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A Green's function solution to the two-dimensional electro-static problem with a planar dielectric discontinuity is formulated. The Green's function for a planar boundary is calculated, and hence this calculation applies only to the case where all gates lie in a plane. The assumption is also made that there is no charge in the oxide. The formalism is then applied to the calculation of the surface potential of a four-phase charge-coupled device (CCD). The calculation involves fairly straightforward integrals over the gates, semiconductor surface, and depletion region.