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Pinned surface and frozen surface approximations are two commonly usedapproximations for the boundary conditions at the exposed surfaces ofsemiconductor structures. We have studied the effect of pinned surface andfrozen surface boundary conditions on the spatial distribution of compressibleand incompressible strips observed in the two dimensional electron gas formedin a GaAs/AlGaAs heterostructure under quantum Hall effect regime. We have usedsemi classical Thomas-Fermi method for describing the many body problem alongwith the Poisson equation for electrostatics. We observe that the boundaryconditions significantly effect the spatial distributions of the compressibleand incompressible strips.

The effect of the frozen and pinned surface approximations on the  spatial distribution of incompressible and compressible strips in quantum  Hall regime