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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Interfacial thermal resistance ： ウィキペディア英語版 Interfacial thermal resistance Interfacial thermal resistance, also known as thermal boundary resistance, or Kapitza resistance, is a measure of an interface's resistance to thermal flow. This thermal resistance differs from contact resistance (not to be confused with electrical contact resistance), as it exists even at atomically perfect interfaces. Due to the differences in electronic and vibrational properties in different materials, when an energy carrier (phonon or electron, depending on the material) attempts to traverse the interface, it will scatter at the interface. The probability of transmission after scattering will depend on the available energy states on side 1 and side 2 of the interface. Assuming a constant thermal flux is applied across an interface, this interfacial thermal resistance will lead to a finite temperature discontinuity at the interface. From an extension of Fourier's law, we can write $Q\; =\; \backslash frac\; =\; G\; \backslash Delta\; T$ where $Q$ is the applied flux, $\backslash Delta\; T$ is the observed temperature drop, $R$ is the thermal boundary resistance, and $G$ is its inverse, or thermal boundary conductance. Understanding the thermal resistance at the interface between two materials is of primary significance in the study of its thermal properties. Interfaces often contribute significantly to the observed properties of the materials. This is even more critical for nanoscale systems where interfaces could significantly affect the properties relative to bulk materials. Low thermal resistance at interfaces is technologically important for applications where very high heat dissipation is necessary. This is of particular concern to the development of microelectronic semiconductor devices as defined by the International Technology Roadmap for Semiconductors in 2004 where an 8 nm feature size device is projected to generate up to 100000 W/cm2 and would need efficient heat dissipation of an anticipated die level heat flux of 1000 W/cm2 which is an order of magnitude higher than current devices.〔Hu, M., Keblinski, P., Wang, JS., and Raravikar, N., Journal of Applied Physics 104 (2008)〕 On the other hand, applications requiring good thermal isolation such as jet engine turbines would benefit from interfaces with high thermal resistance. This would also require material interfaces which are stable at very high temperature. Examples are metal-ceramic composites which are currently used for these applications. High thermal resistance can also be achieved with multilayer systems. As stated above, thermal boundary resistance is due to carrier scattering at an interface. The type of carrier scattered will depend on the materials governing the interfaces. For example, at a metal-metal interface, electron scattering effects will dominate thermal boundary resistance, as electrons are the primary thermal energy carriers in metals. Two widely used predictive models are the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM). The AMM assumes a geometrically perfect interface and phonon transport across it is entirely elastic, treating phonons as waves in a continuum. On the other hand, the DMM assumes scattering at the interface is diffusive, which is accurate for interfaces with characteristic roughness at elevated temperatures. Molecular dynamics (MD) simulations are a powerful tool to investigate interfacial thermal resistance. Recent MD studies have demonstrated that the solid-liquid interfacial thermal resistance is reduced on nanostructured solid surfaces by enhancing the solid-liquid interaction energy per unit area, and reducing the difference in vibrational density of states between solid and liquid.〔(Han Hu and Ying Sun, J. Appl. Phys., 112, (2012) 053508 )〕 == Theoretical models == There are two primary models that are used to understand the thermal resistance of interfaces, the acoustic mismatch and diffuse mismatch models (AMM and DMM respectively). Both models are based only on phonon transport, ignoring electrical contributions. Thus it should apply for interfaces where at least one of the materials is electrically insulating. For both models the interface is assumed to behave exactly as the bulk on either side of the interface (e.g. bulk phonon dispersions, velocities, etc.). The thermal resistance then results from the transfer of phonons across the interface. Energy is transferred when higher energy phonons which exist in higher density in the hotter material propagate to the cooler materials, which in turn transmits lower energy phonons, creating a net energy flux.〔Swartz, E.T, Solid-solid Boundary Resistance, PhD Dissertation, Cornell University 1987〕 A crucial factor in determining the thermal resistance at an interface is the overlap of phonon states. Given two materials, A and B, if material A has a low population (or no population) of phonons with certain k value, there will be very few phonons of that wavevector to propagate from A to B. Further, due to the detailed balance, very few phonons of that wavevector will propagate the opposite direction, from B to A, even if material B has a large population of phonons with that wavevector. Thus as the overlap between phonon dispersions is small, there are less modes to allow for heat transfer in the material, giving at a high thermal interfacial resistance relative to materials with a high degree of overlap.〔Swartz, E.T., Pohl, R.O., Rev. Mod. Phys. 61 605 (1989)〕 Both AMM and DMM reflect this principle, but differ in the conditions they require for propagation across the interface. Neither model is universally effective for predicting the thermal interface resistance (with the exception of very low temperature), but rather for most materials they act as upper and lower limits for real behavior. Both models differ greatly in their treatment of scattering at the interface. In AMM the interface is assumed to be perfect, resulting in no scattering, thus phonons propagate elastically across the interface. The wavevectors that propagate across the interface are determined by conservation of momentum. In DMM, the opposite extreme is assumed, a perfectly scattering interface. In this case the wavevectors that propagate across the interface are random and independent of incident phonons on the interface. For both models the detailed balance must still be obeyed. For both models some basic equations apply. The flux of energy from one material to the other is just: $Q\_\; =\; \backslash sum\_\; n\; \backslash left\; (\; k,T\_1\; \backslash right\; )\; E\; \backslash left\; (\; k\; \backslash right\; )\; \backslash alpha\; \backslash left\; (\; k,T\_1,T\_2\; \backslash right\; )$ where n is the number of phonons at a given wavevector and momentum, E is the energy, and α is the probability of transmission across the interface. The net flux is thus the difference of the energy fluxes: $Q\_\backslash \; =\backslash \; Q\_\backslash \; -\backslash \; Q\_$ Since both fluxes are dependent on T1 and T2, the relationship between the flux and the temperature difference can be used to determine the thermal interface resistance based on: $R\_\backslash \; =\backslash \; \backslash frac$ where A is the area of the interface. These basic equations form the basis for both models. n is determined based on the Debye model and Bose–Einstein statistics. Energy is given simply by: $E\backslash \; =\backslash \; \backslash hbar\backslash \; \backslash omega\; \backslash left\; (\; k\; \backslash right\; )\backslash \; \backslash nu$ where ν is the speed of sound in the material. The main difference between the two models is the transmission probability, whose determination is more complicated. In each case it is determined by the basic assumptions that form the respective models. The assumption of elastic scattering makes it more difficult for phonons to transmit across the interface, resulting in lower probabilities. As a result, the acoustic mismatch model typically represents an upper limit for thermal interface resistance, while the diffuse mismatch model represents the lower limit.〔Zeng, T., and Chen, G., Transactions of the ASME, 123, (2001)〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Interfacial thermal resistance」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.