A New Approach to Calculation of the Kapitza Conductance between Solids

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

“… for the tangent plane to 1 2,eff   for the interface in expression (1) that the well-known relations of the theory of elasticity [23] can be naturally applied to the problem of reflection-refraction of elastic waves at a rough interface between two solids [16]. It should also be noted that when averaging over different angles of inclination of the profile (4), we need to take into account the restrictions on the limits of integration min  and max  [23] that are imposed by the phenomenon of total internal reflection and change the pattern of reflected-refracted waves.…”

“…Figure 1 shows a schematic image of scattering on a rough interface between two bodies (solid 1 and solid 2) [16]. According to the theory of elasticity, a mode transformation occurs at the boundary [23]: an incident wave with index (0) is transformed into two reflected (1) and ( 2) and two refracted (3) and (4) waves. Letters denote polarizations: longitudinal (P) or transverse, where oscillations occur in the plane of propagation (SV) or across it (SH).…”

“…Here we use the elastic wave model with dispersion (EWMD) to calculate the Kapitza conductance. The EWMD is a further development of the acoustic mismatch model (AMM), and it can be found in detail in [5,16,23]. Third, a distinctive feature of this method is that the description of the rough boundary of a sample is based on statistical accounting for the slopes of the real surface profile.…”

“…Next, the problem of the wave propagation through the interface is solved relative to the tangent plane (see Figure 1). First, the transfer coefficient 1 2 0 ( )    is determined as a function of the local incidence angle 0  using the well-known relations from the theory of elasticity [23]. Then using the relationship between 0  , the angle of inclination of the profile  at the scattering point, and the actual angle of incidence  of the wave on the interface, we can pass from the local value 1 2 ( , )…”

The Modeling of the Kapitza Conductance through Rough Interfaces between Solid Bodies

“…The angles θ 1 , θ 2 , θ 3 , and θ 4 are expressed through θ 0 using the Snell law: sinθ n = sinθ 0 . Then the dispersion correlations are generally reduced to the linear form using the Debye approximation (a module with the constant velocity of propagation of the phonon waves), which is a poor approximation for high-frequency phonons [21]. Because of this, we use the real ratio of the dispersion of phonons of the material ω(k) to obtain more accurate results [15], in particular, the frequency-dependent velocities are determined using the expression = ∂ω/∂k.…”