The process of field ionization is considered in this theoretical analysis as a three-dimensional rearrangement collision. The periodic potential variation in the surface region is considered to determine its effect on the field-ionization tunneling probabilities at a specific crystallographic plane. The system considered is hydrogen imaging a tungsten-type metal. A specific crystallographic plane with an interatomic spacing of $\pi$ Å and an externally applied electric field of 2.3 V/Å is considered for numerical results. The analysis shows that the variation of the surface potential along the surface affects the shape of the tail of the electron wave function immediately outside the surface, and the overlap of this wave function with the wave function associated with the incoming atom leads to variation of the tunneling probability on a specific plane. It is concluded that the consideration of fine-surface-structure details does indeed lead to nonuniform tunneling probabilities on a given crystallographic plane in the field-ionization processes.

• Received 30 October 1969

DOI:https://doi.org/10.1103/PhysRevB.2.598