A New Spin on Photoemission Spectroscopy Page: 76 of 259
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For reference, the electric field and potential between the hemispheres as a function of
radial position, r, are given by
E(r) = R ) and (2.36)
(Rout - Rin r2a
R(u R N AV (R
V(r) = Vo - i A - -). (2.37)
(Rout - Rin Ro r
This expression for the electric field is reassuring as it can easily be seen that a dynamical
equilibrium exists for electrons of energy Ep = 1/2mev2 to stay on the central orbit with
radius r = Ro by expressing the force on the electron as F = eE(Ro) and setting it equal
A key characteristic of an energy analyzer is its energy resolution, AE, which is often
discussed as a dimensionless fraction of the pass energy referred to as the resolving power.
For the SDA, the theoretical resolving power is
AE _ S a2
- =2- + 4(2.38)
E, 2r0 4
where S is the average slit width of the hemisphere entrance and exit slits, S = (Si +
S2)/2, and a is the accepted half-angle of electrons through the entrance slits in the energy
dispersion direction. Disregarding the second term on the right, we can see that there are
two ways of improving the resolving power of an SDA - decreasing the entrance/exit slit
widths and increasing ro (the size of the instrument). With these fixed physical dimensions,
the energy resolution can be improved by working at lower pass energy. Equation 2.38 also
shows that the 'Fixed Analyzer Transmission' mode for scanning EK (fixed Ep, swept Vo)
operates with fixed energy resolution throughout the spectrum. Because of this, this is the
method typically used for high resolution experiments.
It can also be shown for an SDA that the measured intensity, I, at the electron detector
is proportional to the pass energy as
I ~ K . (2.39)
Therefore we see that improving the energy resolution by reducing E (equation 2.38) comes
at the price of strongly reduced intensity or count rate at the detector, requiring a longer
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Jozwiak, Chris. A New Spin on Photoemission Spectroscopy, thesis or dissertation, December 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc1014237/m1/76/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.