Hemispherical Analyzer (HSA)
● natural line width of the characteristic radiation used for excitation ∆Ephoto (e.g.
Mg, Kα, Al Kα).
The observed total FWHMtotal is given by the convolution of the single FWHMs, e.g for
gaussian line widths.
FWHM
total
=
E
an
2
E
level
2
E
photo
2
1/2
=
E
(6)
FWHMtotal is usually specified using a sputter-cleaned silver sample and recording the
Ag 3d5/2 level, after linear background subtraction. For Mg Kα excitation, the resolution
at low HSA pass energies for the Ag 3d5/2 level is found to be
(7)
In most practical work, a resolution of 0.9 eV is usually sufficient for high resolution in-
vestigations. For higher instrumental resolution, it is possible to use monochromatized
X-radiation for excitation, e.g. mainly monochromatized Al Kα radiation. For mono-
chromatized Al Kα radiation and for the Ag 3d5/2 level, the extreme resolution is found
to be
(8)
To obtain the extreme resolution of 0.44 eV, the FWHM of the X-ray has to be heavily
restricted, by utilizing only a small part of the X-ray monochromator spot area (due to
the energy dispersion across the spot area), at the expense of a strong loss in intensity.
In practice, a resolution of 0.65 eV is usually sufficient for high resolution investigations
with monochromatized Al Kα excitation. For monochromatic radiation, FWHMtotal is
sometimes specified recording the Si 2p
3/2
level instead of the Ag 3d
5/2
level, which res-
ults in smaller values of FWHMextreme. due to the narrower inherent line width of the Si
2p level.
The integral signal intensity I of the measured particles (the area under the peak with a
background subtracted) is proportional to product of the accepted solid angle Ω
S
, the
accepted sample area A
S
and the HSA resolution ∆E
an
:
I
~
E
an
S
A
S
=
E
an
0
A
0
E
pass
E
kin
~
E
pass
2
E
kin
(9)
where Ω
0
and A
0
are the values of the acceptances for the HSA. They are analyzer con-
stants. The equation results from Liouville’s theorem
1
.
The analyzer can be operated in two different modes:
a) Fixed Retarding Ratio (FRR), the retardation ratio R is defined as
1 For more information there are some excellent publications on analyzers. We recommend two of them:
K. D. Sevier, Low Energy Electron Spectrometry, Wiley-Interscience, 1972
D. Roy and D. Tremblay, Design of Electron Spectrometers, Rep. Prog. Phys. 53, 1621-1674,1990
PHOIBOS 19
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