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.

Simulations of Heat Conduction in Sub-Micron Silicon-on-Insulator Transistors Accounting for Phonon Dispersion and Polarization

2003 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Phonon Dispersion ◽  
Dispersion Model ◽  
Boltzmann Transport Equation ◽  
Silicon On Insulator ◽  
Gray Model ◽  
Boltzmann Transport ◽  
Polarization Effects ◽  
Self Heating ◽  
Dispersion Effects ◽  
Finite Volume Approach

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semicondutors at sub-micron scales. Most studies make a gray assumption and do not account for phonon dispersion or polarization in any detail. In this study, the problem of heat generation in a sub-micron silicon-on-insulator (SOI) transistor is addressed. A model, based on the solution to the BTE incorporating full phonon dispersion effects, is presented and used to study the SOI self-heating problem. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to predictions using the Fourier diffusion equation and also to predictions from the solution to the BTE using a semi-gray model which appears in literature. Significant differences are found between the models and confirm the need for an accounting for phonon dispersion and polarization effects.

Influence of Phonon Dispersion on Transient Thermal Response of Silicon-on-Insulator Transistors Under Self-Heating Conditions

2006 ◽  
Vol 129 (7) ◽  
pp. 790-797 ◽  
Author(s):  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Computational Models ◽  
Phonon Dispersion ◽  
Thermal Response ◽  
Domain Size ◽  
Phonon Transport ◽  
Silicon On Insulator ◽  
Nonlinear Relation ◽  
Temperature Levels ◽  
Transient Thermal ◽  
Transient Thermal Response

Lattice Boltzmann method (LBM) simulations of phonon transport are performed in one-dimensional (1D) and 2D computational models of a silicon-on-insulator transistor, in order to investigate its transient thermal response under Joule heating conditions, which cause a nonequilibrium region of high temperature known as a hotspot. Predictions from Fourier diffusion are compared to those from a gray LBM based on the Debye assumption, and from a dispersion LBM which incorporates nonlinear dispersion for all phonon branches, including explicit treatment of optical phonons without simplifying assumptions. The simulations cover the effects of hotspot size and heat pulse duration, considering a frequency-dependent heat source term. Results indicate that, for both models, a transition from a Fourier diffusion regime to a ballistic phonon transport regime occurs as the hotspot size is decreased to tens of nanometers. The transition is characterized by the appearance of boundary effects, as well as by the propagation of thermal energy in the form of multiple, superimposed phonon waves. Additionally, hotspot peak temperature levels predicted by the dispersion LBM are found to be higher than those from Fourier diffusion predictions, displaying a nonlinear relation to hotspot size, for a given, fixed, domain size.

Modeling of Localized Heating Effect in Sub-Micron Silicon Transistors

2003 ◽  
Author(s):  
Keivan Etessam-Yazdani ◽  
Sadegh M. Sadeghipour ◽  
Mehdi Asheghi
Keyword(s):  
Transport Equation ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Heat Diffusion ◽  
Normal Operation ◽  
Heating Effect ◽  
Boltzmann Transport ◽  
Heat Diffusion Equation ◽  
Localized Heating

The performance and reliability of sub-micron semiconductor transistors demands accurate modeling of electron and phonon transport at nanoscales. The continued downscaling of the critical dimensions, introduces hotspots, inside transistors, with dimensions much smaller than phonon mean free path. This phenomenon, known as localized heating effect, results in a relatively high temperature at the hotspot that cannot be predicted using heat diffusion equation. While the contribution of the localized heating effect to the total device thermal resistance is significant during the normal operation of transistors, it has even greater implications for the thermoelectrical behavior of the device during an electrostatic discharge (ESD) event. The Boltzmann transport equation (BTE) can be used to capture the ballistic phonon transport in the vicinity of a hot spot but many of the existing solutions are limited to the one-dimensional and simple geometry configurations. We report our initial progress in solving the two dimensional Boltzmann transport equation for a hot spot in an infinite media (silicon) with constant temperature boundary condition and uniform heat generation configuration.

From the Casimir Limit to Phononic Crystals: 20 Years of Phonon Transport Studies Using Silicon-on-Insulator Technology

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Amy M. Marconnet ◽  
Mehdi Asheghi ◽  
Kenneth E. Goodson
Keyword(s):  
Room Temperature ◽  
Crystalline Silicon ◽  
Phonon Dispersion ◽  
Single Crystal Silicon ◽  
Phonon Transport ◽  
Silicon On Insulator ◽  
Boundary Scattering ◽  
Porous Films ◽  
Crystal Silicon ◽  
20 Nm

Silicon-on-insulator (SOI) technology has sparked advances in semiconductor and MEMs manufacturing and revolutionized our ability to study phonon transport phenomena by providing single-crystal silicon layers with thickness down to a few tens of nanometers. These nearly perfect crystalline silicon layers are an ideal platform for studying ballistic phonon transport and the coupling of boundary scattering with other mechanisms, including impurities and periodic pores. Early studies showed clear evidence of the size effect on thermal conduction due to phonon boundary scattering in films down to 20 nm thick and provided the first compelling room temperature evidence for the Casimir limit at room temperature. More recent studies on ultrathin films and periodically porous thin films are exploring the possibility of phonon dispersion modifications in confined geometries and porous films.

Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

2007 ◽  
Vol 7 (11) ◽  
pp. 4094-4100 ◽  
Author(s):  
Jae Sik Jin ◽  
Joon Sik Lee
Keyword(s):  
Energy Density ◽  
Group Velocity ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Interaction Model ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering

An electron–phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron–phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron–phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron–phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron–phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon–phonon scattering rates are lower than 4 × 1010 s−1.

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.

Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

2007 ◽  
Vol 7 (11) ◽  
pp. 4094-4100
Author(s):  
Jae Sik Jin ◽  
Joon Sik Lee
Keyword(s):  
Energy Density ◽  
Group Velocity ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Interaction Model ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering

An electron–phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron–phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron–phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron–phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron–phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon–phonon scattering rates are lower than 4 × 1010 s−1.

Simulation of Phonon Transport in Semiconductors Using a Population-Dependent Many-Body Cellular Monte Carlo Approach

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Flavio F. M. Sabatti ◽  
Stephen M. Goodnick ◽  
Marco Saraniti
Keyword(s):  
Monte Carlo ◽  
Phonon Dispersion ◽  
Phonon Transport ◽  
Space Distribution ◽  
Boltzmann Transport ◽  
Many Body ◽  
Simulation Code ◽  
Conservation Of Energy ◽  
Wide Range ◽  
Cellular Monte Carlo

A Monte Carlo rejection technique for numerically solving the complete, nonlinear phonon Boltzmann transport equation (BTE) is presented in this work, including three particles interactions. The technique has been developed to explicitly model population-dependent scattering within a full-band cellular Monte Carlo (CMC) framework, to simulate phonon transport in semiconductors, while ensuring conservation of energy and momentum for each scattering event within gridding error. The scattering algorithm directly solves the many-body problem accounting for the instantaneous distribution of the phonons. Our general approach is capable of simulating any nonequilibrium phase space distribution of phonons using the full phonon dispersion without the need of approximations used in previous Monte Carlo simulations. In particular, no assumptions are made on the dominant modes responsible for anharmonic decay, while normal and umklapp scattering are treated on the same footing. In this work, we discuss details of the algorithmic implementation of both the three-particle scattering for the treatment of the anharmonic interactions between phonons, as well as treating isotope and impurity scattering within the same framework. The simulation code was validated by comparison with both analytical and experimental results; in particular, the simulation results show close agreement with a wide range of experimental data such as thermal conductivity as function of the isotopic composition, the temperature, and the thin-film thickness.

Lattice Boltzmann Modeling of the Thermal Response of Silicon-On-Insulator Transistors Under Joule Heating Including Phonon Dispersion

2005 ◽  
Author(s):  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Joule Heating ◽  
Lattice Boltzmann ◽  
Source Term ◽  
Phonon Dispersion ◽  
Thermal Response ◽  
Phonon Transport ◽  
Silicon On Insulator ◽  
Simplifying Assumptions ◽  
Temperature Levels ◽  
Transient Thermal

Lattice Boltzmann Method (LBM) simulations of phonon transport are performed in a computational model of an Siliconon-Insulator (SOI) transistor to investigate the transient thermal response of the device under Joule heating conditions, which give origin to a non-equilibrium region of high temperature known as hotspot. The gray LBM based on the Debye assumption is compared to a dispersion LBM which incorporates nonlinear dispersion for all phonon branches, including explicit treatment of optical phonons without simplifying assumptions. The simulations cover the effect of hotspot size, heat pulse duration, and source term modeling, as either a constant or frequency-dependent term. Results indicate that hotspot peak temperature levels found by both the dispersion and the gray LBM are higher than Fourier diffusion predictions. Additionally, proper modeling of the source term is found to be critical, in order to accurately predict peak hotspot temperatures.

Electron-Phonon Interaction Model and Thermal Transport Simulation During ESD Event in NMOS Transistor

2007 ◽  
Author(s):  
Jae Sik Jin ◽  
Joon Sik Lee
Keyword(s):  
Group Velocity ◽  
Electron Energy ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Thermal Response ◽  
Interaction Model ◽  
Phonon Interaction ◽  
Nmos Transistor ◽  
Electron Phonon Interaction

An electron-phonon interaction model is proposed and applied to the transient thermal transport simulation during electrostatic discharge (ESD) event in the NMOS transistor. The high electron energy induced by the ESD in the transistor is transferred to the lattice phonons through electron-phonon interaction in the local region of the transistor. Due to this fact, a hot spot turns up, the size of which is much smaller than the phonon mean free path in the silicon layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied to describe the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electronphonon scattering is modeled through the intervalley and intravalley processes by introducing the average electron energy. In the simulation, the electron-phonon interaction model is used in the hot spot region, and then after a quasi-equilibrium state is achieved there, the temperature of lattice phonons in the silicon is calculated by using the phonon-phonon interaction model. The revolution of peak temperature in the hot spot during the ESD event is simulated and compared to that obtained by the previous full phonon dispersion model which treats the electron-phonon scattering as a volumetric heat source. The results show that the lower group velocity phonon modes (i.e. higher frequency) and optical mode of negligible group velocity obtain the highest energy density from electrons during the ESD event, which induces the devices melting phenomenon. The thermal response of phonon is also investigated, and it is found that the ratio of the phonon group velocity to the phonon specific heat can account for the phonon thermal response. If the ratio is higher than 2, the phonon have a good response to the heat input changes.

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