- Email: [email protected]
Cu(111)
Surface Science 121 (1982) 411-420 North-Holland Publishing Company
411
XPS STUDIES AND I/Cu(lll)
OF ADATOM-ADATOM
S.B. DiCENZO,
G.K. WERTHEIM
Bell Laboratories, Received
INTERACTIONS:
and D.N.E.
I/Ag( 111)
BUCHANAN
Murray Hill, New Jersey 07974, USA
1 June 1982
We have studied submonolayer adsorption, at room temperature, of iodine on the (111) faces of silver and copper, using LEED and XPS. In both systems the 6 X 6 LEED pattern appears at -0.2 monolayer (ML) coverage; no other superlattice pattern was observed. The I 4d,,, core eV between very dilute coverage and electron binding energy in both cases decreases by -0.15 0.33 ML. The leveling-off of the binding energy for I/Ag(l 11) for coverages >0.2 ML is shown to be a unique experimental manifestation of an indirect, substrate-mediated adatom-adatom interaction, an attraction of several meV between next-nearest neighbor iodine atoms. The more nearly linear decrease in the I binding energy on Cu( 111) is shown to imply a significantly weaker next-nearest neighbor interaction on this surface. The appearance of the fi X 6 LEED pattern at low coverages on Cu is shown to be consistent with short-range order produced merely by a size effect, that is, by nearest neighbor exclusion. These conclusions are reached with the help of Monte Carlo calculations of a triangular lattice gas.
1. Introduction In earlier work [ 1,2] we have discussed the application of X-ray photoelectron spectroscopy (XPS) to adsorbate systems. In particular, we have described the adatom-substrate interaction as inferred from the XPS data for I/Ag( 111) [2], pointing out that the asymmetric line shape of the I photoemission spectrum indicated screening of the adatom’s core hole by the substrate conduction electrons. The excitation of the silver surface plasmon by the iodine photoelectrons further implied that the I has not formed a compound with the Ag surface. This integrity of the substrate surface was confirmed by the absence of any significant change in either the Ag core spectrum or the Ag valence band. In this paper we combine the I/Ag(lll) data with data for I/Cu( 111) to show that XPS can also give information on the adatom-adatom interaction in these systems. The adatom-adatom interaction is relevant to the study both of ordering phenomena and of heteroepitaxy. Because I atoms adsorbed on these (111) faces occupy the sites of three-fold symmetry [3], each of these systems constitutes a two-dimensional lattice gas, on a triangular net, at submonolayer coverages. The sign and the magnitude of the interactions 0039-6028/82/0000-0000/$02.75
0 1982 North-Holland
412
S.B. DiCenro et al. / XPS studies of adatom -adatom
interactions
between adatoms are therefore of obvious interest. In addition, as the ordered sa tu ra tde overlayer on Cu( 111) is the precursor to coherent epitaxial 0x6 growth of CuI [4], a material whose composition and structure differ from that of the substrate, knowledge of the adatom-adatom interaction is also useful in studying the phenomenon of coherent heteroepitaxy.
2. Experiment
and data analysis
We present a brief summary of the experimental technique, which has been described elsewhere [ 1,2]. Oriented monocrystalline samples were cleaned by Ar sputtering and by annealing in an UHV preparation chamber (base pressure < lop9 Torr), which contains the LEED optics. With the sample at room temperature, the LEED pattern was observed while the preparation chamber was flooded with iodine vapor (- lop8 Torr). The iodine coverage was monitored by tracking the intensities of both the adsorbate and the substrate peaks in the XPS scans. The I 4d spectra and the appropriate substrate core level spectra were analyzed by least-squares fitting using suitable
49.4
-1
. L i._,i,14y2, ,c,.,.., 1 .
l
l
49.3
g a
’
932.9
I
a
I
1
I
I
I
I
I
I
I
l
cu +3/z
932.8
I
I 0.0
I
0.1
I
I
0.3
0.2
COVERABE (ML) Fig. 1. I 4d,,,
and Cu 2p3,z binding
energies,
referenced
to experimental
E,.
S.B. DiCenzo et al. / XPS studies of adatom -ndatom
interactions
413
model functions convolved with an empirically determined spectrometer resolution function. All binding energies were referenced to the substrate Fermi energy, as is usual with XPS. This is the appropriate reference because the adsorbed atoms form chemical bonds, however weak, with the substrate. Run-to-run fluctuations in the I 4d and the substrate core electron binding energies were highly correlated, reflecting the fact that the largest source of error was the uncertainty in locating the Fermi edge. In the work of ref. [2], because the Ag binding energy was clearly constant, the I binding energy was corrected by the fluctuations in the measured Ag binding energy for each run. However, as noted in ref. [l], the Cu core electron binding energy increases with increasing I coverage due to the gradual modification of the surface atom component [5]. Therefore a straight line is fit to the Cu binding energies, as seen in fig. 1, and the fluctuations about this line are used to correct the I core
G 0
3
49.1
P 3
49.0
COVERAGE
(ML)
Fig. 2. Binding energy of the I 4d,,, core electron, as a function of coverage 0, corrected for fluctuations and referenced to the Fermi energy, for the two adsorbate systems I/Cu( 111)and I/Ag( 111). The curves are drawn only to guide the eye.
414
S.B. DiCenzo et al. / XPS studies of adatom -adatom
electron binding binding energy in fig. 2. While this analysis, it ter resolution binding energy
interactions
energies. The result of interest in this discussion, the I 4d,,, as a function of coverage on Ag( 111) and on Cu( 11 l), is shown the variation in binding energy is quite precisely determined by should be noted that the overall shift is less than the spectromewidth; therefore, especially at low coverages, the measured may be an average over distinct energies.
3. Discussion It is known that one can extract physical quantities by a thermodynamical analysis of the shift in core electron binding energy measured in XPS [6]. This is possible because photoemission is an adiabatic process, and thus different paths from an initial state to a final state require the same net energy. Even without knowledge of such quantities as heats of adsorption, we can analyze an adsorption system to determine what terms contribute to the coverage dependence of an adsorbate’s core electron binding energy. We do this by beginning with a finite number of atoms on an infinite surface, for a very dilute coverage at which the adatoms do not interact. We consider one of these atoms, and bring in the other atoms from large separations to their positions for a particular coverage 8. This requires expending an energy
where ci,, the interaction between atoms i andj, is an initial state interaction responsible, e.g., for the adsorbate structure observed by LEED. We may remove a core electron from the chosen atom, allowing the final-state relaxation to occur, at an energy cost of E,(8), which is by definition the XPS binding energy we observe at a coverage of 8. Thus the energy cost of going from a state of infinitely dilute coverage to a finite coverage 8 with one core-ionized, relaxed adatom is (2) Alternatively, we can photoionize the adatom in the dilute compress the adlayer, for a total energy cost of
state,
and
then
IX 4e) + 2 c:k(e)+44% i
Jfk
where k is the index of the adatom under consideration and c’ is the interaction in the final state between the (screened) core hole and the other adatoms. These two paths, (2) and (3), from the dilute state to the same final state must
S.B. DiCenzo et al. / XPS studies of adatom -adatom
require
the same energy,
interactions
415
and thus
(4) i
i
That is, the coverage-dependent part of the XPS binding energy is the difference of two terms: the final state core-hole-adlayer interaction, and the initial state adatom-adlayer interaction. Note that any final state relaxation of the adsorbate layer is included in e’ but we have assumed that the substrate’s response to the core hole is not coverage-dependent and therefore does not contribute to E,(B). This assumption is supported by our observation that the adsorbate’s photoemission lineshape, which is sensitive to the relaxation process, does not change with coverage. In the above expression for E,(8), either the initial state or final state term could dominate. Consider, for example, the Coulomb contributions to these terms in the case where only a small amount of charge is displaced towards the adsorbed atom from the substrate, so that each adatom creates a weak dipole. This is consistent with the weak adsorbate-substrate bonding observed in the two systems under discussion. In this case, there will be a small repulsive adatom-adatom interaction in the initial state, but in the final state, the Coulomb interaction of the core hole with the dipole (adsorbate) layer will be larger by a factor of l/q, where q ec 1 is a measure of the charge transfer per adatom. In a previous publication [l] we have in fact assumed that this final state Coulomb interaction dominates the binding energy shift, and have used the net shift to infer the charge transfer to the iodine atoms; the discussion below demonstrates that the assumption of final state dominance is justified. In the data of fig. 2, the sign of the overall shift (i.e., to lower binding energy) is consistent with a repulsive initial state adatom-adatom interaction, or, equally, with an attractive final state interaction between the core hole and the surrounding adatoms. In the case of I/Ag(l 1l), this ambiguity is resolved by the leveling-off of the binding energy at the higher coverages. Regardless of whether the initial or the final state effects dominate, the constant binding energy indicates that the environment of the photoionized adatom is not varying at these coverages. The adatoms are therefore forming large islands, of 6 X fi structure according to the LEED observations. This clearly implies an attractive initial state interaction at the relevant separation, which is illustrated in fig. 3. Because an initial state attraction cannot cause the observed decrease in binding energy, we conclude that the binding energy shift is dominated by final state effects, as stated earlier. An initial state attraction is in itself interesting. It cannot be due to a Coulomb interaction, which among like entities has to be repulsive, whereas a Van der Waals force can be expected to be weak and therefore dominant only in the case of physisorption of rare gases. Thus the most likely interpretation of this attraction is that it is a substratemediated interaction [7]. This experimental measure of an indirect adatom-
416
S. B. DiCenro et al. / XPS studies
of adatom - adatom interactions
Fig. 3. Illustration of first, or nearest, neighbor distance distance of fia; and third neighbor distance of 2~. Fig. 4. Nearest-neighbor exclusion causes “shadowing” A’s third-neighbor sites (dashed circles).
of la; second,
by second neighbor
or next-nearest,
neighbor
atom B of two of atom
adatom interaction at finite, sub-monolayer coverages is noteworthy. The net shift in binding energy is approximately the same in the I/Cu( 111) data as in the I/Ag( 111) data, suggesting that here, too, the final state effect is dominant. In contrast to the Ag data, the monotonic, nearly linear decrease in binding energy clearly rules out island formation. However, while the XPS data for I/Cu( 111) thus show no evidence for an attractive interaction between adatoms, the \/7X fi LEED pattern nevertheless appears at approximately the same rather low coverages as for I/Ag( 111). To investigate whether this presents conflicting evidence for island formation, and hence for an attractive interaction, we have carried out Monte Carlo calculations for a triangular lattice gas. Two interactions are included in the Monte Carlo calculations: a nearest neighbor (nn) exclusion which results from the large size of the adsorbed iodine atoms, and a next-nearest neighbor (nnn) interaction, in units of kT, which can be varied in sign and magnitude. The relevant distances of la and &a are illustrated in fig. 3. We use a section of a triangular lattice 30 lattice spacings in diameter, and occupied at some chosen coverage. For a chosen value of J/kT, where J is the nnn interaction, the system equilibrates by having randomly chosen atoms hop to randomly chosen adjacent lattices sites, subject to the nn exclusion. The probability of success for each hop is determined by the change in the total energy of the system. Care is taken to of J/kT is increased avoid quenching the system, that is, the magnitude gradually to the desired value. The number of iterations needed to reach equilibrium of course varies with coverage and with initial and final temperature, but typically, for each change in J/kT, each atom attempts at least 400
S. B. DiCenro et al. / XPS studies of adatom - adatom interactions
417
hops and successfully executes 10 or more. Not surprisingly, a strong nnn attraction (J/kT-2) leads to large domains of fi X fi structure, or, islands such as we observe experimentally for I/Ag( 111). A strong nnn repulsion causes domains of 2 X 2 structure to form, especially at coverages near 0.25, the saturation coverage for a 2 X 2 structure. The regions between these 2 X 2 domains are empty at the lower coverages, and contain nnn pairs at coverages > 0.25. For the two adsorbate systems studied, we can rule out a significant nnn repulsion because no 2 X 2 LEED pattern is observed at any coverage. We consider, finally, calculations for the case of weak nnn interactions, that is, J/kT near 0. At moderate coverages ( - 0.2 monolayer), no long-range order is observed in the equilibrated arrays. However, the nn exclusion does introduce short-ranged nnn correlations by a shadowing effect, as illustrated in fig. 4. The nn exclusion increases the number of neighbors at all other distances, particularly at the nnn, or second-neighbor, distance. In addition, each second neighbor will eliminate, again by nn exclusion, one or more third-neighbor sites. A J?; X fi structure is thus enhanced at the expense of, e.g., 1 X 1 and 2 X 2 structure. The short-range fi X fi order induced by nn exclusion is illustrated in fig. 5, which shows the pair correlation function for a r
I
I
v
V
A -0.5
-
I
v
v
A
I
v
A
I
I
I
I
20
3a
40
5a
I NTERATOM I C DISTANCE Fig. 5. Lattice gas calculation of the pair correlation function at a coverage of 0.225 monolayer, assuming nearest-neighbor exclusion and all other interactions zero. The upper set of arrows indicates peaks in the correlation function for the fi X fi ordered structure, and the lower set indicates peaks in the 2 X 2 correlation function.
418
S. B. DiCenzo et al. / XPS studies of adatom -adatom
interactions
coverage of 0.225 ML and J/kT = 0, normalized to what is expected without nn exclusion. It is seen that the J?; X fi distances are enhanced, with the enhancement damping out within a few lattice spacings. The significance of this enhancement may be judged by taking a sample Fourier transform of the equilibrated array; this results in distinct, although broad, peaks at the fi X fi superlattice k-vectors, quite consistent with the LEED observations for I/Cu(lll) in this coverage region. Thus we find that the OX fi LEED pattern observed for I/Cu( 111) is adequately explained by short-range order resulting from the nn exclusion due to the large size of the iodine atoms. The magnitude of the adatom-adatom interaction and its effect on our measurements can be gauged in fig. 6. Here we show the average nnn coordination of an adatom as a function of coverage, for several values of J/kT. The dashed line gives the coordination for J = 0 and no nn exclusion. It is seen that an attractive interaction of - kT is sufficient to produce the leveling-off of the Ag data. It is also clear that a repulsion of the same magnitude would have an unmistakable effect on the coverage dependence of the binding energy. This makes more quantitative our inference, drawn from the LEED observations, that the nnn interaction is not strongly repulsive. Thus we are able to conclude from the XPS data that for I/Ag( 111) there is an attractive adatom-adatom interaction of - - kT at the nnn separation, whereas for I/Cu( 111) the interaction at that distance is significantly weaker, but of undetermined sign. Note that in this model it is the relative value of the nnn interaction that matters, that is, we conclude that the nnn, or second-neighbor, interaction on Ag( 111) is - kT more attractive than other adatom-adatom interactions, most notably the third-neighbor interaction. A similar limitation applies to our characterization of the nnn interaction as weak for I/Cu( 111).
covERAGE
(MONOLAYERS)
Fig. 6. Mean number of next-nearest neighbors per atom as a function of coverage, resulting from Monte Carlo calculations which include nearest-neighbor exclusion and which assume attractive, weak, or repulsive next-nearest neighbor interactions.
S. B. DiCenro ei al. / XPS studies
of adatom -adatom interactions
419
__iATTRACTIVE ’ REPUUIVE
-2.0
.
-1.0
1.0
0
2.0
J/kT Fig. 7. Mean number of second and of third neighbors as a function of the second-neighbor interaction, J/kT, at a coverage of 0.225 monolayers. J/kT =O is the high-temperature limit, while T decreases to the left (right) for an attractive (repulsive) interaction.
Fig. 7 shows how changes in temperature affect the structure of an overlayer in this simple model. For a coverage of 0.225 ML the second- and third-neighbor coordination numbers are plotted as a function of J/kT. The transition between a well-ordered J?; X 6 structure and a somewhat less-ordered 2 X 2 structure occurs smoothly between J/kT = - 1.0 and J/kT = 2.0. The influence of the nn exclusion is especially obvious in the displacement from J/kT = 0 of the intersection of the two curves. Experimenally, these transitions would be easily observed in both the LEED patterns and in the photoemission spectra. Consider a system for which the adatom-adatom interaction is observed to be weak at room temperature. If at an intermediate coverage the system is cooled through its transition temperature, the XPS binding energy will decrease if the adatom-adatom interaction is attractive, and simultaneously the LEED spots will become sharper. If the interaction is repulsive, then the fix fi pattern will gradually evolve into a 2 X 2 pattern as the temperature decreases, while the XPS binding energy increases. It is the binding energy shifts with temperature which would provide the more quantitative measure of the strength of the interaction.
4. Conclusion In summary, room temperature XPS measurements and qualitative LEED data for the adsorbate systems I/Ag( 111) and I/Cu( 111) give straightforward
420
S.B. DiCenro
et al. / XPS studies
of adatom
-adatom
interactions
evidence for an attractive next-nearest neighbor interaction between I atoms on the silver surface; this attraction is furthermore inferred to be a substratemediated, indirect interaction. Monte Carlo calculations for a lattice gas on a triangular net indicate that the magnitude of this interaction is approximately 25 meV, and that the nnn interaction on Cu(ll1) is considerably weaker than this. XPS thus provides a quantitative measure of adatom-adatom interactions. The Monte Carlo calculations further imply that it is possible to observe ordering transitions in the overlayer through changes in the adsorbate core electron binding energy.
References [I] [2] [3] [4] [5] [6]
S.B. DiCenzo, G.K. Wertheim and D.N.E. Buchanan, Phys. Rev. B24 (1981) 6143. G.K. Wertheim, S.B. DiCenzo and D.N.E. Buchanan, Phys. Rev. B25 (1982) 3020. P.H. Citrin, P. Eisenberger and R.C. Hewitt, Phys. Rev. Letters 45 (1980) 1948. S.B. DiCenzo, G.K. Wertheim and D.N.E. Buchanan, Appl. Phys. Letters 40 (1982) 888. P.H. Citrin, G.K. Wertheim and Y. Baer, unpublished. N. Martensson and B. Johansson, Solid State Commun. 32 (1979) 791; Phys. Rev. B21 (1980) 4427. [7] T.B. Grimley, Proc. Phys. Sot. (London) 90 (1967) 751.
411
XPS STUDIES AND I/Cu(lll)
OF ADATOM-ADATOM
S.B. DiCENZO,
G.K. WERTHEIM
Bell Laboratories, Received
INTERACTIONS:
and D.N.E.
I/Ag( 111)
BUCHANAN
Murray Hill, New Jersey 07974, USA
1 June 1982
We have studied submonolayer adsorption, at room temperature, of iodine on the (111) faces of silver and copper, using LEED and XPS. In both systems the 6 X 6 LEED pattern appears at -0.2 monolayer (ML) coverage; no other superlattice pattern was observed. The I 4d,,, core eV between very dilute coverage and electron binding energy in both cases decreases by -0.15 0.33 ML. The leveling-off of the binding energy for I/Ag(l 11) for coverages >0.2 ML is shown to be a unique experimental manifestation of an indirect, substrate-mediated adatom-adatom interaction, an attraction of several meV between next-nearest neighbor iodine atoms. The more nearly linear decrease in the I binding energy on Cu( 111) is shown to imply a significantly weaker next-nearest neighbor interaction on this surface. The appearance of the fi X 6 LEED pattern at low coverages on Cu is shown to be consistent with short-range order produced merely by a size effect, that is, by nearest neighbor exclusion. These conclusions are reached with the help of Monte Carlo calculations of a triangular lattice gas.
1. Introduction In earlier work [ 1,2] we have discussed the application of X-ray photoelectron spectroscopy (XPS) to adsorbate systems. In particular, we have described the adatom-substrate interaction as inferred from the XPS data for I/Ag( 111) [2], pointing out that the asymmetric line shape of the I photoemission spectrum indicated screening of the adatom’s core hole by the substrate conduction electrons. The excitation of the silver surface plasmon by the iodine photoelectrons further implied that the I has not formed a compound with the Ag surface. This integrity of the substrate surface was confirmed by the absence of any significant change in either the Ag core spectrum or the Ag valence band. In this paper we combine the I/Ag(lll) data with data for I/Cu( 111) to show that XPS can also give information on the adatom-adatom interaction in these systems. The adatom-adatom interaction is relevant to the study both of ordering phenomena and of heteroepitaxy. Because I atoms adsorbed on these (111) faces occupy the sites of three-fold symmetry [3], each of these systems constitutes a two-dimensional lattice gas, on a triangular net, at submonolayer coverages. The sign and the magnitude of the interactions 0039-6028/82/0000-0000/$02.75
0 1982 North-Holland
412
S.B. DiCenro et al. / XPS studies of adatom -adatom
interactions
between adatoms are therefore of obvious interest. In addition, as the ordered sa tu ra tde overlayer on Cu( 111) is the precursor to coherent epitaxial 0x6 growth of CuI [4], a material whose composition and structure differ from that of the substrate, knowledge of the adatom-adatom interaction is also useful in studying the phenomenon of coherent heteroepitaxy.
2. Experiment
and data analysis
We present a brief summary of the experimental technique, which has been described elsewhere [ 1,2]. Oriented monocrystalline samples were cleaned by Ar sputtering and by annealing in an UHV preparation chamber (base pressure < lop9 Torr), which contains the LEED optics. With the sample at room temperature, the LEED pattern was observed while the preparation chamber was flooded with iodine vapor (- lop8 Torr). The iodine coverage was monitored by tracking the intensities of both the adsorbate and the substrate peaks in the XPS scans. The I 4d spectra and the appropriate substrate core level spectra were analyzed by least-squares fitting using suitable
49.4
-1
. L i._,i,14y2, ,c,.,.., 1 .
l
l
49.3
g a
’
932.9
I
a
I
1
I
I
I
I
I
I
I
l
cu +3/z
932.8
I
I 0.0
I
0.1
I
I
0.3
0.2
COVERABE (ML) Fig. 1. I 4d,,,
and Cu 2p3,z binding
energies,
referenced
to experimental
E,.
S.B. DiCenzo et al. / XPS studies of adatom -ndatom
interactions
413
model functions convolved with an empirically determined spectrometer resolution function. All binding energies were referenced to the substrate Fermi energy, as is usual with XPS. This is the appropriate reference because the adsorbed atoms form chemical bonds, however weak, with the substrate. Run-to-run fluctuations in the I 4d and the substrate core electron binding energies were highly correlated, reflecting the fact that the largest source of error was the uncertainty in locating the Fermi edge. In the work of ref. [2], because the Ag binding energy was clearly constant, the I binding energy was corrected by the fluctuations in the measured Ag binding energy for each run. However, as noted in ref. [l], the Cu core electron binding energy increases with increasing I coverage due to the gradual modification of the surface atom component [5]. Therefore a straight line is fit to the Cu binding energies, as seen in fig. 1, and the fluctuations about this line are used to correct the I core
G 0
3
49.1
P 3
49.0
COVERAGE
(ML)
Fig. 2. Binding energy of the I 4d,,, core electron, as a function of coverage 0, corrected for fluctuations and referenced to the Fermi energy, for the two adsorbate systems I/Cu( 111)and I/Ag( 111). The curves are drawn only to guide the eye.
414
S.B. DiCenzo et al. / XPS studies of adatom -adatom
electron binding binding energy in fig. 2. While this analysis, it ter resolution binding energy
interactions
energies. The result of interest in this discussion, the I 4d,,, as a function of coverage on Ag( 111) and on Cu( 11 l), is shown the variation in binding energy is quite precisely determined by should be noted that the overall shift is less than the spectromewidth; therefore, especially at low coverages, the measured may be an average over distinct energies.
3. Discussion It is known that one can extract physical quantities by a thermodynamical analysis of the shift in core electron binding energy measured in XPS [6]. This is possible because photoemission is an adiabatic process, and thus different paths from an initial state to a final state require the same net energy. Even without knowledge of such quantities as heats of adsorption, we can analyze an adsorption system to determine what terms contribute to the coverage dependence of an adsorbate’s core electron binding energy. We do this by beginning with a finite number of atoms on an infinite surface, for a very dilute coverage at which the adatoms do not interact. We consider one of these atoms, and bring in the other atoms from large separations to their positions for a particular coverage 8. This requires expending an energy
where ci,, the interaction between atoms i andj, is an initial state interaction responsible, e.g., for the adsorbate structure observed by LEED. We may remove a core electron from the chosen atom, allowing the final-state relaxation to occur, at an energy cost of E,(8), which is by definition the XPS binding energy we observe at a coverage of 8. Thus the energy cost of going from a state of infinitely dilute coverage to a finite coverage 8 with one core-ionized, relaxed adatom is (2) Alternatively, we can photoionize the adatom in the dilute compress the adlayer, for a total energy cost of
state,
and
then
IX 4e) + 2 c:k(e)+44% i
Jfk
where k is the index of the adatom under consideration and c’ is the interaction in the final state between the (screened) core hole and the other adatoms. These two paths, (2) and (3), from the dilute state to the same final state must
S.B. DiCenzo et al. / XPS studies of adatom -adatom
require
the same energy,
interactions
415
and thus
(4) i
i
That is, the coverage-dependent part of the XPS binding energy is the difference of two terms: the final state core-hole-adlayer interaction, and the initial state adatom-adlayer interaction. Note that any final state relaxation of the adsorbate layer is included in e’ but we have assumed that the substrate’s response to the core hole is not coverage-dependent and therefore does not contribute to E,(B). This assumption is supported by our observation that the adsorbate’s photoemission lineshape, which is sensitive to the relaxation process, does not change with coverage. In the above expression for E,(8), either the initial state or final state term could dominate. Consider, for example, the Coulomb contributions to these terms in the case where only a small amount of charge is displaced towards the adsorbed atom from the substrate, so that each adatom creates a weak dipole. This is consistent with the weak adsorbate-substrate bonding observed in the two systems under discussion. In this case, there will be a small repulsive adatom-adatom interaction in the initial state, but in the final state, the Coulomb interaction of the core hole with the dipole (adsorbate) layer will be larger by a factor of l/q, where q ec 1 is a measure of the charge transfer per adatom. In a previous publication [l] we have in fact assumed that this final state Coulomb interaction dominates the binding energy shift, and have used the net shift to infer the charge transfer to the iodine atoms; the discussion below demonstrates that the assumption of final state dominance is justified. In the data of fig. 2, the sign of the overall shift (i.e., to lower binding energy) is consistent with a repulsive initial state adatom-adatom interaction, or, equally, with an attractive final state interaction between the core hole and the surrounding adatoms. In the case of I/Ag(l 1l), this ambiguity is resolved by the leveling-off of the binding energy at the higher coverages. Regardless of whether the initial or the final state effects dominate, the constant binding energy indicates that the environment of the photoionized adatom is not varying at these coverages. The adatoms are therefore forming large islands, of 6 X fi structure according to the LEED observations. This clearly implies an attractive initial state interaction at the relevant separation, which is illustrated in fig. 3. Because an initial state attraction cannot cause the observed decrease in binding energy, we conclude that the binding energy shift is dominated by final state effects, as stated earlier. An initial state attraction is in itself interesting. It cannot be due to a Coulomb interaction, which among like entities has to be repulsive, whereas a Van der Waals force can be expected to be weak and therefore dominant only in the case of physisorption of rare gases. Thus the most likely interpretation of this attraction is that it is a substratemediated interaction [7]. This experimental measure of an indirect adatom-
416
S. B. DiCenro et al. / XPS studies
of adatom - adatom interactions
Fig. 3. Illustration of first, or nearest, neighbor distance distance of fia; and third neighbor distance of 2~. Fig. 4. Nearest-neighbor exclusion causes “shadowing” A’s third-neighbor sites (dashed circles).
of la; second,
by second neighbor
or next-nearest,
neighbor
atom B of two of atom
adatom interaction at finite, sub-monolayer coverages is noteworthy. The net shift in binding energy is approximately the same in the I/Cu( 111) data as in the I/Ag( 111) data, suggesting that here, too, the final state effect is dominant. In contrast to the Ag data, the monotonic, nearly linear decrease in binding energy clearly rules out island formation. However, while the XPS data for I/Cu( 111) thus show no evidence for an attractive interaction between adatoms, the \/7X fi LEED pattern nevertheless appears at approximately the same rather low coverages as for I/Ag( 111). To investigate whether this presents conflicting evidence for island formation, and hence for an attractive interaction, we have carried out Monte Carlo calculations for a triangular lattice gas. Two interactions are included in the Monte Carlo calculations: a nearest neighbor (nn) exclusion which results from the large size of the adsorbed iodine atoms, and a next-nearest neighbor (nnn) interaction, in units of kT, which can be varied in sign and magnitude. The relevant distances of la and &a are illustrated in fig. 3. We use a section of a triangular lattice 30 lattice spacings in diameter, and occupied at some chosen coverage. For a chosen value of J/kT, where J is the nnn interaction, the system equilibrates by having randomly chosen atoms hop to randomly chosen adjacent lattices sites, subject to the nn exclusion. The probability of success for each hop is determined by the change in the total energy of the system. Care is taken to of J/kT is increased avoid quenching the system, that is, the magnitude gradually to the desired value. The number of iterations needed to reach equilibrium of course varies with coverage and with initial and final temperature, but typically, for each change in J/kT, each atom attempts at least 400
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hops and successfully executes 10 or more. Not surprisingly, a strong nnn attraction (J/kT-2) leads to large domains of fi X fi structure, or, islands such as we observe experimentally for I/Ag( 111). A strong nnn repulsion causes domains of 2 X 2 structure to form, especially at coverages near 0.25, the saturation coverage for a 2 X 2 structure. The regions between these 2 X 2 domains are empty at the lower coverages, and contain nnn pairs at coverages > 0.25. For the two adsorbate systems studied, we can rule out a significant nnn repulsion because no 2 X 2 LEED pattern is observed at any coverage. We consider, finally, calculations for the case of weak nnn interactions, that is, J/kT near 0. At moderate coverages ( - 0.2 monolayer), no long-range order is observed in the equilibrated arrays. However, the nn exclusion does introduce short-ranged nnn correlations by a shadowing effect, as illustrated in fig. 4. The nn exclusion increases the number of neighbors at all other distances, particularly at the nnn, or second-neighbor, distance. In addition, each second neighbor will eliminate, again by nn exclusion, one or more third-neighbor sites. A J?; X fi structure is thus enhanced at the expense of, e.g., 1 X 1 and 2 X 2 structure. The short-range fi X fi order induced by nn exclusion is illustrated in fig. 5, which shows the pair correlation function for a r
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I NTERATOM I C DISTANCE Fig. 5. Lattice gas calculation of the pair correlation function at a coverage of 0.225 monolayer, assuming nearest-neighbor exclusion and all other interactions zero. The upper set of arrows indicates peaks in the correlation function for the fi X fi ordered structure, and the lower set indicates peaks in the 2 X 2 correlation function.
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coverage of 0.225 ML and J/kT = 0, normalized to what is expected without nn exclusion. It is seen that the J?; X fi distances are enhanced, with the enhancement damping out within a few lattice spacings. The significance of this enhancement may be judged by taking a sample Fourier transform of the equilibrated array; this results in distinct, although broad, peaks at the fi X fi superlattice k-vectors, quite consistent with the LEED observations for I/Cu(lll) in this coverage region. Thus we find that the OX fi LEED pattern observed for I/Cu( 111) is adequately explained by short-range order resulting from the nn exclusion due to the large size of the iodine atoms. The magnitude of the adatom-adatom interaction and its effect on our measurements can be gauged in fig. 6. Here we show the average nnn coordination of an adatom as a function of coverage, for several values of J/kT. The dashed line gives the coordination for J = 0 and no nn exclusion. It is seen that an attractive interaction of - kT is sufficient to produce the leveling-off of the Ag data. It is also clear that a repulsion of the same magnitude would have an unmistakable effect on the coverage dependence of the binding energy. This makes more quantitative our inference, drawn from the LEED observations, that the nnn interaction is not strongly repulsive. Thus we are able to conclude from the XPS data that for I/Ag( 111) there is an attractive adatom-adatom interaction of - - kT at the nnn separation, whereas for I/Cu( 111) the interaction at that distance is significantly weaker, but of undetermined sign. Note that in this model it is the relative value of the nnn interaction that matters, that is, we conclude that the nnn, or second-neighbor, interaction on Ag( 111) is - kT more attractive than other adatom-adatom interactions, most notably the third-neighbor interaction. A similar limitation applies to our characterization of the nnn interaction as weak for I/Cu( 111).
covERAGE
(MONOLAYERS)
Fig. 6. Mean number of next-nearest neighbors per atom as a function of coverage, resulting from Monte Carlo calculations which include nearest-neighbor exclusion and which assume attractive, weak, or repulsive next-nearest neighbor interactions.
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__iATTRACTIVE ’ REPUUIVE
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.
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J/kT Fig. 7. Mean number of second and of third neighbors as a function of the second-neighbor interaction, J/kT, at a coverage of 0.225 monolayers. J/kT =O is the high-temperature limit, while T decreases to the left (right) for an attractive (repulsive) interaction.
Fig. 7 shows how changes in temperature affect the structure of an overlayer in this simple model. For a coverage of 0.225 ML the second- and third-neighbor coordination numbers are plotted as a function of J/kT. The transition between a well-ordered J?; X 6 structure and a somewhat less-ordered 2 X 2 structure occurs smoothly between J/kT = - 1.0 and J/kT = 2.0. The influence of the nn exclusion is especially obvious in the displacement from J/kT = 0 of the intersection of the two curves. Experimenally, these transitions would be easily observed in both the LEED patterns and in the photoemission spectra. Consider a system for which the adatom-adatom interaction is observed to be weak at room temperature. If at an intermediate coverage the system is cooled through its transition temperature, the XPS binding energy will decrease if the adatom-adatom interaction is attractive, and simultaneously the LEED spots will become sharper. If the interaction is repulsive, then the fix fi pattern will gradually evolve into a 2 X 2 pattern as the temperature decreases, while the XPS binding energy increases. It is the binding energy shifts with temperature which would provide the more quantitative measure of the strength of the interaction.
4. Conclusion In summary, room temperature XPS measurements and qualitative LEED data for the adsorbate systems I/Ag( 111) and I/Cu( 111) give straightforward
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evidence for an attractive next-nearest neighbor interaction between I atoms on the silver surface; this attraction is furthermore inferred to be a substratemediated, indirect interaction. Monte Carlo calculations for a lattice gas on a triangular net indicate that the magnitude of this interaction is approximately 25 meV, and that the nnn interaction on Cu(ll1) is considerably weaker than this. XPS thus provides a quantitative measure of adatom-adatom interactions. The Monte Carlo calculations further imply that it is possible to observe ordering transitions in the overlayer through changes in the adsorbate core electron binding energy.
References [I] [2] [3] [4] [5] [6]
S.B. DiCenzo, G.K. Wertheim and D.N.E. Buchanan, Phys. Rev. B24 (1981) 6143. G.K. Wertheim, S.B. DiCenzo and D.N.E. Buchanan, Phys. Rev. B25 (1982) 3020. P.H. Citrin, P. Eisenberger and R.C. Hewitt, Phys. Rev. Letters 45 (1980) 1948. S.B. DiCenzo, G.K. Wertheim and D.N.E. Buchanan, Appl. Phys. Letters 40 (1982) 888. P.H. Citrin, G.K. Wertheim and Y. Baer, unpublished. N. Martensson and B. Johansson, Solid State Commun. 32 (1979) 791; Phys. Rev. B21 (1980) 4427. [7] T.B. Grimley, Proc. Phys. Sot. (London) 90 (1967) 751.