Width of area of the surface charge in two dimensional metal–two dimensional electron gas at dielectric heterogeneity of the environment

The problem of the equilibrium distribution of potential in the contact two dimensional electron gas–two dimensional metal in the presence of dielectric inhomogeneity of surrounding medium has been considered. It is shown that such inhomogeneity can be taken into account by introducing in the final expressions the effective dielectric constant, equal to the arithmetic average of the dielectric constants of upper and lower mediums surrounding the plane of two dimensional gas.