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Open Access Publications from the University of California

Non-diffusive Heat Conduction in Nano-/Micro-scale Structures

  • Author(s): Wang, Dadong
  • Advisor(s): Ma, Yanbao
  • et al.

Rapid progress has been made in the manufacture of microelectronic and thermoelectric devices. With continuous decrease in the size of devices and structures, the manipulation and control of phonon-mediated heat transfer on the nano-/micro-scale is becoming a bottleneck for the development of many nano-/micro-technologies. To advance these technologies, it is necessary to understand the fundamental mechanisms of thermal transport at nano-/micro-scale. The new feature of heat transfer in nano-/micro-scale systems is non-diffusive thermal transport which cannot be described by Fourier’s law. However, current nano-thermometry of non-diffusive heat transfer still focuses on studying the effective thermal conductivity within the framework of Fourier’s law due to a lack of a well-accepted non-diffusive model. The molecular dynamics (MD) and full spectral Boltzmann transport equation (BTE) are unpractical to be applied for experimental data analysis due to their prohibited computational cost. For Gray BTE and other macroscopic models such as Cattaneo-Vernotte (CV) equation, Guyer-Krumhansl (GK) equation, Dual-phase-lag (DPL) equation and et al., they cannot capture the non-diffusive heat transport accurately.

In this thesis we will develop a high-fidelity model that can accurately describe phonon transport at nano-/micro-scale regime and can replace Fourier’s law for experimental data analysis. The new model named enhanced gray (EG) model is derived from the phonon Boltzmann transport equation (BTE) by considering the second-order terms in Taylor expansion of phonon density distribution. In the proposed enhanced gray BTE (EG-BTE), two parameters associated with inherent material properties, i.e., the ballistic mean free time and the diffusive relaxation time, are used to characterize the non-diffusive nature of heat conduction. Theoretical solutions of EG-BTE

based on Fourier transform are presented in three-dimensional domain for transient thermal grating (TTG) experiments and time domain thermo-reflectance (TDTR) experiments. The reconstructed thermal decays by EG-BTE are in excellent match with the measured signal traces in TTG and TDTR experiments, which demonstrates the validity of our new model. For problems where analytical solutions are not available, an implicit lattice Boltzmann method (LBM) is developed to solve the EG-BTE, which is unconditionally stable and computationally efficient. As an illustrative application, the phonon transport in cryogenic crystals is studied by implicit LBM simulation based on EG-BTE. The heat-pulse experiment conducted in cryogenic crystals observed the only direct evidence of ballistic heat transport. The successive interpretation of this benchmark case by EG-BTE provides a better understanding of the physical nature of non-diffusive heat transfer.

The proposed EG-BTE opens a new avenue to study the unique features of non-diffusive heat transfer. The current interpretations of TDTR experiments is limited by Fourier’s law. For example, the measurements of effective thermal conductivity within the framework of Fourier’s law will provide little insight for non-diffusive heat transfer. By deriving the analytical solution of EG-BTE for TDTR experiments, a new theoretical framework based on EG-BTE that can remove the limit of Fourier law for experimental data analysis is developed and proved. Some unique material thermal properties of non-diffusive heat conduction can be characterized, such as the ballistic mean free time and the diffusive relaxation time. But further development and improvement of the theoretical tool are required to understand other features of non-diffusive heat transfer, such as the interfacial thermal conductance, which can be our future work.

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