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Conversion" [http://fti.neep.wisc.edu/neep602/SPRING00/lecture9.pdf]</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''
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''
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.
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The Kelvin probe technique relies on the detection of an electric field (gradient in ''ϕ'') between a sample material and probe material.
The electric field can be varied by the voltage Δ''
If the voltage is chosen such that the electric field is eliminated (the flat vacuum condition), then
:<math>e\Delta V_{\rm sp} = W_{\rm s} - W_{\rm p}, \quad \text{when}~\phi~\text{is flat}.</math>
Since the experimenter controls and knows Δ''
The only question is, how to detect the flat vacuum condition?
Typically, the electric field is detected by varying the distance between the sample and probe. When the distance is changed but Δ''
Although the Kelvin probe technique only measures a work function difference, it is possible to obtain an absolute work function by first calibrating the probe against a reference material (with known work function) and then using the same probe to measure a desired sample.<ref name="calib"/>
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