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We explore the effects of image potentials on calculated tunnelling rates in field-ion microscopes (FIM's). We introduce a new tunnelling potential for the FIM which includes explicitly the effects of the image potentials. In addition we calculate the change in the effective ionisation energy of the gas atom due to the presence of the image potentials. Calculations of tunnelling rates are then performed using a three-dimensional JWKB method for both flat and curved metal surfaces. The image potentials make the tunnelling potential more repulsive which tends to produce a minimum in the tunnelling rate as a function of the distance of the atom from the atom from the surface. This effect is opposed by the decrease in the effective ionisation energy of the gas atom due to the image interactions, which raises the energy of the tunnelling electron and increases the tunnelling rate. When both effects of the image potentials are included the tunnelling rate is generally a decreasing function of the distance of the gas atom from the surface. We also investigate the effects of the image potentials on the widths of the spatial and energy distributions of ionised atoms.

Ionization rate-constants are calculated for the field-ion microscope using the JWKB method and tunnelling potential introduced by Haydock and Kingham [Surf. Sci. 103 (1981) 239]. The expression for the tunnelling rate-constant given by Haydock and Kingham is inaccurate and we present a new and reliable formula. The prefactor for the tunnelling rate-constant is also calculated by comparing with the ionization rate-constant in a uniform electric field. The resulting rate-constants for helium atoms are significantly larger than those obtained by Kingham and coworkers [J. Phys. (Paris) 45 (1984) 77]. Our results make it possible to calculate ionization rate-constants in the field-ion microscope with greater accuracy than was previously possible.