Abstract Two-dimensional distributions of the potential and the charge near the cross-shaped junction of the crystallites of a polycrystalline semiconductor film are calculated. The electron state charge on the crystal boundaries is assumed to be uniformly distributed over the boundaries. The space charge region is considered in the Schottky approximation. The problem of the nonlinear screening is reduced to that of determining the shape of the boundary of the Schottky layer. It is solved by methods of the theory of functions of a complex variable.