Editing Work function (section)

==== Work function of cold electron collector ====
[[File:Thermionic diode reverse bias.svg|thumb|300px|Energy level diagrams for [[thermionic diode]] in ''retarding potential'' configuration. The barrier is the vacuum near collector surface.]]

The same setup can be used to instead measure the work function in the collector, simply by adjusting the applied voltage.
If an electric field is applied ''away from'' the emitter instead, then most of the electrons coming from the emitter will simply be reflected back to the emitter. Only the highest energy electrons will have enough energy to reach the collector, and the height of the potential barrier in this case depends on the collector's work function, rather than the emitter's.

The current is still governed by Richardson's law. However, in this case the barrier height does not depend on ''W''<sub>e</sub>. The barrier height now depends on the work function of the collector, as well as any additional applied voltages:<ref>G.L. Kulcinski, "Thermionic Energy
Conversion" [http://fti.neep.wisc.edu/neep602/SPRING00/lecture9.pdf] {{Webarchive|url=https://web.archive.org/web/20171117230631/http://fti.neep.wisc.edu/neep602/SPRING00/lecture9.pdf|date=2017-11-17}}</ref>
:<math>E_{\rm barrier} = W_{\rm c} - e (\Delta V_{\rm ce} - \Delta V_{\rm S})</math>
where ''W''<sub>c</sub> is the collector's thermionic work function, Δ''V''<sub>ce</sub> is the applied collector–emitter voltage, and Δ''V''<sub>S</sub> is the [[Seebeck effect|Seebeck voltage]] in the hot emitter (the influence of Δ''V''<sub>S</sub> is often omitted, as it is a small contribution of order 10 mV).
The resulting current density ''J''<sub>c</sub> through the collector (per unit of collector area) is again given by [[Richardson's Law]], except now
:<math>J_{\rm c} = A T_{\rm e}^2 e^{-E_{\rm barrier}/kT_{\rm e}} </math>
where ''A'' is a Richardson-type constant that depends on the collector material but may also depend on the emitter material, and the diode geometry.
In this case, the dependence of ''J''<sub>c</sub> on ''T''<sub>e</sub>, or on Δ''V''<sub>ce</sub>, can be fitted to yield ''W''<sub>c</sub>.

This '''retarding potential method''' is one of the simplest and oldest methods of measuring work functions, and is advantageous since the measured material (collector) is not required to survive high temperatures.