  According to the Kosterlitz-Thouless-Theory two-dimensional solid films melt
by the unbinding of dislocation pairs. A model including quenched random
impurities was already studied by Nelson [Phys. Rev. B 27 (1983) 2902], who
predicted a reentrance into the disordered phase at low temperatures and weak
disorder. New investigations of the physically related XY-model [e.g. T.
Nattermann et al., J. Phys. (France) 5 (1995), 565] and a work of Cha and
Fertig [Phys. Rev. Lett. 74 (1995) 4867] refuse this reentrant melting. In this
work we map the system onto a two-dimensional vector Coulomb gas and via a
renormalization we derive flow equations both for the square and for the
triangular lattice. An analysis of these flow equations shows a new behaviour
in the low-temperature range, where the reentrance into the non-crystalline
phase with short-range order is not found, but the crystalline phase with
quasi-long-range order is preserved below a critical disorder strength of
\bar\sigma_c = 1/16 \pi. Finally we estimate the influence of commensurate
substrates and obtain phase diagrams, which show that the melting by
dislocation unbinding can only be expected, if the lattice constant of the
crystalline film is a multiple of the lattice constant of the substrate
potential.
