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.

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.

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.

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.

Lattice Boltzmann Modeling of Subcontinuum Energy Transport in Crystalline and Amorphous Microelectronic Devices

2006 ◽  
Vol 128 (2) ◽  
pp. 115-124 ◽  
Author(s):  
Rodrigo Escobar ◽  
Brian Smith ◽  
Cristina Amon
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Energy Transport ◽  
Phonon Dispersion ◽  
Numerical Models ◽  
Phonon Transport ◽  
Nonlinear Frequency ◽  
Boltzmann Method

Numerical simulations of time-dependent energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann method is derived from the continuous Boltzmann transport equation assuming first gray dispersion and then nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that a transition from diffusive to ballistic energy transport is found as the characteristic length of the system becomes comparable to the phonon mean free path. The methodology is used in representative microelectronics applications covering both crystalline and amorphous materials including silicon thin films and nanoporous silica dielectrics. Size-dependent thermal conductivity values are also computed based on steady-state temperature distributions obtained from the numerical models. For each case, reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values. Overall, simulations that consider phonon dispersion yield results more consistent with experimental correlations.

Computations of Sub-Micron Heat Transport in Silicon Accounting for Phonon Dispersion

2003 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Phonon Dispersion ◽  
Relaxation Times ◽  
Thermal Response ◽  
Boltzmann Transport ◽  
Proposed Model ◽  
Transverse Acoustic ◽  
Different Temperatures ◽  
Finite Volume Approach ◽  
Transient Thermal ◽  
Transient Thermal Response

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the sub-micron scale. However, most published studies make a gray assumption and do not account for either dispersion or polarization. In this study, we propose a model based on the BTE, accounting for transverse acoustic (TA) and longitudinal acoustic (LA) phonons as well as optical phonons. This model incorporates realistic phonon dispersion curves for silicon. The interactions among the different phonon branches and different phonon frequencies are considered, and the proposed model satisfies energy conservation. Frequency-dependent relaxation times, obtained from perturbation theory, and accounting for phonon interaction rules, are used. In the present study, the BTE is numerically solved using a structured finite volume approach. For a problem involving a film with two boundaries at different temperatures, the numerical results match the analogous exact solutions from radiative transport literature for various acoustic thicknesses. For the same problem, the transient thermal response in the acoustically thick limit matches results from the solution to the parabolic Fourier diffusion equation. Also, in the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model even at coarse phonon frequency band discretization.

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.

Time-Dependent Simulations of Sub-Continuum Heat Generation Effects in Electronic Devices Using the Lattice Boltzmann Method

2003 ◽  
Author(s):  
Rodrigo A. Escobar ◽  
Sartaj S. Ghai ◽  
Cristina H. Amon ◽  
Myung S. Jhon
Keyword(s):  
Lattice Boltzmann Method ◽  
Heat Generation ◽  
Lattice Boltzmann ◽  
Phonon Scattering ◽  
Constant Heat Flux ◽  
Silicon On Insulator ◽  
Wave Nature ◽  
Temperature Levels ◽  
Boltzmann Method ◽  
Fourier Equation

The lattice Boltzmann method (LBM), which accounts for electron-phonon scattering, is used to investigate heat generation effects on silicon-on-insulator (SOI) transistors. The wave nature of the LBM is shown and its influence on subcontinuum dynamics is discussed. The implementation of boundary conditions for constant temperature and constant heat flux is described. SOI devices are modeled as thin films in one dimension. The LBM simulation results for diffusive, transitional, and ballistic regimes are compared with Fourier equation solutions and literature results. For transitional and ballistic regimes, Fourier equation results underpredict the temperature levels obtained by the LBM, which is consistent with the findings previously reported by different authors.

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