The electrostatic potential and field in the surface region of lamina and semi-infinite point charge lattices

General and readily adaptable equations are derived for the Coulomb potential in the surface region of infinite lamina and semi-infinite point charge lattices using the Bertaut method. The expressions which resemble the Ewald formulas used for comparable bulk lattices are cast in terms of charge spreading functions of arbitrary analytical form and are evaluated at real and reciprocal space lattice sites. The significance of the zero reciprocal space vector term is discussed. The convergence behavior of a modified direct summation scheme over the lattice charges compares favorably with that of the Bertaut method.