Would
you expect the binding energy of a C 1s electron to be greater or less than that of an O 1s electron?6.1 Chemical Analysis
References
We’ve already briefly discussed the use of photoelectron spectroscopy to determine the growth modes of adsorbates on surfaces (Section 4.5). In this section we’ll explore in considerably more detail the physics underlying the photoemission process.
The application of photoemission as a technique to study the chemical and electronic structure of solids has its origins in the work of Siegbahn and coworkers in the University of Uppsala, Sweden in the fifties. That group made dramatic improvements in the energy resolution and sensitivity of electron spectrometers, enabling a determination of the binding energies of electrons in a wide range of materials. As we’ll see, from an analysis of the electronic binding energies it was possible to build up a chemical "fingerprint" of the solid. X-ray photoelectron spectroscopy (XPS) (X-ray photoemission) is thus also commonly referred to as Electron Spectroscopy for Chemical Analysis (ESCA). (Siegbahn’s pioneering work earned him the Nobel prize in 1981).
Although synchrotron sources, which provide a continuous range of photon energies (See Section 6.), are very often used in modern high resolution photoemission work, photoemission measurements are still commonly divided into two regimes:
In XPS, X-ray photons from an X-ray tube or a synchrotron (see also Section 6.5) are used whereas in UPS a helium discharge lamp or, again, a synchrotron provides a flux of UV photons.
In each regime, the incident monochromatic radiation ejects an electron from either a valence level or a deeper lying core-level (see Fig 4.16). UV photons have insufficient energy to excite an electron from a core-level and thus can only eject the more weakly bound valence electrons.
The mean free path and surface sensitivity
The photoelectrons that are detected in a photoemission experiment originate only from the uppermost layers of a solid. As we’ll see, with the correct choice of experimental parameters photoemission can be used to probe just the first few monolayers at the surface of a solid. This surface sensitivity arises from the strong interaction of electrons with matter. An electron travelling through a solid will have a certain inelastic mean free path – a characteristic length that it can travel without suffering an energy loss. Thus, electrons ejected from a solid via the photoelectric effect will be of two types:
An electron with energy in the 5 – 2000 eV range passing through a solid can lose energy via a number of processes. Neglecting the minimal energy loss that occurs due to the excitation of phonons, there are three key processes:
The net effect of these processes is that the (inelastic) mean free path of an electron in a solid is strongly dependent on its kinetic energy. A schematic plot of the variation in electron mean free path as a function of electron kinetic energy is shown in Fig. 6.1. At very low kinetic energies the electron simply does not have enough energy to excite the processes listed in 1- 3 above so its mean free path is long. At high kinetic energies the electron spends less time passing through a given thickness of solid and thus is less likely to suffer an energy loss. Hence its mean free path in the solid is again quite long. However between these two regions the mean free path, as is clear from Fig. 6.1, passes through a minimum.
As discussed by Woodruff & Delchar, Prutton and Attard and Barnes the key process determining the minimum in the curve shown in Fig. 6.1 is actually the energy loss due to plasmon excitation. When the kinetic energy of the electron is below the plasmon excitation energy then it can travel for long distances without exciting a plasmon (i.e. it has a long mean free path).
The curve in Fig. 6.1 is usually referred to as the "universal" mean free path curve as it loosely holds for electrons travelling through a very wide range of materials. However, the curve should only be used as a rough guide to the mean free path – the curve is based on an empirically derived relationship. The actual value of the mean free path in a given material may fall some way off the curve.
(NOTE: Woodruff & Delchar, Chapter 3 and Prutton, p. 24 make the point that the inelastic mean free path referred to above is actually more correctly referred to as the electron attenuation length. This is because elastic scattering processes in the solid, although not changing the energy of the electron will increase the distance it needs to travel through the solid. This in turn leads to a larger probability of an inelastic scattering event (processes 1 – 3) occurring. However, it is still very common in the surface science literature for the attenuation length to be referred to simply as the mean free path and I will use the latter term throughout
).The most important point to be gained from the above discussion is that electrons with kinetic energies in the ~ 40 – 150 eV range have the shortest mean free paths and at the minimum of the "universal" curve the mean free path is ~ 1 nm. Even for quite high electron energies ( 1- 2 keV) the mean free path is still only a few nm. This is a very significant result as regards the use of photoelectron spectroscopy as a surface sensitive probe. It means that even though the penetration depth of the incident X-rays is typically of the order of microns, the electrons that escape from the solid, due to their mean free path, will only have originated from the top few layers.
Up to this point we have implicitly considered that the angle between the entrance to the electron spectrometer (see Section 6.4 for a discussion of electron spectrometers) and the surface normal is 0 (Fig. 6.2). That is, we have a normal emission geometry for photoelectron collection. If, however, we rotate the spectrometer (or sample) so that the electrons are collected at a glancing angle (again, see Fig. 6.2), the electrons have to traverse a longer distance in the solid (d cos q ). The larger the angle, the greater the path length for the electrons and, thus, the higher the surface sensitivity of the photoemission measurement.
Electronic energy levels and the photoemission spectrum
As mentioned above, in XPS we are concerned with the excitation of electrons lying in the tightly bound core-levels whereas UPS is used to probe the valence levels. The key equation underlying both processes is Einstein’s equation:
EKE = hn - EB
where EKE is the kinetic energy of the electron ejected from the solid, hn is the photon energy and EB is the binding energy of the electron in the solid.
XPS may be used to provide a chemical "fingerprint" of a surface. This is because the binding energies of the electrons in the core-levels (see Fig. 6.3) are representative of the atomic species. That is, an electron in a 1s level of oxygen has a particular binding energy which will differ from that of a Si 1s electron, a Ga 3d electron, a C 1s electron etc…
Although, as we’ll see, the binding energy will vary depending on the chemical environment of the atom in the solid, the energy differences are generally small enough so that the presence of a particular element may be unequivocally identified from an XPS spectrum.
A simple (and poorly drawn!) schematic of a photoemission spectrum is shown in Fig. 6.3. Electrons are excited from filled states out of the solid with a particular kinetic energy. Measurement of the intensities and energies of the outgoing electrons with an electron spectrometer (Section 6.4) produces a photoemission spectrum that mirrors the distribution of filled levels in the solid. Importantly, the binding energies are referenced to the Fermi level of the sample - we'll come back to this point later. In addition, you’ll note that there is a background signal underlying the valence band and core-level derived peaks.
Can you suggest an origin for the background in the photoemission spectrum?
A typical XPS spectrum covering a large energy range is shown in Fig. 6.4 (Taylor et al., Nottingham Nanoscience Group 1999, unpublished). There are a number of sharp core-level peaks clearly visible – from the known photon energy and the measured kinetic energies we can determine the binding energies of these peaks. Then, from previously published tables of binding energies for elemental electronic energy levels we can determine which chemical species are present at our sample surface.
Photoemission: the key physics
In this section I’ll briefly discuss some of the key physics underlying photoemission.We first need to consider the nomenclature used for the electronic levels in a solid. In common with most atomic spectroscopies, in XPS the principal quantum number of an electronic energy level is usually designated by a letter. Thus the n=1 level is the K shell, the n=2 level the L shell and the n=3 level the M shell. For the K shell there is one possible value of orbital angular momentum quantum number, l, and that is 0 (for n=1, we can only have an s orbital) and thus there are no subshells associated with the K shell.
As the principal quantum number increases, the possible values of l also increase (l=(n-1)…0). So for the L shell, we have two values of orbital angular momentum (0,1 corresponding to s and p orbitals) and for the M shell we have 3 values of orbital angular momentum (l =0,1,2 i.e. s, p and d orbitals).
The photoemission process involves the excitation of an electron from an initial state (for our purposes, an atomic orbital) to a final state. The intensity of a photoemission peak depends on both the initial and final state wavefunctions and the vector potential of the incident electromagnetic field. We will not discuss in any detail the (rather involved) quantum mechanics underlying the photoemission process. Just note that the photoemission rate is given by the square of the matrix element <f | H | i> where | f> and | i> are the final and initial states respectively and H is the interaction Hamiltonian (H=-(e/2mc)(p· A+A· p), p is the electron momentum operator and A is the vector potential of the field).
The binding energy, EB, is simply the energy difference between the (N-1) electron final state and the N electron initial state. That is:
EB=Efinal(N-1) – Einitial(N)
If we assume that no rearrangement of the electrons - either within the atom from which the photoelectron originated or in the neighbouring atoms of the material - occurs following the ejection of the photoelectron (an approximation known as Koopman’s theorem) then the binding energy of the electron is simply the negative of the atomic orbital energy (-e k, where the subscript k labels the energy level from which the electron was removed).
Final state effects
Koopman’s theorem is a severe approximation. The ejection of a photoelectron creates a positively charged core-hole in the atom. Just as we discussed in Sections 4 and 5, electrons in the vicinity of the positive charge will rearrange to screen it i.e. reduce its energy. The energy reduction is called the relaxation energy and can originate both from the electrons on the atom containing the core-hole (intra-atomic screening) and from those on surrounding atoms (interatomic screening). Relaxation/screening is thus a final state effect.
The photoelectron can also interact with other electrons when departing the atom. For example, it may excite a valence electron to an unfilled (conduction band) state and lose an amount of kinetic energy equal to the excitation energy. This is called a shake-up process. Similarly, the departing photoelectron might transfer sufficient energy to the valence electron to remove it entirely from the atom: a shake-off process.
Spin-orbit (l-s) coupling
A very important final state effect for any orbital with orbital angular momentum> 0 is spin-orbit coupling/ splitting. This is a magnetic interaction between an electron’s spin and its orbital angular momentum. We'll consider a p orbital (though spin/orbit coupling holds equally for d and f orbitals). After removal of an electron from the p orbital through photoemission, the remaining electron can adopt one of two configurations - a spin-up or spin-down state (see Fig. 6.5(i))). With no spin-orbit interaction these states would have equal energy. However, spin-orbit coupling lifts the degeneracy and we need to consider the quantum number, j, the total angular momentum quantum number. The value of j is given by l + s where s is the spin quantum number (±½). For a p orbital j=1/2 or 3/2. Thus the final state of the system may be either p1/2 or p3/2 and this gives rise to a splitting of the core-level into a doublet.
The degeneracies of the two spin-orbit split levels are given by (2j+1). (Fig. 6.5(ii)). The degeneracy determines the probability of that state being the final state of the system. The relative intensities of the peaks in the core-level doublet are thus given by the ratio of the degeneracies of the spin-orbit split states.(Fig. 6.5(iii)).
Fig. 6.6 shows a Si 2p XPS spectrum from a silicon sample where the photon energy and emission angle have been chosen to enhance the signal from the bulk of the sample (we’ll shortly consider what happens to the spectrum as the surface sensitivity is increased). As discussed above, spin-orbit interactions split the 2p peak into a doublet. The higher angular momentum state (j=3/2) appears at lower binding energy in the spectrum. The value of the energy splitting between the components of the doublet is, as you might expect, called the spin orbit splitting whereas the intensity ratio is termed the branching ratio (see Fig. 6.5(iii)).
What is the branching ratio for a Ga 3d level? A C 1s level?
XPS Peak broadening
You'll note that the peaks in the Si 2p spectrum shown in Fig. 6.6 are not particularly sharp. Having discussed the intensities and energies of XPS peaks, we now need to consider their widths. The first contribution to the peak widths is Gaussian broadening which arises from a number of sources. The primary contributions to Gaussian broadening are:
The second type of peak width broadening is Lorentzian broadening. The core-hole that the incident photon creates has a particular lifetime which is dependent on how quickly the hole is filled by an electron from another shell. From Heisenberg’s uncertainty principle, the finite lifetime will produce a broadening of the peak.
Initial state effects: chemical shifts
At this point we can start to discuss just why XPS is such a powerful method of probing the chemical structure of a surface. Throughout the module I’ve stressed how the valence electron distribution at the surface of a solid will differ from that of the bulk solid (sometimes weakly, as for certain metal surfaces, or dramatically, as for a large number of semiconductors (Si(111)(7x7) perhaps being the best example)). Importantly, variations in the valence electron distribution will affect the potential a core-level electron feels. Therefore, the binding energy of a core-level electron in an atom at the surface will generally differ from that in a bulk atom.
The precise binding energy of a core-level electron depends critically on its chemical environment. Both clean and adsorbate covered surfaces represent chemical environments that differ from that "seen" by an atom in the bulk. The change in the chemical environment produces a shift in the core-level. The magnitude of this chemical shift varies dramatically (from <0.1 eV to ~ 10 eV) from system to system.
Chemical shifts are generally interpreted in terms of the initial state of the system (i.e. before the photoelectron has been ejected). (However, this approach needs to be adopted with care… see below). Charge transfer will either decrease or increase the charge density of an atom, leading to increased or decreased Coulombic attraction between the nucleus and the core electrons. Thus an atom that has donated a considerable amount of valence charge - or, to use the correct chemistry terminology, is in a high oxidation state - will produce an XPS peak at a higher binding energy than that of an atom in a lower oxidation state.
A good example of a chemically shifted XPS peak is shown in Fig. 6.7 (a). This is some of the Nottingham Nanoscience group’s photoemission data from an oxidised Si(100) surface (Cotier et al., 1999, unpublished). The Si 2p core-level (doublet) peak appears at ~ 100 eV binding energy. However, at approximately 4 eV above the Si 2p peak lies a broad peak due to the oxidised atoms at the Si surface. As we anneal the sample surface we can desorb this oxidised layer and produce a clean Si(100) surface. For the clean surface, the chemically shifted peak due to the oxidised Si atoms is missing (Fig. 6.7 (b)).
However, the Si 2p spectrum shown in Fig. 6.7(b) is somewhat more complex than the doublet spectrum we discussed above (Fig. 6.6). This is because on desorbing the oxide the Si(100) surface forms a (2x1) reconstruction. Surface reconstruction means that the chemical environments (valence charge density, bond lengths) of the surface atoms differ from that in the bulk. Photoemission from the surface atoms thus leads to the appearance of core-level peaks with different energies than that of the bulk. Using sophisticated curve-fitting algorithms it is possible to decompose the Si 2p spectrum into its constituent bulk and surface related components – an example is shown in Fig. 6.8. (Note that Fig. 6.8 is a lower resolution spectrum than Fig. 6.7(b) - for example, the shoulder on the high kinetic energy side of the spectrum is not as well defined as it is in Fig. 6.7(b)).
I am not going to cover the minutiae of the spectral decomposition shown in Fig. 6.8. (In fact, to some extent, the precise origins and positions of the peaks are still being debated). You should just note that the core-level consists of:
How
might we make the photoemission measurement more surface sensitive?!
From an analysis of the energies and intensities of the surface core-level shifted (SCLS) components, we can derive a great deal of information about the chemistry and, to some extent, structure of the surface. Note that if we now expose the Si(100) surface to an adsorbate the core-level line-shape will change because, again, we are modifying the valence electron distribution at the surface. A particularly good example of adsorbate-induced core-level peak changes is the H/Si(111) system. The Si(111)(7x7) surface is associated with a very complex core-level spectrum due to the large number of chemically distinct sites at the surface (see Fig. 2.6(a)). Each one of these sites, in principle, can give rise to a core-level component. With high resolution photoemission measurements (and a large data set covering a range of photon energies and emission angles) it is possible to decompose the Si 2p core-level from the (7x7) surface into its component bulk and surface related features. However, for a Si(111) surface terminated with a monolayer of hydrogen atoms, the Si 2p core-level lineshape is significantly less complex.
At this point I should mention that we have assumed that the core-level shifts observed at clean and adsorbate surfaces arise solely from the variation in the charge state of the atom before the photoemission process - that is, are purely initial state effects. You should realise that differing chemical environments will also change the screening of a core-hole and this will in turn affect the photoemission relaxation energy. However, a very large number of photoemission studies have successfully interpreted surface core-level shifts on a wide range of semiconductor surfaces solely in terms of initial state variations. For the purposes of this module we will neglect the role of final state effects in core-level shifts.
Binding energy referencing
For the type of core-level analysis we have discussed above we must have accurate measurements of the core-level binding energies. In this final section on core-level photoemission the issue of binding energy referencing will be discussed. I will assume that the photoemission measurements are for conducting samples (metals or semiconductors). (Things get somewhat more complicated for insulators!). Referring to Fig. 6.9, both the spectrometer and the sample are electrically grounded and, hence their Fermi levels will align. The sample and spectrometer will have different workfunctions as shown. The binding energy of the photoelectron is referenced to the Fermi level (i.e. the zero of the binding energy scale is at the Fermi level). A close examination of Fig. 6.9 shows that the binding energy of the photoelectron is given by:
EB=hn - EKE - f SP
where f SP is the spectrometer work function. Hence, it is the spectrometer and not the sample work function that must be accurately known. The spectrometer is generally calibrated using standard samples prior to the photoemission experiments and its work function determined.
For semiconductors, the onset of photoemission occurs not at the Fermi level but at the valence band edge. However, we still reference the photoemission measurements to the semiconductor Fermi level. This is achieved by measuring the onset of photoemission from a metal in electrical contact with the semiconductor. Again, if the metal and semiconductor are in electrical contact the Fermi levels must align. Thus the Fermi level position in the metal equals that in the semiconductor and may be used as the energy reference.
A second important electron spectroscopy used in surface science is Auger electron spectroscopy(AES). Auger electrons are named after their discoverer, Pierre Auger and arise from what is termed an autoionisation process which is illustrated in Fig. 6.10. An electron is ejected from a core-level either by a photon (as in conventional photoemission) or by an incident high energy electron. The core-hole is filled by an electron from a higher energy level. The energy lost by that electron may be given up in the form of an X-ray photon or the quantum of energy is transferred (non-radiatively) to another electron in the atom. That electron (the Auger electron) is thus released from the atom.
The kinetic energy of the Auger electron, unlike that of a photoelectron, is not dependent on the energy of the incident radiation (or electron) that produced the initial core hole. Thus, Auger electrons have energies that are characteristic of the atom from which they arose and may be used for elemental identification.
The notation associated with Auger transitions is also shown in Fig. 6.10 and relies on the shell nomenclature discussed earlier in this section. Note that if the valence levels are involved in the Auger process these are denoted by a V.
Generally Auger electron spectroscopy is carried out using an electron gun to produce relatively high energy electrons (in the 2 to 5 keV range) for initial core-level excitation. The Auger peaks are superimposed on the secondary electron background and are generally quite weak. Therefore, the Auger spectrum is usually electronically (sometimes numerically) differentiated to highlight the Auger peaks.
In addition to chemical "fingerprinting" of a sample, a very common application of Auger spectroscopy is in the determination of growth modes (Section 4.4). An analysis of the attenuation of a substrate Auger peak as a function of coverage, in an identical manner to that discussed for photoemission peaks in Section 4.4., enables a determination of whether the growth mode is of Frank-van der Merwe, Vollmer-Weber or Stranski-Krastanov character.