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Binding energies and reference levels in photoelectron spectroscopy
293
Journal of Electron Spectroscopy and Related Pherwmena, 52 (1990) 293-302 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
BINDING ENERGIES AND REFERENCE PHOTOELECTRON SPECTROSCOPY
LEVELS IN
SE. ANDERSON and G.L. NYBERG Chemistry Department, La Trobe University, Bundoora, Vie., 3083 (Australia)
ABSTRACT Measurements on solids enable the Fermi level to be positioned relative to the spectrometer vacuum level; those on gases should in turn allow placement of the latter with respect to the vacuum level at infinity. A combination of the two would therefore position the Fermi energy on an absolute scale. The separation between EF and V, corresponds to the spectrometer electrochemical potential. This is the quantity which must be added to binding energies measured relative to EF to reference them to V,, ie 6, = BF + &p. The requirements for performing this alignment are discussed, and &+, is measured on the present spectrometer. The value of 4.1 eV which is obtained should supplant the use of sample work functions in the alignment procedure.
INTRODUCTION
Whereas in the photoelectron spectroscopy of gases there has never been any question but that the electron binding energies are referenced to the vacuum level at infinity (V,), in the case of solids it is normal to express binding energies relative to the Fermi level ( EF). This is done not just for experimental convenience, but because of the uncertainty in converting these values to an absolute scale. This uncertainty has included not only how to align them with the vacuum level at infinity, but also whether this is indeed the “proper” reference level. While this deficiency is largely unimportant for purely experimental studies of solids, it becomes significant whenever comparison is made with either theoretical calculations or gas phase measurements, both of which are referenced to V,. The instance where this most commonly arises is in photoemission studies of adsorbates, where it is usual to want to compare the adsorbate spectrum with that of the free molecule. The objectives here are to achieve a correct alignment of the two spectra to aid in band assignment, and to further identify the shift of those bands involved in chemisorption bonding. There have thus been several studies which have addressed the problems of converting binding energies (BF) relative to the Fermi level to those (B,) relative to the vacuum level at infinity, the significance of the adsorption shifts so obtained, and of possibly more appropriate reference levels. Since the principle of photoelectron spectroscopy is based on the (extended) Einstein photoelectric equation (for solids) hv = (BF + @)+ K (1) (where K is the electron kinetic energy upon ejection), and for gases hv = B, + K (2) 0363-2043/90/$03.50
1990 Elsavier Science Publishers B.V.
it is natural that the method of conversion from BF to B, has been to add the value of the work function $, ie B_= BF+$ (3) Just which work function, though, has been a matter of contention. The original choice [l] in adsorbate studies was that of the clean substrate surface (I&,,), but subsequently the value of the adsorbate-saturated surface ($a&) was advocated [2], and adopted in some instances. However it was pointed out by Carley, Joyner and Roberts [3] that since 4 refers to the vacuum level local to the surface (Vtocat; either V, or Va&), and not to V,, then there is no value of the work function per se which can be appropriate. In the final discussion around that time Broughton and Perry 143agreed, but concluded that em was nevertheless “the most meaningful practical approach’, and subsequently this has been most commonly employed. In these discussions, attention has focussed upon whether the resulting adsorbate binding energy shifts AB = Bg - Ba (4) (the difference between the binding energies of a band in the gas-phase and in the adsorbate spectrum) are “chemically meaningful” [4,5], and emphasis has been placed on the value of o that is required for this to be so. Now while this is undoubtedly an important matter, it implies (as will be seen) a value of Ba other than B,a (and so is experimentally not well defined). The primary concern of the current study is instead the determination of this latter quantity, with the interpretation of the resulting value of AB a matter of only secondary consideration. We have taken-up this topic again because we wish to question one of the underlying assumptions of previous discussions - that the measured electron kinetic energies of solids cannot be related to V,. Since there is no ‘calibrant solid’, we accept that this is true for measurements purely on solids; for gases, though, there are calibrants. Hence by combining both types of measurements on the one spectrometer it would seem as though it should be possible to establish a common absolute reference level. SPECTROMETER WORK FUNCTION AND VACUUM LEVEL (SOLIDS) It seems to us that progress in this area has been experimentally led, based on certain observed constancies. Thus right at the beginning of photoelectron spectroscopy Siegb,ahn et al [6] observed in regard to eqn (1) that the experimental value of hv - (BF + K) ‘I... does not depend on the source material and [consequently] one and the same work function correction can be applied to all the measurements” (irrespective of the work function of the sample). They therefore concluded that, in PES measurements, the appropriate value of e was that pertaining to the material of the spectrometer; in other words, the spectrometer had an effective work function,
I$~+.,. This is illustrated in Fig la, which shows the situation for sample work functions (assumed metals) both less (&,,,) and greater (@m,) than &u. In Fig la, it has been assumed that sample and spectrometer are in thermodynamic equilibrium, so that the Fermi levels of both are aligned. When ejected, the photoelectrons move from the local environment (and potential) of the metal into that of the spectrometer; in so doing they either lose or ,gain kinetic energy, depending on whether $,,, is less or greater than asp. This serves to emphasise that the electron kinetic energy will depend on the particular spectrometer, each of which has its own spectrometer vacuum level VSPm, situated above EF by the amount $sp. The superscript ‘m’ is added to Vsp to emphasise that it is obtained by measurement on metal (solid) samples. There are two further consequences of the above observation. One relates to the measurement of work functions, from the full-width of the photoemission spectrum (ie, from the Fermi level to the secondary-electron cut-off). For any sample for which om is less than asp, the cut-off will lie hv below not Vm but Vap, and the fullwidth will yield not em but $sp. This difficulty can of course be overcome by floating the sample, so that its V, lies at or above Vsp (ie by applying a voltage to the sample to raise its Fermi level above that of the spectrometer by the appropriate amount). In the present context, though, the important point is that asp is readily determined. The other consequence, which is rather an aside, relates to angle-resolved studies. The difference between V, and V,, will cause a distortion of the angular distribution, which will increase as both the binding energy and the emission angle increase. This also can be eliminated by floating the sample, so that these vacuum levels match. SPECTROMETER VACUUM LEVEL (GASES) Although the concept of a spectrometer vacuum level [7] arises most naturally in the context of the photoemission spectra of solids, it does not add materially to their interpretation. Where it is most useful is in thinking about gases, and of the relationship between the two. It is well appreciated in gas-phase studies that binding (ionization) energies are not directly given by the difference between the photon energy and the (spectrometermeasured) kinetic energy. The technique employed there is to add a calibrant or reference gas (rg) whose ionization energy has been determined optically (eg from Rydberg series), and then to correct the apparent binding energies of the sample gas (sg) appropriately, viz: B,sS = Bspsg + (B-Q - Bsp’g) = (hv - Kspsg) +(B,‘g - hv + KspW) = B_Q + (KspW - Kspsg) (3 The determination thus involves two kinetic energies measured under the same conditions, namely, the environment of the spectrometer. What this again recognises is that kinetic energies are measured relative to the vacuum level of the spectrometer, and furthermore that this is not equal to the vacuum level at infinity.
296
Metal Spectrometer Work Function
Spectrometer Vacuum Level
(d)
@I
V,
Spectrometer Electrochemical Potential
Absolute Binding Energies
Figure 1. Relationship of the Fermi level, the spectrometer Work Function, the spectrometer Vacuum Level, the Vacuum Level at infinity, the spectrometer Electrochemical Potential (and Outer Potential), the Binding Energy relative to the Fermi level, the absolute Binding Energy (relative to the vacuum level at infinity), and the Binding Energy Shift (upon adsorption).
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An alternative way to do the experiment would be to measure the two gases sequentially. Measuring Ksp of the reference gas first establishes the position of V,,, relative to V,: e(Vsp - V,) I eAV,,, = hv - B,XI - K,orS g K,rg - K,,,‘S (6) This is illustrated in Fig lb. The subsequently measured Ksp for the sample gas can then be converted to KJB,: (hv - B,sg) P K_,sg = K,osg + eAV,,, (7) The drawback with this procedure in practice is that some gases contaminate the spectrometer, in which case the measurement environment in the two instances would be different. This contamination is the result of adsorption onto the spectrometer (particularly the walls of the ionization chamber, and the entrance slits). This results in a change in the spectrometer work function, and so also in the spectrometer vacuum level. The simultaneous measurement of the reference gas and the sample circumvents this difficulty, and is by far the simpler practical procedure. In order to establish the position of Vsp relative to V,, though, it is necessary to carry out the first of the above steps. Naturally this should be done employing noncontaminating gases. In addition, the kinetic energies should be measured as a function of decreasing gas pressure. The reason for this is to eliminate any pressureshift, which can arise from the attraction of the departing electrons to the remaining positive ions in the ionization region [8]. The resulting value of the spectrometer vacuum level is labelled V&P+O) in Fig lb. SPECTROMETER ELECTROCHEMICAL POTENTIAL We have seen how the concept of a spectrometer vacuum level arises naturally in the spectroscopy of both solids and gases. The question then follows as to whether these levels are identical in the two cases. It would be easy to label both simply as Vsu and thereby ignore this question. By deliberately labelling them separately we are required to explicitly justify this critical step in our argument. Our view is that they are not necessarily the same, but will be so under the appropriate measurement conditions. A typical experimental sequence in the measurement of solids is that the spectrometer is under ultrahigh vacuum, is brought up to something like 10-4 torr during argon ion bombardment of the sample, then returned to UHV. Were this gas one that chemisorbed (at room temperature) then there would be more than enough opportunity for monolayer coverage over the entire spectrometer. Separate studies on argon (and other inert gas) adsorption show, however, that this is not the case, so it can be assumed that the spectrometer remains clean, and esp unaltered. The situation with the gas measurements is not very different. At the ionization centre the pressure may be something like 10-3 torr, and 10-6 ton: in the rest of the spectrometer (and maintained constant throughout the course of the measurement).
Whether or not a monolayer adsorbs on the spectrometer surfaces (assumed initially clean) again depends on the nature of the gas being studied. lf these are inert gases there is no more reason than in the case above for the spectrometer to be contaminated. Under these circumstances the two spectrometer vacuum levels are thus the same. Should, however, the gaseous sample be one which strongly adsorbed, then it is entirely possible that a quite different spectrometer vacuum level would be developed, due to the changed work function of the spectrometer surfaces. When using inert gases, though, the outcome of this discussion is that, as indicated in Figlc, &pm = vsps = v,,. Having established the relative positions of V,, Vsp, and EF, it is appropriate to introduce some further terminology. By definition [4, & refs therein], the difference between V, and EF is known as the electrochemical potential ( cl), and that between Vlocal and V, as the Outer Potential (+Outer/e). Whereas the latter depends on the particular surface, the former does not (it is a property of the entire sample). The quantity AVsp determined from the gas-phase measurements is thus the Outer Potential of the spectrometer potential-defining surfaces (@spouter/e). The difference between &+, (determined from solids) and eAVsp is thus ksp; ie &p = h.p - eAVsp These quantities are illustrated in Fig lc.
(8)
Although the electrochemical potential so derived is that of the spectrometer, because (under the usual circumstances) dre Fermi levels of spectrometer and sample are aligned, it follows that the same value of G must apply to the sample as well. It might therefore seem that the subscript ‘sp’ could be dropped. We will not do so, however, since the Fermi level of a sample will adjust itself from one spectrometer to another, and it is by no means obvious that isp should be the same for different spectrometers. ABSOLUTE BINDING ENERGIES Having established Lp, that is, the position of V, with respect to EF, it is a simple matter to obtain absolute binding energies of solids, viz: B, = BF+ &p (9) This is illustrated in Fig Id, and the same adjustment applies to the levels of both the substrate and the adsorbate. This transference of Lsp clearly also depends on the Fermi level of the sample being aligned with that of the spectrometer. Besides the obvious instances involving sample-charging when this will not be so, there are examples involving physisorbed multilayers which also have been interpreted otherwise [9]. These cases would generally be considered, though, to be particular exceptions to the rule of Fermi level alignment. It is pertinent to comment further on the distinction between eqns (9) and (3). Since Q(m)varies from one crystal face to another, a band which has the same value of BF would, according to (3), give different values of B, on two different faces. Now
because of valence band dispersion, both the nature and the binding energy of the bands varies from face to face, so this anomoly is not so evident in UPS. These variations do not apply to core orbitals, however, which could be expected to have the same values of both BF and B, irrespective of the face exposed (in contrast to (3) but in .accordance with (9)). Indeed, it was just such a constancy, observed in their XPS measurements, which led Carley er al [3] to conclude that the quantity which needed to be added to BF in order to obtain B, is “of the order of a typical work function but is a constant not necessarily equal to any particular work function”. Eqn (9) completely concurs with this, and furthermore provides the interpretation of this constant. ADSORBATE BINDING (AND BONDING) ENERGY SHIFTS Having established the absolute binding energies of the adsorbate, these can now be compared to their gas phase values, and so the binding energy shifts determined, as illustrated in Fig Id. The question then arises, though, as to whether such shifts are “chemically meaningful”. By this is meant, ‘Does the resulting shift reflect the magnitude of the chemical bonding interaction between the adsorbate and the substrate?’ The answer previously given [4,5], and with which we concur, is ‘No’. The well-appreciated reason for this is that there are various ‘physical’ factors (such as the image charge) which will affect the binding energy of a molecule-locallised electron even if there is no chemical bonding between the adsorbate and the metal substrate. While a partial solution to this problem is provided by another well established, experimentally-originating, procedure - that of dividing the Binding Energy Shift into separate Relaxation and Bonding contributions [lo], ie (10) AB = ABBonding+ Al&taxation two difficulties remain. One is identifying bands of the adsorbate which are not involved in the bonding. However this can usually be done fairly unambiguously for some of the valence orbitals of larger polyatomic molecules, and for the core orbitals of any molecule (such orbitals not overlapping with those of the substrate). What cannot be overcome [ 111, though, is the likelihood that the bonding orbitals will have a different relaxation shift from their nonbonding counterparts. What the present procedure allows, therefore, is not a determination of nett Bonding Shifts, but (through the absolute alignment of the two binding energy scales) an accurate measurement of the Relaxation Shift (of the nonbonding orbitals). This can then be compared to calculated values of all extramolecular relaxation/polarization effects, such as final state screening and the influence of the image charge, and all other such non-chemical-bonding effects involved in photoemission from adsorbed species. -
300
IMPLEMENTATION The concepts discussed above arose in our own (UPS) case largely because the spectrometer (described previously [ 121) readily allows gas-phase measurements, as well as those on solids. The determination of V, relative to Van was undertaken observing all the cautions outlined above. ‘Ihe calibration gases employed were Ar, Xe and N2 in conjunction with He I radiation, and Ne and N2 with He II. The consequent wide range of kinetic energies enables the presence of any nonlinearity to be readily detected; there is none. The results obtained can be represented by the equation (hv - B,) = K, = 0.98 K,P + 0.77 eV (11) and the negligible scatter is reflected in the correlation coefficient of 1.000. This equation corresponds to (7), but differs in the coefficient of K,,. This deviation of the slope from unity represents the error in the calibration of the analogue electronics (gain of the voltage amplifiers). While of practical importance in the determination of binding energies on the present spectrometer, it is of no conceptual significance. The more important term in the present context is the constant (0.77 eV), which yields the position of V, relative to Vat,. The calibration is completed by directly measuring the kinetic energy of a Fermi level electron. With 21.22 eV photons this gave Ksp(E~) = 16.69 eV, hence via eqn (1 l), B,(EF) = 4.09 eV. This, the energy of the Fermi level relative to the vacuum level at infinity, is the experimentally determined value of &n. This is the number which must be added to all binding energies measured relative to EF in order to convert them to absolute values. Finally, it is interesting for comparison to note that the value of the spectrometer work function (eat,) is (4.09 + 0.77) = 4.86 eV. DISCUSSION There is a final issue which should now be addressed, which is equivalent to that also raised by Carley et al. This concerns the matter alluded to in the final paragraph of a previous section, viz, the extent to which j&, might be constant (or vary) from one spectrometer to another. It is generally considered that BFS are a property of the sample (ie are independent of the spectrometer). Since the value of B, must be absolute, it therefore follows from (9) that so also must be isp. That is, there is a common value of F for all spectrometers (and samples). This ‘terrestrial constant’ conclusion is the one reached by Carley et al. The only alternative which is allowed by eqn (9) is that both BF and i are spectrometer dependent. While this is not the usual view, the possibility of varying BF.S has been previously raised [13], and it does seem to us that it is tenable. A completely a priori calculation of the band structure of a solid would necessarily be referenced to the vacuum level at infinity. The bands are thus fixed relative to this
301
level, whereas the position of the Fermi level is determined only consequentially, by the electron occupancy. Should this occupancy change, then any BF value would change correspondingly. Hence when a sample’s EF realigns to that of the spectrometer there should be a change in its BFS. Of course this ‘initial’ change is impossible to measure; all that is experimentally accessible is the variation between different spectrometers. The consequence, though, of variable BFS is that &os could likewise vary. Irrespective, though, of whether or not any change in BFS/ &+s is theoretically expected, the experimental results (ie for equivalent samples in different spectrometers) would seem to indicate that in practice BFS are nevertheless constant to within at least 0.1 eV. We would therefore have to conclude that z should indeed have a value which is spectrometer-invariant to within the same margin. A plausible explanation of why this should be so could lie in the effective electrical similarity of electron spectrometers, perhaps due to the coating of electron-exposed surfaces with colloidal graphite, a practice which is almost universal. CONCLUSION This paper has addressed the question of referencing the binding energies of solids to an absolute scale (ie to the vacuum level at infinity). This is quite different from (and complimentary to) the practically important but conceptually straightforward task of calibrating the spectrometer energy scale (relative to EF) [14]. It has been shown that this absolute referencing is indeed possible. To do so, the quantity which needs to be added to the binding energy measured relative to the Fermi level is the spectrometer electrochemical potential. In the present spectrometer &,, = 4.09 eV. Whereas the spectrometer work function can be found from measurements on a (single) solid, to determine its electrochemical potential requires measurements also on a calibrant gas. By this means the vacuum level at infinity is located relative to the spectrometer vacuum level, as also is the Fermi level. A necessary condition for this determination is that the spectrometer work function remain the same for both sets of measurements. This would, we note, be possible also in non-UHV instruments. Although most UHV spectrometers are not set up for gas-phase measurements, and so the independent determination of their electrochemical potentials is not possible, it would appear that the value of 4.1M.l eV for & is likely to be generally applicable. (We observe that it does correspond to the (average) difference between B, and BF values noted in the table of binding energies by Carlson [15]). Since this difference has now been reaffirmed as not the work function of the substrate (neither clean nor adsorbate-saturated), adoption of the above figure would certainly seem preferable to persisting with current usage.
ACKNOWLEDGEMENTS We would like to thank the A.R.G.S. for financial University for a Postgraduate Scholarship (SEA).
support,
and La Trobe
REFERENCES 1 D.E. Eastman and J.K. Cashion, Phys. Rev. Letts, 27 (1971) 1520. 2 H.H. Hagstrum, Surf. Sci., 54 (1976) 197. 3 A.F. Carley, R.W. Joyner and M.W. Roberts, Chem. Phys. Letts, 27 (1974) 580. 4 J.Q. Broughton and D.L. Perry, Surf. Sci., 74 (1978) 307. 5 J.W. Gadzuk, Phys. Rev. B, 14 (1976) 2267. 6 K. Siegbahn et al, ESCA, Almqvist and Wiksell, Uppsala, 1967. 7 S. Evans, Chem. Phys. Lens, 23 (1973) 134; and [14] ~121. 8 K. Kimura, T. Yamazaki and K. Osafune, J. Elec. Spec., 6 (1975) 391. 9 K. Jacobi and H.H. Rotermund, Surf. Sci., 116 (1982) 435. 10 J.E. Demuth and D.E. Eastman, Phys. Rev. Letts, 32 (1974) 1123. 11 C.R. Brundle and A.F. Carley, Farad. Discuss. Chem. Sot., 60 (1975) 51. 12 S.E. Anderson and G.L. Nyberg, Surf. Sci., 207 (1989) 233. 13 D. Menzel in: Farad. Discuss. Chem. Sot., 58 (1974) 91. 14 M.T. Anthony and M.P. Seah, Surf. Interface Anal., 6 (1984) 95 15 T.A. Carlson, Photoelectron and Auger Spectroscopy, Plenum Press, New York, 1975, p337.
ADDENDUM
Further discussions’
following the acceptance of this paper have indicated another
interpretation of the gas-phase measurements. Rather than remaining fixed at V,, the molecular ionization threshold is instead pinned at the effective spectrometer potential Vso (and all energy levels move up by a constant eAV&. The 0.77 eV kinetic energy offset is then due entirely to a spectrometer correction (arising from contact potential differences,
stray magnetic fields, etc).
This requires some amendments to Fig 1
(particularly Fig 1b), together with the associated discussion, but the conclusion of Fig Id remains unaltered.
However the value of
&,
is then not given by the gas-phase
measurements, but rather is the average value* of asp over all spectrometer analyser surfaces (including those not directly viewed by the photoelectrons). In this case a value of Fsp slightly larger than 4.1 eV (though not so large as 4.9 eV) is indicated. 1D.R. LLoyd, personal communication. 2W.F. Egelhoff, Surf. Sci. Reports, 6 (1987) 253.
Journal of Electron Spectroscopy and Related Pherwmena, 52 (1990) 293-302 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
BINDING ENERGIES AND REFERENCE PHOTOELECTRON SPECTROSCOPY
LEVELS IN
SE. ANDERSON and G.L. NYBERG Chemistry Department, La Trobe University, Bundoora, Vie., 3083 (Australia)
ABSTRACT Measurements on solids enable the Fermi level to be positioned relative to the spectrometer vacuum level; those on gases should in turn allow placement of the latter with respect to the vacuum level at infinity. A combination of the two would therefore position the Fermi energy on an absolute scale. The separation between EF and V, corresponds to the spectrometer electrochemical potential. This is the quantity which must be added to binding energies measured relative to EF to reference them to V,, ie 6, = BF + &p. The requirements for performing this alignment are discussed, and &+, is measured on the present spectrometer. The value of 4.1 eV which is obtained should supplant the use of sample work functions in the alignment procedure.
INTRODUCTION
Whereas in the photoelectron spectroscopy of gases there has never been any question but that the electron binding energies are referenced to the vacuum level at infinity (V,), in the case of solids it is normal to express binding energies relative to the Fermi level ( EF). This is done not just for experimental convenience, but because of the uncertainty in converting these values to an absolute scale. This uncertainty has included not only how to align them with the vacuum level at infinity, but also whether this is indeed the “proper” reference level. While this deficiency is largely unimportant for purely experimental studies of solids, it becomes significant whenever comparison is made with either theoretical calculations or gas phase measurements, both of which are referenced to V,. The instance where this most commonly arises is in photoemission studies of adsorbates, where it is usual to want to compare the adsorbate spectrum with that of the free molecule. The objectives here are to achieve a correct alignment of the two spectra to aid in band assignment, and to further identify the shift of those bands involved in chemisorption bonding. There have thus been several studies which have addressed the problems of converting binding energies (BF) relative to the Fermi level to those (B,) relative to the vacuum level at infinity, the significance of the adsorption shifts so obtained, and of possibly more appropriate reference levels. Since the principle of photoelectron spectroscopy is based on the (extended) Einstein photoelectric equation (for solids) hv = (BF + @)+ K (1) (where K is the electron kinetic energy upon ejection), and for gases hv = B, + K (2) 0363-2043/90/$03.50
1990 Elsavier Science Publishers B.V.
it is natural that the method of conversion from BF to B, has been to add the value of the work function $, ie B_= BF+$ (3) Just which work function, though, has been a matter of contention. The original choice [l] in adsorbate studies was that of the clean substrate surface (I&,,), but subsequently the value of the adsorbate-saturated surface ($a&) was advocated [2], and adopted in some instances. However it was pointed out by Carley, Joyner and Roberts [3] that since 4 refers to the vacuum level local to the surface (Vtocat; either V, or Va&), and not to V,, then there is no value of the work function per se which can be appropriate. In the final discussion around that time Broughton and Perry 143agreed, but concluded that em was nevertheless “the most meaningful practical approach’, and subsequently this has been most commonly employed. In these discussions, attention has focussed upon whether the resulting adsorbate binding energy shifts AB = Bg - Ba (4) (the difference between the binding energies of a band in the gas-phase and in the adsorbate spectrum) are “chemically meaningful” [4,5], and emphasis has been placed on the value of o that is required for this to be so. Now while this is undoubtedly an important matter, it implies (as will be seen) a value of Ba other than B,a (and so is experimentally not well defined). The primary concern of the current study is instead the determination of this latter quantity, with the interpretation of the resulting value of AB a matter of only secondary consideration. We have taken-up this topic again because we wish to question one of the underlying assumptions of previous discussions - that the measured electron kinetic energies of solids cannot be related to V,. Since there is no ‘calibrant solid’, we accept that this is true for measurements purely on solids; for gases, though, there are calibrants. Hence by combining both types of measurements on the one spectrometer it would seem as though it should be possible to establish a common absolute reference level. SPECTROMETER WORK FUNCTION AND VACUUM LEVEL (SOLIDS) It seems to us that progress in this area has been experimentally led, based on certain observed constancies. Thus right at the beginning of photoelectron spectroscopy Siegb,ahn et al [6] observed in regard to eqn (1) that the experimental value of hv - (BF + K) ‘I... does not depend on the source material and [consequently] one and the same work function correction can be applied to all the measurements” (irrespective of the work function of the sample). They therefore concluded that, in PES measurements, the appropriate value of e was that pertaining to the material of the spectrometer; in other words, the spectrometer had an effective work function,
I$~+.,. This is illustrated in Fig la, which shows the situation for sample work functions (assumed metals) both less (&,,,) and greater (@m,) than &u. In Fig la, it has been assumed that sample and spectrometer are in thermodynamic equilibrium, so that the Fermi levels of both are aligned. When ejected, the photoelectrons move from the local environment (and potential) of the metal into that of the spectrometer; in so doing they either lose or ,gain kinetic energy, depending on whether $,,, is less or greater than asp. This serves to emphasise that the electron kinetic energy will depend on the particular spectrometer, each of which has its own spectrometer vacuum level VSPm, situated above EF by the amount $sp. The superscript ‘m’ is added to Vsp to emphasise that it is obtained by measurement on metal (solid) samples. There are two further consequences of the above observation. One relates to the measurement of work functions, from the full-width of the photoemission spectrum (ie, from the Fermi level to the secondary-electron cut-off). For any sample for which om is less than asp, the cut-off will lie hv below not Vm but Vap, and the fullwidth will yield not em but $sp. This difficulty can of course be overcome by floating the sample, so that its V, lies at or above Vsp (ie by applying a voltage to the sample to raise its Fermi level above that of the spectrometer by the appropriate amount). In the present context, though, the important point is that asp is readily determined. The other consequence, which is rather an aside, relates to angle-resolved studies. The difference between V, and V,, will cause a distortion of the angular distribution, which will increase as both the binding energy and the emission angle increase. This also can be eliminated by floating the sample, so that these vacuum levels match. SPECTROMETER VACUUM LEVEL (GASES) Although the concept of a spectrometer vacuum level [7] arises most naturally in the context of the photoemission spectra of solids, it does not add materially to their interpretation. Where it is most useful is in thinking about gases, and of the relationship between the two. It is well appreciated in gas-phase studies that binding (ionization) energies are not directly given by the difference between the photon energy and the (spectrometermeasured) kinetic energy. The technique employed there is to add a calibrant or reference gas (rg) whose ionization energy has been determined optically (eg from Rydberg series), and then to correct the apparent binding energies of the sample gas (sg) appropriately, viz: B,sS = Bspsg + (B-Q - Bsp’g) = (hv - Kspsg) +(B,‘g - hv + KspW) = B_Q + (KspW - Kspsg) (3 The determination thus involves two kinetic energies measured under the same conditions, namely, the environment of the spectrometer. What this again recognises is that kinetic energies are measured relative to the vacuum level of the spectrometer, and furthermore that this is not equal to the vacuum level at infinity.
296
Metal Spectrometer Work Function
Spectrometer Vacuum Level
(d)
@I
V,
Spectrometer Electrochemical Potential
Absolute Binding Energies
Figure 1. Relationship of the Fermi level, the spectrometer Work Function, the spectrometer Vacuum Level, the Vacuum Level at infinity, the spectrometer Electrochemical Potential (and Outer Potential), the Binding Energy relative to the Fermi level, the absolute Binding Energy (relative to the vacuum level at infinity), and the Binding Energy Shift (upon adsorption).
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An alternative way to do the experiment would be to measure the two gases sequentially. Measuring Ksp of the reference gas first establishes the position of V,,, relative to V,: e(Vsp - V,) I eAV,,, = hv - B,XI - K,orS g K,rg - K,,,‘S (6) This is illustrated in Fig lb. The subsequently measured Ksp for the sample gas can then be converted to KJB,: (hv - B,sg) P K_,sg = K,osg + eAV,,, (7) The drawback with this procedure in practice is that some gases contaminate the spectrometer, in which case the measurement environment in the two instances would be different. This contamination is the result of adsorption onto the spectrometer (particularly the walls of the ionization chamber, and the entrance slits). This results in a change in the spectrometer work function, and so also in the spectrometer vacuum level. The simultaneous measurement of the reference gas and the sample circumvents this difficulty, and is by far the simpler practical procedure. In order to establish the position of Vsp relative to V,, though, it is necessary to carry out the first of the above steps. Naturally this should be done employing noncontaminating gases. In addition, the kinetic energies should be measured as a function of decreasing gas pressure. The reason for this is to eliminate any pressureshift, which can arise from the attraction of the departing electrons to the remaining positive ions in the ionization region [8]. The resulting value of the spectrometer vacuum level is labelled V&P+O) in Fig lb. SPECTROMETER ELECTROCHEMICAL POTENTIAL We have seen how the concept of a spectrometer vacuum level arises naturally in the spectroscopy of both solids and gases. The question then follows as to whether these levels are identical in the two cases. It would be easy to label both simply as Vsu and thereby ignore this question. By deliberately labelling them separately we are required to explicitly justify this critical step in our argument. Our view is that they are not necessarily the same, but will be so under the appropriate measurement conditions. A typical experimental sequence in the measurement of solids is that the spectrometer is under ultrahigh vacuum, is brought up to something like 10-4 torr during argon ion bombardment of the sample, then returned to UHV. Were this gas one that chemisorbed (at room temperature) then there would be more than enough opportunity for monolayer coverage over the entire spectrometer. Separate studies on argon (and other inert gas) adsorption show, however, that this is not the case, so it can be assumed that the spectrometer remains clean, and esp unaltered. The situation with the gas measurements is not very different. At the ionization centre the pressure may be something like 10-3 torr, and 10-6 ton: in the rest of the spectrometer (and maintained constant throughout the course of the measurement).
Whether or not a monolayer adsorbs on the spectrometer surfaces (assumed initially clean) again depends on the nature of the gas being studied. lf these are inert gases there is no more reason than in the case above for the spectrometer to be contaminated. Under these circumstances the two spectrometer vacuum levels are thus the same. Should, however, the gaseous sample be one which strongly adsorbed, then it is entirely possible that a quite different spectrometer vacuum level would be developed, due to the changed work function of the spectrometer surfaces. When using inert gases, though, the outcome of this discussion is that, as indicated in Figlc, &pm = vsps = v,,. Having established the relative positions of V,, Vsp, and EF, it is appropriate to introduce some further terminology. By definition [4, & refs therein], the difference between V, and EF is known as the electrochemical potential ( cl), and that between Vlocal and V, as the Outer Potential (+Outer/e). Whereas the latter depends on the particular surface, the former does not (it is a property of the entire sample). The quantity AVsp determined from the gas-phase measurements is thus the Outer Potential of the spectrometer potential-defining surfaces (@spouter/e). The difference between &+, (determined from solids) and eAVsp is thus ksp; ie &p = h.p - eAVsp These quantities are illustrated in Fig lc.
(8)
Although the electrochemical potential so derived is that of the spectrometer, because (under the usual circumstances) dre Fermi levels of spectrometer and sample are aligned, it follows that the same value of G must apply to the sample as well. It might therefore seem that the subscript ‘sp’ could be dropped. We will not do so, however, since the Fermi level of a sample will adjust itself from one spectrometer to another, and it is by no means obvious that isp should be the same for different spectrometers. ABSOLUTE BINDING ENERGIES Having established Lp, that is, the position of V, with respect to EF, it is a simple matter to obtain absolute binding energies of solids, viz: B, = BF+ &p (9) This is illustrated in Fig Id, and the same adjustment applies to the levels of both the substrate and the adsorbate. This transference of Lsp clearly also depends on the Fermi level of the sample being aligned with that of the spectrometer. Besides the obvious instances involving sample-charging when this will not be so, there are examples involving physisorbed multilayers which also have been interpreted otherwise [9]. These cases would generally be considered, though, to be particular exceptions to the rule of Fermi level alignment. It is pertinent to comment further on the distinction between eqns (9) and (3). Since Q(m)varies from one crystal face to another, a band which has the same value of BF would, according to (3), give different values of B, on two different faces. Now
because of valence band dispersion, both the nature and the binding energy of the bands varies from face to face, so this anomoly is not so evident in UPS. These variations do not apply to core orbitals, however, which could be expected to have the same values of both BF and B, irrespective of the face exposed (in contrast to (3) but in .accordance with (9)). Indeed, it was just such a constancy, observed in their XPS measurements, which led Carley er al [3] to conclude that the quantity which needed to be added to BF in order to obtain B, is “of the order of a typical work function but is a constant not necessarily equal to any particular work function”. Eqn (9) completely concurs with this, and furthermore provides the interpretation of this constant. ADSORBATE BINDING (AND BONDING) ENERGY SHIFTS Having established the absolute binding energies of the adsorbate, these can now be compared to their gas phase values, and so the binding energy shifts determined, as illustrated in Fig Id. The question then arises, though, as to whether such shifts are “chemically meaningful”. By this is meant, ‘Does the resulting shift reflect the magnitude of the chemical bonding interaction between the adsorbate and the substrate?’ The answer previously given [4,5], and with which we concur, is ‘No’. The well-appreciated reason for this is that there are various ‘physical’ factors (such as the image charge) which will affect the binding energy of a molecule-locallised electron even if there is no chemical bonding between the adsorbate and the metal substrate. While a partial solution to this problem is provided by another well established, experimentally-originating, procedure - that of dividing the Binding Energy Shift into separate Relaxation and Bonding contributions [lo], ie (10) AB = ABBonding+ Al&taxation two difficulties remain. One is identifying bands of the adsorbate which are not involved in the bonding. However this can usually be done fairly unambiguously for some of the valence orbitals of larger polyatomic molecules, and for the core orbitals of any molecule (such orbitals not overlapping with those of the substrate). What cannot be overcome [ 111, though, is the likelihood that the bonding orbitals will have a different relaxation shift from their nonbonding counterparts. What the present procedure allows, therefore, is not a determination of nett Bonding Shifts, but (through the absolute alignment of the two binding energy scales) an accurate measurement of the Relaxation Shift (of the nonbonding orbitals). This can then be compared to calculated values of all extramolecular relaxation/polarization effects, such as final state screening and the influence of the image charge, and all other such non-chemical-bonding effects involved in photoemission from adsorbed species. -
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IMPLEMENTATION The concepts discussed above arose in our own (UPS) case largely because the spectrometer (described previously [ 121) readily allows gas-phase measurements, as well as those on solids. The determination of V, relative to Van was undertaken observing all the cautions outlined above. ‘Ihe calibration gases employed were Ar, Xe and N2 in conjunction with He I radiation, and Ne and N2 with He II. The consequent wide range of kinetic energies enables the presence of any nonlinearity to be readily detected; there is none. The results obtained can be represented by the equation (hv - B,) = K, = 0.98 K,P + 0.77 eV (11) and the negligible scatter is reflected in the correlation coefficient of 1.000. This equation corresponds to (7), but differs in the coefficient of K,,. This deviation of the slope from unity represents the error in the calibration of the analogue electronics (gain of the voltage amplifiers). While of practical importance in the determination of binding energies on the present spectrometer, it is of no conceptual significance. The more important term in the present context is the constant (0.77 eV), which yields the position of V, relative to Vat,. The calibration is completed by directly measuring the kinetic energy of a Fermi level electron. With 21.22 eV photons this gave Ksp(E~) = 16.69 eV, hence via eqn (1 l), B,(EF) = 4.09 eV. This, the energy of the Fermi level relative to the vacuum level at infinity, is the experimentally determined value of &n. This is the number which must be added to all binding energies measured relative to EF in order to convert them to absolute values. Finally, it is interesting for comparison to note that the value of the spectrometer work function (eat,) is (4.09 + 0.77) = 4.86 eV. DISCUSSION There is a final issue which should now be addressed, which is equivalent to that also raised by Carley et al. This concerns the matter alluded to in the final paragraph of a previous section, viz, the extent to which j&, might be constant (or vary) from one spectrometer to another. It is generally considered that BFS are a property of the sample (ie are independent of the spectrometer). Since the value of B, must be absolute, it therefore follows from (9) that so also must be isp. That is, there is a common value of F for all spectrometers (and samples). This ‘terrestrial constant’ conclusion is the one reached by Carley et al. The only alternative which is allowed by eqn (9) is that both BF and i are spectrometer dependent. While this is not the usual view, the possibility of varying BF.S has been previously raised [13], and it does seem to us that it is tenable. A completely a priori calculation of the band structure of a solid would necessarily be referenced to the vacuum level at infinity. The bands are thus fixed relative to this
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level, whereas the position of the Fermi level is determined only consequentially, by the electron occupancy. Should this occupancy change, then any BF value would change correspondingly. Hence when a sample’s EF realigns to that of the spectrometer there should be a change in its BFS. Of course this ‘initial’ change is impossible to measure; all that is experimentally accessible is the variation between different spectrometers. The consequence, though, of variable BFS is that &os could likewise vary. Irrespective, though, of whether or not any change in BFS/ &+s is theoretically expected, the experimental results (ie for equivalent samples in different spectrometers) would seem to indicate that in practice BFS are nevertheless constant to within at least 0.1 eV. We would therefore have to conclude that z should indeed have a value which is spectrometer-invariant to within the same margin. A plausible explanation of why this should be so could lie in the effective electrical similarity of electron spectrometers, perhaps due to the coating of electron-exposed surfaces with colloidal graphite, a practice which is almost universal. CONCLUSION This paper has addressed the question of referencing the binding energies of solids to an absolute scale (ie to the vacuum level at infinity). This is quite different from (and complimentary to) the practically important but conceptually straightforward task of calibrating the spectrometer energy scale (relative to EF) [14]. It has been shown that this absolute referencing is indeed possible. To do so, the quantity which needs to be added to the binding energy measured relative to the Fermi level is the spectrometer electrochemical potential. In the present spectrometer &,, = 4.09 eV. Whereas the spectrometer work function can be found from measurements on a (single) solid, to determine its electrochemical potential requires measurements also on a calibrant gas. By this means the vacuum level at infinity is located relative to the spectrometer vacuum level, as also is the Fermi level. A necessary condition for this determination is that the spectrometer work function remain the same for both sets of measurements. This would, we note, be possible also in non-UHV instruments. Although most UHV spectrometers are not set up for gas-phase measurements, and so the independent determination of their electrochemical potentials is not possible, it would appear that the value of 4.1M.l eV for & is likely to be generally applicable. (We observe that it does correspond to the (average) difference between B, and BF values noted in the table of binding energies by Carlson [15]). Since this difference has now been reaffirmed as not the work function of the substrate (neither clean nor adsorbate-saturated), adoption of the above figure would certainly seem preferable to persisting with current usage.
ACKNOWLEDGEMENTS We would like to thank the A.R.G.S. for financial University for a Postgraduate Scholarship (SEA).
support,
and La Trobe
REFERENCES 1 D.E. Eastman and J.K. Cashion, Phys. Rev. Letts, 27 (1971) 1520. 2 H.H. Hagstrum, Surf. Sci., 54 (1976) 197. 3 A.F. Carley, R.W. Joyner and M.W. Roberts, Chem. Phys. Letts, 27 (1974) 580. 4 J.Q. Broughton and D.L. Perry, Surf. Sci., 74 (1978) 307. 5 J.W. Gadzuk, Phys. Rev. B, 14 (1976) 2267. 6 K. Siegbahn et al, ESCA, Almqvist and Wiksell, Uppsala, 1967. 7 S. Evans, Chem. Phys. Lens, 23 (1973) 134; and [14] ~121. 8 K. Kimura, T. Yamazaki and K. Osafune, J. Elec. Spec., 6 (1975) 391. 9 K. Jacobi and H.H. Rotermund, Surf. Sci., 116 (1982) 435. 10 J.E. Demuth and D.E. Eastman, Phys. Rev. Letts, 32 (1974) 1123. 11 C.R. Brundle and A.F. Carley, Farad. Discuss. Chem. Sot., 60 (1975) 51. 12 S.E. Anderson and G.L. Nyberg, Surf. Sci., 207 (1989) 233. 13 D. Menzel in: Farad. Discuss. Chem. Sot., 58 (1974) 91. 14 M.T. Anthony and M.P. Seah, Surf. Interface Anal., 6 (1984) 95 15 T.A. Carlson, Photoelectron and Auger Spectroscopy, Plenum Press, New York, 1975, p337.
ADDENDUM
Further discussions’
following the acceptance of this paper have indicated another
interpretation of the gas-phase measurements. Rather than remaining fixed at V,, the molecular ionization threshold is instead pinned at the effective spectrometer potential Vso (and all energy levels move up by a constant eAV&. The 0.77 eV kinetic energy offset is then due entirely to a spectrometer correction (arising from contact potential differences,
stray magnetic fields, etc).
This requires some amendments to Fig 1
(particularly Fig 1b), together with the associated discussion, but the conclusion of Fig Id remains unaltered.
However the value of
&,
is then not given by the gas-phase
measurements, but rather is the average value* of asp over all spectrometer analyser surfaces (including those not directly viewed by the photoelectrons). In this case a value of Fsp slightly larger than 4.1 eV (though not so large as 4.9 eV) is indicated. 1D.R. LLoyd, personal communication. 2W.F. Egelhoff, Surf. Sci. Reports, 6 (1987) 253.