Reflection and transmission of electrons through surface potential barriers

A numerical treatment has been made of the reflection properties of several 1-dimensional surface potential barrier models. Curves of reflection coefficient versus energy have been obtained for the classical image barrier, the modified or corrected image barrier and the Bardeen potential in both the zero and finite field cases. For zero field, the smoothly varying Bardeen potential yields smaller reflection except for energies close to zero. This result suggests that the presence of the discontinuous derivative in the potential function introduces spurious reflection. There is no appearance of the elastic scattering component found in low-energy electron diffraction for any of the 1-dimensional models investigated. With fields, the curves are qualitatively similar except near the barrier maximum. However, for incident energies above the barrier, the image and modified image are larger in magnitude than the Bardeen model. The present treatment is compared with a recent numerical computation of the periodic deviations in the Schottky effect.