  We study the ground state of two-dimensional classical electron solids under
the influence of modulation-doped impurities by using a simulated annealing
molecular dynamics method. By changing the setback distance as a parameter, we
find that in the strong disorder limit the ground state configuration contains
both isolated dislocations and disclinations, whereas in the weak disorder
regime only dislocations are present. We show, via continuum elasticity theory,
that the ground state of the lattice should be unstable against a proliferation
of free disclinations above a critical dislocation density. Associated with
this, the behavior of the threshold electric field as a function of the setback
distance changes.
