Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Thesis.pdf (3.97 MB)

ETD Abstract Container

Abstract Header

A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation

Allu, Pareekshith
http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769

Abstract Details

2016, Master of Science, Ohio State University, Mechanical Engineering.
Thermal related issues are among the most common causes for semiconductor device failure. With the current generation microprocessors having an exceedingly high power density, efficient heat removal from transistor to the chip surface level has been a major bottleneck in further miniaturization performance improvements. As a result, understanding the physical mechanisms underlying thermal transport at the device scales, which usually range from a few tens of nanometers to a few micrometers, is critical to designing efficient heat removal strategies. At room temperature, the energy carrying wave packets (or phonons) in silicon have an average mean free path around 300nm, which is comparable to or larger than the device length scales. Thermal transport in such regimes is referred to as non-equilibrium transport and the Boltzmann Transport Equation (BTE) is a powerful tool that can model heat conduction in non-equilibrium conditions. Although the BTE has witnessed great success, it is an eight-dimensional partial differential equation which makes it quite challenging and computationally intensive to solve. In this study, a general-purpose deterministic hybrid ballistic-diffusive method is developed to enhance the computational efficiency of solving the transient and frequency dependent (non-gray) BTE. To achieve this, phonon transport is demarcated using a cutoff Knudsen number into two distinct regimes namely, the ballistic (when phonon mean free paths are larger than the device length scales) and diffusive (when phonon mean free paths are smaller than the device length scales) regimes. The original BTE is then discretized in frequency space, and for all those spectral bands whose Knudsen number is larger than the cutoff Knudsen number, the CADOM is applied, and in order to increase the efficiency, the spherical harmonics (P1) approximation is invoked in the remainder of the spectral bands. The end result is a hybrid methodology that is able to solve the BTE in all transport regimes more efficiently than previously used methods while compromising little on accuracy. The accuracy and efficiency of the hybrid method is tested over a broad temperature range spanning 195K – 205K, 245K – 255K and 295K – 305K for two- and three-dimensional configurations both at steady state and under transient conditions. Overall, it was found that the hybrid method is more accurate than the diffuse P1 approximation while being computationally more efficient than the CADOM for transient simulation studies at all temperature ranges. For steady state simulations, the hybrid method is more accurate than the P1 method in operating temperature ranges of 195K – 205K and 245K – 255K, while it performs similar to the P1 approximation in the diffuse regime at 295K – 305K. Overall, the performance of the hybrid method can be tweaked by adjusting the cutoff Knudsen number to yield the desired gains in either accuracy or efficiency. The development of the hybrid method serves as a significant step toward advancement of methods for solving the phonon BTE. Accurate and efficient simulation of sub-micron thermal transport in semiconductors ultimately lead to better thermal management strategies that can aid in the further advancement and miniaturization of microprocessors in the semiconductor industry.
Sandip Mazumder (Advisor)
Seung Hyun Kim (Committee Member)
167 p.
Energy; Mechanical Engineering
Sub micron scale heat transfer; Non-equilibrium heat conduction; Boltzmann transport equation

Recommended Citations

Citations

  • Allu, P. (2016). A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769

    APA Style (7th edition)

  • Allu, Pareekshith. A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation. 2016. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769.

    MLA Style (8th edition)

  • Allu, Pareekshith. "A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation." Master's thesis, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769

    Chicago Manual of Style (17th edition)

osu1451998769
655
© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.