Frequency-dependent Monte Carlo simulations of phonon transport in two-dimensional porous silicon with aligned pores
TL;DR: In this paper, a boundary condition based on the periodic heat flux with constant virtual wall temperature is developed for the studied periodic structures, which enable the simulation of the lattice thermal conductivities with a minimum computational domain.
Abstract: In this work, phonon transport in two-dimensional (2D) porous silicon structures with aligned pores is investigated by Monte Carlo simulations considering the frequency-dependent phonon mean free paths (MFPs). A boundary condition based on the periodic heat flux with constant virtual wall temperature is developed for the studied periodic structures. Such periodic boundary conditions enable the simulation of the lattice thermal conductivities with a minimum computational domain. For the 2D case, it is found that phonon size effects caused by the periodically arranged pores can be remarkable even when the pore size and spacing are much larger than the averaged phonon MFPs. Our results show the importance of considering the frequency dependence of phonon MFPs in the analysis of micro- and nanostructured materials.
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TL;DR: In this article, Minnich et al. reviewed the progress made in thermoelectrics over the past two years on charge and heat carrier transport, strategies to improve the thermiolectric figure of merit, with new discussions on device physics and applications.
Abstract: This review is an update of a previous review (A. J. Minnich, et al., Energy Environ. Sci., 2009, 2, 466) published two years ago by some of the co-authors, focusing on progress made in thermoelectrics over the past two years on charge and heat carrier transport, strategies to improve the thermoelectric figure of merit, with new discussions on device physics and applications, and assessing challenges on these topics. Understanding of phonon transport in bulk materials has advanced significantly as the first-principles calculations are applied to thermoelectric materials, and experimental tools are being developed. Some new strategies have been developed to improve electron transport in thermoelectric materials. Fundamental questions on phonon and electron transport across interfaces and in thermoelectric materials remain. With thermoelectric materials reaching high ZT values well above one, the field is ready to take a step forward and go beyond the materials' figure of merit. Developing device contacts and module fabrication techniques, developing a platform for efficiency measurements, and identifying applications are becoming increasingly important for the future of thermoelectrics.
1,049 citations
01 Jan 2012
TL;DR: In this article, Minnich et al. reviewed the progress made in thermoelectrics over the past two years on charge and heat carrier transport, strategies to improve the thermiolectric figure of merit, with new discussions on device physics and applications.
Abstract: This review is an update of a previous review (A. J. Minnich, et al., Energy Environ. Sci., 2009, 2, 466) published two years ago by some of the co-authors, focusing on progress made in thermoelectrics over the past two years on charge and heat carrier transport, strategies to improve the thermoelectric figure of merit, with new discussions on device physics and applications, and assessing challenges on these topics. Understanding of phonon transport in bulk materials has advanced significantly as the first-principles calculations are applied to thermoelectric materials, and experimental tools are being developed. Some new strategies have been developed to improve electron transport in thermoelectric materials. Fundamental questions on phonon and electron transport across interfaces and in thermoelectric materials remain. With thermoelectric materials reaching high ZT values well above one, the field is ready to take a step forward and go beyond the materials' figure of merit. Developing device contacts and module fabrication techniques, developing a platform for efficiency measurements, and identifying applications are becoming increasingly important for the future of thermoelectrics.
826 citations
TL;DR: In this paper, the authors systematically summarize the molecular level understanding on the thermal transport mechanisms in polymers in terms of polymer morphology, chain structure and inter-chain coupling, and highlight the rationales in recent efforts in enhancing the thermal conductivity of nanostructured polymers and polymer nanocomposites.
Abstract: Polymers are widely used in industry and in our daily life because of their diverse functionality, light weight, low cost and excellent chemical stability. However, on some applications such as heat exchangers and electronic packaging, the low thermal conductivity of polymers is one of the major technological barriers. Enhancing the thermal conductivity of polymers is important for these applications and has become a very active research topic over the past two decades. In this review article, we aim to: 1). systematically summarize the molecular level understanding on the thermal transport mechanisms in polymers in terms of polymer morphology, chain structure and inter-chain coupling; 2). highlight the rationales in the recent efforts in enhancing the thermal conductivity of nanostructured polymers and polymer nanocomposites. Finally, we outline the main advances, challenges and outlooks for highly thermal-conductive polymer and polymer nanocomposites.
471 citations
TL;DR: This work experimentally measures the intrinsic spectral distribution of energy among heat carriers by probing quasi-ballistic transport near nanostructured heaters down to 30 nm using ultrafast optical spectroscopy, providing a new fundamental understanding of thermal transport.
Abstract: Controlling thermal properties is central to many applications, such as thermoelectric energy conversion and the thermal management of integrated circuits. Progress has been made over the past decade by structuring materials at different length scales, but a clear relationship between structure size and thermal properties remains to be established. The main challenge comes from the unknown intrinsic spectral distribution of energy among heat carriers. Here, we experimentally measure this spectral distribution by probing quasi-ballistic transport near nanostructured heaters down to 30 nm using ultrafast optical spectroscopy. Our approach allows us to quantify up to 95% of the total spectral contribution to thermal conductivity from all phonon modes. The measurement agrees well with multiscale and first-principles-based simulations. We further demonstrate the direct construction of mean free path distributions. Our results provide a new fundamental understanding of thermal transport and will enable materials design in a rational way to achieve high performance.
301 citations
Cites background from "Frequency-dependent Monte Carlo sim..."
...Anharmonic scattering is processed as a probabilistic step following the energy sampling [7]....
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...If interface scattering occurs, a random number is generated and compared with the relevant phonon’s transmissivity to determine whether transmission or reflection occurs subsequently [7]....
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TL;DR: In this article, a Monte Carlo method for obtaining solutions of the Boltzmann equation to describe phonon transport in micro-and nanoscale devices is presented, which can resolve arbitrarily small signals at small constant cost and thus represents a considerable improvement compared to traditional Monte Carlo methods, whose cost increases quadratically with decreasing signal.
Abstract: We present a Monte Carlo method for obtaining solutions of the Boltzmann equation to describe phonon transport in micro- and nanoscale devices. The proposed method can resolve arbitrarily small signals (e.g., temperature differences) at small constant cost and thus represents a considerable improvement compared to traditional Monte Carlo methods, whose cost increases quadratically with decreasing signal. This is achieved via a control-variate variance-reduction formulation in which the stochastic particle description solves only for the deviation from a nearby equilibrium, while the latter is described analytically. We also show that simulation of an energy-based Boltzmann equation results in an algorithm that lends itself naturally to exact energy conservation, thereby considerably improving the simulation fidelity. Simulations using the proposed method are used to investigate the effect of porosity on the effective thermal conductivity of silicon. We also present simulations of a recently developed thermal conductivity spectroscopy process. The latter simulations demonstrate how the computational gains introduced by the proposed method enable the simulation of otherwise intractable multiscale phenomena.
268 citations
Cites background or methods from "Frequency-dependent Monte Carlo sim..."
...es by V g;i t. The sampling substep during which the temperature (T) and pseudo-temperature (T loc) are locally measured. They are calculated by inverting the local energy (E) and pseudo-energy (E~) [10] relations E= N eff X i ~! i= V Z ! max !=0 X p D(!;p)~! exp ~! k bT 1 d! (7) and E~ = N eff X i ~! i ˝(! i;p i;T) = V Z ! max !=0 X p D(!;p)~! ˝(!;p;T) 1 exp ~! k bT loc 1 d! (8) respectively...
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...odic unit cell boundary conditions Heat transfer in periodic nanostructures is a subject of considerable interest in the context of many applications. Such nanostructures are considered in Hao et al. [10], in Huang et al. [21] and in Jeng et al. [4]. Hao et al. developed periodic boundary conditions that allow ecient simulation of such structures by considering only one unit cell (period). In this se...
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... method for eciently treating transmission and re ection of phonons at material interfaces and used this method to model the thermal conductivity of nanoparticle composites [4]. Hao et al. developed [10] a formulation for periodic boundary conditions in order to study the thermal conductivity of periodic nanoporous materials while only simulating one unit cell (period). The work presented here introd...
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...olution (56). Figure 4 shows a comparison between this solution and the variance-reduced Monte Carlo result. The simulation was run with T eq = T 0 and the phonon velocity was taken to be 12;360m:s 1 [10]. Excellent agreement is observed. 4.2 Heat ux and thermal conductivity in a thin slab In this section we continue to validate our formulation by calculating the thermal conductivity of a thin silicon...
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...lar by nature to a black body, have been used in several studies [8, 9]. Adiabatic boundaries also naturally appear [8, 20]. Recently, a class of periodic boundary conditions has also been introduced [10]. The deviational formulation adapts remarkably well to these dierent classes of boundary conditions. 3.5.1 Adiabatic boundaries Adiabatic boundaries re ect all incident phonons. This re ection proce...
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References
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TL;DR: Electrical transport measurements, coupled with microstructure studies and modeling, show that the ZT improvement is the result of low thermal conductivity caused by the increased phonon scattering by grain boundaries and defects, which makes these materials useful for cooling and power generation.
Abstract: The dimensionless thermoelectric figure of merit (ZT) in bismuth antimony telluride (BiSbTe) bulk alloys has remained around 1 for more than 50 years. We show that a peak ZT of 1.4 at 100°C can be achieved in a p-type nanocrystalline BiSbTe bulk alloy. These nanocrystalline bulk materials were made by hot pressing nanopowders that were ball-milled from crystalline ingots under inert conditions. Electrical transport measurements, coupled with microstructure studies and modeling, show that the ZT improvement is the result of low thermal conductivity caused by the increased phonon scattering by grain boundaries and defects. More importantly, ZT is about 1.2 at room temperature and 0.8 at 250°C, which makes these materials useful for cooling and power generation. Cooling devices that use these materials have produced high-temperature differences of 86°, 106°, and 119°C with hot-side temperatures set at 50°, 100°, and 150°C, respectively. This discovery sets the stage for use of a new nanocomposite approach in developing high-performance low-cost bulk thermoelectric materials.
4,695 citations
Journal Article•
4,230 citations
TL;DR: A review of the literature on thermal transport in nanoscale devices can be found in this article, where the authors highlight the recent developments in experiment, theory and computation that have occurred in the past ten years and summarizes the present status of the field.
Abstract: Rapid progress in the synthesis and processing of materials with structure on nanometer length scales has created a demand for greater scientific understanding of thermal transport in nanoscale devices, individual nanostructures, and nanostructured materials. This review emphasizes developments in experiment, theory, and computation that have occurred in the past ten years and summarizes the present status of the field. Interfaces between materials become increasingly important on small length scales. The thermal conductance of many solid–solid interfaces have been studied experimentally but the range of observed interface properties is much smaller than predicted by simple theory. Classical molecular dynamics simulations are emerging as a powerful tool for calculations of thermal conductance and phonon scattering, and may provide for a lively interplay of experiment and theory in the near term. Fundamental issues remain concerning the correct definitions of temperature in nonequilibrium nanoscale systems. Modern Si microelectronics are now firmly in the nanoscale regime—experiments have demonstrated that the close proximity of interfaces and the extremely small volume of heat dissipation strongly modifies thermal transport, thereby aggravating problems of thermal management. Microelectronic devices are too large to yield to atomic-level simulation in the foreseeable future and, therefore, calculations of thermal transport must rely on solutions of the Boltzmann transport equation; microscopic phonon scattering rates needed for predictive models are, even for Si, poorly known. Low-dimensional nanostructures, such as carbon nanotubes, are predicted to have novel transport properties; the first quantitative experiments of the thermal conductivity of nanotubes have recently been achieved using microfabricated measurement systems. Nanoscale porosity decreases the permittivity of amorphous dielectrics but porosity also strongly decreases the thermal conductivity. The promise of improved thermoelectric materials and problems of thermal management of optoelectronic devices have stimulated extensive studies of semiconductor superlattices; agreement between experiment and theory is generally poor. Advances in measurement methods, e.g., the 3ω method, time-domain thermoreflectance, sources of coherent phonons, microfabricated test structures, and the scanning thermal microscope, are enabling new capabilities for nanoscale thermal metrology.
2,933 citations
TL;DR: In the temperature range 600 to 900 kelvin, the AgPbmSbTe2+m material is expected to outperform all reported bulk thermoelectrics, thereby earmarking it as a material system for potential use in efficient thermoeLECTric power generation from heat sources.
Abstract: The conversion of heat to electricity by thermoelectric devices may play a key role in the future for energy production and utilization. However, in order to meet that role, more efficient thermoelectric materials are needed that are suitable for high-temperature applications. We show that the material system AgPb m SbTe 2+ m may be suitable for this purpose. With m = 10 and 18 and doped appropriately, n -type semiconductors can be produced that exhibit a high thermoelectric figure of merit material ZT max of ∼2.2 at 800 kelvin. In the temperature range 600 to 900 kelvin, the AgPb m SbTe 2+ m material is expected to outperform all reported bulk thermoelectrics, thereby earmarking it as a material system for potential use in efficient thermoelectric power generation from heat sources.
2,716 citations
TL;DR: In this article, a phenomenological model is developed to facilitate calculation of lattice thermal conductivities at low temperatures, where the phonon scattering processes can be represented by frequency-dependent relaxation times.
Abstract: A phenomenological model is developed to facilitate calculation of lattice thermal conductivities at low temperatures. It is assumed that the phonon scattering processes can be represented by frequency-dependent relaxation times. Isotropy and absence of dispersion in the crystal vibration spectrum are assumed. No distinction is made between longitudinal and transverse phonons. The assumed scattering mechanisms are (1) point impurities (isotopes), (2) normal three-phonon processes, (3) umklapp processes, and (4) boundary scattering. A special investigation is made of the role of the normal processes which conserve the total crystal momentum and a formula is derived from the Boltzmann equation which gives their contribution to the conductivity. The relaxation time for the normal three-phonon processes is taken to be that calculated by Herring for longitudinal modes in cubic materials. The model predicts for germanium a thermal conductivity roughly proportional to ${T}^{\ensuremath{-}\frac{3}{2}}$ in normal material, but proportional to ${T}^{\ensuremath{-}2}$ in single-isotope material in the temperature range 50\ifmmode^\circ\else\textdegree\fi{}-100\ifmmode^\circ\else\textdegree\fi{}K. Magnitudes of the relaxation times are estimated from the experimental data. The thermal conductivity of germanium is calculated by numerical integration for the temperature range 2-100\ifmmode^\circ\else\textdegree\fi{}K. The results are in reasonably good agreement with the experimental results for normal and for single-isotope material.
2,390 citations