Image potential for nonplanar metal surfaces

In this report we apply a method for solving Poisson’s equation in the presence of a nonplanar conducting boundary. The classical electrostatic potential and the interaction energy of the point-charge–conductor system (or image potential) is derived in a perturbative-expansion scheme in terms of a surface structure function h(r${\to }_{\mathrm{para}}$). The first-order correction is shown to be equivalent to Hadamard’s theorem and to a work-energy theorem that we have previously reported. In addition, we derive expressions for the image potential for a general slowly varying surface structure, for a periodic or corrugated surface, and a general surface whose structure function h(r${\to }_{\mathrm{para}}$) can be expressed in a Fourier-series, or Fourier-integral, expansion. In the latter case, it is found that the image potential assumes a particularly simple form and has many advantages in its application to both ion and electron scattering from surfaces. We briefly discuss applications to angular distributions of ions produced by stimulated desorption, in the former case, and to angle-resolved photoemission and inverse photoemission in the detection of image-induced surface states, in the latter case.