Thermal transport in beta-gallium oxide thin-film using non-gray Boltzmann transport equation

2021 ◽  
Author(s):  
Nitish Kumar ◽  
Matthew Barry ◽  
Satish Kumar
Keyword(s):  
Thin Films ◽  
Temperature Distribution ◽  
Energy Dissipation ◽  
Thermal Transport ◽  
Energy Exchange ◽  
Domain Size ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Abstract Phonon transport  in β-Ga2O3 thin films and metal–oxide field effect transistors (MESFETs) are investigated using non-gray Boltzmann transport equations (BTE) to decipher the effect of  ballistic-diffusive phonon transport. The effects of domain size, and  energy dissipation to various phonon modes and subsequent phonon-phonon energy exchange on the thermal transport and temperature distribution is investigated using non-gray BTE. Our analysis deciphered that domain size plays a major role in thermal transport in β-Ga2O3 but energy dissipation to various phonon modes and subsequent phonon-phonon energy exchange does not affect the temperature field significantly.   Phonon transport in β-Ga2O3 MESFETs on diamond substrate is investigated using coupled non-gray BTE and Fourier model. It is established that the ballistic effects need to be considered for devices with β-Ga2O3 layer thickness less than 1 µm. A non-gray phonon BTE model should be used near hotspot in the thin β-Ga2O3 layer as the Fourier model may not give accurate temperature distribution. The results from this work will help in understanding the mechanism of phonon transport in the β-Ga2O3 thin films and energy efficient design of its FETs.

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.

scholarly journals Computational Study of In-Plane Phonon Transport in Si Thin Films

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Xinjiang Wang ◽  
Baoling Huang
Keyword(s):  
Thin Films ◽  
Thermal Transport ◽  
Computational Study ◽  
Isotope Effects ◽  
Phonon Transport ◽  
Phonon Confinement ◽  
Phonon Modes ◽  
Scattering Rate ◽  
Si Films ◽  
Thermal Conductivities

Abstract We have systematically investigated the in-plane thermal transport in Si thin films using an approach based on the first-principles calculations and lattice dynamics. The effects of phonon mode depletion induced by the phonon confinement and the corresponding variation in interphonon scattering, which may be important for the thermal conductivities of ultra-thin films but are often neglected in precedent studies, are considered in this study. The in-plane thermal conductivities of Si thin films with different thicknesses have been predicted over a temperature range from 80 K to 800 K and excellent agreements with experimental results are found. The validities of adopting the bulk phonon properties and gray approximation of surface specularity in thin film studies have been clarified. It is found that in ultra-thin films, while the phonon depletion will reduce the thermal conductivity of Si thin films, its effect is largely offset by the reduction in the interphonon scattering rate. The contributions of different phonon modes to the thermal transport and isotope effects in Si films with different thicknesses under various temperatures are also analyzed.

DSMC Scheme for Phonon Transport in Solid Thin Films

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Mitsuhiro Matsumoto ◽  
Masaya Okano ◽  
Yusuke Masao
Keyword(s):  
Thin Films ◽  
Input Parameter ◽  
Direct Simulation Monte Carlo ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Phonon Dynamics ◽  
Solid Thin Films ◽  
Simulation Monte Carlo ◽  
Phonon Model

Analysis of phonon dynamics based on a linearized Boltzmann transport equation is widely used for thermal analysis of solid thin films, but couplings among various phonon modes appear in some situations. We propose a direct simulation Monte Carlo (DSMC) scheme to simulate the phonon gas starting without the conventional linearization approximation. This requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes. A prototype code based on a simple phonon model was developed, and energy flux was evaluated for thin films of various thickness as a test calculation.

FREQUENCY DEPENDENT PHONON TRANSPORT IN TWO-DIMENSIONAL SILICON AND DIAMOND THIN FILMS

2012 ◽  
Vol 26 (17) ◽  
pp. 1250104 ◽  
Author(s):  
B. S. YILBAS ◽  
S. BIN MANSOOR
Keyword(s):  
Thin Films ◽  
Boltzmann Transport Equation ◽  
Diamond Films ◽  
Equilibrium Temperature ◽  
Phonon Transport ◽  
Two Dimensional ◽  
Boltzmann Transport ◽  
Frequency Dependent ◽  
Aluminum Films ◽  
The Difference

Phonon transport in two-dimensional silicon and aluminum films is investigated. The frequency dependent solution of Boltzmann transport equation is obtained numerically to account for the acoustic and optical phonon branches. The influence of film size on equivalent equilibrium temperature distribution in silicon and aluminum films is presented. It is found that increasing film width influences phonon transport in the film; in which case, the difference between the equivalent equilibrium temperature due to silicon and diamond films becomes smaller for wider films than that of the thinner films.

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.

Heat Conduction in Nanostructured Materials Predicted by Phonon Bulk Mean Free Path Distribution

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Giuseppe Romano ◽  
Jeffrey C. Grossman
Keyword(s):  
Free Path ◽  
Nanostructured Materials ◽  
Thermal Transport ◽  
High Efficiency ◽  
Theoretical Models ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Computational Effort ◽  
Boltzmann Transport ◽  
Computational Framework

We develop a computational framework, based on the Boltzmann transport equation (BTE), with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path (MFP) distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with the frequency-dependent (FD) approach. Second, when the MFP distribution is available from theoretical models, our approach allows one to include easily the material dispersion in the calculations without discretizing the phonon frequencies for all polarizations thereby reducing considerably computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multiscale method that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon MFP distributions length. After validating our model against the FD approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has the potential to advance high-efficiency thermoelectric devices.

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.

Thermal Conductivity of Phonon Modes in Graphene Nanoribbon at Localized High Heating

2015 ◽  
Author(s):  
Tatiana Zolotoukhina
Keyword(s):  
Thermal Conductivity ◽  
Thermal Transport ◽  
Single Layer ◽  
Phonon Transport ◽  
Graphene Nanoribbon ◽  
Single Layer Graphene ◽  
Quasi Equilibrium ◽  
Phonon Modes ◽  
Limited Region ◽  
Small Areas

The spectral components of the phonon transport in the locally thermally excited graphene samples were studied by molecular dynamics (MD) method. In order to be able to select and analyze separate phonon modes in the time of propagation, the transient Green-Kubo approach to the definitions of density of states (DOS) and thermal conductivity was tested in quasi-equilibrium regimes for limited region of the graphene sample studied. Propagation of single modes at the background of diffusional phonon distribution and energy decay of such modes are studied by calculation of the DOS and dispersion relations, their dependence on the heating condition and temperature is studied. Similar conditions can be generated at localized heating of small areas of graphene structures in electronic devices. In transient regime, many issues of thermal transport evaluation still remain not sufficiently tested, especially phonon dynamics. Thermal conductivity of graphene samples related to transport of separate phonon modes is still not completely investigated, however, recent result give indication on the difference in the contribution of phonon modes. In the study, we consider mostly high temperature transport modes that are generated at the heated spot in order to be able to define their velocities and lifetimes in the limit of transient MD sampling. The single-layer graphene nanoribbon of 150 nm to 40 nm was relaxed and prepared in equilibrium in zigzag and armchair orientations. REBO potential for graphene was utilized. Our calculation has shown that at the heating to high temperatures of 1000K and higher, the G mode of graphene remains stationary and has a minimal contribution into thermal transport by coherent modes. The coherent phonon mode or modes that contribute the most into thermal transport were confined in the vicinity of 30 THz and can possibly be attributed to the D modes of graphene.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films: Role of Optical Phonons

2009 ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Optical Phonons ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

The Monte Carlo (MC) method has found prolific use in the solution of the Boltzmann Transport Equation (BTE) for phonons for the prediction of non-equilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions—in particular, optical phonons. A procedure to calculate scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that Transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T > 200K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes. At room temperature, optical modes are found to carry about 25% of the energy at steady state in Silicon thin films. Most importantly, inclusion of optical phonons results in better match with experimental observations for Silicon thin-film thermal conductivity.

Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization

2001 ◽  
Vol 123 (4) ◽  
pp. 749-759 ◽  
Author(s):  
Sandip Mazumder ◽  
Arunava Majumdar
Keyword(s):  
Thin Films ◽  
Monte Carlo ◽  
Monte Carlo Study ◽  
Past Research ◽  
Phonon Transport ◽  
Solution Technique ◽  
Boltzmann Transport ◽  
Linear Dispersion ◽  
Silicon Thin Films ◽  
Solid Thin Films

The Boltzmann Transport Equation (BTE) for phonons best describes the heat flow in solid nonmetallic thin films. The BTE, in its most general form, however, is difficult to solve analytically or even numerically using deterministic approaches. Past research has enabled its solution by neglecting important effects such as dispersion and interactions between the longitudinal and transverse polarizations of phonon propagation. In this article, a comprehensive Monte Carlo solution technique of the BTE is presented. The method accounts for dual polarizations of phonon propagation, and non-linear dispersion relationships. Scattering by various mechanisms is treated individually. Transition between the two polarization branches, and creation and destruction of phonons due to scattering is taken into account. The code has been verified and evaluated by close examination of its ability or failure to capture various regimes of phonon transport ranging from diffusive to the ballistic limit. Validation results show close agreement with experimental data for silicon thin films with and without doping. Simulation results show that above 100 K, transverse acoustic phonons are the primary carriers of energy in silicon.

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