A New Approach to Calculation of the Kapitza Conductance between Solids
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Approach to Calculation of the Kapitza Conductance between Solids V. I. Khvesyuka, B. Liua*, and A. A. Barinova a
Bauman Moscow State Technical University, Moscow, 105005 Russia *e-mail: [email protected] Received May 6, 2020; revised June 16, 2020; accepted July 7, 2020
Abstract—The problem of calculation of Kapitza contact thermal resistances between different materials is very urgent in view of the development of various nanosystems (computer electronic circuits, thermoelectric devices, quantum cascade lasers, etc.). An improved acoustic mismatch model is proposed for calculating Kapitza conductivities. A drawback of the current model is the use of the Debye approximation. This leads to limitation of the model’s applicability by the low-temperature region. It is shown that consideration of the wave dispersion ensures good agreement between the theoretical and experimental data in a much wider temperature range in comparison with the application of modern models. Keywords: Kapitza conductance, micro and nano heat transfer, Kapitza resistance, phonon transport. DOI: 10.1134/S1063785020100065
Development of methods for calculating so-called “Kapitza conductance” (KC) is an important line of research in the modern theory of heat transfer in nanostructures because of the development of various nanoelectronics technologies such as computer electronic circuits, thermoelectric devices, and quantum cascade lasers [1–3]. A key parameter in calculation of KC is the coefficient of energy transfer through the interface. There are two models for determining the transfer coefficient. The first one is the acoustic mismatch model (AMM) [4]. It is based on an analysis of acoustic wave transport through the interface [5]. This model has both an advantage (physical clarity of the transport processes) and a drawback (it yields good results only in a narrow temperature range that is close to absolute zero). The second model called diffuse mismatch model (DMM) is based on an analysis of phonon transport through the interface. The advantage of DMM is that it can be used in a wider temperature range than the AMM. There are two different versions of the AMM. The first version is based on the use of elasticity theory methods [5]. In this case, the problem is reduced to solution of a system of differential equations to determine the amplitudes of the scattered and refracted waves during their passage through the interface. This makes it possible to determine the fraction of the total energy incident on the interface, which is transferred from the first medium to the second one. This version was formulated for the first time in [6]. It is referred to as an “elastic wave model” (EWM). The second ver-
sion for determining a transferred-energy fraction uses the Rayleigh formulas [4]. It allows one to deal without solution of the system of equations. In this Letter, we report the results of calculations using both approaches. A drawback of these models is that it does not include the dispersion properties of elastic waves, i.e., dependenc
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