In the first lecture we have learned about UHV techniques and how to keep surfaces clean for a long time. The next questions is obviously how to obtain a clean surface in the first place. There are various ways of doing this, the most common being
Cleaving a bulk crystal is a very elegant way of obtaining a clean surface but it can only be applied to materials which have a natural cleavage plane. Important examples are some semiconductors and layered compounds like graphite or the new high TC superconductors as well as molecular crystals which are merely bound by van der Waals forces like fcc C60. A disadvantage of cleaving is the fact that a new preparation requires a new cleavage and most samples can only be cleaved once. Another potential problem is that the surface structure obtained by cleaving might be a meta-stable structure. The surface atoms may be left at the bulk position while the most stable structure would actually be a reconstruction . Yet another problem is that some samples are so unstable, that some of their constituents are evaporating out of the freshly cleaved surface and are thus depleted in the vicinity of the surface. An example is the oxygen depletion in certain high TC superconductors which occurs unless the cleavage is performed at very low temperatures.
Some materials can simply be cleaned by heating, in order to flash off an oxide layer and all contaminations. The most important examples are Si and the refractory metals Mo and W. For most materials, however, the bulk melting point lies under the temperature which would be required to clean the sample. Even below the melting temperature, heating might damage the crystal too much by changing the stoichiometry.
Ion bombardment (sputtering) of the sample is a very broadly used method, especially for metals. It is possible to clean the surface but the cost is that the surface is heavily damaged. This damage can often be repaired by heating. This, in turn, might cause impurities from the bulk to migrate to the surface such that more ion bombardment is needed and so on. Usually many cycles are needed to obtain a clean surface. When used for compounds, ion bombardment has the problem, that some elements in the compound are more easily removed than others. This leads to a sample with the wrong stoichiometry.
The sample can be chemically treated in order to “react the impurities away”. Carbon contaminations can often be removed by heating the sample in a low oxygen pressure (to create desorbing CO ) and the remaining oxygen can be removed by a hydrogen treatment (to create desorbing water).
Chemical analysis is essential for almost every experiment in surface science. Many questions are concerned with chemical reactions on surfaces where one has to learn about the reactants and the products and last but not least one has to determine if the surface is indeed clean after cleaning it.
We want to concentrate on non-destructive techniques for analysing the chemical composition of a surface. One can probe the geometric, electronic or vibrational properties in order to check if they correspond to those of the clean surface. The electronic structure is of particular importance because the binding energies of the core electrons, i.e. the electron in the atom’s inner shells, are very characteristic for the different elements. The techniques of x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) rely on this. An alternative is to probe the surface vibrations. Adsorbed atoms or molecules have characteristic vibrational modes which often have higher energies than the bulk vibrational frequencies.
In the following we will describe XPS in some detail and Auger rather briefly. The reason is the higher potential in the former technique. XPS can not only give an answer about which elements are present on the surface, it can also give some information about the chemical state the elements are in.
XPS relies on the photoelectric effect. In the most simple picture, the photons which hit the solid kick out electrons which are detected outside. The photon energy must be high enough for the electrons to overcome the work function of the solid. If one analyses the energy distribution outside the solid, it reflects the density of states inside (see Fig. 5.1). The energy is conserved:
| Ekin=h ν − Ebin− Φ, (5.1) |
where Ekin is the kinetic energy, h ν is the photon energy,
Ebin is the binding energy and Φ is the work function. For
XPS the photon energy has to be high enough to ionize the core levels
from the atoms of interest. Fig. 5.1 suggests that the
photoemission intensity I(Ekin) is simply given by
I(Ekin)=DOS(hν− Ebin− Φ) where DOS(E) is the density
of states of the sample as a function of binding energy. We shall see
later that this simple picture is rather poor, in particular for
spectroscopy of the valence states.
Figure 5.1: Sketch of the energies involved in photoelectron spectroscopy.
We have to keep in mind, however, that identifying the photoemission intensity with the occupied density of states is much too simple, mainly because of the fact that the photoemission intensity depends strongly on photon energy and emission direction.
To make use of the difference in core-level binding energies for
chemical analysis, one needs a monochromatic x-ray source.
Most x-ray sources are based on the following principle: a hole
is created in the inner-shell core levels of the atoms in an anode by
bombardment with high-energy electrons. There are two competing
ways to fill up this hole: x-ray emission and Auger decay
. Both are
shown in Fig. 5.2.
Figure 5.2: Decay of a core-hole by x-ray emission or the Auger process.
The Auger process is important for relatively low core-binding energies and for light elements. Below 10 keV binding energy and Z = 12 (Mg), the x-ray decay is extremely unlikely.
For the x-ray sources employed in surface chemical analysis, one normally uses Al or Mg as an anode material. The most intense lines are called Kα1 and Kα2, according the the old x-ray nomenclature (see Fig. 5.3). Often the doublet is viewed as one line and called Kα12. It has an energy of 1253.6 eV and 1486.6 eV, for Al and Mg, respectively. Note that in the light of what we have just said about the probability of an x-ray decay, these sources are very un-efficient. Why does one use these materials anyway?
Figure 5.3: Nomenclature in the x-ray decay in Al and Mg.
The Kα12 is the most intense line in the x-ray spectrum but not the only one. The most important other contributions are due to double-ionization (the Kα34 line), transitions from the valence band (the Kβ line) and a bremsstrahlungs background caused by the de-acceleration of the fast electrons in the material. These lines lead to “satellite” peaks in the spectra. The Kα1 and Kα2 lines do also have a certain width themselves which, together with their separation, determines the ultimate resolution achievable with an x-ray source. It is determined by lifetime of the core hole. The total width for the Al and Mg Kα12 line is of the order of 1 eV.
For a detailed chemical analysis, it is very desirable to have a higher energy resolution. In order to achieve this, the x-ray source can be equipped with a monochromator. This will increase the energy resolution and at the same time remove the “satellite” lines which are due to photoemission induced by, for example, the Kα34 line.
Alternatively, one can use synchrotron radiation
as an x-ray
source. This radiation is caused by accelerating ultra-relativistic
charged particles (mostly electrons), typically by forcing them to
go around the corners of a storage ring
(see Fig. 5.4).
Figure 5.4: Acceleration of electrons in a storage ring and emission of synchrotron radiation.
This leads to a continuos spectrum from the infrared over the visible
and uv to the x-ray regime (see Fig. 5.5)
Figure 5.5: Spectral distribution of synchrotron radiation.
Above the so-called critical energy, the synchrotron radiation intensity drops quickly to zero. The critical energy is given by the kinetic energy of the electrons in the ring
| EC ∝ |
| , (5.2) |
where R is the bending radius in the ring. If one wants to do XPS at a synchrotron radiation source, one does of course also need a monochromator.
Synchrotron radiation has several advantages over conventional sources: the resolution can be very high, the radiation is polarized and, most importantly here, the photon energy can be changed. The last point allows us to shift the peaks in an x-ray spectrum to exactly the kinetic energy we want. In surface science, this is often the energy where the mean free path of the electrons is shortest. The obvious disadvantage of synchrotron radiation is that you have to build a storage ring to get it.
The XPS cross section is given by a matrix element <f|H′|i>. The field-atom interaction hamilton can be written as
| H′=− |
| (pA+Ap) −eΦ+ |
| |A|2 (5.3) |
This may be simplified using various approximations (for a detailed discussion of the photoemission process, see section 8.3.2). The result is
| <f|H′|i>= |
| <f|p|i>. (5.4) |
Decomposing this into a radial part and an angular part gives the dipole-selection rules
| l′=l ± 1 and m′=m,m ± 1. (5.5) |
The actual cross section is contained in the radial integral. As a rule of thumb, the cross section for a given initial state, e.g. the 1s electron, increases very rapidly with the atomic number of the element. This means that it is easier to see a contamination of oxygen than a contamination of carbon when looking at a conventional XPS spectrum from a surface.
Qualitatively, a lot can be learned about the cross sections by just looking at the radial part of the atomic, i.e. bound, wave function and of the free electron wave leaving the atom. Fig. 5.6 shows such a comparison. Consider first the upper part which shows the radial wave function of Ne 2p together with the radial part of the photoemitted electron just at the threshold, i.e. at zero kinetic energy. Qualitatively, the matrix element is given by the integral over the product of the two wave functions. This integral is positive. When we now increase the energy of the outgoing electron then the wavelength of the photoelectron will become smaller and the value of the integral will increase. At very high energies, on the other hand, the wavelength of the outgoing electron will be so short, that the integral contains very many positive and negative contributions of equal size and vanishes. This means that for increasing the photoelectron energy, we expect the photoemission cross section to increase right after the threshold, to rise to a maximum value and to decrease slowly after reaching this value.
Now consider the case of Ar 3p. The behaviour here is
qualitatively different because the radial wave function of the atom
has a node. Right at threshold the integral is large and negative.
Increasing the energy of the outgoing electron will lead to a
situation where the first node of the outgoing wave divides the
large negative area of the 3p area in almost equal parts. At this
point, the integral will be close to zero. Upon a further increase of
the energy, the integral will also increase again. Finally, for very
high energies, it will vanish for the same reasons as above. The
minimum occurring in the cross sections for initial states with a
radial node is called a Cooper minimum.
Figure 5.6: Radial part of the Ne 2p and Ar 3p wave functions together width the continuum wave function for the l+1 channel at zero kinetic energy. After Ref. [14].
Fig. 5.7 shows an XPS spectrum from an Al surface. The most pronounced peaks in the spectrum are due to the excitation of the Al core levels and the corresponding plasmon losses. Apart from these, several other structures are visible. Some can be identified as lines from contaminations which are adsorbed on the surface. One is due to an Auger transition which occurs to fill up the core hole under the emittance of an electron. When using synchrotron radiation, it is simple to distinguish between the Auger and the XPS peaks: One takes the same spectrum at a slightly different photon energy. The XPS peaks will also shift in kinetic energy by the same amount but the Auger peaks will not. They have a fixed kinetic energy. The possibility of moving the photon energy is also very useful if some adsorbate XPS peaks fall to close to some substrate Auger peaks and are therefore invisible.
There is also a background under the whole spectrum which is caused by inelastically scattered electrons. This background is quite structureless, only increasing at low kinetic energies. We see that we can really distinguish between the directly emitted electrons and those which have undergone an inelastic scattering process.
For a practical surface chemical analysis one can compare the
measured spectra to tabulated data, like in the “Handbook of x-ray
photoelectron spectroscopy” [17].
The precise value of the XPS binding energy gives very valuable information about the system. However, an exact understanding of the observed binding energy is rather complicated. We distinguish between initial state effects and final state effect. The former affect the binding energy of the initial state before the photoemission event, for example by the chemical environment of the atom of interest. The latter are due to the photoemission event itself and the nature of the final state.
Let us start with the initial state effects.
If one finds, for example, a C 1s
peak in the XPS spectrum from a surface, then one may be able to
decide if the carbon is present in a CO2 or in a CF4
molecule. The reason is, that the electronic environment of the
carbon atom determines the electrostatic potential at the position
of the carbon core. In the case of CF4 the F atoms draw the
C valence electrons strongly away from the carbon. For the 1s
electron, this leads to an effective increase of the nuclear charge
and it therefore increases the binding energy observed in XPS. Fig.
5.8 shows the measured and calculated (see below) binding
energies for the C 1s line in different chemical environments.
The chemical shift
over the whole range is rather large, so large
that it can be observed even with a conventional x-ray source.
Figure 5.8: Comparison between experimental and calculated (from Koopman’s theorem ) C1s binding energies. Note that the agreement is very good but only if one of the axes is shifted by 15 eV. The good agreement is underlined by the line of slope 1 After Ref. [15].
The use of synchrotron radiation
and the high resolution associated
with this permits now the observation of much smaller shifts. Fig. 5.9
shows the Ru 3d core level spectrum from a clean Ru surface.
Figure 5.9: A Ru 3d5/2 core level spectrum from a clean Ru surface. Apart from the bulk peak two surface-related peaks are visible, one from the first and one from the second layer. After Ref. [16].
Apart from the bulk peak two others are visible which can be
assigned to emission from the first two layers of this surface. Such
surface core level shifts (SCLS)
have often been observed for
the transition metals and have been explained using the simple
picture given in Fig. 5.10. When the surface is created,
the d-band is narrowed due to the smaller number of nearest
neighbours. Consider the case of less than half filling. A band
narrowing would also move the whole band over the Fermi level. This
would mean that the surface is charged: it is at a chemical
potential different from the bulk. In order to avoid this
energy-expensive situation, an
electrostatic potential is needed which shifts the whole band down
to lower energies. This electrostatic potential does also shift the
core level. The analogue argument is made for the case of more than
half filling.
Figure 5.10: Surface core level shift caused by d-band narrowing and an electrostatic shift for transition metals with less and more than half filling of the d shell.
So far, we have only considered initial state effects on shifting the binding energy. We have not said anything about the importance of final state effects or how to calculate the binding energy in the first place. The most simple assumption for such a calculation is that the measured binding energy is the orbital energy of the photoionized electron. This is known as Koopman’s theorem . It has been used to calculate the binding energies in Fig. 5.8 and obviously leads to a large but constant error of about 15 eV.
The most severe error in Koopman’s theorem is the following: if an electron is adiabatically removed from the core, the other electrons in the system have to reach a new ground state. This new ground state has a lower energy due to the increased effective nuclear number of the photoemitting atom. The relaxation energy associated with reaching the new ground state is partially transferred on the photoelectron (Fig. 5.11). This increases the kinetic energy and decreases the apparent binding energy. We can write:
| Ekin=h ν − Ebin + Er=h ν −( Ebin − Er) (5.6) |
We assume a zero work function here for simplicity. The expression in
brackets would be the binding energy determined by the experiment.
The picture where the electron is taken out of the system
adiabatically, i.e. very slowly, is actually not a good one. On the
contrary, we should rather think of the electron as being removed
very quickly. In such a situation, the system is not necessarily left
in the ground state. It could be in some excited state and the energy
of this excitation would be missing from the photoelectrons. This
leads to satellite peaks in the photoemission spectra
. In the case
of metals the most pronounced satellite peaks correspond to plasmon
excitation. The excitation of electron-hole pairs, on the other hand,
does not lead to separate peaks but it renders the lineshape of the
core level peak itself asymmetric.
Figure 5.11: Final state effects in the photoemission process.
In summary, we can note that the precise binding energy of a core electron is very sensitive to the environment of the emitting atom and much can be learned from the XPS spectra. On the other hand, one has to be very careful when it comes to interpreting spectra with several shifted components because the shift itself is a very complicated interplay of initial and final state effects. An “intuitive” assignment of the various peaks could be wrong.
Auger electron spectroscopy can be used for surface chemical analysis in a way very similar to XPS. Since core levels are involved, the energy of the Auger electrons is also very characteristic for the various elements. AES is, however, rather limited when it comes to very high resolution studies. Therefore, we discuss it only briefly here. On the other hand, a qualitative chemical analysis of the surface is still very often performed using AES with a simple spectrometer based on a cylindrical mirror analyser . The importance of AES for the practitioner justifies a short discussion.
The Auger effect (depicted in Fig. 5.2) was discovered by Pierre Auger in 1923. In photoemission experiments, he observed electrons with kinetic energies independent of the incident x-rays.
The process starts from an atom with a core hole in the level A. This core hole is filled by an electron from the level B. The remaining energy is used to kick out an electron from the level C. The kinetic energy of an Auger electron is then
| Ekin=EA−EB− EC− Φ (5.7) |
This formula is not a very good one because it is only based on the atomic levels. Actually we are concerned with a transition from an atom with one core hole to an atom with two core holes. One often takes this into account (with little justification but some success) by inserting the average between the Z and Z+1 energy levels for EB and EC into equations (5.7).
The Auger nomenclature follows the old x-ray notations. The Auger transitions are labelled ABC for the initial state hole (A) and the two final state holes (B) and (C). For A, B and C one inserts the letter denoting the shell. A KLL Auger transition would be a transition starting from a hole in the 1s level which would be filled up from the 2p level. A 2p electron would also be emitted. The more complicated nature of the upper levels causes a multiplet splitting in the Auger spectra.
An important point in AES is, that it does not make any difference, how the initial core hole is created. In most practical cases this is achieved by bombarding the sample with electrons of 2-3 keV kinetic energy. The Auger electrons are detected with the electron analysers we have already discussed. For a quantitative analysis, the energy of the exciting electrons does, however, come into play because of the energy- and element-dependent ionization probability.
Fig. 5.12 shows a typical Auger spectrum from a Cu surface.
It shows pronounced peaks due to the Cu Augers peaks and some small peaks
which have been assigned to contaminations of the surface. Note that
the spectrum is taken in a derivative mode using a lock-in amplifier
in order to reduce the contribution of the inelastically scattered
electrons.
Figure 5.12: Typical Auger spectrum from a Cu surface.
An example for the quantitative analysis of Auger spectra is given in the Exercises.
If you are interested in preparational details for a specific system, it is best to consult some recent original publications (if these do not exist you have to try for yourself!). XPS and AES are discussed in most surface science books and in great detail in [2].