An effective potential is derived, including both the classical image potential and quantum-mechanical boundary-condition effects, for an electron outside a stepped dielectric surface approximated to the first order of the step height in the infinitely-high-barrier approximation. The results show that the boundary condition cancels the effect of the nonplanar surface on the surface electron states through the image potential. The potential-energy minimum of the averaged effective potential over the electron distribution in the direction normal to the surface is on the lower part of the step, showing that the electron will be attracted to the lower part of the step, in contrast to the conclusion of Clinton et al. [Phys. Rev. B 31, 722 (1985)], which applies to conductor stepped surfaces and not to those of dielectrics. The ground-state energy of the bound states parallel to the surface are calculated variationally for step-conductor and liquid-He surfaces, which shows that the ground-state energy of the stepped dielectric surface is lowered compared with that of the planar dielectric surface. The effects of the nonplanar surface on the experiments, such as the microwave absorption by the electron in the vicinity of a liquid-He surface, are discussed.

• Received 19 April 1989

DOI:https://doi.org/10.1103/PhysRevB.41.3145