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.

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.

Modeling Nanoscale Thermal Transport via the Boltzmann Transport Equation

2004 ◽  
Author(s):  
Cristina H. Amon ◽  
Jayathi Y. Murthy ◽  
Sreekant V. J. Narumanchi
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Group Velocity ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Solution Methods

In modern microelectronics, where extreme miniaturization has led to feature sizes in the sub-micron and nanoscale range, Fourier diffusion has been found to be inadequate for the prediction of heat conduction. Over the past decade, the phonon Boltzmann transport equation (BTE) in the relaxation time approximation has been employed to make thermal predictions in dielectrics and semiconductors at micron and nanoscales. This paper presents a review of the BTE-based solution methods widely employed in the literature. Particular attention is given to the problem of self-heating (hotspot) in sub-micron transistors. First, the solution approaches based on the gray formulation of the BTE are presented. In this class of solution methods, phonons are characterized by one single group velocity and relaxation time. Phonon dispersion is not accounted for in any detail. This is the most widely employed approach in the literature. The semi-gray BTE approach, moments of the Boltzmann equation, the lattice Boltzmann approach, and the ballistic-diffusive approximation are presented. Models which incorporate greater details of phonon dispersion are also discussed. This includes a full phonon dispersion model developed recently by the authors. This full phonon dispersion model satisfies energy conservation, incorporates the different phonon modes, and well as the interactions between the different modes, and accounts for the frequency dependence for both the phonon group velocity and relaxation times. Results which illustrate the differences between some of these models reveal the importance of developing models that incorporate substantial details of phonon physics.

Thermal Characterization of Cu/CoFe Multilayer for Giant Magnetoresistive (GMR) Head Applications

2004 ◽  
Author(s):  
Y. Yang ◽  
M. Asheghi
Keyword(s):  
Giant Magnetoresistance ◽  
Room Temperature ◽  
Boltzmann Transport Equation ◽  
Thermal Characterization ◽  
Disk Drive ◽  
Boltzmann Transport ◽  
Self Heating ◽  
Superlattice Structure ◽  
Metallic Ferromagnet

Giant Magnetoresistance (GMR) head technology is one of the latest advancement in hard disk drive (HDD) storage industry. The GMR head superlattice structure consists of alternating layers of extremely thin metallic ferromagnet and paramagnet films. A large decrease in the resistivity from antiparallel to parallel alignment of the film magnetizations can be observed, known as giant magnetoresistance (GMR) effect. The present work characterizes the in-plane electrical and thermal conductivities of Cu/CoFe GMR multilayer structure in the temperature range of 50 K to 340 K using Joule-heating and electrical resistance thermometry in suspended bridges. The thermal conductivity of the GMR layer monotonously increased from 25 Wm−1K−1 (at 55 K) to nearly 50 Wm−1K−1 (at room temperature). We also report the GMR ratio of 17% and a large negative magnetothermal resistance effect (GMTR) of 33% in Cu/CoFe superlattice structure. The Boltzmann transport equation (BTE) is used to estimate the GMR ratio, and to investigate the effect of repeats, as well as the spin-dependent interface and boundary scatting on the transport properties of the GMR structure. Aside from the interesting underlying physics, these data can be used in the predictions of the Electrostatic Discharge (ESD) failure and self-heating in GMR heads.

Solution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules

2006 ◽  
Author(s):  
Tianjiao Wang ◽  
Jayathi Y. Murthy
Keyword(s):  
Thin Film ◽  
Energy Conservation ◽  
Transport Equation ◽  
Phonon Dispersion ◽  
Boltzmann Transport Equation ◽  
Physical Space ◽  
Finite Volume Scheme ◽  
Boltzmann Transport ◽  
Bulk Silicon ◽  
Silicon Thin Film

A finite volume scheme is developed to solve the phonon Boltzmann transport equation in an energy form accounting for phonon dispersion and polarization. The physical space and the first Brillouin zone are discretized into finite volumes and the phonon BTE is integrated over them. Second-order accurate differencing schemes are used for the discretization. The scattering term employs a rigorous implementation of phonon momentum and energy conservation laws in determining the rate of normal and Umklapp processes. The method is applied to a variety of bulk silicon and silicon thin-film conduction problems and shown to perform satisfactorily.

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.

Submicron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization

2004 ◽  
Vol 126 (6) ◽  
pp. 946-955 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Thermal Conductivity ◽  
Phonon Dispersion ◽  
Transport Model ◽  
Relaxation Times ◽  
Thermal Response ◽  
Boltzmann Transport ◽  
Wide Range ◽  
Submicron Scale ◽  
Different Temperatures ◽  
Finite Volume Approach

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the submicron 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 and longitudinal acoustic 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. In the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model. Experimental in-plane thermal conductivity data for silicon thin films over a wide range of temperatures are also matched satisfactorily.

Ballistic-Diffusive Approximation for Phonon Transport Accounting for Polarization and Dispersion

2003 ◽  
Author(s):  
J. Y. Murthy ◽  
S. R. Mathur
Keyword(s):  
Thermal Conductivity ◽  
Diffusion Approximation ◽  
Phonon Dispersion ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Conductivity Measurements ◽  
Bulk Silicon ◽  
Medium Component ◽  
Diffusive Approximation

A ballistic-diffusive approximation to the Boltzmann transport equation is developed for describing phonon transport in semi-conductors and dielectrics. The model incorporates the effects of phonon dispersion and polarization by considering longitudinal, transverse and optical branches. Each branch is divided into frequency bands, and scattering between branches and bands is incorporated subject to conservation rules. The phonon energy in each band is divided into a boundary and a medium component, with the latter being computed using a diffusion approximation. The approximation is shown to work well by comparing its predictions to exact solutions as well thermal conductivity measurements for bulk silicon.

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