  We study the effects of finite chemical potential and impurity scattering on
dynamical fermion mass generation in (2+1)-dimensional quantum electrodynamics.
In any realistic systems, these effects usually can not be neglected. The
longitudinal component of gauge field develops a finite static length produced
by chemical potential and impurity scattering, while the transverse component
remains long-ranged because of the gauge invariance. Another important
consequence of impurity scattering is that the fermions have a finite damping
rate, which reduces their lifetime staying in a definite quantum state. By
solving the Dyson-Schwinger equation for fermion mass function, it is found
that these effects lead to strong suppression of the critical fermion flavor
$N_c$ and the dynamical fermion mass in the symmetry broken phase.
