Schottky effect

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The Schottky effect or field enhanced thermionic emission is a phenomenon in condensed matter physics named after Walter H. Schottky. In electron emission devices, especially electron guns, the thermionic electron emitter will be biased negative relative to its surroundings. This creates an electric field of magnitude F at the emitter surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has height W equal to the local work-function. The electric field lowers the surface barrier by an amount ΔW, and increases the emission current. It can be modeled by a simple modification of the Richardson equation, by replacing W by (W − ΔW). This gives the equation J ( F , T , W ) = A G T 2 e − ( W − Δ W ) k T {\displaystyle J(F,T,W)=A_{\mathrm {G} }T^{2}e^{-(W-\Delta W) \over kT}} Δ W = q e 3 F 4 π ϵ 0 , {\displaystyle \Delta W={\sqrt {q_{e}^{3}F \over 4\pi \epsilon _{0}}},} where J is the emission current density, T is the temperature of the metal, W is the work function of the metal, k is the Boltzmann constant, qe is the Elementary charge, ε0 is the vacuum permittivity, and AG is the product of a universal constant A0 multiplied by a material-specific correction factor λR which is typically of order 0.5. The expression is sometimes written as [ q e F / ( 4 π ϵ 0 ) ] 1 / 2 {\displaystyle [q_{e}F/(4\pi \epsilon _{0})]^{1/2}} , in which case Δ W {\displaystyle \Delta W} is expressed as a voltage. Electron emission that takes place in the field-and-temperature-regime where this modified equation applies is often called Schottky emission. This equation is relatively accurate for electric field strengths lower than about 108 V m−1. For electric field strengths higher than 108 V...