor (NS) interface, we find that the minimum conductivity stays the same. This is explained as a manifestation of pseudo-diffusive conduction at the Dirac point. As a generalization of our results for a ballistic system,…
We report the observation of commensurability oscillations in an AlAs two-dimensional electron system where two conduction-band valleys with elliptical in-plane Fermi contours are occupied. The Fourier power spectrum of the oscillations shows two frequency components consistent with those expected for the Fermi contours of the two valleys. From an analysis of the spectra we deduce $m_l/m_t=5.2\pm0.5$ for the ratio of the longitudinal and transverse electron effective masses.
Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows i) …
Electrical conductance is quantized in units of $σ_{\rm Q}=2e^2/h$ in ballistic one-dimensional conductors. Similarly, thermal conductance at temperature $T$ is expected to be limited by the quantum of thermal conductance of one mode, $G_{\rm Q} = \frac{πk_{\rm B}^2}{6\hbar}T$, when physical dimensions are small in comparison to characteristic wavelength of the carriers. The relation between $σ_{\rm Q}$ and $G_{\rm Q}$ obeys the Wiedemann-Franz law for ballistic electrons (apart from factor 2 in $σ_{\rm Q}$ due to spin degeneracy), but somewhat amazingly the same expression of $G_{\rm Q}$ is e…
At micro- to nano-scales, classical size effects in heat conduction play an important role in suppressing the thermal transport process. Such effects occur when the characteristic lengths become commensurate to the mean free paths (MFPs) of heat carriers that are mainly phonons for nonmetallic crystals. Beyond existing experimental efforts on thin films using laser-induced thermal gratings, this work provides the complete theoretical analysis for a new approach to extract the effective phonon MFP distribution for the in-plane heat conduction within a thin film or flake-like sample. In this app…
Ballistic conductance through a single atom adsorbed on a metallic surface and probed by a scanning tunneling microscope (STM) tip can be decomposed into eigenchannel contributions, which can be potentially obtained from shot noise measurements. Our density functional theory calculations provide evidence that transmission probabilities of these eigenchannels encode information on the modifications of the adatom's local density of states caused by its interaction with the STM tip. In the case of open shell atoms, this can be revealed in nonmonotonic behavior of the eigenchannel's transmissions …
Cross-plane heat transport in thin films with thickness comparable to the phonon mean free paths is of both fundamental and practical interest. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes frequency-dependence of phonon properties. Further, our method is more than three o…
The thermal conductance of straight and corrugated monocrystalline silicon nanowires has been measured between 0.3 K and 5 K. The difference in the thermal transport between corrugated nanowires and straight ones demonstrates a strong reduction in the mean free path of the phonons. This averaged mean free path is remarkably smaller than the smaller diameter of the nanowire, evidencing a phonon thermal transport reduced below the Casimir limit. Monte Carlo simulations highlight that this effect can be attributed to significant multiple scattering of ballistic phonons occuring on the corrugated …
Short-range order in strongly disordered structures plays an important role in their heat conduction property. Using numerical and analytical methods, we show that short-range spatial correlation (with a correlation length of $Λ_{m}$) in the mass distribution of the one-dimensional (1D) alloy-like random binary lattice leads to a dramatic enhancement of the high-frequency phonon transmittance but also increases the low-frequency phonon opacity. High-frequency semi-extended states are formed while low-frequency modes become more localized. This results in ballistic heat conduction at finite len…
Graphane and graphene are both two-dimensional materials but of different bonding configurations, which can result in distinct thermal conduction properties. We simulate thermal conduction in graphane nanoribbons (GANRs) using the nonequilibrium Green's function method. It is found that GANRs have lower ballistic thermal conductance and stronger thermal conductance anisotropy than the graphene counterparts. Furthermore, hydrogen vacancies of GANRs considerably suppress thermal conduction, accompanied by enhanced thermal conductance anisotropy. The tunable thermal conduction, realized by contro…
Electronic transport in a carbon nanotube (CNT) metal-oxide-semiconductor field effect transistor (MOSFET) is simulated using the non-equilibrium Green's functions method with the account of electron-phonon scattering. For MOSFETs, ambipolar conduction is explained via phonon-assisted band-to-band (Landau-Zener) tunneling. In comparison to the ballistic case, we show that the phonon scattering shifts the onset of ambipolar conduction to more positive gate voltage (thereby increasing the off current). It is found that the subthreshold swing in ambipolar conduction can be made as steep as 40mV/d…
The propagation of a heat pulse in a single crystal and across grain boundaries (GBs) is simulated using a concurrent atomistic-continuum method furnished with a coherent phonon pulse model. With a heat pulse constructed based on a Bose-Einstein distribution of phonons, this work has reproduced the phenomenon of phonon focusing in single and polycrystalline materials. Simulation results provide visual evidence that the propagation of a heat pulse in crystalline solids with or without GBs is partially ballistic and partially diffusive, i.e., there is a co-existence of ballistic and diffusive th…
Unusual features in the bias dependence of spin transport are observed in a Co/Au/NiFe spin valve fabricated on a highly textured Cu(100)/Si(100) Schottky interface, exploiting the local probing capabilities of a Ballistic electron magnetic microscope (BEMM). This arises due to local differences in the strain and the presence of misfit dislocations at the Schottky interface that enhances spin flip scattering and broadens the energy and angular distribution of the transmitted electrons. Cumulatively, these enable the transmitted hot electrons to probe the different conduction band minima in Si,…
Transient grating (TG) spectroscopy is an important experimental technique to measure mean free path (MFP) spectra using observations of quasiballistic heat conduction. To obtain MFP spectra, the measurements must be interpreted within the framework of the frequency-dependent Boltzmann transport equation (BTE), but previous solutions have restricted validity due to simplifying assumptions. Here, we analyze heat conduction in TG using a new analytical solution of the frequency-dependent BTE that accurately describes thermal transport from the diffusive to ballistic regimes. We demonstrate that …
We report an experimental study of one-dimensional (1D) electronic transport in an InSb semiconducting nanowire. Three bottom gates are used to locally deplete the nanowire creating a ballistic quantum point contact with only a few conducting channels. In a magnetic field, the Zeeman splitting of the corresponding 1D subbands is revealed by the emergence of conductance plateaus at multiples of $e^2$/h, yet we find a quantized conductance pattern largely dependent on the configuration of voltages applied to the bottom gates. In particular, we can make the first plateau disappear leaving a first…
In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire have been explained by coherent and dissipationless transmission of individual electrons across a one-dimensional barrier. This leaves untouched the central issue of conduction: a quantum wire, albeit ballistic, has finite resistance and so must dissipate energy. Exactly HOW does the quantum wire shed its excess electrical energy? We show that the answer is provided, uniquely, by many-body quantum kinetics. Not only does this inevitably lead to universal quantization of the conductance, in spite of dissipation;…
Heat transport in nanoscale systems is both hard to measure microscopically, and hard to interpret. Ballistic and diffusive heat flow coexist, adding confusion. This paper looks at a very simple case: a nanoscale crystal repeated periodically. This is a popular model for simulation of bulk heat transport using classical molecular dynamics (MD), and is related to transient thermal grating experiments. Nanoscale effects are seen in perhaps their simplest form. The model is solved by an extension of standard quasiparticle gas theory of bulk solids. Both structure and heat flow are constrained by …
We present a first-principles study of the cross-plane thermal conductivity $κ_{\perp}$ in a wide variety of semiconductor thin films. We introduce a simple suppression model that matches variance-reduced Monte Carlo simulations with ab-initio phonon dispersions and scattering rates within $\leq 5\%$ even for anisotropic compounds. This, in turn, enables accurate $κ_{\perp}$ reconstruction from tabulated cumulative conductivity curves $κ_Σ(Λ_{\perp})$. We furthermore reveal, and explain, a distinct quasiballistic regime characterised by a fractional thickness dependence $κ_{\perp} \sim L^{2-α}…
Quasiparticle theory gives a local relation between heat current and temperature gradient, provided the quasiparticle mean free path is smaller than the scale of variation of temperature. When mean free paths are comparable to sample size, the relation becomes non-local. This non-local relation is formulated for phonon carriers; an explicit form is found in the approximation where current relaxation rates are replaced by quasiparticle relaxation rates. A quasiparticle definition of local temperature is offered. To extract the spatial variation of the temperature gradient requires inverting the…
Based on generalized quantum Langevin equations for the tight-binding wave function amplitudes and lattice displacements, electron and phonon quantum transport are obtained exactly using molecular dynamics (MD) in the ballistic regime. The electron-phonon interactions can be handled with a quasi-classical approximation. Both charge and energy transport and their interplay can be studied. We compare the MD results with that of a fully quantum mechanical nonequilibrium Green's function (NEGF) approach for the electron currents. We find a ballistic to diffusive transition of the electron conducti…
I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and De…
Microscopic current fluctuations are inseparable from conductance. We give an integral account of both quantized conductance and nonequilibrium thermal noise in one-dimensional ballistic wires. Our high-current noise theory opens a very different window on such systems. Central to the role of nonequilibrium ballistic noise is its direct and robust dependence on the statistics of carriers. For, with increasing density, they undergo a marked crossover from classical to strongly degenerate behavior. This is singularly evident where the two-probe conductance shows quantized steps: namely, at the d…
A race is held between ten species of organic gas molecules on a graphene substrate driven by thermal gradients via molecular dynamics. Fast conduction of the molecules is observed with selectivity for aromatic compounds. This selectivity stems from the fact that the planar structure of the aromatic molecule helps keep a shorter distance to the substrate, which is the key to the driving force at the gas-solid interface. The drift velocity monotonically increases with decreasing molecule density, with no ballistic transport observable even for a single molecule. A non-linear regime is discovere…
The standard physical model of contemporary mesoscopic noise and transport consists in a phenomenologically based approach, proposed originally by Landauer and since continued and amplified by Buettiker (and others). Throughout all the years of its gestation and growth, it is surprising that the Landauer-Buettiker approach to mesoscopics has matured with scant attention to the conservation properties lying at its roots: that is, at the level of actual microscopic principles. We systematically apply the conserving sum rules for the electron gas to clarify this fundamental issue within the stand…
We study the transport properties of deeply scaled monolayer MoS2 n-channel metal-oxide-semiconductor field effect transistors (MOSFETs) using full-band ballistic quantum transport simulations with an atomistic tight-binding Hamiltonian obtained from density functional theory. Our simulations suggest that monolayer MoS2 MOSFETs can provide near-ideal subthreshold slope, and suppression of drain-induced barrier lowering (DIBL) and gate-induced drain leakage (GIDL). However, these full-band simulations also exhibit limited transconductance. These ballistic simulations also exhibit negative diffe…
For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean free path and arbitrary shape of the conduction band edge profile. Universal formulas are obtained for the current-voltage characteristic in the nondegenerate case and for the zero-bias conductance in the degenerate case, which describe in a transparent manner the interplay of ballistic and diffusive transport. The semiclassical approach is adopted, but quantum…
Ballistic transport occurs whenever electrons propagate without collisions deflecting their trajectory. It is normally observed in conductors with a negligible concentration of impurities, at low temperature, to avoid electron-phonon scattering. Here, we use suspended bilayer graphene devices to reveal a new regime, in which ballistic transport is not limited by scattering with phonons or impurities, but by electron-hole collisions. The phenomenon manifests itself in a negative four-terminal resistance that becomes visible when the density of holes (electrons) is suppressed by gate-shifting th…
Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that both steady state and modulated components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path, and they exhibit the diffusive behavior as predicted by the Fourier law of heat conduction when this ratio is much larger than the unity. In contrast, in the balli…
We study dynamic nonequilibrium electron charging phenomena in ballistic molecular devices at room temperature that compromise their response to bias and whose nature is evidently distinguishable from static Schottky-type potential barriers. Using various metallic/semiconducting carbon nanotubes and alkane dithiol molecules as active parts of a molecular bridge, we perform self-consistent quantum transport calculations under the nonequilibrium Green's function formalism coupled to a three-dimensional Poisson solver for a mutual description of chemistry and electrostatics. Our results sketch a …
We develop a computational framework, based on the Boltzmann transport equation, with the ability to compute the thermal transport in nanostructured materials of any geometry using as the only input the bulk thermal conductivity accumulation function. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with a frequency-dependent approach. Second, when phonon dispersions…
Departures in phonon heat conduction from diffusion have been extensively observed in nanostructures through their thermal conductivity reduction and largely explained with classical size effects neglecting phonon's wave nature. Here, we report localization-behavior in phonon heat conduction due to multiple scattering and interference of phonon waves, observed through measurements of the thermal conductivities of GaAs/AlAs superlattices with ErAs nanodots randomly distributed at the interfaces. Near room temperature, the measured thermal conductivities increased with increasing number of SL pe…
For quantum ballistic transport of electrons through a short conduction channel, the role of Coulomb interaction may significantly modify the energy levels of an electron pair at low temperatures as the channel becomes wide. In this regime, the Coulomb effect on the orbital triplet and singlet electron-pair state is calculated and found to lead to four split energy levels, including two hybrid and two unhybrid states. Moreover, due to the interplay of hybrid and unhybrid Coulomb interactions between two electrons, our calculations reveal that the ground pair-state will switch from one hybrid o…
We have used the scanning charged tip of an Atomic Force Microscope (AFM) to produce images of the conductance variation of a quantised 1D ballistic channel. The channel was formed using electron beam defined 700 nm wide split gate surface electrodes over a high mobility GaAs/AlGaAs heterostructure with a two dimensional electron gas (2DEG) 98 nm beneath the surface. We operate the AFM at 1.5 K and 4.2 K in magnetic fields up to 2 T to observe several phenomena. With a dc voltage on the AFM tip we have produced conduction images of the tip potential perturbation, as the channel is a sensitive …
We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane's concept of fractional statistics (FES) and the Landauer formulation of transport theory. We show that the 1D ballistic thermal conductance is independent of the statistics obeyed by the carriers and is governed by the universal quantum $ (π^2 k^2_B T)/(3h) $ in the degenerate regime. By contrast, the electrical conductance of FES systems is statistics-dependent. This work unifies previous theories of electron and phonon systems and explains an interesting commonality in their behavior.
Nonequilibrium molecular dynamics (NEMD) has been extensively used to study thermal transport at various length scales in many materials. In this method, two local thermostats at different temperatures are used to generate a nonequilibrium steady state with a constant heat flux. Conventionally, the thermal conductivity of a finite system is calculated as the ratio between the heat flux and the temperature gradient extracted from the linear part of the temperature profile away from the local thermostats. Here we show that, with a proper choice of the thermostat, the nonlinear part of the temper…
A new non-ballistic analytical model for the intrinsic channel region of MOSFET-like single-walled carbon-nanotube field-effect transistors with ohmic contacts has been developed which overcomes the limitations of existing models and extends their applicability toward high bias voltages needed for analog applications. The new model comprises an improved description of electron-phonon scattering mechanism taking into account the accumulation of electrons at the bottom of conduction subband due to back scattering by optical phonons. The model has been justified by a Boltzmann transport equation …
