is often performed using a nonlinear least squares algorithm.

This approach is widely used and has provided important insights into a wide range of metal-semiconductor interfaces \cite{}. A drawback, however, is that the microscopic information about the interface is averaged into a single number, the interface conductance, obscuring the microscopic detail. Hopkins et al used TDTR measurements on a variety of metal films with varying phonon cutoff frequencies to extract spectral information about phonon transmission[@Cheaito2015]. However, determining transmission coefficients is still challenging due to variations in phonon density of states in each metal.

In this work, we aim to directly extract the transmission coefficients from TDTR data by replacing the macroscopic transfer function based on Fourier’s law with a microscopic transfer function based on ab-initio phonon transport modeling. Just as in the traditional approach, we seek to identify the parameters that best fit the TDTR data sets. Although this fitting process is much more complex than the traditional approach, in principle it is the same widely-used procedure.

There are several conditions that must be satisfied to successfully extract transmission coefficients using this approach. First, it is essential that part of the non-equilibrium phonon distribution emerging from the interface propagate into 