  Temperature dependence of vibrational modes in semiconductors depends on
lattice thermal expansion and anharmonic phonon-phonon scattering. Evaluating
the two contributions from experimental data is not straightforward, especially
for epitaxial layers that present mechanical deformation and anisotropic
lattice expansion. In this work, a temperature-dependent Raman study in
epitaxial Ge and Ge$_{1-x}$Sn$_{x}$ layers is presented. A model is introduced
for the Raman mode energy shift as a function of temperature, comprising
thermal expansion of the strained lattice and anharmonic corrections. With
support of x-ray diffraction, the model is calibrated on experimental data of
epitaxial Ge grown on Si and Ge$_{1-x}$Sn$_{x}$ grown on Ge/Si, finding that
the main difference between bulk and epitaxial layers is related to the
anisotropic lattice expansion. The phonon anharmonicity and other parameters do
not depend on dislocation defect density (in the range $7\cdot 10^6$ - $4\cdot
10^8$ cm$^{-2}$) nor on alloy composition in the range 5-14 at.%. The
strain-shift coefficient for the main model of Ge and for the Ge-Ge vibrational
mode of Ge$_{1-x}$Sn$_{x}$ is weakly dependent on temperature and is around
-500 cm$^{-1}$. In Ge$_{1-x}$Sn$_{x}$, the composition-shift coefficient
amounts to -100 cm$^{-1}$, independent of temperature and strain.
