= Emission-limited thermionic current
An <emission-limited thermionic current> is set by the rate at which the heated surface supplies <Electrons>, with nearly complete collection. At fixed <temperature>, increasing the attracting <electric potential difference> then produces an approximate collection plateau. That plateau is the useful regime for fitting the <Richardson-Dushman law>, provided the <electric field> has not significantly lowered the surface barrier.
The emitting surface still matters in this regime. <Adsorption> changes the <work function>; different crystal faces can have different barriers. Heating may desorb contaminants or change a coating, so repeated measurements at the same <temperature> need not agree unless the surface preparation is controlled. For fixed $A,T$, a barrier change $\Delta W$ multiplies $J$ by $e^{-\Delta W/(k_BT)}$. In the chosen model at $1000\,\mathrm K$, raising the barrier by $0.10\,\mathrm{eV}$ reduces $J$ to about 0.313 of its previous value.
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