ThesisMSME_Krishna_AM_FS_JW_RevFinal.pdf (2.98 MB)

Download file# Active Tuning of Thermal Conductivity in Single layer Graphene Phononic crystals using Engineered Pore Geometry and Strain

Understanding thermal transport across length scales lays the foundation to developing high-performance electronic devices. Although many experiments and models of the past few decades have explored the physics of heat transfer at nanoscale, there are still open questions regarding the impact of periodic nanostructuring and coherent phonon effects, as well as the interaction of strain and thermal transport. Thermomechanical effects, as well as strains applied in flexible electronic devices, impact the thermal transport. In the simplest kinetic theory models, thermal conductivity is proportional to the phonon group velocity, heat capacity, and scattering times. Periodic porous nanostructures impact the phonon dispersion relationship (group velocity) and the boundaries of the pores increase the scattering times. Strain, on the other hand, affects the crystal structure of the lattice and slightly increases the thermal conductivity of the material under compression. Intriguingly, applying strain combined with the periodic porous structures is expected to influence both the dispersion relation and scattering rates and yield the ability to tune thermal transport actively. But often these interrelated effects are simplified in models.

This work evaluates the combination of structure and strain on thermal conductivity by revisiting some of the essential methods used to predict thermal transport for a single layer of graphene with a periodic porous lattice structure with and without applied strain. First, we use the highest fidelity method of Non-Equilibrium Molecular Dynamics (NEMD) simulations to estimate the thermal conductivity which considers the impact of the lattice structure, strain state, and phononic band structure together. Next, the impact of the geometry of the slots within the lattice is interrogated with Boltzmann Transport Equation (BTE) models under a Relaxation Time Approximation. A Monte Carlo based Boltzmann Transport Equation (BTE) solver is also used to estimate the thermal conductivity of phononic crystals with varying pore geometry. Dispersion relations calculated from continuum mechanics are used as input here. This method which utilizes a simplified pore geometry only partially accounts for the effects of scattering on the pore boundaries. Finally, a continuum level model is also used to predict the thermal conductivity and its variations under applied strain. As acoustic phonon branches tend to carry the most heat within the lattice, these continuum models and other simple kinetic theories only consider their group velocities to estimate their impact on phonon thermal conductivity. As such, they do not take into account the details of phonon transport across all wavelengths.

By comparing the results from these different methods, each of which has different assumptions and simplifications, the current work aims to understand the effects of changes to the dispersion relationship based on strain and the periodic nanostructures on the thermal conductivity. We evaluate the accuracy of the kinetic theory, ray tracing, and BTE models in comparison to the MD results to offer a perspective of the reliability of each method of thermal conductivity estimation. In addition, the effect of strain on each phononic crystal with different pore geometry is also predicted in terms of change to their in-plane thermal anisotropy values. To summarize, this deeper understanding of the nanoscale thermal transport and the interrelated effects of geometry, strain, and phonon band structure on thermal conductivity can aid in developing lattices specifically designed to achieve the required dynamic thermal response for future nano-scale thermoelectric applications.

This work evaluates the combination of structure and strain on thermal conductivity by revisiting some of the essential methods used to predict thermal transport for a single layer of graphene with a periodic porous lattice structure with and without applied strain. First, we use the highest fidelity method of Non-Equilibrium Molecular Dynamics (NEMD) simulations to estimate the thermal conductivity which considers the impact of the lattice structure, strain state, and phononic band structure together. Next, the impact of the geometry of the slots within the lattice is interrogated with Boltzmann Transport Equation (BTE) models under a Relaxation Time Approximation. A Monte Carlo based Boltzmann Transport Equation (BTE) solver is also used to estimate the thermal conductivity of phononic crystals with varying pore geometry. Dispersion relations calculated from continuum mechanics are used as input here. This method which utilizes a simplified pore geometry only partially accounts for the effects of scattering on the pore boundaries. Finally, a continuum level model is also used to predict the thermal conductivity and its variations under applied strain. As acoustic phonon branches tend to carry the most heat within the lattice, these continuum models and other simple kinetic theories only consider their group velocities to estimate their impact on phonon thermal conductivity. As such, they do not take into account the details of phonon transport across all wavelengths.

By comparing the results from these different methods, each of which has different assumptions and simplifications, the current work aims to understand the effects of changes to the dispersion relationship based on strain and the periodic nanostructures on the thermal conductivity. We evaluate the accuracy of the kinetic theory, ray tracing, and BTE models in comparison to the MD results to offer a perspective of the reliability of each method of thermal conductivity estimation. In addition, the effect of strain on each phononic crystal with different pore geometry is also predicted in terms of change to their in-plane thermal anisotropy values. To summarize, this deeper understanding of the nanoscale thermal transport and the interrelated effects of geometry, strain, and phonon band structure on thermal conductivity can aid in developing lattices specifically designed to achieve the required dynamic thermal response for future nano-scale thermoelectric applications.