Effect of Sub-Continuum Energy Transport on Effective Thermal Conductivity in Nanoporous Silica (Aerogel)

Author(s):  
Brian R. Smith ◽  
Cristina H. Amon

This paper analyzes the effect of Fourier vs. subcontinuum heat transport through thin layers of nanoporous silica (aerogel) in the framework of an infrared focal plane array (IRFPA) sensor system. Aerogel is introduced as a compatible material for emerging microsystems applications and the comparison between aerogel and conventional insulation systems is analyzed. Correlations between aerogel’s macro-scale thermal properties and its nano-scale structure are discussed to address the effect of the material’s amorphous structure and sub-continuum phonon transport phenomena on macro-scale thermal conductivity. Simulations using the Lattice Boltzmann Method (LBM) quantify the effect of phonon scattering on silica conductivity. Techniques for extending the analysis to a three-dimensional silica matrix are discussed in light of recent advances in the simulation of aerogel morphology.

Author(s):  
Jungwan Cho ◽  
Pane C. Chao ◽  
Mehdi Asheghi ◽  
Kenneth E. Goodson

Silicon films of thickness near and below one micrometer play a central role in many advanced technologies for computation and energy conversion. Numerous data on the thermal conductivity of silicon thin films are available in the literature, but mainly for the in-plane thermal conductivity of polycrystalline and single-crystal films. Here we use picosecond time-domain thermoreflectance (TDTR), transmission electron microscopy, and phonon transport theory to investigate heat conduction normal to polycrystalline silicon films on diamond substrates. The data agree with predictions that account for the coupled effects of phonon scattering on film boundaries and defects concentrated near grain boundaries. Using the data and the model, we estimate the polysilicon-diamond interface resistance to be 6.5–8 m2 K GW−1.


2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Lina Yang ◽  
Austin J. Minnich

Abstract Nanocrystalline thermoelectric materials based on Si have long been of interest because Si is earth-abundant, inexpensive, and non-toxic. However, a poor understanding of phonon grain boundary scattering and its effect on thermal conductivity has impeded efforts to improve the thermoelectric figure of merit. Here, we report an ab-initio based computational study of thermal transport in nanocrystalline Si-based materials using a variance-reduced Monte Carlo method with the full phonon dispersion and intrinsic lifetimes from first-principles as input. By fitting the transmission profile of grain boundaries, we obtain excellent agreement with experimental thermal conductivity of nanocrystalline Si [Wang et al. Nano Letters 11, 2206 (2011)]. Based on these calculations, we examine phonon transport in nanocrystalline SiGe alloys with ab-initio electron-phonon scattering rates. Our calculations show that low energy phonons still transport substantial amounts of heat in these materials, despite scattering by electron-phonon interactions, due to the high transmission of phonons at grain boundaries, and thus improvements in ZT are still possible by disrupting these modes. This work demonstrates the important insights into phonon transport that can be obtained using ab-initio based Monte Carlo simulations in complex nanostructured materials.


Author(s):  
Dhruv Singh ◽  
Jayathi Y. Murthy ◽  
Timothy S. Fisher

This paper examines the thermodynamic and thermal transport properties of the 2D graphene lattice. The interatomic interactions are modeled using the Tersoff interatomic potential and are used to evaluate phonon dispersion curves, density of states and thermodynamic properties of graphene as functions of temperature. Perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. An algorithm to accurately quantify the contours of energy balance for three-phonon scattering events is presented and applied to calculate the net transition probability from a given phonon mode. Under the linear approximation, the Boltzmann transport equation (BTE) is applied to compute the thermal conductivity of graphene, giving spectral and polarization-resolved information. Predictions of thermal conductivity for a wide range of parameters elucidate the behavior of diffusive phonon transport. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided, contrasting graphene with other materials, along with implications for graphene electronics. We also highlight the specific scattering processes that are important in Raman spectroscopy based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.


2020 ◽  
Vol 93 (11) ◽  
Author(s):  
Neophytos Neophytou ◽  
Vassilios Vargiamidis ◽  
Samuel Foster ◽  
Patrizio Graziosi ◽  
Laura de Sousa Oliveira ◽  
...  

Abstract The field of thermoelectric materials has undergone a revolutionary transformation over the last couple of decades as a result of the ability to nanostructure and synthesize myriads of materials and their alloys. The ZT figure of merit, which quantifies the performance of a thermoelectric material has more than doubled after decades of inactivity, reaching values larger than two, consistently across materials and temperatures. Central to this ZT improvement is the drastic reduction in the material thermal conductivity due to the scattering of phonons on the numerous interfaces, boundaries, dislocations, point defects, phases, etc., which are purposely included. In these new generation of nanostructured materials, phonon scattering centers of different sizes and geometrical configurations (atomic, nano- and macro-scale) are formed, which are able to scatter phonons of mean-free-paths across the spectrum. Beyond thermal conductivity reductions, ideas are beginning to emerge on how to use similar hierarchical nanostructuring to achieve power factor improvements. Ways that relax the adverse interdependence of the electrical conductivity and Seebeck coefficient are targeted, which allows power factor improvements. For this, elegant designs are required, that utilize for instance non-uniformities in the underlying nanostructured geometry, non-uniformities in the dopant distribution, or potential barriers that form at boundaries between materials. A few recent reports, both theoretical and experimental, indicate that extremely high power factor values can be achieved, even for the same geometries that also provide ultra-low thermal conductivities. Despite the experimental complications that can arise in having the required control in nanostructure realization, in this colloquium, we aim to demonstrate, mostly theoretically, that it is a very promising path worth exploring. We review the most promising recent developments for nanostructures that target power factor improvements and present a series of design ‘ingredients’ necessary to reach high power factors. Finally, we emphasize the importance of theory and transport simulations for materialoptimization, and elaborate on the insight one can obtain from computational tools routinely used in the electronic device communities. Graphical abstract


2006 ◽  
Vol 128 (2) ◽  
pp. 115-124 ◽  
Author(s):  
Rodrigo Escobar ◽  
Brian Smith ◽  
Cristina Amon

Numerical simulations of time-dependent energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann method is derived from the continuous Boltzmann transport equation assuming first gray dispersion and then nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that a transition from diffusive to ballistic energy transport is found as the characteristic length of the system becomes comparable to the phonon mean free path. The methodology is used in representative microelectronics applications covering both crystalline and amorphous materials including silicon thin films and nanoporous silica dielectrics. Size-dependent thermal conductivity values are also computed based on steady-state temperature distributions obtained from the numerical models. For each case, reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values. Overall, simulations that consider phonon dispersion yield results more consistent with experimental correlations.


Author(s):  
Ankur Chattopadhyay ◽  
Arvind Pattamatta

Heat transport at nanoscales departs substantially from the well established classical laws governing the physical processes at continuum level. The Fourier Law of heat conduction cannot be applied at sub-continuum level due to its inability in modeling non-equilibrium energy transport. Therefore one must resort to a rigorous solution to the Boltzmann Transport Equation (BTE) in the realm of nanoscale transport regime. Some recent studies show that a relatively inexpensive and accurate way to predict the behavior of sub continuum energy transport in solids is via the discrete representation of the BTE referred to as the Lattice Boltzmann method (LBM). Although quite a few numerical simulations involving LBM have been exercised in the literature, there has been no clear demonstration of the accuracy of LBM over BTE; also there exists an ambiguity over employing the right lattice configurations describing phonon transport. In the present study, the Lattice Boltzmann Method has been implemented to study phonon transport in miniaturized devices. The initial part of the study focuses upon a detailed comparison of the LBM model with that of BTE for one dimensional heat transfer involving multiple length and time scales. The second objective of the present investigation is to evaluate different lattice structures such as D1Q2, D1Q3, D2Q5, D2Q8, D2Q9 etc. for 1-D and 2-D heat conduction. In order to reduce the modeling complexity, gray model assumption based on Debye approximation is adopted throughout the analysis. Results unveil that the accuracy of solution increases as the number of lattice directions taken into account are incremented from D2Q5 to D2Q9. A substantial increase in solution time with finer directional resolutions necessitates an optimum lattice. A novel lattice dimension ‘Mod D2Q5’ has been suggested and its performance is also compared with its compatriots. It is also demonstrated that the inclusion of the center point within a particular lattice structure can play a significant role in the prediction of thermal conductivity in the continuum level. However, as the size of the device comes down to allow high Knudsen numbers, in the limiting case of ballistic phonon transport, the choice of lattice seems to have negligible effect on thermal conductivity.


Nanoscale ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 4971-4977
Author(s):  
Tatsuhiko Taniguchi ◽  
Tsukasa Terada ◽  
Yuki Komatsubara ◽  
Takafumi Ishibe ◽  
Kento Konoike ◽  
...  

Ballistic phonon transport was observed in Si films containing Ge nanodots. In SiGe films containing Ge nanodots, thermal conductivity was drastically reduced close to that of amorphous materials due to alloy phonon scattering and nanodot scattering.


2007 ◽  
Vol 1053 ◽  
Author(s):  
Travis Z. Fullem ◽  
Eric J. Cotts

AbstractWhile detailed theories exist for thermal conduction due to electrons and phonons in crystalline solids, phonon scattering and transmission at solid/solid interfaces is not as well understood. Steady increases in the power density of microelectronic devices have resulted in an increasing need in the electronics industry for an understanding of thermal conduction in multilayered structures. The materials of interest in this study consist of a polymer matrix in which small (on the order of microns to tens of microns) highly conductive filler particles (such as Ag or alumina) are suspended. These materials are used to form a thermal interface material bondline (a fifty to several hundred micron bonding layer) between a power device and a heat spreader. Such a bondline contains many polymer/filler interfaces. Using a micro Fourier apparatus, the thermal conductivities of such thermal interface material (TIM) bondlines of various thicknesses, ranging from fifty microns to several hundred microns, have been measured. The microstructure of these bondlines has been investigated using optical microscopy and acoustic microscopy. Measured values of thermal conductivity are compared to values for bulk samples, and considered in terms of microstructural features such as filler particle depleted regions. The influence of polymer/filler particle interfaces in the TIM bondline on phonon transport through the bondline is also considered.


2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Jungwan Cho ◽  
Daniel Francis ◽  
Pane C. Chao ◽  
Mehdi Asheghi ◽  
Kenneth E. Goodson

Silicon films of submicrometer thickness play a central role in many advanced technologies for computation and energy conversion. Numerous thermal conductivity data for silicon films are available in the literature, but they are mainly for the lateral, or in-plane, direction for both polycrystalline and single crystalline films. Here, we use time-domain thermoreflectance (TDTR), transmission electron microscopy, and semiclassical phonon transport theory to investigate thermal conduction normal to polycrystalline silicon (polysilicon) films of thickness 79, 176, and 630 nm on a diamond substrate. The data agree with theoretical predictions accounting for the coupled effects of phonon scattering on film boundaries and defects related to grain boundaries. Using the data and the phonon transport model, we extract the normal, or cross-plane thermal conductivity of the polysilicon (11.3 ± 3.5, 14.2 ± 3.5, and 25.6 ± 5.8 W m−1 K−1 for the 79, 176, and 630 nm films, respectively), as well as the thermal boundary resistance between polysilicon and diamond (6.5–8 m2 K GW−1) at room temperature. The nonuniformity in the extracted thermal conductivities is due to spatially varying distributions of imperfections in the direction normal to the film associated with nucleation and coalescence of grains and their subsequent columnar growth.


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