11.8.2 Space-Charge Effects
The pulse of photons from a synchrotron radiation source creates a cloud of electrons
with a finite size on its way to the analyzer. The initial distribution of energies and
momenta will be altered by the mutual Coulomb repulsions between the electrons—
so-called space-charge effects (Fig. 11.13) [549].
Of course, the significance of space-charge effects depends on the energy or
momentum resolution that is required. One estimate suggests that to keep the energy
distortions below 50 meV, the linear photoelectron density per photon pulse must be
limited to less than ~10
4 mm
À1 . As with sample charging, these issues become
especially important when using very short pulses such as from free-electron lasers
described in Chap. 12.
11.8.2.1 Radiation Damage
By now, we should not need a reminder that X-rays are ionizing radiation. The
degree to which different samples are susceptible to radiation damage varies enormously with chemical composition. Metals and many other materials such as Si and
diamond are almost impervious to damage—witness their use in mirrors and monochromators. At the other extreme, organometallic complexes such as Fe carbonyl or
cyanide complexes undergo rapid photochemistry (Fig. 11.13). In Chap. 12 we will
learn about free-electron lasers that can literally vaporize samples. Any X-ray
spectroscopy study should include an assessment of possible radiation damage
effects, but this is particularly important for photon-in electron-out methods where
the sample volume is small and the dose to sample ratio is large.
11.9 Suggested Exercises
1. Estimate the energy of a 2p 3/2 photoelectron from Cu metal if the incident X-ray
energy is 10 keV.
2. Use the TTM-2 algorithm to estimate the mean free path for a 1 keV electron in
silicon.
3. Estimate by what factor the mean free path increases for a 5 keV electron in
silicon, using the exponential approximation.
4. Use the Chung and Jenkins formula to estimate the KL 3 L 2 Auger energy for Fe.
5. Estimate the peak photon intensity (photons s
À1 mm
À2 ) at 10 keV on a Cu surface
that would exceed the proposed space-charge limit of ~10
4 photoelectrons mm
À1 .
11.9 Suggested Exercises
293
The pulse of photons from a synchrotron radiation source creates a cloud of electrons
with a finite size on its way to the analyzer. The initial distribution of energies and
momenta will be altered by the mutual Coulomb repulsions between the electrons—
so-called space-charge effects (Fig. 11.13) [549].
Of course, the significance of space-charge effects depends on the energy or
momentum resolution that is required. One estimate suggests that to keep the energy
distortions below 50 meV, the linear photoelectron density per photon pulse must be
limited to less than ~10
4 mm
À1 . As with sample charging, these issues become
especially important when using very short pulses such as from free-electron lasers
described in Chap. 12.
11.8.2.1 Radiation Damage
By now, we should not need a reminder that X-rays are ionizing radiation. The
degree to which different samples are susceptible to radiation damage varies enormously with chemical composition. Metals and many other materials such as Si and
diamond are almost impervious to damage—witness their use in mirrors and monochromators. At the other extreme, organometallic complexes such as Fe carbonyl or
cyanide complexes undergo rapid photochemistry (Fig. 11.13). In Chap. 12 we will
learn about free-electron lasers that can literally vaporize samples. Any X-ray
spectroscopy study should include an assessment of possible radiation damage
effects, but this is particularly important for photon-in electron-out methods where
the sample volume is small and the dose to sample ratio is large.
11.9 Suggested Exercises
1. Estimate the energy of a 2p 3/2 photoelectron from Cu metal if the incident X-ray
energy is 10 keV.
2. Use the TTM-2 algorithm to estimate the mean free path for a 1 keV electron in
silicon.
3. Estimate by what factor the mean free path increases for a 5 keV electron in
silicon, using the exponential approximation.
4. Use the Chung and Jenkins formula to estimate the KL 3 L 2 Auger energy for Fe.
5. Estimate the peak photon intensity (photons s
À1 mm
À2 ) at 10 keV on a Cu surface
that would exceed the proposed space-charge limit of ~10
4 photoelectrons mm
À1 .
11.9 Suggested Exercises
293