Calculation of Band-Structure Effects in Field-Emission Tunneling from Tungsten

A calculation was made to determine whether band-structure effects in field emission, as described in the Stratton theory of tunneling from a metal, could explain the anomalous total energy distribution (TED) for the $〈100〉$ directions of tungsten obtained by Swanson and Crouser. In applying the Stratton theory, a simple model for the tungsten energy bands based on Loucks's calculated relativistic augmented-plane-wave band structure was chosen. The results are in fair qualitative agreement with the experimental data of Swanson and Crouser with two important differences: (1) Swanson and Crouser observed merely a shoulder in the TED, but our results show a small peak; (2) Swanson and Crouser observed an anomaly centered around $\epsilon \cong -2.0d$, but our peak is located at $\epsilon \cong -2.5d$, where $d$ is determined by the applied field. These discrepancies between theory and experiment may be due to the crudeness of the band-structure model used.