Simulation of Sub-Micron Thermal Transport in a MOSFET Using a Hybrid Fourier-BTE Model

2010 ◽  
Author(s):  
James M. Loy ◽  
Dhruv Singh ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Transport ◽  
Source Term ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Computational Cost ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Hybrid Solver ◽  
Solution Methodology ◽  
Electron Phonon Scattering

Self-heating has emerged as a critical bottleneck to scaling in modern transistors. In simulating heat conduction in these devices, it is important to account for the granularity of phonon transport since electron-phonon scattering occurs preferentially to select phonon groups. However, a complete accounting for phonon dispersion, polarization and scattering is very expensive if the Boltzmann transport equation (BTE) is used. Moreover, difficulties with convergence are encountered when the phonon Knudsen number becomes small. In this paper we simulate a two-dimensional bulk MOSFET hotspot problem using a partially-implicit hybrid BTE-Fourier solver which is significantly less expensive than a full BTE solution, and which shows excellent convergence characteristics. Volumetric heat generation from electron-phonon collisions is taken from a Monte Carlo simulation of electron transport and serves as a heat source term in the governing transport equations. The hybrid solver is shown to perform well in this highly non-equilibrium situation, matching the solutions obtained from a pure all-BTE solution, but at significantly lower computational cost. The paper establishes that this new model and solution methodology are viable for the simulation of thermal transport in other emerging transistor designs and in other nanotechnology applications as well.

scholarly journals Thermal transport in nanocrystalline Si and SiGe by ab initio based Monte Carlo simulation

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Lina Yang ◽  
Austin J. Minnich
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Ab Initio ◽  
Grain Boundaries ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Computational Study ◽  
Phonon Transport ◽  
Nanocrystalline Si

Abstract Nanocrystalline thermoelectric materials based on Si have long been of interest because Si is earth-abundant, inexpensive, and non-toxic. However, a poor understanding of phonon grain boundary scattering and its effect on thermal conductivity has impeded efforts to improve the thermoelectric figure of merit. Here, we report an ab-initio based computational study of thermal transport in nanocrystalline Si-based materials using a variance-reduced Monte Carlo method with the full phonon dispersion and intrinsic lifetimes from first-principles as input. By fitting the transmission profile of grain boundaries, we obtain excellent agreement with experimental thermal conductivity of nanocrystalline Si [Wang et al. Nano Letters 11, 2206 (2011)]. Based on these calculations, we examine phonon transport in nanocrystalline SiGe alloys with ab-initio electron-phonon scattering rates. Our calculations show that low energy phonons still transport substantial amounts of heat in these materials, despite scattering by electron-phonon interactions, due to the high transmission of phonons at grain boundaries, and thus improvements in ZT are still possible by disrupting these modes. This work demonstrates the important insights into phonon transport that can be obtained using ab-initio based Monte Carlo simulations in complex nanostructured materials.

Spectral Detail of Phonon Conduction and Scattering in Graphene

2011 ◽  
Author(s):  
Dhruv Singh ◽  
Jayathi Y. Murthy ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Conductivity ◽  
Phonon Scattering ◽  
Interatomic Potential ◽  
Phonon Dispersion ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Phonon Transport ◽  
Temperature Perturbation ◽  
Boltzmann Transport ◽  
Wide Range

This paper examines the thermodynamic and thermal transport properties of the 2D graphene lattice. The interatomic interactions are modeled using the Tersoff interatomic potential and are used to evaluate phonon dispersion curves, density of states and thermodynamic properties of graphene as functions of temperature. Perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. An algorithm to accurately quantify the contours of energy balance for three-phonon scattering events is presented and applied to calculate the net transition probability from a given phonon mode. Under the linear approximation, the Boltzmann transport equation (BTE) is applied to compute the thermal conductivity of graphene, giving spectral and polarization-resolved information. Predictions of thermal conductivity for a wide range of parameters elucidate the behavior of diffusive phonon transport. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided, contrasting graphene with other materials, along with implications for graphene electronics. We also highlight the specific scattering processes that are important in Raman spectroscopy based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.

Phonon Transport in SiGe-Based Nanocomposites and Nanowires for Thermoelectric Applications

2015 ◽  
Vol 1735 ◽  
Author(s):  
M. Upadhyaya ◽  
Z. Aksamija
Keyword(s):  
Thermal Conductivity ◽  
Silicon Germanium ◽  
Thermal Transport ◽  
Lattice Thermal Conductivity ◽  
Phonon Scattering ◽  
Voronoi Tessellation ◽  
Phonon Transport ◽  
Interface Properties ◽  
Boltzmann Transport ◽  
Rough Interfaces

ABSTRACTSilicon-germanium (SiGe) superlattices (SLs) have been proposed for application as efficient thermoelectrics because of their low thermal conductivity, below that of bulk SiGe alloys. However, the cost of growing SLs is prohibitive, so nanocomposites, made by a ball-milling and sintering, have been proposed as a cost-effective replacement with similar properties. Lattice thermal conductivity in SiGe SLs is reduced by scattering from the rough interfaces between layers. Therefore, it is expected that interface properties, such as roughness, orientation, and composition, will play a significant role in thermal transport in nanocomposites and offer many additional degrees of freedom to control the thermal conductivity in nanocomposites by tailoring grain size, shape, and crystal angle distributions. We previously demonstrated 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. Here we adapt the model to a broad range of SiGe nanocomposites. We model nanocomposite structures using a Voronoi tessellation to mimic the grains and their distribution in the nanocomposite and show excellent agreement with experimentally observed structures, while for nanowires we use the Monte Carlo method to solve the phonon Boltzmann equation. In order to accurately treat phonon scattering from a series of atomically rough interfaces between the grains in the nanocomposite and at the boundaries of nanowires, we employ a momentum-dependent specularity parameter. Our results show thermal transport in SiGe nanocomposites and nanowires is reduced significantly below their bulk alloy counterparts.

A Fast Hybrid Fourier–Boltzmann Transport Equation Solver for Nongray Phonon Transport

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
James M. Loy ◽  
Jayathi Y. Murthy ◽  
Dhruv Singh
Keyword(s):  
Transport Equation ◽  
Thermal Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Phonon Transport ◽  
Computational Effort ◽  
Boltzmann Transport ◽  
Knudsen Numbers ◽  
Sequential Solution ◽  
Hybrid Solver

Nongray phonon transport solvers based on the Boltzmann transport equation (BTE) are being increasingly employed to simulate submicron thermal transport in semiconductors and dielectrics. Typical sequential solution schemes encounter numerical difficulties because of the large spread in scattering rates. For frequency bands with very low Knudsen numbers, strong coupling between other BTE bands result in slow convergence of sequential solution procedures. This is due to the explicit treatment of the scattering kernel. In this paper, we present a hybrid BTE-Fourier model which addresses this issue. By establishing a phonon group cutoff Knc, phonon bands with low Knudsen numbers are solved using a modified Fourier equation which includes a scattering term as well as corrections to account for boundary temperature slip. Phonon bands with high Knudsen numbers are solved using the BTE. A low-memory iterative solution procedure employing a block-coupled solution of the modified Fourier equations and a sequential solution of BTEs is developed. The hybrid solver is shown to produce solutions well within 1% of an all-BTE solver (using Knc = 0.1), but with far less computational effort. Speedup factors between 2 and 200 are obtained for a range of steady-state heat transfer problems. The hybrid solver enables efficient and accurate simulation of thermal transport in semiconductors and dielectrics across the range of length scales from submicron to the macroscale.

scholarly journals Simulation of Heat Transport in Graphene Nanoribbons Using the Ab-Initio Scattering Operator

2014 ◽  
Author(s):  
Colin D. Landon ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Ab Initio ◽  
Heat Transport ◽  
Density Functional ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Graphene Nanoribbons ◽  
Phonon Transport ◽  
Stochastic Algorithm ◽  
Boltzmann Transport ◽  
Scattering Operator

We present a deviational Monte Carlo method for simulating phonon transport in graphene using the ab initio 3-phonon scattering operator. This operator replaces the commonly used relaxation-time approximation, which is known to neglect, among other things, coupling between out of equilibrium states that are particularly important in graphene. Phonon dispersion relations and transition rates are obtained from density functional theory calculations. The proposed method provides, for the first time, means for obtaining solutions of the Boltzmann transport equation with ab initio scattering for time- and spatially-dependent problems. The deviational formulation ensures that simulations are computationally feasible for arbitrarily small temperature differences; within this formulation, the ab initio scattering operator is treated using an efficient stochastic algorithm which, in the limit of large number of states, outperforms the more traditional deterministic methods used in solutions of the homogeneous Boltzmann equation. We use the proposed method to study heat transport in graphene ribbons.

Coupled Electro-Thermal Simulation of MOSFETs

2009 ◽  
Author(s):  
Chunjian Ni ◽  
Zlatan Aksamija ◽  
Jayathi Y. Murthy ◽  
Umberto Ravaioli
Keyword(s):  
Thermal Transport ◽  
Phonon Scattering ◽  
Field Effect Transistors ◽  
Device Simulation ◽  
Heat Fluxes ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Conduction Model ◽  
Electron Phonon Scattering

Thermal transport in metal-oxide-semiconductor field effect transistors (MOSFETs) due to electron-phonon scattering is simulated using phonon generation rates obtained from an electron Monte Carlo device simulation. The device simulation accounts for a full band description of both electrons and phonons considering 22 types of electron-phonon scattering events. Detailed profiles of phonon emission/absorption rates in the physical and momentum spaces are generated and are used in a MOSFET thermal transport simulation with a recently-developed anisotropic relaxation time model based on the Boltzmann transport equation (BTE). Comparisons with a Fourier conduction model reveal that the anisotropic heat conduction model predicts higher maximum temperatures because it accounts for the bottlenecks in phonon scattering pathways. Heat fluxes leaving the boundaries associated with different phonon polarizations and frequencies are also examined to reveal the main modes responsible for transport. It is found that though the majority of the heat generation is in the optical modes, the heat generated in the acoustic modes is not negligible. The modes primarily responsible for the transport of heat are found to be medium-to-high frequency acoustic phonon modes.

scholarly journals Body-centered-cubic structure and weak anharmonic phonon scattering in tungsten

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Yani Chen ◽  
Jinlong Ma ◽  
Shihao Wen ◽  
Wu Li
Keyword(s):  
Phonon Scattering ◽  
Phonon Transport ◽  
High Symmetry ◽  
Body Centered Cubic ◽  
Phonon Branch ◽  
High Frequencies ◽  
Transverse Acoustic ◽  
Two Factors ◽  
Electron Phonon Scattering ◽  
Isotropy Condition

Abstract It was recently found that the anharmonic phonon–phonon scattering in tungsten is extremely weak at high frequencies, leading to a predominance of electron–phonon scattering and consequently anomalous phonon transport behaviors. In this work, we calculate the phonon linewidths of W along high-symmetry directions from first principles. We find that the weak phonon–phonon scattering can be traced back to two factors. The first is the triple degeneracy of the phonon branches at the P and H points, a universal property of elemental body-centered-cubic (bcc) structures. The second is a relatively isotropic character of the phonon dispersions. When both are met, phonon–phonon scattering rates must vanish at the P and H points. The weak phonon–phonon scattering feature is also applicable to Mo and Cr. However, in other elemental bcc substances like Na, the isotropy condition is violated due to the unusually soft character of the lower transverse acoustic phonon branch along the Γ-N direction, opening emission channels and leading to much stronger phonon–phonon scattering. We also look into the distributions of electron mean-free paths (MFPs) at room temperature in tungsten, which can help engineer the resistivity of nanostructured W for applications such as interconnects.

Statistical Phonon Transport Model of Thermal Transport in Silicon

2009 ◽  
Vol 1229 ◽  
Author(s):  
Thomas W Brown ◽  
Edward Hensel
Keyword(s):  
Thermal Transport ◽  
Lattice Dynamics ◽  
Transport Model ◽  
Silicon Nanowire ◽  
Boltzmann Transport Equation ◽  
Momentum Conservation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Crystalline Materials ◽  
Statistical Framework

AbstractThermal transport in crystalline materials at various length scales can be modeled by the Boltzmann transport equation (BTE). A statistical phonon transport (SPT) model is presented that solves the BTE in a statistical framework that incorporates a unique state-based phonon transport methodology. Anisotropy of the first Brillouin zone (BZ) is captured by utilizing directionally-dependent dispersion curves obtained from lattice dynamics calculations. A rigorous implementation of phonon energy and pseudo-momentum conservation is implemented in the ballistic thermal transport regime for a homogeneous silicon nanowire with adiabatic specular boundary conditions.

Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors

2005 ◽  
Vol 127 (7) ◽  
pp. 713-723 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Phonon Transport ◽  
Silicon On Insulator ◽  
Boltzmann Transport ◽  
Transport Models ◽  
Microelectronic Devices ◽  
Finite Volume Approach ◽  
Spot Temperature

The problem of self-heating in microelectronic devices has begun to emerge as a bottleneck to device performance. Published models for phonon transport in microelectronics have used a gray Boltzmann transport equation (BTE) and do not account adequately for phonon dispersion or polarization. In this study, the problem of a hot spot in a submicron silicon-on-insulator transistor is addressed. A model based on the BTE incorporating full phonon dispersion effects is used. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to those obtained using a Fourier diffusion model. Comparisons are also made to previously published BTE models employing gray and semi-gray approximations. Significant differences are found in the maximum hot spot temperature predicted by the different models. Fourier diffusion underpredicts the hot spot temperature by as much as 350% with respect to predictions from the full phonon dispersion model. For the full phonon dispersion model, the longitudinal acoustic modes are found to carry a majority of the energy flux. The importance of accounting for phonon dispersion and polarization effects is clearly demonstrated.

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