Calculation of Modal Contributions to Heat Transfer across Si/Ge Interfaces
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Calculation of Modal Contributions to Heat Transfer across Si/Ge Interfaces Kiarash Gordiz1 and Asegun Henry1,2 1 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta GA, 30332, USA 2 School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta GA, 30332, USA ABSTRACT Using our newly proposed interface conductance modal analysis (ICMA) formalism, we study the modal contributions to thermal interface conductance ( G ) across the interface of crystalline silicon and crystalline germanium. We present the accumulation functions of G at different temperatures and predict G as a function of temperature after proper quantum-corrections have been applied. Different classes of vibration are identified across the interface, among which interfacial modes are determined to have the highest per mode contribution to G . The results demonstrate the ability of ICMA in not only calculating the spectral contributions to G but exactly pinpointing the shape of each vibrational eigen state. INTRODUCTION When heat flows through the adjoining interface of two different materials a temperature discontinuity appears across the interface ( ΔT ), the magnitude of which is proportional to the heat flux through the interface ( Q ), and the constant of proportionality is the thermal interface conductance ( G ) (i.e., Q = G ΔT ). Due to tremendous advances in nanostructuring in recent years [1, 2], we can now exquisitely fabricate structures with characteristic lengths on the order of nanometers for applications in nanoelectronics [3] and nanoscale energy conversion [4]. In these small scales, interfaces quickly become the dominant resistance to heat transfer, which on one side impedes the progress towards achieving improved performances in nanoelectronics [5] and on the other side sets interface engineering as a promising path to reach higher ZT thermoelectric (TE) materials through reducing thermal conductivity (e.g., by making grain boundaries [6] or superlattices [6]). Since the first experimental observation of thermal interface resistance [7], characterizing the exact modal contributions to interface heat transfer has long been a challenge. In this regard, a number of different methods have been proposed, including acoustic mismatch model [8], diffuse mismatch model [9], atomistic Green's function (AGF) [10], wave packet simulations [11], and harmonic lattice-dynamics (LD) based approaches [12, 13], but none of these methods are able to include both anharmonicity and the detailed configuration of atoms around the interface at the same time in the calculations. It has been shown that details of atomic positions around the interface (e.g., degree of interface roughness) can either decrease [14] or increase[15] G , and anharmonicity can become increasingly important especially above cryogenic temperatures, which has been investigated both theoretically [16] and experimentally [17]. Therefore, inclusion of these two effects into interface heat transfer analysis seems essential. T
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