  Pinned surface and frozen surface approximations are two commonly used
approximations for the boundary conditions at the exposed surfaces of
semiconductor structures. We have studied the effect of pinned surface and
frozen surface boundary conditions on the spatial distribution of compressible
and incompressible strips observed in the two dimensional electron gas formed
in a GaAs/AlGaAs heterostructure under quantum Hall effect regime. We have used
semi classical Thomas-Fermi method for describing the many body problem along
with the Poisson equation for electrostatics. We observe that the boundary
conditions significantly effect the spatial distributions of the compressible
and incompressible strips.
