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When accounting for thermal excitation in a system that is not in thermal equilibrium, heat is constantly flowing through a material, should I account for the thermal excitation in the work function equation as well as the Richardson-Dushmann equation? Due to the fact that the Fermi level will change when accounting for thermal excitation, which variables should I alter in accounting for heat? Here's an equation which may be relevant: $$J=A_G T^2 \cdot\exp{\cfrac{-W}{kT}} \, .$$

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  • $\begingroup$ Titles should not have a question mark unless it's actually an English question, and should only capitalize the first word and any proper nouns. See this meta post for information on titles. Also, I modified the last part of the question to be a complete sentence. Please modify to make it more clear what that equation actually is. $\endgroup$ – DanielSank Jul 31 '15 at 21:07
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The Fermi level in the Richardson-Dushman equation is already the Fermi level at the temperature your system has. You do not have to account for thermal excitations seperately. Usually the equation is applied with a high temperature and is intended for just this.

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