A new technique for modelling phonon scattering processes at rough interfaces and free boundaries of solids

Scattering processes at interfaces and free boundaries of solids strongly affect heat transfer in micro- and nanostructures such as integrated circuits, periodic nanostructures, multilayer thin films, and other nanomaterials. Among many influencing factors, surface roughness due to atomic disorder plays a significant role in the rate of thermal transport. Existing approaches have been developed only for the limiting cases of smooth or completely diffuse surfaces. We have developed a new effective and simple method based on a direct consideration of the scattering of elastic waves from a statistically random profile (using a normal Gaussian surface as an example). This approach, first, allows to generalize common methods for determining the thermal properties of a real random rough surface using simple modifications, and, second, provides a tool for calculating the Kapitza conductance and the effective longitudinal thermal conductivity and studying the influence of roughness on heat transfer.

Generalized model of Kapitza conductance across rough interfaces

This paper is devoted to the theoretical prediction of the interfacial heat transfer in nanostructured materials. The main task of this work is the analysis of interaction of elastic waves with the rough interface between two different solids. The presence of toughness leads to a significant increase in the resistance to heat transfer in nanostructures. This fundamental problem is discussed in relation to the commonly used method of wave scattering at rough surface: the Kirchhoff tangent plane method. The method assumes that at the point of the rough surface profile, the surface is regarded as locally smooth, and the reflection and transmission of the incident wave can be described by the scattering at the tangent plane of this point. Based on the elastic wave theory, we use the frequency-dependent continuity conditions to calculate the energy transmission coefficient at the interface. And then its effective value at the rough interface is estimated by using the Kirchhoff method. By substituting this effective value into the formula of Kapitza conductance, we can calculate the Kapitza conductance at the rough interface and analyze the effect of roughness on the interfacial heat transfer.

Моделирование проводимости Капицы через шероховатые интерфейсы между твердыми телами

In this work, we have formulated and solved the problem of determining the Kapitza conductance across the interface between two solids, taking into account the interface roughness. We use a modified acoustic mismatch model (AMM). The difference from the classic model is that the dispersion properties of acoustic waves are considered. A significant advantage of this model is that the theoretical prediction agrees well with experimental data over a wide temperature range: from 30K to more than 300K. Finally, a theoretical method with the statistical distribution of roughness profiles is used to determine the energy transmission coefficient across the interface.

Новый подход к расчету проводимости Капицы между твердыми телами

In connection with the development of various nanosystems (computer electronic circuits, thermoelectric devices, quantum cascade lasers, etc.), the problem of calculating the Kapitza conductance between various materials is very acute. An improved acoustic mismatch model for calculating the Kapitza conductance is proposed. The disadvantage of the currently existing model is that it uses the Debye approximation. This limits the applicability of the model to the low temperature region. It is shown that taking into account the dispersion of the waves ensures good agreement between the theory and experiment in a much wider temperature range than with modern models.

Cryogenic design for a high intensity ultracold neutron source at TRIUMF

The TUCAN (TRIUMF Ultra-Cold Advanced Neutron) collaboration has been developing a source of high-intensity ultra-cold neutrons for use in a neutron electric dipole search. The source is composed of a spallation neutron source and a superfluid helium ultra-cold neutron converter, surrounded by a cold moderator. The temperature of the superfluid helium needs to be maintained at approximately 1.0 K to suppress up-scattering by phonons. The Kapitza conductance and the heat transport by the superfluid helium are key parameters which need to be well characterized. We have therefore investigated them in first experiments. Current efforts are directed at optimizing the design of the helium cryostat.

Impact of Grain Boundaries on the Heat Conductivity of Mono-Layer Hexagonal Boron Nitride

Reverse nonequilibrium molecular dynamics modeling is used to study the influence of grain boundaries on thermal properties of mono–layer hexagonal boron nitride (h–BN) nanoribbons. We consider symmetric grain boundaries consisting of series of pentagon–heptagon ring defects. Our results show a jump in the temperature profile at the location of grain boundary. The jump is consistently increasing with increase in the mis-orientation angle of nanoribbons with grain boundaries. This is attributed to an increase in the pentagon–heptagon defect density along the grain boundary. The temperature profile is used to calculate the Kapitza (interface) conductance of grain boundaries as a function of the misorientation angle of grain boundaries. Our results show that Kapitza conductance of the grain boundaries decreases with increase in the misorientation angle. Zigzag nanoribbons show slightly higher Kapitza conductance than armchair nanoribbons.