Figure 1 exhibits the ingredients of a modern PE experiment. The light source is either a gas discharge lamp, an X-Ray tube, or a synchrotron radiation source. The light (vector potential A) impinges on the sample, which is a gas or the surface of a solid, and the electrons excited by the photoelectric effect are then analyzed with respect to their kinetic energy Ekin and their momentum p in an electrostatic analyzer.
Figure 2 shows schematically how the energy-level diagram and the energy distribution of photoemitted electrons relate to each other. The solid sample has core levels and a valence band. In the present case of a metal, the Fermi energy EF is at the top of the valence band and has a separation W0 from the vacuum level Evac. If photoabsortion takes place in a core level with binding energy EB (EB = 0 at EF) the photoelectrons can be detected with kinetic energy Ekin = hv-W0-EB in the vacuum. If the energy distribution of the emitted electron is plotted as in Figure 2, their number per energy interval often gives a replica of the electron-energy distribution in the solid. This is an attractive feature of PES; it is able to provide us information on the electron energy distribution in a material.
But modern photoemission spectroscopy can only be available in 1970's because we need the electron energy analyzer and ultra high vacuum (UHV) environment to get the undistorted data.
one reason we need the UHV condition is the short escape depth of electron for study of dolid surface, which is typically of the order of a few angstrom. This means that any spectroscopy of a solid suface involving electrons samples only electrons from a very thin layer of the sample. Thus if one wishes to learn about the bulk properties of the solid, one has to work with atomically clean surfaces.
Surface contamination is another reason for UHV. Typically the measure time for PES is of the order of ten minutes, so if the UHV condition is not satisfied, the signal come from not sample but contaminants. The required minimal pressure to experiment PES is around low 10-9 torr and the lower the better.
2. X-ray Photoemission Spectroscopy (XPS)
XPS is photoemission spectroscopy using X-ray as a photon source.
The energy range of X-ray in XPS is usually more than 1000 eV. X-ray of these energy range can be obtained by using characteristic x-ray line spectrum, which is due to transition of electron from high energy state to low one. When an atom is bombarded by high energy electrons, some inner atomic electrons are sometimes knocked out, leaving vacancies in the inner shell. These vacancies are filled by electrons with outter high energy states, in which process the X-ray emits correspondig the energy difference between these two states.
Most widely used targets to obtain X-ray in XPS are Al and Mg. The energy of Al K-alpha line is 1486.6 eV and Mg K-alpha 1253.6 eV.
Figure 3 shows the XPS spectrum of pure Au. In this spectrum we can easily see the core level electron energy states and the crude valence band shape of Au together. Although we can see the valence band with XPS, the energy resolution is not so high, it is limited to study the valence band in detail. Instead, because the XPS spectrum is sensitive to chemical environment, it is usually used to analyze the chemical state of the sample. The name ESCA (Electron Spectroscopy for Chemical Analysis) has been invented for this technique.
3. Ultraviolet Photoemission Spectroscopy (UPS)
UPS is one of the most useful tools to study the valence band structure of the condensed matters. It usually uses the He I line (hv = 21.22 eV) or He II line (hv = 40.8) as a photon source. Comparing with XPS, the resolution of the UPS is rather high (~meV), so this is adequate for studying band structures though it is more surface sensitive than XPS.
Figure 4 shows UPS spectrum from a (110) face of Cu. From this spectrum, after substracting secondaries due to background inelastic scattering we can obtain the 'replica' of the density of the states (DOS) of the sample. In this figure we can idensify the 3d band, flat 4s band and Fermi edge.
4. Angle Resolved Photoelectron Spectroscopy (ARPES)
In ARPES another experimental parameter is introduced, i. e. momentum vector k of the photoelectron. When the photoelectrons are emitted from the sample surface, we can measure not only the energy but also the angles relative to crystal axis of the sample, and from angle and energy we can determine the momentum of the electrons. If we know the energy distribution and momentum distribution of the crystals, we can determine the band structure of the crystal. Thus ARPES can make band mapping possible though some assumptions are needed to this end.
Figrue 5 shows typical ARPES spectrum. In this figure we can see the band dispersion as the angle varies. Each angle corresponds to a certain crystal momentum in solid, so in crude picture, the dashed lines can be regarded as spaghettis in band map.
5. Surface Magneto-Optical Kerr Effect (SMOKE)
Magneto-optic Kerr effect is a rotation of the plane of polarization of a light during reflection from a magnetized material. Rotation of the polarization during transimission is Faraday effect. Usually samples are not so thin or transparancy, Kerr effect is useful. In general, the rotation in ferromagnetic material is order of mdeg, but it is very large compared to that in non-mangetic material. Microscopically, electric field of light is coupled with electron spin. Macroscopically, electron feels Lorentz force in magnetic field, so dielectric constant is changed, and the reflectivity is changed. So if incident light is linear polarized, reflected light is eliptically polarized. The rotation of polarization is known as proportional to the magnetization of sample, so we can measure the magnetization using Kerr effect.
Figure 6: Schematic diagram of SMOKE setup. Inset: An example
of SMOKE data
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