If we bombard a sample with electrons or photons, electrons will be emitted which have an energy spectrum, shown schematically in diagram 70 for the case of electron bombardment. The most well-known historical example is the photoelectric effect, and the modern version in UHV is called Photoemission. Electron emission is also commonly used; for example secondary electrons are the signal normally used to form an image in the Scanning Electron Microscope (SEM), and AES uses Auger electrons to determine surface chemical composition. Ion emission is also known, but is less widely used.
The problem of measuring the energy spectrum is non-trivial. There are various possible geometries for the analyzers and the measurements can be performed in an angle-integrated or angle-resolved (AR) mode. Thus we have a profusion of acronyms, e.g. UPS, Ultra-violet Photoelectron Spectroscopy, not a parcels service; ARUPS, the angular resolved version of the same technique, which is used to study surface states; XPS, X-ray Photoelectron Spectroscopy, also known as ESCA, Electron Spectroscopy for Chemical Analysis; and Electron Energy Loss Spectroscopy, which comes in two varieties (EELS and (High Resolution) HREELS).
These various analysers also have acronyms (diagram 71, Prutton), and the techniques are all related, as shown in diagrams 72 and 75. First, analyzers: the magnetic sector spectrometer (diagram 71a) may be familiar from analysis using EELS in conjunction with TEM. It has very good energy resolving power, but collects over a small angular range; this is well suited to the strongly forward peaked scattering which we have at TEM energies (> 100 keV). The Retarding Field Analyzer (RFA) is the same arrangement as used for LEED; the only difference is that one now ramps, and probably modulates, the retarding voltage V on the grid (or the sample) and collects all the electrons with energy > eV, i.e. it is a high pass filter. The advantage is simplicity and availability, plus the very large angular collection range. The disadvantage lies in the poor signal to noise ratio inherent in differentiating the collected signal (once or twice) to get the spectrum of interest. Draw a spectrum and show that an N(E) spectrum corresponds to differentiating once, and a dN/dE spectrum corresponds to differentiating twice. These two types of spectrum are shown in diagram 73, ignoring the difference between N(E) and E.N(E), which is discussed next.
The electron energy analysers in common use are the Cylindrical Mirror Analyzer (CMA) and Concentric Hemispherical Analyzer (CHA), shown in diagram 71c and d. These are both band pass filters, passing a band of energy (ΔE) at a pass energy E, typically by adjusting a slit width (w) to change the energy resolution ΔE/E. These analyzers can be operated with retardation, so that the pass energy is less than the energy of the electron being analyzed; this is easier for the CHA, with retarding lenses in front of the analyzer, and can lead to a high energy resolution in the resulting spectrum. If the analyzer is retarded to a constant pass energy, then the spectrum reflects N(E), which is often peaked at low energies, since secondary electron emission is strong. If there is no retardation, of if the pass energy is a constant fraction of the analyzed energy, then the spectrum reflects E.N(E).
The goal of energy analysis is to combine high energy resolving power ρ = (E/ΔE), with a high collection solid angle, Ω. It is not very surprising that nature doesn't like you doing that: it smacks of getting something for nothing. So the various analyzers have been optimized by all the tricks one can think of, such as second order focusing, where changing the angle of incidence to the optic axis, α, produces aberrations of order α2 or higher. The net result is that the energy resolution looks like E/ΔE = A(w/L) + Bαn, where L is a characteristic size of the analyzer, and A, B and n~2 are constants for the equipment.
A comparison of the three main analytical techniques which use electron emission are shown in diagram 75. UPS uses ultra-violet radiation as the probe, and collects electrons from the valence band, whereas XPS excites a core hole with X-rays. The third technique is AES, which can be excited by (X-ray) photons or, more usually, electrons. AES involves three electrons, and leaves the atom doubly ionised. In general, XPS and AES are used for species identification, and core level shifts in XPS can also give chemical state identification. AES is routinely used to check surface cleanliness. UPS, especially ARUPS, is the main technique for determining band structure (of solids, not just the surface) and can also identify surface states. The surface sensitivity depends primarily on the energy of the outgoing electron.
The nature of the spectrum for XPS and UPS is shown in diagram 76. The core line is often split by spin-orbit interactions, whereas the valence line is wider because of band broadening. These techniques, when photons are used as the probe, only involve one electron, and so are relatively simple to understand. Luth gives an outline of the theory of photoemission in Chapter 6.
Luth gives some details about the X-ray sources and monochromators used (diagram 77), and emphasises the importance of synchrotron radiation sources to current research. These sources have high intensity and very well defined direction, so that they are well suited to AR- studies. An example of ARUPS from a metal (Au) is shown in diagram 78; we can see that details of the band structure can be mapped out from such data, but it is quite difficult to separate surface and bulk states from a single set of spectra such as this. The extraction of the surface state part of the spectrum for Si(100)2x1 is shown in diagram 79, where it is seen that the data agree best with the dimer (pairing) model of the reconstruction. Surface States, particularly of semiconductors, would be a suitable topic for a talk or mini-project.
Much work has been done over the last 20 years or so using synchrotron radiation at several large laboratories around the world. The web pages of the facilities can be accessed from my Synchrotron Radiation Sources page, for more details.
These energies are given by various formulae, such as
where the use of the average energy is due to being unable to tell which transition happened 'first'. Δ is used to indicate that the final emission is from an ion, not a neutral atom. This shifts the final energies downwards slightly. In practice, for standard analysis, you need to know that these energies are known, and are typically displayed on a chart in every Surface Science laboratory. The energy measured does, however, depend on whether you are measuring in the N'(E) mode, where the negative-going peak is typically quoted, or in the N(E), or E.N(E), mode, where the positive-going peak is quoted (see diagram 73). These can be separated by several eV; the width of the Auger peak is typically 1-2 eV, due to a rather short lifetime before Auger emission, but this can be further broadened by overlapping peaks and by analyzers which are set to increase sensitivity at the expense of resolution. In addition, to quote the absolute energy relative to the vacuum level of the element, a negative correction equal to the work function of the analyzer (4.5 eV typically) is needed; however, if one quotes energies relative to the Fermi level, this correction is not required.
The theory of Auger emission is rooted in atomic physics, and is only modified slightly by solid state and surface effects. First, the proper notation would take into account whether the atom in question is L-S or j-j coupled. The Si example is a case of L-S coupling, since the atomic number is small (diagram 101). A high energy resolution spectrum will show these effects, as indicated in diagram 102. This figure also shows that what one can see in the spectrum depends on both energy resolution and signal to noise ratio. If X-ray excitation is used, the secondary electron background can be much reduced over electron excitation. So the peak to background ratio (P/B), while very useful for analysis as we shall see later, does depend on the analyser settings and mode of excitation.
The other point which is clear from the atomic physics is that X-ray and Auger emission are alternatives: either/or, not both. For low energy transitions, Auger emission is strongly favored. This Auger efficiency
The Auger transition rate was solved very early in the history of Quantum Mechanics by Wentzel (1927), who calculated transition matrix elements (Fermi's Golden Rule) between the initial (atomic) and the final (continuum) states based on the Coulomb interaction. This is set out in detail in D. Chattarji 'The Theory of Auger Transitions' (1976). There are simple arguments which bring out what is going on, as follows. The Auger transition rate,
where ψf = emitted electron (continuum) and χf = electron in the lower band. On the other hand, the X-ray fluorescence yield is the one electron dipole matrix element, namely
where the constant k = 4/3(ω/c)3, with the radiation frequency ω/2π given by hω/2π = EK -EL. Now if we assume Bohr-like atoms EK ~ -Ze2/r and r ~ a0/Z, with the Bohr radius a0 = h2/(4π2me2), we can deduce that ωK ~ Z2, and ω3r2 ~ Z4. So the K-shell X-ray fluorescence yield is
as shown in diagram 103.
To recap: these theories all depend on atomic and ionic wavefunctions for energies, transition rates, fluorescence yields, and are not specific to solids or surfaces. Note that many books on surface analysis pitch straight into the technical details without mentioning any of this at all.
The state of matter affects the lineshape, and the energy shift. If the transitions involve the valence band, then we refer to LVV etc. For example, Si LVV has a transtion at ~90 eV; these transitions are sensitive to chemical state (diagrams 105 and 106) and Al LVV has a different lineshape in metallic Al and in Aluminum Oxide (diagram 105). Other workers have studied core level shifts in photoemission. A personal account of this history is given by D. Menzel, Surface Sci 299/300 (1994) 170. This paper stresses the use of spectral shapes as 'fingerprints' of particular chemisorbed states.
The precise shape of an Auger or Photoelectron line is an ongoing topic which is researched in a few specialist groups worldwide. The lineshape of LVV Auger transitions is thought to reflect the self-convolution of the valence band density of states, whereas the UPS spectrum reflects the density of states directly. This is because of the two valence electrons involved in the Auger process. But in fact it is more complicated than this (diagrams 107-109). The final electron is emitted at a later time, so that it is possible that another electron has arrived in the locality to neutralise the core hole first. This depends on the energy cost of localising two holes on the same atom (the correlation energy U, often associated with the 'Hubbard' model), versus the valence band width, W. If U/W is much less than 1, we see an unshifted self convolution (self fold) of the valence band, whereas in the other limit (W/U much less than 1) we see a shifted, but atomic like, line. As a result the lineshape can switch from one type to the other across a series of alloys. A look at these effects in more detail is suitable for a talk or mini-project.
All these electron spectroscopies derive their surface sensitivity from the low inelastic mean free path (imfp) of electrons, which has a minimum in the neighborhood of 100 eV, and a typical minimum value of, say, 0.5 nm (C.J. Powell, Surf. Sci. 299/300 (1994) 34; there are also many previous, and indeed subsequent papers). Knowing the inelastic mean free path has become a major industry in its own right, but it is only in special cases that it can be readily determined experimentally. One case which is soluble is growth in a layer by layer mode. We will look into this in connection with the question of Quantification of Auger Spectroscopy in the next section. Because of time, we wonít be looking at quantification of other techniques: the approaches and problems are all very similar.
The general form of λ(E) has been given as λ (in ML) = 538/E2 + 0.41(aE)1/2, where a is the ML thickness in nm (diagram 110). This widely used formula correctly shows a minimum at about 50eV, but the form used is not rigorous, and if you are doing detailed work, you may well need a more precise expression. The underlying physics is that at high E, we have the Bethe loss law for scattering, which shows that (-dE/dx) ~ E-1ln(E/I), with I a typical electron excitation energy, of order 10-15eV. λ(E) increases as E/ln(E/I), (approximated as E1/2 in the formula given), since λ is ~ (-dE/dx)-1. At lower energy λ(E) goes up strongly as E decreases, because of the lack of states into which the electron can be scattered. For example, if the main scattering mechanism is creation of plasmons, with energies of 15 eV, then if the energy is within 15 eV of the Fermi level, the scattering canít occur because the final state is already occupied. This then becomes a phase space limitation at low E.
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