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Results of an international leed intensity project
39B
Surface Science 192 (1987) 398-413 North-Holland, Amsterdam
RESULTS OF AN INTERNATIONAL LEED INTENSITY PROJECT I. Reproducibility of experimental spectra F. JONA College of Engineering and Applied Science, State University of New York at Stony Brook, Stony Brook, NY 11794, USA Received 20 May 1987; accepted for publication 27 July 1987
Five laboratories participated in a project consisting in the collection of LEED (low-energy electron diffraction) data from a self-prepared Cu{OOI} surface for the purpose of testing methodologies and reproducibility. Each of the five data sets consists of normal-incidence I-V spectra for the four degenerate 10·, 11- and 20-type beams and for some of the eight degenerate 21-type beams, the electron energy varying in the range from 20 to 300 eV somewhat differently in different sets. Although equivalent I - V curves look very similar to one another a quantitative analysis reveals that the energy scale may be shifted by as much as 10 eV from laboratory to laboratory, the peak positions may fluctuate by ±2.S eV and the peak intensities may vary by as much as 70%.
1. History and scope On 19 June 1980, at the IBM conference on the determination of surface structures by LEED (low-energy electron diffraction) [1], a self-appointed group of LEED workers agreed to launch an international project aimed at comparing to one another the experimental LEED intensities collected in different laboratories from the same or equivalent surfaces. Such intensities constitute the first step in a LEED surface structure analysis. In fact, presentday procedures in LEED crystallography consist in collecting experimental intensity-versus-energy curves (called alternatively 1- V curves, LEED spectra or I-V spectra) over energy ranges of the order of 250-300 eV for several diffracted beams from the surface under study and then comparing the results of model calculations to those experimental curves. Thus, it appeared desirable to check the reproducibility of experimental data collected in different laboratories with different equipment. The scope of the project was to invite a large number of workers in different laboratories to collect specific sets of intensity data from a specific test surface and then to determine the differences, if any, between the various sets. It was agreed to pick Cu{OOl} as the test surface because it can be cleaned without appreciable difficulty and it is more inert than most non-reconstructed 0039-6028/87/$03.50 © Elsevier Science Publishers B.V. (N orth-Holland Physics Publishing Division)
F. JOlla / Results 01 an internat ional LEED intensi ty project 1
399
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metal surfaces. Two data sets were to be collected, both in the energy range from 20 to 300 eV, the first set with the incident electron beam perpendicular to the surface plane (normal incidence), the second set with the incident beam at 15 0 to the surface normal ({} = 15 0 ) and with projection onto the surface plane either parallel or antiparallel (r:p = 0 0 or 180 0 ) to the k; axis (see fig. 1). The normal-incidence set was to include all or as many as possible of the non-s pecular beams in the first 4 shells of the LEED pattern (see fig. 1), i.e., the four 10· , 11-, and 20-type beams and the eight 21-type beams. The non-normal-incidence set was to include the specular beam and as many as possible of the other beams in the first 4 shells. A sheet of ins tructions was to be sent to each laboratory participating in the project. In addition, each p articipant was to complete a questionnaire including several queries about surface preparation, experimental conditions and d ata collect ion. The above work was to be done on two samples, denoted A and B, respectively. Sample A was to be provided in experiment-ready form by one laboratory. Realizing that the surface would be affected by the in-situ cleaning process that is necessary for a LEED experiment, the group rejected the idea of sending the same sample, sequentially, to all participants, Instead, several "identical" A samples were to be prepared by one laboratory, and one such
400
F Jona / Results of an international LEED intensity project. I
sample was to be sent to each participant. Dr. J. Noonan of the Oak Ridge National Laboratory graciously agreed to prepare and characterize (by X-ray diffraction) the A samples. Sample B was to be provided and prepared by each participant in the way and with the procedures customary to that participant's laboratory. In July 1980, letters were sent to 38 laboratories around the world with invitations to participate in the project. Fourteen laboratories answered in the affirmative, 7 declined and 17 did not answer. Since difficulties were being encountered in the preparation of the A samples it was not until May 1981 that a follow-up letter was sent to the 14 laboratories which had agreed to participate. This letter asked the participants to proceed with the work on sample B while waiting for sample A. At that point in time only 8 laboratories were still willing to participate in the project. One A sample was sent to each of the 8 laboratories in November 1982. It turns out that, unfortunately, none of these A samples was used for the LEED intensity project. The reasons for the failure of this part of the project probably were, among others, the size of the samples (25 mm diameter and 3 mm thickness, notably larger than the samples commonly used in LEED experiments) and, of course, the demand on time for the experimental execution of the project. The B part of the project fared a little better. Between September 1982 and May 1985, intensity data from Cu{001} were received from 5 laboratories, although not all of them included the non-normal-incidence set. Evaluation of the 5 normal-incidence sets was carried out at Stony Brook in the period between January and August 1985. Preliminary results were presented orally at the International Seminar on Surface Structure Determination by LEED and Other Methods in Erlangen, Fed. Rep. of Germany, on 25 September 1985. The final results are presented and discussed below in abbreviated form.
2. Experimental details and methodology The project was reduced to the study of 5 normal-incidence sets collected from Cu{DOl} samples prepared domestically by each participating laboratory. Not all sets included all the degenerate beams in anyone shell of the LEED pattern, and the energy ranges varied for the same beam type in the different sets. Although 5 sets are not quite enough for a meaningful statistical study of differences and fluctuations we decided to proceed with the project anyway because there is, to date, little information about reproducibility and reliability of LEED intensity data from different sources for LEED surface structure determinations [2]. Since the goal of the project was to provide just such information, i.e., to give a picture of the state of the art of LEED intensity measurements (and not to "rate" either participants or methodologies or instrumentations) it was decided that the data would not be publicly
F. Jona / Results of an international LEED intensity project. I
401
associated with specific individuals or laboratories. Rather, the laboratories and the corresponding data sets will be identified by numbers, 1 through 5, assigned arbitrarily at random. With a larger number of data sets we would have hoped to be able to recognize some trends in the data gathered with anyone method of data collection and perhaps draw some conclusions about the advantages and disadvantages of such method. As it turns out, this approach was not possible: two laboratories used the brightness-spot-photometer method, two used the Faraday-box method, and one used the TV-camera method. Only two laboratories reported the quoted purity of the Cu crystal from which their {DOl} sample was obtained (99.995% and 99.999%, respectively). Three laboratories reported the value of base pressure reached in the experimental chamber during the LEED experiment (the values ranged from 5 X 10- 10 to 5 X 1O-1l Torr), and the in-situ cleaning procedures prior to data collection (series of Ar ion bombardments of 30 min to 8 h at argon pressures of (1-5) X 10- 4 Torr, ion current densities of 0.5-2 j.tA/cm2 at 300 eV, annealing cycles of 30 min to 1 h at 650 to 700 0 C). Data collection with a Faraday box required longer times (3-10 min/curve), of course, than data collection with a TV camera (0.5 min/curve), with the spot-photometer collection times in between (2-5 min/curve). Only one laboratory corrected the energy scale of the LEED spectra for the contactpotential difference between sample and electron-gun cathode, and only two removed the background from the curves. Finally, one laboratory held their sample at 120 K during data collection, another held theirs at 160 K, and the rest collected all data with the sample at room temperature. At the outset, the methodology to be used for the evaluation of the 5 data sets was not obvious. Use of reliability factors to quantify the differences between curves in the same set or in different sets was not deemed appropriate because one would have to choose among several factors, none of which is universally accepted, all emphasizing different features of LEED spectra and all designed specifically for theory-experiment, rather than experiment-experiment, comparisons. It was therefore decided to carry out a direct quantitative comparison of: (1) the positions of intensity peaks in equivalent beams of the same and different sets, and (2) the magnitudes of equivalent intensity peaks and the ratios of magnitudes of neighboring intensity peaks in equivalent 1- V spectra. For this purpose, the data sets, all received on magnetic tape, were read into a main-frame computer, re-formatted in order to suit the available plotting routines and plotted for visual inspection and study. 3. Evaluation and results
We examined first how equal to one another the degenerate beams in any given set are. As examples, we show in figs. 2, 3 and 4 the 10, 11 and 20 sets,
402
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respectively, from three laboratories, proving that degenerate spectra were indeed very similar to one another. A more quantitative measure of reproducibility, however, is the comparison of peak positions and peak heights in the same and in different sets. For this purpose, we determined the positions of some (2-4) major peaks in each spectrum and then examined first the fluctuations of such positions in degenerate beams of the same data set as measured by the same laboratory. Table 1 gives an example of such a study, whence we see that the standard deviation fluctuates between 0 and 2.0 eV. These fluctuations were encountered in all 5 sets, the maximum standard deviation of these equivalent-peak positions being 2.5 eV. The maximum standard deviation of equivalent-peak intensities was found to be 63%. Next, we compared peak positions in equivalent beams of different sets. Table 2 shows such a comparison for the 11 and the II beam - the maximum deviation is 4.15 eV here, but is as large as 5 eV for other beams. The ratios of any two adjacent peaks in equivalent beams change by 20% to 125% in different sets. We then proceeded to average the degenerate I-V spectra of the same
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F Jona / Results of an international LEED intensity project. I
Table 1 Selected peak positions (in eV) in degenerate beams of one data set; mean values and standard deviations (SD) are given for each selected peak position Beam
1st peak
2nd peak
3rd peak
4th peak
114.0 115.0 114.5 0.71
154.0 154.0 154.0 0.0
190.0 189.0 189.5 0.71
252.0 252.0 252.0 252.0 252.0 0.0
271.0 271.0 270.0 271.0 270.75 0.5
10 10 01 01 Mean SD
76.0 76.0 76.0 76.0 76.0 0.0
144.0 144.0 144.0 144.0 144.0 0.0
11
62.0 61.0 61.5 0.71
n
Mean SD 20 20 02 02 Mean SD
144.0 144.0 140.0 144.0 143.0 2.0
215.0 215.0 215.0 215.0 215.0 0.0
21 12 21
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278.0 280.0 280.0 278.0 279.0 1.15
12 Mean SD
beam type in each set and we plotted such averaged curves for all five sets to allow visual comparison of the curves from different sets. Figs. 5 and 6 depict, as examples, the averaged 10-type and ll-type spectra, respectively, from the five sets. Realizing that only one of the data sets had been corrected for the contact-potential difference between sample and electron-gun cathode (a correction usually of the order of 1 to 3.5 eV), and that therefore different sets had energy scales shifted by different amounts with respect to one another, we attempted to determine both the average energy-scale shifts and the eventual fluctuations about this average shifts as follows. For each of the four beam types (10, 11, 20 and 21) in each of the five sets we determined the average positions of the major peaks (see table 3). Then we chose (arbitrarily) set 1 as a reference set and determined the difference .a k 1 between the (average) peak positions in set k and those in set 1. The average value of these differences should be the same for all beam types in the same set, since it represents a constant shift of the energy scale. Table 3 shows that this average shift is not
F. Jona / Results of an international LEED intensity project. I
405
Table 2 Selected peak positions in two LEED spectra (11 and II) from 5 different laboratories; mean values over the 5 laboratories and standard deviations (SD) are also given Laboratory
11 Beam 1st peak
1 2 3 4 5
60.0
Mean SD
62.0 61.0 1.41
2nd peak
3rd peak
4th peak
116.0 111.0 118.0 116.0 114.0 115.0 2.65
156.0 150.0 156.0 156.0 154.0 154.4 2.61
191.0 185.0 192.0 192.0 190.0 190.0 2.92
2nd peak
3rd peak
4th peak
116.0 111.0 117.0 116.0 115.0 115.0 2.35
156.0 149.0 156.0 158.0 154.0 154.6 3.44
191.0 185.0 193.0 196.0 189.0 190.8 4.15
EBeam 1st peak 1 2 3 4 5
60.0
Mean SD
61.0 60.5 0.71
constant but varies by as much as 2.7 eV in any given set. Finally, we determined the fluctuations €k of peak positions around the average shift: table 3 shows that these fluctuations range from - 2.2 to + 2.7 eV. We note that a constant shift of the energy scale affects "only" the value of the real part of the inner potential that is usually determined by LEED intensity analysis - this shift may vary, as we see in table 3, from approximately + 2 to - 8 eV. But the fluctuations of peak positions about the average are certain to affect the structural parameters. How large the effect of the observed fluctuations is on the structural parameters cannot be immediately gauged because intensity calculations are required to determine it (see part II of this report [3]), but the range is unexpectedly large, considering the care with which LEED intensity data intended for structure determinations are usually taken. A comparison of the magnitudes of peak intensities in corresponding beams of different sets is less straightforward because none of the participants measured absolute intensities. It is in fact customary, in LEED crystallography, to monitor diffracted intensities in arbitrary units. Thus, some kind of normalization procedure had to be found and applied before comparison between different sets could be done. We chose to apply a normalization procedure described in the following. For each 1- V spectrum we determined the maximum range !:J.E = E, - E, common to all data sets, we calculated the
406
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factor F = 11 £/ 1/ r / dE and then mult iplied all intensities in that I-V spectrum with F. This' pr ocedu re ensures that after no rmalization all t.: V spectra have the same value of the integral between E, and E f , namely, ff. rInorm dE = /1E. After this normalization, the heights of corresponding peaks in degenerate beams (e.g., 10, 10, 01 and 01) of the same set were averaged. Such averaged values (and their standard deviations) are listed in table 4 for each of the five data sets, together with the average peak positions already scrutinized in table 3. Thus, the two quantities considered important in LEED intensity analysis (peak position and peak intensity) can be compared among different sets across each horizontal line in table 4. In order to reduce further the effect of different detectors in the different sets we have also calculated (and listed in
Table 3 Average positions (Ek ) of equivalent peaks in LEED spectra of different sets(1 through 5), shifts ~ k1 = Ek (k about the average of li kl LEED spectra
Peak
10
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20
21
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Set 2
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137.8 208.5 245.5 264.2 Ave.
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Table 4 Average energies (E), and in ten sities (1) of intensity peaks in LEED spectra of different sets (SD = stan dard deviation) LEED spectra
10
Peak
I
2
3 4
Set 1
Set 3
Set 2
E (SD)
I (SD)
E (SD)
1 (SD)
E (SD)
47.3 (0.58) 77.7 (0.58) 145.7 (0.58) 241.7 (0.58)
12.0 (3.95) 26.3 (2.85) 28.2 (0048) 14.9 (2.78)
43.0 (0.82) 73.5 (1.0) 140.0 (0.0) 234.0 (0.0)
15.6 (11.6) 14.8 (10.7) 16.5 (lOA) 6.6 (4.1)
76.2 (050) 144.8 (0.50) 242.0 (0.82)
Set 4
I (SD)
-
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21.6 (2.69) 29.6 (2.00) 16.2 (LlO)
E (SD)
77.9 (0.71) 145.5 (0.71) 243.5 (0.71)
Set 5
I (SD)
E (SD)
-
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76.0 (0.0) 144.0 (O.O) -
17.0 (054) 35.2 (5.01) 12.7 (0.84)
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Mean (SD)
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0.93
0.89
0.72
0048
0.47
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2.48
1.83
2.76
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11
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116.0 (0.0) 156.0 (O.O) 191.0 (0.0)
9.6 (1.16) 5.3 (1.3) 19.5 (4.13)
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59.8 (0.50) 111.8 (0.96) 149.5 (0.58) 185.0 (0.0)
53.3 (16.1) 11.9 (3.06) 6.0 (1.55) 16.2 (4.27)
117.5 (1.29) 156.5 (0.58) 192 .5 (0.58)
11.7 (1.56) 5.8 (Ll5) 24.5 (4.30)
116.2 (0.50) 156.2 (1.26) 193.2 (2.22)
11.6 (3.66) 4.9 (0.93) 28.1 (6.93)
61.5 (0.71) 114 .5 (0.71) 154.0 (0.0) 189.5 (0.71)
25.6 (0.16) IDA
(1.95) 5.7 (0.3) 17.1 (1.95)
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4.47
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2.45
121 13
1.81
1.99
1.99
2.36
1.81
13 / 14
0.27
0.37
0.24
0.17
0.34
1 2 3 4
146.0 (0.0) 216.0 (0.0) 255.3 (2.31) 271.7 (0.58)
3.7 (0.0) 22.4 (1.95) 11.2 (1.23) 11.8 (1.58)
137.8 (0.96) 208.5 (0.58) 245.5 (0.58) 264.2 (LSD)
41.5 (12.5) 24.1 (3.82) 9.4 (1.53) 9.8 (1.66)
218.0 (0.0) 255.2 (0.50) 273.8 (0.50)
33.7 (5.31) 11.2 (1.40) 9.3 (1.41)
215.0 (0.0) 257.0 (0.0) 276.0 (1.41)
34.3 (0.12) 10.6 (1.69) 11.1 (2.55)
143 .0 (2.00) 215.0 (0.0) 252.0 (0.0) 270.8 (0 .50)
3.46 (1.43) 1.99 (0.22) 0.28 (0.08)
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27 .3 (2.98) 29.1 (3.34) 12.2 (1.44) 12.9 (1.75)
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1.72
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0.94
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2.00
2.57
3.00
3.25
2.38
131 14
0.95
0.96
1.21
0.95
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188 .0 (0 .63) 279.3 (0.82)
35.6 (3.86) 28.9 (2.08)
Ratios ofpeak intensities: 1.23 121/3
128.0 (2.5&) 181.8 (0.50) 270.3 (0.50)
94.9 (15 .6) 55.0 (8.83) 26.9 (3.92)
2.05
281.0 (0.53)
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43.6 (5. 87)
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table 4) the ratios 11112' 12/13 , etc. of intensities of first and second, second and third, etc. peaks, respectively, in the LEED spectra. The standard deviations from the mean of these intensity ratios vary from 11% to 83%.
4. Conclusions
The results of the LEED intensity project may be summarized as follows: (1) Within anyone of the five sets, the standard deviations from the mean peak positions in degenerate LEED spectra are as large as 2.5 eV. No obvious difference was detected between different methods of intensity data collection (Faraday box, spot photometer or TV camera).
F. JOlla / Results of an international LEED intensity project. I
411
(2) Comparison between different sets reveals that equivalent peak positions may vary by as much as 10 eV from one set to another, with standard deviations varying between 1 and 5 eV. A rigid shift of one set of data with respect to another may be present because of the lack of correction for contact-potential difference between electron-gun cathode and sample (correction which is presumably applied when the data are used for surface structure determinations and which, at or near normal incidence, affects only the real part of the inner potential). However, when we attempt to determine the magnitude of such a shift by comparing all data to the same reference set (table 3) we find that even within the same set the fluctuations of the mean shift can be as large as 2.7 eV for different LEED spectra. The (more important) fluctuations around the mean rigid shift are as large as ± 2.5 eV. (3) Peak intensities vary considerably. Within any given set (i.e., for data collected from the same surface and with the same method) the intensities of equivalent peaks in degenerate beams differ mostly by 10% to 30% and occasionally by as much as 70%. In different sets (i.e., for data collected from different samples and with different equipment) the differences can also be large (- 50%) [4] while the ratios of intensities of neighboring peaks differ mostly by 30-40%, with occasional large disagreements of the order of 80%. The above results suggest a few comments. Discrepancies between different sets may be attributed, in part, to the fact that the samples were different (different surface preparation, orientation, purity, etc.) and the data collection methods were different. It may be of interest, in this respect, to note that a round robin of Auger electron spectroscopy CAES) data from copper and gold, involving 28 different instruments, revealed substantial variations in reported kinetic energies and relative intensities [2]. The spread in reported kinetic energic values ranged from 7 eV at a kinetic energy of 60 eV to 32 eV at a kinetic energy of 2025 eV. The spread in intensity ratios ranged from a factor of about 38 for the - 60 eV and - 920 eV AES peaks of Cu to a factor of about 120 for the - 70 eV and - 2025 eV AES peaks of Au [5]. Thus, since it is reasonable to assume that the participants to our LEED intensity project used AES for checking surface cleanliness, we must conclude that substantial interlaboratory variations were almost certain to occur with regards to the magnitude of surface contaminants in the LEED project. Surface contaminants may affect the intensity peaks and therefore the ratios of adjacent peaks in a LEED spectrum. However, small amounts of contaminants, especially if disordered, are less likely to affect the peak positions (at least at the submonolayer level) than are misorientations of the different surfaces used in the different laboratories [6]. More puzzling are the variations in peak positions and peak heights in degenerate beams of the same set. One possible cause of such variations may indeed be a misorientation of the surface. Other causes may be deviations from normal incidence, the presence of residual fields, most likely magnetic
412
F. lana
I
Results of an international LEED intensity project. I
fields, and of course, inaccurate voltmeters (vide, e.g., the results of the AES round robin mentioned above). If the LEED intensities are measured via the brightness of spots on the fluorescent screen of a display-type apparatus (either with a spot-photometer or with a television camera) one may argue that inhomogeneities, i.e., different responses of different regions of the screen could cause variations of intensity values. But there is no evidence that the data collected with a Faraday box, which should not have this problem, have smaller fluctuations of peak intensities in degenerate beams than the data collected on a fluorescent screen (see the standard deviation values of the averaged intensity values in table 4). Inasmuch as the results of the present project may be interpreted to give information about the accuracy (as opposed to the precision) of LEED intensity data, we may conclude that in a routinely but carefully monitored 1- V curve: (a) at normal incidence (and presumably at any known angle of incidence) peak positions may be uncertain by about ± 2.5 eV; (b) the energy scale may be uncertain by 5 or 10 eV; and (c) the intensities and the intensity ratios may be uncertain by about 60%.
Acknowledgements Thanks are due to the following people who were instrumental in providing the data on which this report is based: R.J. Behm, H.L. Davis, K. Muller, J.R. Noonan, D. Wolf, W.S. Yang and E. Zanazzi. T.S. Joh helped in the analysis of the data. The work was sponsored in part by the National Science Foundation with Grant No. DMR8301l65AOl.
References [11 The proceedings of this conference (without mention of the project described in this report) are published in book form with the title: Determination of Surface Structure by LEED, Eds. P.M. Marcus and F. Jona (Plenum, New York, 1984). [2] In 1977, the results of three independent studies of a clean Si{OOl} surface were compared to one another (A. Ignatiev, F. Jona, M. Debe, D.E. Johnson, SJ. White and D.P. Woodruff, J. Phys. CIO (1977) 1109). However, the comparison was mostly qualitative and visual, i.e., no attempt was made to quantify the differences in peak positions and peak intensities, and no structure analysis was carried out. Furthermore, Si{OOl} is reconstructed and is known to have coexisting domains with different reconstructions. None of these complications occurs on Cu{OOl}. [3] F. Jona, P. Jiang and P.M. Marcus, Surface Sci. 192 (1987) 414. [4] Although two of the data sets were collected from samples cooled below room temperature (120 and 160 K, respectively) no attempt was made to take this fact into account, as the temperature effects on the diffracted intensities is known to be much less than the observed spread in intensities from different data sets.
F. J ana / Results of an international LEED intensity project. I
413
[5] C.l. Powell, N.E. Erickson and T.E. Madey, J. Electron Spetrosc. Related Phenomena 25 (1982) 87. [6] The effect of deviations from ideal conditions of a surface (i.e., disordered contaminants, imperfections, etc.) upon LEED spectra has never been studied systematically and quantitatively. The main difficulty in such a study is the measurement of the magnitude of the deviation from ideal conditions. If this difficulty could be overcome such a study would be very interesting indeed.
Surface Science 192 (1987) 398-413 North-Holland, Amsterdam
RESULTS OF AN INTERNATIONAL LEED INTENSITY PROJECT I. Reproducibility of experimental spectra F. JONA College of Engineering and Applied Science, State University of New York at Stony Brook, Stony Brook, NY 11794, USA Received 20 May 1987; accepted for publication 27 July 1987
Five laboratories participated in a project consisting in the collection of LEED (low-energy electron diffraction) data from a self-prepared Cu{OOI} surface for the purpose of testing methodologies and reproducibility. Each of the five data sets consists of normal-incidence I-V spectra for the four degenerate 10·, 11- and 20-type beams and for some of the eight degenerate 21-type beams, the electron energy varying in the range from 20 to 300 eV somewhat differently in different sets. Although equivalent I - V curves look very similar to one another a quantitative analysis reveals that the energy scale may be shifted by as much as 10 eV from laboratory to laboratory, the peak positions may fluctuate by ±2.S eV and the peak intensities may vary by as much as 70%.
1. History and scope On 19 June 1980, at the IBM conference on the determination of surface structures by LEED (low-energy electron diffraction) [1], a self-appointed group of LEED workers agreed to launch an international project aimed at comparing to one another the experimental LEED intensities collected in different laboratories from the same or equivalent surfaces. Such intensities constitute the first step in a LEED surface structure analysis. In fact, presentday procedures in LEED crystallography consist in collecting experimental intensity-versus-energy curves (called alternatively 1- V curves, LEED spectra or I-V spectra) over energy ranges of the order of 250-300 eV for several diffracted beams from the surface under study and then comparing the results of model calculations to those experimental curves. Thus, it appeared desirable to check the reproducibility of experimental data collected in different laboratories with different equipment. The scope of the project was to invite a large number of workers in different laboratories to collect specific sets of intensity data from a specific test surface and then to determine the differences, if any, between the various sets. It was agreed to pick Cu{OOl} as the test surface because it can be cleaned without appreciable difficulty and it is more inert than most non-reconstructed 0039-6028/87/$03.50 © Elsevier Science Publishers B.V. (N orth-Holland Physics Publishing Division)
F. JOlla / Results 01 an internat ional LEED intensi ty project 1
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metal surfaces. Two data sets were to be collected, both in the energy range from 20 to 300 eV, the first set with the incident electron beam perpendicular to the surface plane (normal incidence), the second set with the incident beam at 15 0 to the surface normal ({} = 15 0 ) and with projection onto the surface plane either parallel or antiparallel (r:p = 0 0 or 180 0 ) to the k; axis (see fig. 1). The normal-incidence set was to include all or as many as possible of the non-s pecular beams in the first 4 shells of the LEED pattern (see fig. 1), i.e., the four 10· , 11-, and 20-type beams and the eight 21-type beams. The non-normal-incidence set was to include the specular beam and as many as possible of the other beams in the first 4 shells. A sheet of ins tructions was to be sent to each laboratory participating in the project. In addition, each p articipant was to complete a questionnaire including several queries about surface preparation, experimental conditions and d ata collect ion. The above work was to be done on two samples, denoted A and B, respectively. Sample A was to be provided in experiment-ready form by one laboratory. Realizing that the surface would be affected by the in-situ cleaning process that is necessary for a LEED experiment, the group rejected the idea of sending the same sample, sequentially, to all participants, Instead, several "identical" A samples were to be prepared by one laboratory, and one such
400
F Jona / Results of an international LEED intensity project. I
sample was to be sent to each participant. Dr. J. Noonan of the Oak Ridge National Laboratory graciously agreed to prepare and characterize (by X-ray diffraction) the A samples. Sample B was to be provided and prepared by each participant in the way and with the procedures customary to that participant's laboratory. In July 1980, letters were sent to 38 laboratories around the world with invitations to participate in the project. Fourteen laboratories answered in the affirmative, 7 declined and 17 did not answer. Since difficulties were being encountered in the preparation of the A samples it was not until May 1981 that a follow-up letter was sent to the 14 laboratories which had agreed to participate. This letter asked the participants to proceed with the work on sample B while waiting for sample A. At that point in time only 8 laboratories were still willing to participate in the project. One A sample was sent to each of the 8 laboratories in November 1982. It turns out that, unfortunately, none of these A samples was used for the LEED intensity project. The reasons for the failure of this part of the project probably were, among others, the size of the samples (25 mm diameter and 3 mm thickness, notably larger than the samples commonly used in LEED experiments) and, of course, the demand on time for the experimental execution of the project. The B part of the project fared a little better. Between September 1982 and May 1985, intensity data from Cu{001} were received from 5 laboratories, although not all of them included the non-normal-incidence set. Evaluation of the 5 normal-incidence sets was carried out at Stony Brook in the period between January and August 1985. Preliminary results were presented orally at the International Seminar on Surface Structure Determination by LEED and Other Methods in Erlangen, Fed. Rep. of Germany, on 25 September 1985. The final results are presented and discussed below in abbreviated form.
2. Experimental details and methodology The project was reduced to the study of 5 normal-incidence sets collected from Cu{DOl} samples prepared domestically by each participating laboratory. Not all sets included all the degenerate beams in anyone shell of the LEED pattern, and the energy ranges varied for the same beam type in the different sets. Although 5 sets are not quite enough for a meaningful statistical study of differences and fluctuations we decided to proceed with the project anyway because there is, to date, little information about reproducibility and reliability of LEED intensity data from different sources for LEED surface structure determinations [2]. Since the goal of the project was to provide just such information, i.e., to give a picture of the state of the art of LEED intensity measurements (and not to "rate" either participants or methodologies or instrumentations) it was decided that the data would not be publicly
F. Jona / Results of an international LEED intensity project. I
401
associated with specific individuals or laboratories. Rather, the laboratories and the corresponding data sets will be identified by numbers, 1 through 5, assigned arbitrarily at random. With a larger number of data sets we would have hoped to be able to recognize some trends in the data gathered with anyone method of data collection and perhaps draw some conclusions about the advantages and disadvantages of such method. As it turns out, this approach was not possible: two laboratories used the brightness-spot-photometer method, two used the Faraday-box method, and one used the TV-camera method. Only two laboratories reported the quoted purity of the Cu crystal from which their {DOl} sample was obtained (99.995% and 99.999%, respectively). Three laboratories reported the value of base pressure reached in the experimental chamber during the LEED experiment (the values ranged from 5 X 10- 10 to 5 X 1O-1l Torr), and the in-situ cleaning procedures prior to data collection (series of Ar ion bombardments of 30 min to 8 h at argon pressures of (1-5) X 10- 4 Torr, ion current densities of 0.5-2 j.tA/cm2 at 300 eV, annealing cycles of 30 min to 1 h at 650 to 700 0 C). Data collection with a Faraday box required longer times (3-10 min/curve), of course, than data collection with a TV camera (0.5 min/curve), with the spot-photometer collection times in between (2-5 min/curve). Only one laboratory corrected the energy scale of the LEED spectra for the contactpotential difference between sample and electron-gun cathode, and only two removed the background from the curves. Finally, one laboratory held their sample at 120 K during data collection, another held theirs at 160 K, and the rest collected all data with the sample at room temperature. At the outset, the methodology to be used for the evaluation of the 5 data sets was not obvious. Use of reliability factors to quantify the differences between curves in the same set or in different sets was not deemed appropriate because one would have to choose among several factors, none of which is universally accepted, all emphasizing different features of LEED spectra and all designed specifically for theory-experiment, rather than experiment-experiment, comparisons. It was therefore decided to carry out a direct quantitative comparison of: (1) the positions of intensity peaks in equivalent beams of the same and different sets, and (2) the magnitudes of equivalent intensity peaks and the ratios of magnitudes of neighboring intensity peaks in equivalent 1- V spectra. For this purpose, the data sets, all received on magnetic tape, were read into a main-frame computer, re-formatted in order to suit the available plotting routines and plotted for visual inspection and study. 3. Evaluation and results
We examined first how equal to one another the degenerate beams in any given set are. As examples, we show in figs. 2, 3 and 4 the 10, 11 and 20 sets,
402
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respectively, from three laboratories, proving that degenerate spectra were indeed very similar to one another. A more quantitative measure of reproducibility, however, is the comparison of peak positions and peak heights in the same and in different sets. For this purpose, we determined the positions of some (2-4) major peaks in each spectrum and then examined first the fluctuations of such positions in degenerate beams of the same data set as measured by the same laboratory. Table 1 gives an example of such a study, whence we see that the standard deviation fluctuates between 0 and 2.0 eV. These fluctuations were encountered in all 5 sets, the maximum standard deviation of these equivalent-peak positions being 2.5 eV. The maximum standard deviation of equivalent-peak intensities was found to be 63%. Next, we compared peak positions in equivalent beams of different sets. Table 2 shows such a comparison for the 11 and the II beam - the maximum deviation is 4.15 eV here, but is as large as 5 eV for other beams. The ratios of any two adjacent peaks in equivalent beams change by 20% to 125% in different sets. We then proceeded to average the degenerate I-V spectra of the same
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F Jona / Results of an international LEED intensity project. I
Table 1 Selected peak positions (in eV) in degenerate beams of one data set; mean values and standard deviations (SD) are given for each selected peak position Beam
1st peak
2nd peak
3rd peak
4th peak
114.0 115.0 114.5 0.71
154.0 154.0 154.0 0.0
190.0 189.0 189.5 0.71
252.0 252.0 252.0 252.0 252.0 0.0
271.0 271.0 270.0 271.0 270.75 0.5
10 10 01 01 Mean SD
76.0 76.0 76.0 76.0 76.0 0.0
144.0 144.0 144.0 144.0 144.0 0.0
11
62.0 61.0 61.5 0.71
n
Mean SD 20 20 02 02 Mean SD
144.0 144.0 140.0 144.0 143.0 2.0
215.0 215.0 215.0 215.0 215.0 0.0
21 12 21
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278.0 280.0 280.0 278.0 279.0 1.15
12 Mean SD
beam type in each set and we plotted such averaged curves for all five sets to allow visual comparison of the curves from different sets. Figs. 5 and 6 depict, as examples, the averaged 10-type and ll-type spectra, respectively, from the five sets. Realizing that only one of the data sets had been corrected for the contact-potential difference between sample and electron-gun cathode (a correction usually of the order of 1 to 3.5 eV), and that therefore different sets had energy scales shifted by different amounts with respect to one another, we attempted to determine both the average energy-scale shifts and the eventual fluctuations about this average shifts as follows. For each of the four beam types (10, 11, 20 and 21) in each of the five sets we determined the average positions of the major peaks (see table 3). Then we chose (arbitrarily) set 1 as a reference set and determined the difference .a k 1 between the (average) peak positions in set k and those in set 1. The average value of these differences should be the same for all beam types in the same set, since it represents a constant shift of the energy scale. Table 3 shows that this average shift is not
F. Jona / Results of an international LEED intensity project. I
405
Table 2 Selected peak positions in two LEED spectra (11 and II) from 5 different laboratories; mean values over the 5 laboratories and standard deviations (SD) are also given Laboratory
11 Beam 1st peak
1 2 3 4 5
60.0
Mean SD
62.0 61.0 1.41
2nd peak
3rd peak
4th peak
116.0 111.0 118.0 116.0 114.0 115.0 2.65
156.0 150.0 156.0 156.0 154.0 154.4 2.61
191.0 185.0 192.0 192.0 190.0 190.0 2.92
2nd peak
3rd peak
4th peak
116.0 111.0 117.0 116.0 115.0 115.0 2.35
156.0 149.0 156.0 158.0 154.0 154.6 3.44
191.0 185.0 193.0 196.0 189.0 190.8 4.15
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60.0
Mean SD
61.0 60.5 0.71
constant but varies by as much as 2.7 eV in any given set. Finally, we determined the fluctuations €k of peak positions around the average shift: table 3 shows that these fluctuations range from - 2.2 to + 2.7 eV. We note that a constant shift of the energy scale affects "only" the value of the real part of the inner potential that is usually determined by LEED intensity analysis - this shift may vary, as we see in table 3, from approximately + 2 to - 8 eV. But the fluctuations of peak positions about the average are certain to affect the structural parameters. How large the effect of the observed fluctuations is on the structural parameters cannot be immediately gauged because intensity calculations are required to determine it (see part II of this report [3]), but the range is unexpectedly large, considering the care with which LEED intensity data intended for structure determinations are usually taken. A comparison of the magnitudes of peak intensities in corresponding beams of different sets is less straightforward because none of the participants measured absolute intensities. It is in fact customary, in LEED crystallography, to monitor diffracted intensities in arbitrary units. Thus, some kind of normalization procedure had to be found and applied before comparison between different sets could be done. We chose to apply a normalization procedure described in the following. For each 1- V spectrum we determined the maximum range !:J.E = E, - E, common to all data sets, we calculated the
406
F. JOlla / Results of all international L EED intensity proj ect. I
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factor F = 11 £/ 1/ r / dE and then mult iplied all intensities in that I-V spectrum with F. This' pr ocedu re ensures that after no rmalization all t.: V spectra have the same value of the integral between E, and E f , namely, ff. rInorm dE = /1E. After this normalization, the heights of corresponding peaks in degenerate beams (e.g., 10, 10, 01 and 01) of the same set were averaged. Such averaged values (and their standard deviations) are listed in table 4 for each of the five data sets, together with the average peak positions already scrutinized in table 3. Thus, the two quantities considered important in LEED intensity analysis (peak position and peak intensity) can be compared among different sets across each horizontal line in table 4. In order to reduce further the effect of different detectors in the different sets we have also calculated (and listed in
Table 3 Average positions (Ek ) of equivalent peaks in LEED spectra of different sets(1 through 5), shifts ~ k1 = Ek (k about the average of li kl LEED spectra
Peak
10
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20
21
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Set 2
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59.8 111.8 149.5 135.0 Ave.
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1st 2nd 3rd 4th
146.0 216.0 255.3 271.7
137.8 208.5 245.5 264.2 Ave.
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10
Peak
I
2
3 4
Set 1
Set 3
Set 2
E (SD)
I (SD)
E (SD)
1 (SD)
E (SD)
47.3 (0.58) 77.7 (0.58) 145.7 (0.58) 241.7 (0.58)
12.0 (3.95) 26.3 (2.85) 28.2 (0048) 14.9 (2.78)
43.0 (0.82) 73.5 (1.0) 140.0 (0.0) 234.0 (0.0)
15.6 (11.6) 14.8 (10.7) 16.5 (lOA) 6.6 (4.1)
76.2 (050) 144.8 (0.50) 242.0 (0.82)
Set 4
I (SD)
-
-
21.6 (2.69) 29.6 (2.00) 16.2 (LlO)
E (SD)
77.9 (0.71) 145.5 (0.71) 243.5 (0.71)
Set 5
I (SD)
E (SD)
-
-
-
76.0 (0.0) 144.0 (O.O) -
17.0 (054) 35.2 (5.01) 12.7 (0.84)
I (SD)
Mean (SD)
l:l
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<,
-
~
~
t:
16.1 (1.0)
~
.Q,
34.3
l:l ;,
(1.46)
;;'
-
~
l:l
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Ratios ofpeak intensities: 0046 lJiI2
-
1.05
-
0.76 (0042)
12 / I3
0.93
0.89
0.72
0048
0.47
/3//4
1.89
2.48
1.83
2.76
-
0.70 (0.22) 2.24 (0045)
11
-
1 2 3
4
116.0 (0.0) 156.0 (O.O) 191.0 (0.0)
9.6 (1.16) 5.3 (1.3) 19.5 (4.13)
~
~ ;,
59.8 (0.50) 111.8 (0.96) 149.5 (0.58) 185.0 (0.0)
53.3 (16.1) 11.9 (3.06) 6.0 (1.55) 16.2 (4.27)
117.5 (1.29) 156.5 (0.58) 192 .5 (0.58)
11.7 (1.56) 5.8 (Ll5) 24.5 (4.30)
116.2 (0.50) 156.2 (1.26) 193.2 (2.22)
11.6 (3.66) 4.9 (0.93) 28.1 (6.93)
61.5 (0.71) 114 .5 (0.71) 154.0 (0.0) 189.5 (0.71)
25.6 (0.16) IDA
(1.95) 5.7 (0.3) 17.1 (1.95)
r-
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Ratios ofpeak intensities: IJl12
20
4.47
-
-
2.45
121 13
1.81
1.99
1.99
2.36
1.81
13 / 14
0.27
0.37
0.24
0.17
0.34
1 2 3 4
146.0 (0.0) 216.0 (0.0) 255.3 (2.31) 271.7 (0.58)
3.7 (0.0) 22.4 (1.95) 11.2 (1.23) 11.8 (1.58)
137.8 (0.96) 208.5 (0.58) 245.5 (0.58) 264.2 (LSD)
41.5 (12.5) 24.1 (3.82) 9.4 (1.53) 9.8 (1.66)
218.0 (0.0) 255.2 (0.50) 273.8 (0.50)
33.7 (5.31) 11.2 (1.40) 9.3 (1.41)
215.0 (0.0) 257.0 (0.0) 276.0 (1.41)
34.3 (0.12) 10.6 (1.69) 11.1 (2.55)
143 .0 (2.00) 215.0 (0.0) 252.0 (0.0) 270.8 (0 .50)
3.46 (1.43) 1.99 (0.22) 0.28 (0.08)
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27 .3 (2.98) 29.1 (3.34) 12.2 (1.44) 12.9 (1.75)
l:l
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at:
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s·
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l:l
Ratios of peak intensities: 0.16 IJ11 2
1.72
-
-
0.94
12 / 13
2.00
2.57
3.00
3.25
2.38
131 14
0.95
0.96
1.21
0.95
0.95
0.94 (0.78) 2.64 (0.50) 1.00 (0 .12)
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S· t;;
S.
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21
1 2 3
188 .0 (0 .63) 279.3 (0.82)
35.6 (3.86) 28.9 (2.08)
Ratios ofpeak intensities: 1.23 121/3
128.0 (2.5&) 181.8 (0.50) 270.3 (0.50)
94.9 (15 .6) 55.0 (8.83) 26.9 (3.92)
2.05
281.0 (0.53)
-
-
43.6 (6.00)
-
-
-
-
-
-
-
-
280.4 (1. 52)
43.6 (5. 87)
185.5 (0.58) 279.0 (Ll5)
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65.2 (11.3) 39.5 (5.12)
1.65
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F. lana / Results of an international LEED intensity project. I
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Fig. 6. Averaged l l-type LEED spectra from set 1 through 5.
table 4) the ratios 11112' 12/13 , etc. of intensities of first and second, second and third, etc. peaks, respectively, in the LEED spectra. The standard deviations from the mean of these intensity ratios vary from 11% to 83%.
4. Conclusions
The results of the LEED intensity project may be summarized as follows: (1) Within anyone of the five sets, the standard deviations from the mean peak positions in degenerate LEED spectra are as large as 2.5 eV. No obvious difference was detected between different methods of intensity data collection (Faraday box, spot photometer or TV camera).
F. JOlla / Results of an international LEED intensity project. I
411
(2) Comparison between different sets reveals that equivalent peak positions may vary by as much as 10 eV from one set to another, with standard deviations varying between 1 and 5 eV. A rigid shift of one set of data with respect to another may be present because of the lack of correction for contact-potential difference between electron-gun cathode and sample (correction which is presumably applied when the data are used for surface structure determinations and which, at or near normal incidence, affects only the real part of the inner potential). However, when we attempt to determine the magnitude of such a shift by comparing all data to the same reference set (table 3) we find that even within the same set the fluctuations of the mean shift can be as large as 2.7 eV for different LEED spectra. The (more important) fluctuations around the mean rigid shift are as large as ± 2.5 eV. (3) Peak intensities vary considerably. Within any given set (i.e., for data collected from the same surface and with the same method) the intensities of equivalent peaks in degenerate beams differ mostly by 10% to 30% and occasionally by as much as 70%. In different sets (i.e., for data collected from different samples and with different equipment) the differences can also be large (- 50%) [4] while the ratios of intensities of neighboring peaks differ mostly by 30-40%, with occasional large disagreements of the order of 80%. The above results suggest a few comments. Discrepancies between different sets may be attributed, in part, to the fact that the samples were different (different surface preparation, orientation, purity, etc.) and the data collection methods were different. It may be of interest, in this respect, to note that a round robin of Auger electron spectroscopy CAES) data from copper and gold, involving 28 different instruments, revealed substantial variations in reported kinetic energies and relative intensities [2]. The spread in reported kinetic energic values ranged from 7 eV at a kinetic energy of 60 eV to 32 eV at a kinetic energy of 2025 eV. The spread in intensity ratios ranged from a factor of about 38 for the - 60 eV and - 920 eV AES peaks of Cu to a factor of about 120 for the - 70 eV and - 2025 eV AES peaks of Au [5]. Thus, since it is reasonable to assume that the participants to our LEED intensity project used AES for checking surface cleanliness, we must conclude that substantial interlaboratory variations were almost certain to occur with regards to the magnitude of surface contaminants in the LEED project. Surface contaminants may affect the intensity peaks and therefore the ratios of adjacent peaks in a LEED spectrum. However, small amounts of contaminants, especially if disordered, are less likely to affect the peak positions (at least at the submonolayer level) than are misorientations of the different surfaces used in the different laboratories [6]. More puzzling are the variations in peak positions and peak heights in degenerate beams of the same set. One possible cause of such variations may indeed be a misorientation of the surface. Other causes may be deviations from normal incidence, the presence of residual fields, most likely magnetic
412
F. lana
I
Results of an international LEED intensity project. I
fields, and of course, inaccurate voltmeters (vide, e.g., the results of the AES round robin mentioned above). If the LEED intensities are measured via the brightness of spots on the fluorescent screen of a display-type apparatus (either with a spot-photometer or with a television camera) one may argue that inhomogeneities, i.e., different responses of different regions of the screen could cause variations of intensity values. But there is no evidence that the data collected with a Faraday box, which should not have this problem, have smaller fluctuations of peak intensities in degenerate beams than the data collected on a fluorescent screen (see the standard deviation values of the averaged intensity values in table 4). Inasmuch as the results of the present project may be interpreted to give information about the accuracy (as opposed to the precision) of LEED intensity data, we may conclude that in a routinely but carefully monitored 1- V curve: (a) at normal incidence (and presumably at any known angle of incidence) peak positions may be uncertain by about ± 2.5 eV; (b) the energy scale may be uncertain by 5 or 10 eV; and (c) the intensities and the intensity ratios may be uncertain by about 60%.
Acknowledgements Thanks are due to the following people who were instrumental in providing the data on which this report is based: R.J. Behm, H.L. Davis, K. Muller, J.R. Noonan, D. Wolf, W.S. Yang and E. Zanazzi. T.S. Joh helped in the analysis of the data. The work was sponsored in part by the National Science Foundation with Grant No. DMR8301l65AOl.
References [11 The proceedings of this conference (without mention of the project described in this report) are published in book form with the title: Determination of Surface Structure by LEED, Eds. P.M. Marcus and F. Jona (Plenum, New York, 1984). [2] In 1977, the results of three independent studies of a clean Si{OOl} surface were compared to one another (A. Ignatiev, F. Jona, M. Debe, D.E. Johnson, SJ. White and D.P. Woodruff, J. Phys. CIO (1977) 1109). However, the comparison was mostly qualitative and visual, i.e., no attempt was made to quantify the differences in peak positions and peak intensities, and no structure analysis was carried out. Furthermore, Si{OOl} is reconstructed and is known to have coexisting domains with different reconstructions. None of these complications occurs on Cu{OOl}. [3] F. Jona, P. Jiang and P.M. Marcus, Surface Sci. 192 (1987) 414. [4] Although two of the data sets were collected from samples cooled below room temperature (120 and 160 K, respectively) no attempt was made to take this fact into account, as the temperature effects on the diffracted intensities is known to be much less than the observed spread in intensities from different data sets.
F. J ana / Results of an international LEED intensity project. I
413
[5] C.l. Powell, N.E. Erickson and T.E. Madey, J. Electron Spetrosc. Related Phenomena 25 (1982) 87. [6] The effect of deviations from ideal conditions of a surface (i.e., disordered contaminants, imperfections, etc.) upon LEED spectra has never been studied systematically and quantitatively. The main difficulty in such a study is the measurement of the magnitude of the deviation from ideal conditions. If this difficulty could be overcome such a study would be very interesting indeed.