In this paper, a numerical simulation of thermal transport at the nanoscale is developed by solving the phonon Boltzmann transport equation by the Monte Carlo method. A full phonon dispersion is used to determine accurately the vibrational frequencies and group velocities of all phonon modes. Simultaneous conservation of energy and momentum in anharmonic phonon-phonon scattering events in enabled by a novel algorithm developed in this work. The inclusion of rough boundaries and the treatment of their impact on phonon transport is also discussed. The results demonstrate the convergence, accuracy, and efficiency of the proposed simulation.

We simulate phonon transport in suspended graphene nanoribbons (GNRs) with real-space edges and experimentally relevant widths and lengths (from submicron to hundreds of microns). The full-dispersion phonon Monte Carlo simulation technique, which we describe in detail, involves a stochastic solution to the phonon Boltzmann transport equation with the relevant scattering mechanisms (edge, three-phonon, isotope, and grain boundary scattering) while accounting for the dispersion of all three acoustic phonon branches, calculated from the fourth-nearest-neighbor dynamical matrix. We accurately reproduce the results of several experimental measurements on pure and isotopically modified samples [S. Chen et al., ACS Nano 5, 321 (2011);S. Chen et al., Nature Mater. 11, 203 (2012); X. Xu et al., Nat. Commun. 5, 3689 (2014)]. We capture the ballistic-to-diffusive crossover in wide GNRs: room-temperature thermal conductivity increases with increasing length up to roughly 100 μm, where it saturates at a value of 5800 W/m K. This finding indicates that most experiments are carried out in the quasiballistic rather than the diffusive regime, and we calculate the diffusive upper-limit thermal conductivities up to 600 K. Furthermore, we demonstrate that calculations with isotropic dispersions overestimate the GNR thermal conductivity. Zigzag GNRs have higher thermal conductivity than same-size armchair GNRs, in agreement with atomistic calculations.

scattering from the grain boundary roughness. Thermal transport in the large-area sample is considered in the Corbino-membrane geometry, with heatflowing through a network of thermal resistors and away from a pointlike heat source. The thermal transport in polycrystalline graphene is shown to be highly anisotropic, depending on the individual properties of the grains (their size and boundary roughness), as well as on grain connectivity. Strongest heat conduction occurs along large-grain filaments, while the heat flow is blocked through regions containing predominantly small grains. We discuss how thermal transport in CVD graphene can be tailored by controlling grain disorder.

A 3-D full-band particle Monte Carlo (MC) simulator, with full electron and phonon dispersion and a 2-D quantum correction is self-consistently coupled to a phonon MC simulator. The coupling entails feeding the phonon data obtained from the 3-D electrical MC to the phonon MC. The phonon MC reciprocates by providing the resulting spatial temperature map, which is used in the electron MC, with temperature-dependent scattering table, in a self-consistent manner. A key feature of our model is its ability to delineate the influence of the various phonon modes on the electronic transport through the application of anharmonic phonon decay and full phonon dispersion. The electrothermal simulator developed is utilized to assess the performance of silicon-on-insulator (SoI) multigate (MG) MOSFET with nanoscale cross sections. This paper shows that the hotspot in inversion mode SoI MG MOSFET with 20-nm gate length permeates into the channel as the cross section is reduced (covering ~ 50% of the channel for the 5 nm × 5 nm cross section). Furthermore, cross-sectional scaling, a key design rule to mitigate short-channel effects, degenerates device performance well beyond the ideal current gain limits of MG MOSFET architecture of double-gate, trigate, and gate-all-around MOSFET. Consequently, at the sub-20-nm scale adding more gate does not necessarily improve performance.

We investigate thermal transport in Si/Ge and Si1−xGex /Si1−yGey alloy superlattices based on solving the single-mode phonon Boltzmann transport equation in the relaxation-time approximation and with full phonon dispersions. We derive an effective interface scattering rate that depends both on the interface roughness (captured by a wave-vector-dependent specularity parameter) and on the efficiency of internal scattering mechanisms (mass-difference and phonon-phonon scattering). We provide compact expressions for the calculations of in-plane and cross-plane thermal conductivities in superlattices. Our numerical results accurately capture both the observed increase in thermal conductivity as the superlattice period increases and the in-plane vs cross-plane anisotropy of thermal conductivity. Owing to the combined effect of interface and internal scattering, an alloy/alloy superlattice has a lower thermal conductivity than bulk SiGe with the same alloy composition. Thermal conductivity can be minimized by growing short-period alloy/alloy superlattices or Si/Si1−xGex superlattices with the SiGe layer thicker than the Si one.

Time-of-flight (TOF) mass spectrometry has been considered as the method of choice for mass analysis of large intact biomolecules, which are ionized in low charge states by matrix-assisted-laser-desorption/ionization (MALDI). However, it remains predominantly restricted to the mass analysis of biomolecules with a mass below about 50,000 Da. This limitation mainly stems from the fact that the sensitivity of the standard detectors decreases with increasing ion mass. We describe here a new principle for ion detection in TOF mass spectrometry, which is based upon suspended silicon nanomembranes. Impinging ion packets on one side of the suspended silicon nanomembrane generate nonequilibrium phonons, which propagate quasi-diffusively and deliver thermal energy to electrons within the silicon nanomembrane. This enhances electron emission from the nanomembrane surface with an electric field applied to it. The nonequilibrium phonon-assisted field emission in the suspended nanomembrane connected to an effective cooling of the nanomembrane via field emission allows mass analysis of megadalton ions with high mass resolution at room temperature. The high resolution of the detector will give better insight into high mass proteins and their functions.

Submitted for the MAR13 Meeting of The American Physical Society Phonon Surface Scattering in Monte Carlo Simulations LEON MAURER, ZLATAN AKSAMIJA, University of Wisconsin-Madison, EDWIN RAMAYYA, Intel Corporation, AMIRHOSSEIN DAVOODY, IRENA KNEZEVIC, University of Wisconsin-Madison — Surface roughness has a significant impact on the thermal conductivity and thermoelectric properties of nanowires. We investigate the effect of surface roughness on thermal transport using a phonon Monte Carlo simulation. In addition to allowing us to simulate a wide range of wire dimensions and surface topographies, Monte Carlo enables us to investigate different models for surface scattering: constant specularity parameters, momentum-dependent specularity parameters, and specular scattering from randomly generated rough surfaces. We investigate the relative merits of different surface scattering models and the limitations on their validity. Leon Maurer University of Wisconsin-Madison Date submitted: 09 Nov 2012 Electronic form version 1.4

Thermal conductivity of graphene and graphene-based nanostructures [1], such as graphene nanoribbons (GNRs) [2], CVD-grown polycrystalline graphene (PCG) [3], and nanopatterned single-layer graphene (SLG) is of great interest due to their potential applications as logic devices, high-frequency amplifiers, and heat spreaders in future nanoelectronic circuits [4]. Device applications of graphene typically rely on samples supported on SiO2 and cut into ribbons [5]. For switching applications, GNR-FETs have to be made from very narrow ribbons in order to lithographically tune the band-gap and achieve the required on-off ratios. High-frequency applications also lead to strong dissipation in GNR-FET [6], which further motivates the present interest in the thermal properties of narrow, suspended and supported ribbons. Line edge roughness along the sides of narrow graphene ribbons has been shown to reduce the lattice thermal conductivity relative to its value in large flakes [7]. Initially, it was found that the ballistic thermal conductivity of graphene is isotropic; however, it was subsequently discovered that, when graphene is cut into nanoribbons, directional anisotropy of thermal conductivity appears [2]. Despite tremendous experimental and theoretical progress, a study treating both substrate and edge roughness effects on thermal transport, as well as their mutual interplay and the anisotropy of the lattice thermal conductivity tensor, has been lacking. We explore lattice thermal transport in supported graphene nanoribbons (GNRs). We demonstrate the sensitivity of the lattice thermal conductivity in GRNs to the edge properties, based on solving the phonon Boltzmann transport equation (pBTE) under the relaxation time approximation. We derive a solution to the pBTE in the cross-ribbon direction with partially diffuse edges in the presence of competing scattering from the substrate, umklapp phononphonon, and isotope scattering processes, as depicted schematically in Figure 1. We compute the lattice thermal conductivity tensor, with excellent agreement with experiment (Figure 3) and show that is has two very distinct components: one along the ribbon, and another one in the crossribbon direction, as shown in Figure 2 (b-c). The parallel/cross-ribbon anisotropy increases in narrower ribbons and with increased line edge roughness, shown in Figure 4 (a-c). In supported nanoribbons, we identify three ranges based on the width W of the GNR and the competition between edge roughness and substrate scattering: narrow ribbons (W<100 nm), where line edge roughness scattering dominates and anisotropy is very high, medium ribbons (100 nm1um) where substrate scattering dominates and thermal transport becomes nearly isotropic, shown in Figure 4 (d). Based on our model, we conclude that thermal conductivity of narrow GNRs can be effectively controlled by controlling their width and edge properties. Coupled with good electronic transport properties, this opens up the possibility of using GNRs for high-efficiency thermoelectric conversion. High degree of anisotropy in narrow ribbons also opens up the possibility of using GNRs as heat guides to move heat in a directed way by patterning the graphene ribbons into heat conduits.

We present a theoretical model for thermal transport in graphene nanoribbons (GNRs) on SiO2 based on solving the phonon Boltzmann transport equation. Thermal transport in supported GNRs is characterized by a complex interplay between line edge roughness (LER) and internal scattering, as captured through an effective LER scattering rate that depends not only on the surface roughness features, but also on the strength of internal scattering mechanisms (substrate, isotope, and umklapp phonon scattering). Substrate scattering is the dominant internal mechanism, with a mean free path (mfp) of approximately 67 nm. In narrow supported GNRs ( W 1 μm) is dominated by substrate scattering and spatially isotropic. Thermal transport in supported GNRs can be tailored by controlling the ribbon width and edge roughness. We conclude that narrow ribbons act as longitudinal heat conduits while wide ribbons act as good omnidirectional heat spreaders.

One of the limiting factors for the room-temperature continuous-wave (RT-cw) operation of quantum cascade lasers (QCLs) is the high temperature in the active region that stems from the high electrical power and poor heat extraction [1]. In order to simulate the thermal behavior of QCLs, the heat diffusion equation with appropriate source and boundary conditions needs to be solved. However, the heat generation rate of the active region under a given bias is both space- and temperature-dependent. In this paper, we present a method of extracting the heat generation rate by recording the electron-optical phonon scattering during the ensemble Monte Carlo (EMC) simulation of electron transport under different temperatures. The extracted nonlinear heat source together with appropriate thermal conductivity models enable self-consistent calculation of temperature distribution throughout QCLs. We apply the thermal model to investigate the cross-plane temperature distribution of a 9.4 μm infrared GaAs-based QCL [2]. The nonlinear effects stemming from the temperature dependence of thermal conductivity and the heat generation rate are studied.

In this paper, we demonstrate the sensitivity of the lattice thermal conductivity in SLs to the interface properties, based on solving the phonon Boltzmann transport equation under the relaxation time approximation. Previous calculations relied on treating the interface scattering with an empirical specularity parameter, which is then adjusted to fit measured data. In this work, in order to accurately treat phonon scattering from a series of rough interfaces with a given rms roughness height (Δ), we employ a momentum-dependent specularity parameter p(q) that is the fraction of specular reflections to the total number of reflections from a rough boundary (0 ≤ p(q⃗) ≤ 1).