Energy Distributions of Field Emitted Electrons

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Abstract
The total and normal energy distributions of electrons, emitted from a semiconductor conduction or valence band, by quantum mechanical tunneling through a surface potential barrier in vacuum, have been derived. General results, which apply for arbitrary emitter band structures, barrier shapes and distribution functions in momentum space, are given. Specific formulas are worked out for the case of spherical energy surfaces, an image force barrier and Fermi-Dirac statistics. The emitter band structure only affects the emitted electron energy distribution if the important energy surfaces in momentum space are very small. Thus, appreciable effects occur only for non- or semidegenerate semiconductors with low effective masses. The prevailing lack of agreement between theory and experiment and some difficulties in interpreting results of retarding potential measurements are discussed.