  Structuring materials is one mechanism to influence the thermal conductivity
and thus thermoelectric efficiency. In order to investigate the scattering of
phonons in multilayer structures we developed a beam matching technique, which
is based on the concept of individual phonons and their scattering at
interfaces. One of the major goals is to efficiently determine the complex band
structure of the bulk materials. The complex band structure is determined using
selected k-points on a triangulated grid in the complex plane of wave vectors
perpendicular to the interface. Matching the phonon modes at an interface is
translated to a singular value problem. Its null-vectors provide the coupling
coefficients of the phonon modes across the interface. Besides giving explicit
access to the modes as they scatter at the interface, the technique provides
the transfer matrices, that provide the transmission coefficient of any
multilayer structure. The transmission coefficient, in turn, yields the
phononic thermal conductance for coherent transport. The knowledge of the
matched phonons forms the basis of investigating incoherent transport under the
influence of phonon-phonon or impurity scattering.
