Electron Reflection Coefficient at Zero Energy. II. Computer Experiments on the Reflection of Slow Electrons in the Electrostatic Field of Surface Patches

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Abstract
As reported in paper I, the zero-energy reflection coefficient of electrons at a polycrystalline silver surface has been measured to be (7±1)%. A theory consistent with this experimental result is presented below. This theory shows that the zero-energy reflection coefficient may be fully explained by the effect of patches of different work functions. The different potentials presented at the surface of a metal by the differently oriented crystal surfaces converge exponentially to the average potential as one moves away from the surface. The potential variation with the largest spatial period extends farthest from the surface. It will be shown that this component alone determines the reflection behavior at the threshold of energy. Because the surface presents a two-dimensional distribution, two independent periods must be considered which range in their aspect ratio from a square checkerboard to long stripes. The reflection coefficient is found to be independent of patch size and patch potential amplitude, and is (7.73±0.03)% for the stripe-type and (5.4±0.2)% for the square-checkerboard-type patches. The reflection coefficient jumps abruptly from 100% below the threshold of energy to some 6% at an energy immediately above threshold; therefore, it is not surprising that recent energy analyses with a simple patchy counterfield electrode of several-hundred-millivolt patch amplitude can resolve fine structure in the energy of less than 10 meV, as exhibited in the energy spectrum of electrons field-emitted from a liquid-helium-cooled tip.