THEORY OF FIELD-IONIZATION

We describe calculations of tunnelling rate constants for the field ion microscope (FIM) using various model potentials, and potentials obtained from self-consistent electronic structure calculations incorporating the full screening of an applied electric field. For our tunnelling calculations we have used the JWKB method of Haydock and Kingham. The expression for the tunnelling rate constant for a flat surface given by Haydock and Kingham is inaccurate and we have derived a new and reliable formula. We have also introduced a new tunnelling potential for the FIM which includes explicitly the effects of image potentials. None of the potentials for smooth surfaces give ionization zone widths which are narrow enough to account for experimental values. However, the width of the ionization zone is found to be a strongly decreasing function of the corrugation of the surface potential, and for large corrugations we can obtain results in plausible agreement with experimental values. For corrugated model surfaces we have found cross-surface variations in the tunnelling rate constant which may be sufficient to account for the atomic resolution of the FIM under normal operating conditions at liquid nitrogen temperatures.