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The coefficient $A$ has dimensions of electric current density divided by squared temperature. For ideal nonrelativistic particles with the free electron mass, two spin states, a planar uniform surface, and unit escape transmission, the thermionic tail-flux derivation giveswhere $e$ is the positive elementary charge and $h$ is the Planck constant. The two area units differ by a factor of $10^4$. A fitted $A$ need not equal $A_0$: reflection at the surface, the electronic band structure, and uncertain emitting area affect the inferred coefficient. A constant escape transmission $\tau$ would give $A=\tau A_0$ in this simple model; an energy-dependent transmission generally requires an integral instead.

The name joins Owen Willans Richardson with Saul Dushman. Dushman's 1923 paper develops a thermodynamic treatment of Electron emission analogous to evaporation and evaluates the prefactor using quantum ideas.^[ref]