Multi-scale simulation of phonon transport across heterogeneous interfaces
Heat transfer at lengths scales less than the mean free path of thermal energy carriers has emerged as a critical research topic, driven in part by the downscaling of integrated circuits. This work focuses on investigating phonon transport at heterogeneous interfaces and the corresponding interface resistance, which has been shown to comprise a significant part of the total thermal impendence. The goal is to develop a relationship among interface geometry, atomic structure, and the resultant interface resistance for use in the optimization of heat transfer in multiscale system simulations. ^ The traditional Fourier heat conduction model is inapplicable at length scales below the mean free path. Therefore, developing new thermal measurement and simulation methods is crucially important for investigating sub-micron thermal energy transport phenomena. In this work, an extension of the atomistic Green’s function (AGF) method is developed to model phonon wave characteristics and to quantify phonon transport properties at the nanometer scale. The AGF results are then integrated with a particle-based non-gray Boltzmann transport equation (BTE) model that treats phonons as semi-classical particles; the resulting simulation approach offers a comprehensive treatment of phonon duality and extends the application of the BTE to heat conduction in domains with heterogeneous interfaces. ^ In response to the growing interest in graphene-related material research, the AGF approach is applied to the study of thermal conductance in graphene sheets and graphene nanoribbons (GNRs). At isotope-doped interfaces, the phonon transmission function of each vibrational branch in at heterogeneous interface is calculated, and the major and minor channels of phonon transport through graphene are identified. Further, phonon wave effects in zigzag and armchair edge ribbons are investigated. Phonon transmission functions and thermal conductances are found to be sensitive to the edge shape of the structure. The phonon transmission functions of nanoribbons with defects are evaluated by artificially creating mismatches at interfaces. By comparing the transmission function of different defect patterns and the corresponding thermal conductances, the reduction of phonon transport is quantified. The length of defects is found to be important to phonon transport. These results offer a useful reference and suggest directions for future research on the thermal applications of this material. ^ This work also considers phonon transport behavior in GNRs that bridge semi-infinite graphene contacts. Thermal conductances are found to be sensitive to the edge shape of the ribbons; a sandwiched zigzag GNR structure has almost twice the thermal conductance of the corresponding armchair structure. Results show that the graphene-GNR interface moderately reduces phonon conductance compared to a freestanding GNR. At fixed device lengths, conductance increases with the width of GNR. On the other hand, conductance decreases with GNR length. The zigzag ribbons show smaller reduction with increasing GNR length than armchair ribbons; the conductances of both ribbons converge to a length-independent value. For very short devices, thermal conductance can exceed that of a single graphene-GNR interface. ^ The AGF method is also used to study phonon transport in a heterogeneous interface between bulk TiC substrate and GNRs. The force constants that govern the lattice dynamical equations are obtained from first-principles density functional theory (DFT) calculations and then optimized for the Green’s function study after truncation on interatomic interactions is introduced. Phonon vibrational properties of TiC and GNRs are investigated by lattice dynamics (LD) calculation with the optimized constants and limited difference is found between the LD results and direct DFT calculation results. Thermal conductances of TiC-GNR-TiC cases are studied together with TiC-GNR structures. The conductances of TiC-GNR interfaces are normalized by ribbon width and are found to converge. The converged value is used to estimate the interface resistance of multi-walled carbon nanotubes (MWCNTs) grown on metal catalyst support substrates. The estimated resistance is found to match experiment results in an order of magnitude sense. The results reveal that covalent bonds might be formed during CNT synthesis and phonon wave mismatch between materials can severely reduce interface energy transport. ^
Timothy S. Fisher, Purdue University, Jayathi Y. Murthy, Purdue University.
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