  The temperature dependence of the Seebeck coefficient of homoepitaxial metal
organic vapor phase (MOVPE) grown, silicon doped $\beta$-Ga$_2$O$_3$ thin films
was measured relative to aluminum. For room temperature we found the relative
Seebeck coefficient of
$S_{\beta\text{-Ga}_2\text{O}_3\text{-Al}}=(-300\pm20)\;\mu$V/K. At high bath
temperatures $T>240$ K, the scattering is determined by
electron-phonon-interaction. At lower bath temperatures between $T=100$ K and
$T=300$ K, an increase in the magnitude of the Seebeck coefficient is explained
in the frame of Strattons formula. The influence of the different scattering
mechanisms on the magnitude of the Seebeck coefficient is discussed and
compared with Hall measurement results.
