A tungsten surface coated with a caesium monolayer has a reduced work function and an…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Condensed Matter, Materials & Soft Matter · Data analysis and model fitting in the laboratory

Solid State Physics, Ch The degenerate electron gas, finished

Problem

A tungsten surface coated with a caesium monolayer has a reduced work function

\phi = 1.36\,\mathrm{eV}

and an effective Richardson constant

A_0 = 3.0\,\mathrm{A\,cm^{-2}K^{-2}}

, well below the universal value because of the altered barrier at the surface. ((a)) Use the Richardson equation to find the saturated emission current density

J

T=800\,\mathrm{K}

and at

T=1000\,\mathrm{K}

. ((b)) Convert both results into the coordinates

\left(1/T,\ \ln(J/T^2)\right)

used for a Richardson plot, and find the slope between the two points. ((c)) Check that this slope agrees with

-\phi/k_B

computed directly from the given

\phi

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