Discussion of the band structure effects on thermoemission as deduced from a simple model

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Abstract
The exact treatment of tunnelling of Caroli et al. is used to study thermoemission. The current is computed in the presence of the image-force potential and quantum mechanical correction. The effect of this correction is shown to be negligible. Band structure effects are taken into account through a one-dimensional Krônig-Penney model. The current, in this situation, is not obtained simply by replacing m by m* in the expression for the current obtained when the metal is described by a free electron gas, even close to band edges. Moreover, the current depends strongly on the location of the boundary between the metal and the vacuum. It is also shown that, depending on the location of the vacuum level with respect to the band gaps, the well-accepted Richardson-Laue-Dushman law may or may not be valid

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