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.

THERMAL INVESTIGATION OF COMMON 2D FETs AND NEW GENERATION OF 3D FETs USING BOLTZMANN TRANSPORT EQUATION IN NANOSCALE

2013 ◽  
Vol 24 (09) ◽  
pp. 1350064 ◽  
Author(s):  
R. S. SAMIAN ◽  
A. ABBASSI ◽  
J. GHAZANFARIAN
Keyword(s):  
Transport Equation ◽  
Thermal Performance ◽  
Field Effect Transistors ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Heat Diffusion ◽  
Equal Weight ◽  
Boltzmann Transport ◽  
Oxide Interface ◽  
New Generation

The thermal performance of two-dimensional (2D) field-effect transistors (FET) is investigated frequently by solving the Fourier heat diffusion law and the Boltzmann transport equation (BTE). With the introduction of the new generation of 3D FETs in which their thickness is less than the phonon mean-free-path it is necessary to carefully simulate the thermal performance of such devices. This paper numerically integrates the BTE in common 2D transistors including planar single layer and Silicon-On-Insulator (SOI) transistor, and the new generation of 3D transistors including FinFET and Tri-Gate devices. In order to decrease the directional dependency of results in 3D simulations; the Legendre equal-weight (PN-EW) quadrature set has been employed. It is found that if similar switching time is assumed for 3D and 2D FETs while the new generation of 3D FETs has less net energy consumption, they have higher hot-spot temperature. The results show continuous heat flux distribution normal to the silicon/oxide interface while the temperature jump is seen at the interface in double layer transistors.

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar
Keyword(s):  
Gallium Nitride ◽  
Transport Equation ◽  
Thermal Transport ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Significant Loss ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Thermal Transport ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.

Heat Pulse Propagation in Silicon Nanostructures by Solving Phonon Transport Equation

2008 ◽  
Author(s):  
Damian Terris ◽  
Karl Joulain ◽  
Denis Lemonnier
Keyword(s):  
Transport Equation ◽  
Pulse Propagation ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Isotropic Scattering ◽  
Silicon Nanostructures ◽  
Boltzmann Transport ◽  
Discrete Ordinate ◽  
Rectangular Mesh ◽  
Angle Space

The temperature evolution prediction of silicon nanofilms and nanowires can be useful to safeguard high technology systems of its deterioration. The simulation of a level and a pulse in these nanostructures is then made with Boltzmann Transport Equation (BTE) resolution using the single time approximation. The Discrete Ordinate (DO) method helps to numerate the angle space. BTE is written in cylindrical coordinates which corresponds to wires. Therefore, the cylindrical plane is considered as an isotropic scattering to mimic a nanowire and then, as a specular reflexion (which conserve z momentum) to simulate a nanofilm. Using the axisymmetry done with a specular reflexion, the cylinder is two dimensionally discretized with a regular rectangular mesh.

scholarly journals Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5110
Author(s):  
Yangyu Guo ◽  
Masahiro Nomura ◽  
Sebastian Volz ◽  
Jose Ordonez-Miranda
Keyword(s):  
Heat Transport ◽  
State Of The Art ◽  
Boltzmann Transport Equation ◽  
Thermal Conductance ◽  
Heat Diffusion ◽  
Heat Sources ◽  
Boltzmann Transport ◽  
Heat Diffusion Equation ◽  
Current State ◽  
Linear Behavior

Heat transport guided by the combined dynamics of surface phonon-polaritons (SPhPs) and phonons propagating in a polar nanowire is theoretically modeled and analyzed. This is achieved by solving numerically and analytically the Boltzmann transport equation for SPhPs and the Fourier’s heat diffusion equation for phonons. An explicit expression for the SPhP thermal conductance is derived and its predictions are found to be in excellent agreement with its numerical counterparts obtained for a SiN nanowire at different lengths and temperatures. It is shown that the SPhP heat transport is characterized by two fingerprints: (i) The characteristic quantum of SPhP thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 μm supporting the ballistic propagation of SPhPs. (ii) The deviation of the temperature profile from its typical linear behavior predicted by the Fourier’s law in absence of heat sources. For a 150 μm-long SiN nanowire maintaining a quasi-ballistic SPhP propagation, this deviation can be as large as 1 K, which is measurable by the current state-of-the-art infrared thermometers.

The first-principles and BTE investigation of phonon transport in 1T-TiSe2

2021 ◽  
Author(s):  
Zhao-Liang Wang ◽  
Guofu Chen ◽  
Xiaoliang Zhang ◽  
Dawei Tang
Keyword(s):  
Density Functional Theory ◽  
Transport Equation ◽  
First Principles ◽  
Density Functional ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Functional Theory

Through the first-principles density functional theory and the phonon Boltzmann transport equation, we investigated the phonon transport characteristics inside 1T-TiSe2.

A Generalized Enhanced Fourier Law

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Ashok T. Ramu ◽  
John E. Bowers
Keyword(s):  
Heat Flux ◽  
Transport Equation ◽  
Phonon Mode ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Fourier Law ◽  
Transport Effects

A generalized enhanced Fourier law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables is derived from the Boltzmann transport equation. It generalizes the previously reported EFL from a gray phonon population to an arbitrary quasi-ballistic phonon mode population, the chief advantage being its formulation in terms of observables like the heat flux and temperature, in a manner akin to the Fourier law albeit rigorous enough to describe quasi-ballistic phonon transport.

Improved Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2009 ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation ◽  
Thermal Conductivities

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time phonon BTE model employs a single-mode relaxation time idea, but the relaxation time is a function of wave-vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior as well as relaxation times satisfying conservation rules. A critical issue in the model development is the accounting for the role of three-phonon N scattering processes. Direct inclusion of N processes into the anisotropic relaxation time model is not possible because such an inclusion would engender thermal resistance. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulation by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted bulk thermal conductivities of silicon and silicon thin-film thermal conductivities with experimental measurements.

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