Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


SyedAliDissertation.pdf (4.11 MB)

ETD Abstract Container

Abstract Header

Phonon Boltzmann Transport Equation (BTE) Based Modeling of Heat Conduction in Semiconductor Materials at Sub-Micron Scales

Ali, Syed Ashraf
http://rave.ohiolink.edu/etdc/view?acc_num=osu1482776207590992

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Mechanical Engineering.
Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In the first part of this dissertation, strategies and algorithms for large-scale parallel computation of the frequency and polarization dependent phonon BTE are presented, that has been discretized using an unstructured finite volume method and control angle discrete ordinates method for spatial discretization and angular discretization, respectively. The single-time relaxation approximation is used to treat phonon-phonon scattering. For large-scale computation, three different parallelization strategies are explored: (a) band-wise, (b) direction-wise, and (c) hybrid band/cell-wise. Transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral control volumes, 40 spectral bins for spectral discretization and 400 angles for angular discretization. This resulted in ~9.7 x 109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-wise and hybrid band/cell-wise parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy (about 88%) was found to be superior to that of the direction-wise strategy, and is recommended as the preferred strategy for even larger scale computations. In the second part of this dissertation, interface models were developed and implemented in the BTE solver in order to extend it to multi-materials. Two models for phonon transmission across semiconductor interfaces are investigated and demonstrated in the context of large-scale spatially three-dimensional calculations of the phonon Boltzmann Transport Equation (BTE). These include two modified forms of the classical diffuse mismatch model: one, in which dispersion is accounted for, and another, in which energy transfer between longitudinal and transverse acoustic phonons is disallowed. The present study considers the interplay between the interface and intrinsic (volumetric) scattering of phonons by incorporating the interface models into the parallel solver developed for the full seven-dimensional BTE for phonons, which is an advancement over the vast majority of previous studies where the interface is treated in isolation, and the thermal boundary conductance is calculated using closed-form analytical formulations. A verification study is conducted by comparing thermal boundary resistance of a silicon/germanium interface predicted by the BTE, against previously reported results of molecular dynamics calculations. The BTE solutions over-predicted the interfacial resistance, and the reasons for this discrepancy are discussed. It is found that due to the interplay between intrinsic and interface scattering, the interfacial thermal resistance across a Si(hot)/Ge(cold) bilayer is different from that of a Si(cold)/Ge(hot) bilayer. Finally, the phonon BTE is solved for a nanoscale three-dimensional heterostructure, comprised of multiple blocks of silicon and germanium, and the time evolution of the temperature distribution is predicted, and compared against predictions using the Fourier law of heat conduction. The most important input to the phonon BTE is the spectral mean free path of the phonons, which constitutes the product of group velocity of the phonons and the phonon-phonon scattering time-scale. Time Domain Thermo-Reflectance (TDTR) experiments have been recently identified as a viable pathway toward extracting the phonon mean free path spectrum of semiconductor materials. In the third part of this work, TDTR experiments are simulated using large-scale parallel computations of the phonon BTE in a two-dimensional computational domain. Simulations are performed for multiple pulse and modulation cycles of the TDTR pump laser. This requires resolution of a picosecond laser pulse within a computational timeframe that spans several hundreds of nanoseconds. The metallic transducer layer on top of the silicon substrate is modeled using the Fourier law and is coupled to the BTE. Studies are conducted for four different laser spot sizes and two different modulation frequencies. The BTE results are fitted to the Fourier law, and effective thermal conductivities of the substrate are extracted. It is demonstrated that the time delay of the probe laser could have a significant effect on the fitted (extracted) thermal conductivity value. The modulation frequency is found to have negligible effect on the thermal conductivity, while the spot size variation exhibits significant impact. Both trends are found to be in agreement with experimental observations. The thermal conductivity accumulation function is also computed, and the effect of the mean free path spectrum on the thermal conductivity suppression is delineated. This dissertation has three major contributions in the field of non-equilibrium phonon mediated thermal transport. First, parallelization strategies were developed and demonstrated for a 3D device-like geometry with about 9.7 x 109 unknowns, which is approximately 3 orders of magnitude lager than previously reported in this area. Second, interface models were developed and implemented with the parallel phonon BTE solver in order to extend the capability of the BTE solver to simulate semiconductor heterostructures. The prediction of this simulation was also compared with the prediction with the Fourier law of heat conduction to highlight the importance of simulation of non-equilibrium heat transport. Calculations of such large-scale 3D heterostructures are the first of their kind. Finally, TDTR experiments were simulated using the phonon BTE for multiple pulses and modulation cycles of the TDTR pump laser. This is in contrast with previous studies where only one pulse of the pump laser has been simulated. The TDTR simulations lay the foundation for future inverse calculation for extracting the phonon mean free path spectrum directly experimental data.
Sandip Mazumder, Dr. (Advisor)
Vishwanath Subramaniam, Dr. (Committee Member)
Marat Khafizov, Dr. (Committee Member)
P Sadayappan, Dr. (Committee Member)
222 p.
Mechanical Engineering

Recommended Citations

Citations

  • Ali, S. A. (2017). Phonon Boltzmann Transport Equation (BTE) Based Modeling of Heat Conduction in Semiconductor Materials at Sub-Micron Scales [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1482776207590992

    APA Style (7th edition)

  • Ali, Syed. Phonon Boltzmann Transport Equation (BTE) Based Modeling of Heat Conduction in Semiconductor Materials at Sub-Micron Scales . 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1482776207590992.

    MLA Style (8th edition)

  • Ali, Syed. "Phonon Boltzmann Transport Equation (BTE) Based Modeling of Heat Conduction in Semiconductor Materials at Sub-Micron Scales ." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1482776207590992

    Chicago Manual of Style (17th edition)

osu1482776207590992
3,808
© 2017, some rights reserved.Creative Commons License Phonon Boltzmann Transport Equation (BTE) Based Modeling of Heat Conduction in Semiconductor Materials at Sub-Micron Scales by Syed Ashraf Ali is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.