  Considering screeening of electron scattering interactions in terms of the
finite-temperature STLS theory and solving the linearized Boltzmann equation
(with no appeal to a relaxation time approximation), we present a theoretical
analysis of the low-temperature Seebeck effect in two-dimensional
semiconductors with dilute electron densities. We find that the temperature
($T$) dependencies of the diffusion and phonon-drag thermoelectric powers
($S_d$ and $S_g$) can no longer be described by the conventional simple
power-laws. As temperature increases, $|S_d|/T$ decreases when $T\gtrsim 0.1
\epsilon_F$ ($\epsilon_F$ is the Fermi energy), while $|S_g|$ first increases
and then falls, resulting a peak located at a temperature between
Bloch-Gr\"uneisen temperature and $\epsilon_F$.
