Diffusion of individual adatoms

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Surface Science 2YY/300

(1994) 62X-642

of individual

Received

1993; accepted

E.W. adsorbed

29 April

Miiller‘s

invention

on crystals,

experiments

for publication

18 May

of the field ion microscope

1. Introduction In the standard view of growth phenomena from the vapor, which dates back some 60 years to Stranski and Volmer [l-3], the transport of adatoms toward lattice steps is one of the primary events leading to growth. In view of the intense interest during the last decade in the growth of.crystals and overlayers, it is natural that atomic diffusion on surfaces has become a topic of interest and activity in its own right: there is now available a significant body of information dealing with the diffusion of single metal atoms on crystal planes. The situation 30 years ago was remarkably different. At that time, techniques for examining surface properties on the atomic level did not exist, and no experimental data on the behavior of single adatoms could be found in the literature. The migration of metal atoms, especially of the alkali and alkaline earths, had been examined by various macroscopic methods starting in the 1930s primarily in connection with thermionic emission phenomena [4]. Although valuable in establishing the importance of diffusion over surfaces, these early studies generally were not done on well-defined crystal planes, and long-range interactions played an important part in these measurements, so that the overall understanding 0

1994 - Elsevier

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in the 10.50s for the first time made it possible to see single metal atom‘.

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studies on individual

adatoms.

The

background

probing the motion of single adatoms is sketched briefly, as are yome of the significant developments

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adatoms

have taken place over the last three decades and have provided

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quite a detailed

and beginning

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of the individual atomic events was limited. ‘I’hc development of the field emission microscope in the late 1930s began to change this situation [S,6], but World War II intervened. In the immediate post-war years, observations of diffusion in metal deposits were started again. In Berlin, Stranski and other notable scientists had found a home in what is now the Fritz Haber Institute [3,7]. In Stranski’s group, Erwin Miller. who had been closely involved in the development of the field emission microscope, undertook extensive observations on the transport of tungsten deposited on tungsten surfaces in such a microscope [8]. Some years later, Drechsler and Vanselow [9,10] at the same institute extended observations to tantalum, molybdenum, and nickel. and further refined the work on tungsten. These studies already provided interesting insights into the importance of surface structure in affecting migration, and gave some ideas about the energetics of atom transfer from lattice steps. Quantitative data on atomic events in diffusion was beyond the power of the techniques available. The picture began to change in the 1950s with Erwin Miiller’s invention [l 11of the field ion microscope (FIM). This was the first instrument to depict surfaces with atomic resolution, and it was immediately clear that the FIM would change the scientific landscape.

Science B.V. All rights reserved

G. Ehrlich / Diffusion of individual adatoms

The ability to visualize individual atoms for the first time opened the possibility of obtaining direct information about the migration of atoms on crystals, and this hope has, in fact, been realized. Essentially all the quantitative information about the behavior of individual metal atoms now available has been derived from observations in the FIM. How studies on the motion of individual atoms began and evolved will be the main theme of this personal account. The overall state of various diffusion studies has been reviewed only recently [12-141, and will therefore be of only incidental concern.

2. Background

to single-atom

studies

In a paper [15] entitled “Experiments with atomic crystal building blocks in the FIM”, published in 1957, not too long after Miiller moved to Penn State and perfected the field ion microscope, he not only outlined the principles of the technique, but also sketched areas of research that could be fruitfully explored. He stressed field evaporation and the condensation of individual atoms on surfaces, and emphasized the possibility of measuring the binding energy of atoms by determining the field strength at which they were removed from the surface. Miiller was also interested in ion bombardment of crystals, and the feasibility of examining the damage caused by single-ion impacts. In this connection, he pointed out that by “stepwise heating of the tungsten tip at 700 to 800 K, the changes brought about by the surface diffusion of individual atoms can be studied after cooling”. This technique, he felt, would be especially useful for following the annealing of defects induced by ion bombardment. In his subsequent efforts, Miiller [16] concentrated upon perfecting the operation of the microscope, gaining a better understanding of the physics of the imaging process and of field evaporation, and developing more powerful instruments, such as the atom probe, the combination of the FIM with a time-of-flight mass spectrometer. Among the many subjects examined in his laboratory, the study of defects of one kind or another was emphasized. That nothing further

629

was done to examine the migration of atoms is not too surprising. Much of his early effort was devoted to surveying the operation and capabilities of the microscope, and a premium was therefore placed on easy replacement of samples. The earliest microscopes, which had been of all-glass construction and capable of achieving ultrahigh vacuum conditions, were soon replaced by demountable models, often relying on greased joints to make access simple. In subsequent studies in Miiller’s laboratories, high fields were maintained on the surface to field ionize impinging gases that might otherwise contaminate the sample. These are not conditions appropriate for examining the ordinary thermal properties of atoms at the surface, and diffusion studies developed elsewhere. In the early postwar years, J.H. Hollomon had created at the GE Research Laboratory in Schenectady a department devoted to modern materials studies. In 1953 I joined David Turnbull’s group there and immersed myself in studies of chemisorption phenomena on metal surfaces. After developing thermal desorption methods and quantitatively characterizing adsorption processes on macroscopic surfaces, it became clear that more microscopic techniques would be desirable [171. This led to adsorption studies using the field emission microscope [ 181, and, less successfully, the field ion microscope [19]. Although my own efforts were focussed upon chemisorption, David Turnbull was deeply involved with diffusion phenomena, both in the bulk and at surfaces, because of their importance in the kinetics of growth and transformations. Occasionally Charles Frank or Nicolas Cabrera would visit the laboratory, and I had the opportunity of talking with them about their work on crystal growth [20]. In this marvelously stimulating environment, it was natural to take at least a brief look at metal atoms in our FIM.

3. Early work on single metal atoms At the beginning of the 60s my assistant Frank Hudda and I began to examine the behavior of single tungsten atoms deposited on a tungsten surface from a nearby evaporator. The first stud-

ies. in 1953, were exploratory and devoted to transient diffusion during deposition, a topic that has again become of interest recently 121-241. Through our involvement in the kinetics of chemisorption, Bruce McCarroll and I [2S] had become concerned about how atoms from the vapor give up their energy on colliding with a surface to eventually equilibrate with it. Calculations with one-dimensional models suggested that for atoms striking their own lattice, energy transfer would be quite an efficient process. Metal atoms deposited on their own lattice should therefore come to rest close to their original point of impact. If this view was indeed correct, then on an emitter tip illuminated by atoms from one side, the deposit should follow the shadow line. Experiments with tungsten atoms from an evaporator at - 3000 K falling on a tungsten surface at - 20 K suggested that, within the limits of our ability to define the geometry, the tungsten atoms did not transgress significantly beyond the shadow line, and that just a few collisions with the lattice served to im~lobilizc the atoms on the surface 126,271. At the same time these experiments were underway, other laboratories were also beginning to use the FIM for exploring surface diffusion. S.S. Brenner [2X], at US Steel, surveyed changes in the shapes of field-evaporated tungsten tips on heating, in an endeavor to establish how transport over the surface depended upon surface structure. More detailed experiments of this sort were subsequently undertaken at the National Chemical Laboratories in England, where David Bassett observed the atomic rearrangement of field-evaporated tungsten surfaces [29]. He was able to establish that changes occurred in different temperature regimes for different crystallographic regions, and to relate these to the diffusion of atoms bound at different types of lattice steps. Studies of transient diffusion were also started up in a collaboration between groups at Yale and the National Bureau of Standards [30,31]. Their work, published in 1965, again suggested that tungsten atoms condensing on atomicaily rough surfaces of tungsten came to rest in the immediate vicinity of the point of impact. At the GE Research Labs, observations on

chemis~~rption phen(~mena were c~~nt~n~ling. Trevor Delchar had arrived at the laboratory from England in 1963 and had initiated some of the first single-crystal studies [33]. Frank Hudda and I were therefore able to concentrate on new experiments. probing the mobility of W atoms on different planes of tungsten. Atoms wcrc deposited on a cold emitter and their location was established by imaging with helium ions. Thercafter. the surfaces were heated, in the ahscncc of any applied fields, and displacements were noted after allowing the surface to cool again to cryogenic temperatures. The results were surprising [27]. Atoms became mobile around room temperaturc, that is at less than l/l0 the melting point of tungsten. On the rough (211) surface, mobility of tungsten atoms already was pronounced at temperatures at which atoms deposited on the smoothest plane of tungsten, the (1101, did not undergo any displacements. More quantitative measurements were obviously required for further explorations, and above all a technique had to be devised to deduce diffLIsivitics from ohscrvations on individual atoms. In the past, regardless of observational technique, surface diffusion had always been examined in a chemical potential gradient. These wcrc the first observations of surface diffusion in an equilibrium system. How should the diffusion of a few atoms on a small crystal plane, less than 100 A across, bc analyzed? As a graduate student. 1 had run across C‘handrasckhar’s article “Stochastic problems in physics and astronomy” [33]; based on what I had learned there I considered two possibilities. One was to describe the motion of the atoms as a random walk, and to extract the diffusivity from the measured mean-square displacement ( 3 .t-’ ). relying on the Einstein relation [34] (AX’)

= 2Dt.

(1)

Quite another method of analysis was also possible. That was to measure the mean-square successive difference ([ n( 7) - u(O)]~ ) in the number of atoms II present in a small area element ,4 a time interval T after the start of observations. and to extract the diffusivity D much as Smoluchowski had analyzed the diffusivity of colloidal

G. Ehrlich / Diffusion of individual adatoms

particles. At the beginning of the century, Smoluchowski [35] showed that for an area element surrounded by an infinite reservoir of atoms, values of the mean-square successive difference, and of ((An2)), the mean amplitude of fluctuations in the number of particles, are related to the diffusivity D through the after-effect factor P by (in(~)

-n(0)]2>/[2((An2)>]

The after-effect sivity D by

=P.

(2)

factor is in turn tied to the diffu-

exp[ -(R,

X //

-R,)2/(4D1)]

dR, dR,.

A (3)

The diffusivity on the plane of interest can therefore be derived from observations of the number of atoms present in the area element A. This second method was rejected, however, as the small planes on which observations are made in the FIM seemed to violate Smoluchowski’s assumptions. The Einstein relation between the mean-square displacement ( Ax2) of an adatom and the diffusivity D in eq. (1) also has its limitations. It is valid only for a random walk on a large plane on which atoms are not constrained by the presence of boundaries. To make this approach applicable to studies on the small planes accessible in the FIM, corrections to the simple random walk relation therefore had to be worked out [36]. For mean-square displacements small compared to the plane diameter a, the Einstein relation was replaced by the approximation (Ax2> = 2Dt[l

and (321), the only ones for which quantitative information is available to this day; qualitative observations, about the much lower mobility on (310) and (111) were reported as well. It was demonstrated that atomic motion was diffusive the mean square displacement increased linearly with time t, as expected, and interactions with plane boundaries were briefly examined. The temperature dependence of the diffusivity was analyzed according to the usual Arrhenius relation 1381 D = D, exp( - E,/kT)

P = 1 - 1/(4rDrA)

- (4/3a)(4Dt/#‘].

(4)

This made it possible to extract the diffusivity D from the mean-square displacement measured on a plane of finite size. Diffusion experiments on tungsten atoms deposited on different planes of tungsten were carried out over the course of a few years, and were reported in 1966 [37]. It was quite a different era from now. Quantitative observations were made on three differently structured planes, (1101, (211),

631

.

(5)

Here EA is the barrier opposing jumps, and D, is a prefactor, related to the entropy of activation AS, and the jump length e by D, = v,t2

exp(AS,/k),

(6)

where v0 is a vibrational frequency of the adatom. The results were surprising. On (321) and (110) planes, behavior conformed to that for a random walk between nearest-neighbor sites, for which D, is expected to be - lop3 cm2/s. The activation energy for diffusion on the (110) plane, the most densely packed plane of the bee lattice, amounted to only 22 kcal/mol, compared with the heat of vaporization of > 200 kcal/mol, or with an activation energy of > 40 kcal/mol reported for surface rearrangement. Diffusion of atoms over a flat plane obviously required little energy. Motion on the much rougher (321) occurred over a barrier of only 20 kcal/mol. On the (211) plane, whose structure is close to that of (3211, diffusion was definitely anomalous, with a prefactor D, = 2 x lo-’ cm’/s and a barrier of only 13 kcal/mol. The activation energies differed from anything expected for models based on pairwise interactions between atoms. However, one observation was entirely in agreement with expectations [9] - the directional dependence of atom motion. On the channelled planes (211) and (321), diffusion was always observed along the direction of the dose-packed [ill] rows of the substrate, just as for a marble running along a trough. In contrast, on the (110) plane, motion appeared two-dimensional. Details of the atomic jump processes involved in diffusion were also probed. In experiments on

small planes, atoms execute only a few jumps during any given diffusion interval. The usual Gaussian expression [33] for the probability of finding an atom at a distance Ax from the origin would therefore not be valid. With the help of Bruce McCarroll, a close colleague at GE, the distribution of displacements expected in a random walk with a small number of jumps, itself subject to fluctuations, was derived as [36] ~,=cxp[-(N)I,((N))]:

(7)

here (N) is the average number of jumps during the diffusion interval, and Z,(u) the modified Bessel function of order z. Unbeknownst to us, Feller at Princeton had just arrived at the same result [39]. The very sparse data that had been gathered about the distribution of displacements appeared to be in agreement with this relation, suggesting that diffusion conformed to the traditional picture of a random walk between nearest-neighbor sites. Although the analysis of these experiments was quite sophisticated, the experiments themselves were carried out with rudimentary instrumentation. That the experiments were done at all owed everything to the skill and persistence of Frank Hudda. In the earliest work, images of the surface under study were obtained by allowing the helium ions created at the surface to fall directly on a Willemite screen. These images were recorded on a Polaroid camera extracted from an old oscilloscope and required exposures on the order of ten minutes in absolute darkness. The small darkroom, where the ultrahigh vacuum system was housed, initially did not have air-conditioning. During the summer, temperatures would rise well above 100 F, yet it was crucial to remain alert, as we were operating at voltages up to 30 kV, using glass equipment cooled with liquid hydrogen. It was therefore natural to maximize the amount of information obtained by doing experiments with several atoms deposited on one plane. The attendant problems of assigning displacements were recognized at the time; the more subtle effects of interactions upon diffusion were not. With information about the energetics of atomic diffusion in hand, it was obviously of

interest to compare this with the binding energy of adatoms on the same planes. Miiller [15.16] had proposed that the removal of metal atoms from a surface by high fields was limited by evaporation of metal ions over a so-called Schottky saddle. If this is true, the desorption energy can be simply deduced from measured values of the field required for evaporation at low temperatures. Experiments to derive binding cncrgics of tungsten atoms on various planes of tungsten were undertaken by Kirk [40]. and evaporation fields were determined on ( I 10). (21 I), (310). (321). and (411) plants. It is now rccognizcd that the basic assumption of desorption over a Schottky barrier is not valid [41] and that binding cncrgies cannot be obtained this simply, but ncithct the measured desorption fields, nor the apparent binding energies, showed any unusual differences between the (211) and (321) planes. To account for the surprisingly low activation energy for diffusion that had been observed on W(21 I ), it was proposed that adatoms diffuse along a [i 1 l] channel during a fluctuation: the channel atoms move outward so that the adatom can then jump t’rom one binding site to another over a much rcduccd energy barrier. This model did not, however. account for the unusually low prefactor D,, found for the diffusion of tungsten atoms on this plant. These early results were soon related to mass transfer processes on macroscopic surfaces [42], but at GE examination of individual atoms came to an end in 1968, as the author moved to the University of Illinois. Interesting studies on single metal atoms had in the meantime begun at other laboratories. Late in 1968, Plummer and Rhodin [43] reported on field evaporation studies of individual atoms, done at Cornell. This work greatly expanded on the GE studies, in dealing with a variety of different metals held on the more prominent planes of tungsten, but still was subject to the same fundamental limitations. In the next few years, detailed measurements of atomic diffusion using the FIM began to appear from Imperial College, where David Bassett had moved from the National Chemical Lab. In an impressive study, Bassett and Parsley [44] deposited Ta, MO, W, Re, Ir and Pt atoms on a tungsten emitter. For Ta, W, and Re, they were

G. Ehrlich / Diffusion of individual adatoms

able to deduce activation energies and prefactors on W(llO), (2111, and (321) planes; for Ir atoms, only the behavior on the first two planes was characterized. The overall techniques were quite similar to the earlier studies at GE, and their results for tungsten atoms were in very good agreement with the previous data. Again the activation energy on (211) was much lower than on (320, while the behavior on that plane was quite close to that found on (1101. This pattern was observed not only for W atoms, but also for Ta and Ir, but not Re. All but the latter again showed unusually low prefactors. The directional dependence of diffusion for all the atoms studied conformed to what had been found earlier for tungsten - one-dimensional on the channeled (211) and (321) planes, two-dimensional motion on (1101. Bassett and Parsley were able to correlate the activation energy for the chemically different adatoms with the binding energies reported for these atoms by Plummer and Rhodin [431. We now recognize that this correlation is not soundly based. It is of interest to note that neither do the diffusion barriers for the different adatoms follow the trends in the heat of vaporization of the respective elements - clearly there is room for further study here. All of these early observations were done on tungsten, a material relatively simple to clean and also quite robust, for which surface studies date back to the 1920s. To establish a reasonable understanding of surface diffusion, it obviously was important to extend measurements to other substrates, and this effort was pioneered by Guy Ayrault at Illinois. On transferring activities from GE to Urbana, the plan had been to concentrate entirely on the chemisorption of gases on crystals. In keeping with this focus, three different projects were started. Probe hole field emission microscopy was put into place to examine chemisorption on smooth, low-index planes. Molecular beam lines were built to do studies of diffraction and also of chemical reactions on large-scale surfaces, and an atom probe system was set up to provide chemical information about chemisorption on the atomic level. Field ion microscopic examination of atomic behavior was not in the original plan; that it was continued at

633

Illinois was due entirely to Guy Ayrault. Because of a deep interest in radiation damage, he had started work with one of my colleagues and had begun to build a field ion microscope system. The project was entirely in his own hands, with occasional help from Mike Wald (who had done FIM studies at Cambridge University, but was working on different projects nearby). This, however, proved too great an undertaking for a single student and in the spring of 1969 he joined the surface group. Here he initiated diffusion studies on rhodium, a material of considerable catalytic interest, whose behavior in chemisorption was being examined by others in the group. Rhodium is an fee metal, and the intent of the diffusion studies was to determine if the pattern of behavior found on tungsten would extend to different materials. Instrumentation for these experiments was much improved. The introduction of channel plate image intensifiers built into the microscope [45-461 made it much quicker to collect data. Studies on rhodium would otherwise have been extremely hard. Neon had to be used as imaging gas, so as to operate at lower fields which would not perturb the adsorbed atoms. Direct imaging on an unintensified phosphor screen would have made it difficult to gather adequate statistics. Another improvement had been the change to liquid helium as a coolant for the FIM. This had become inevitable, as at Illinois liquid hydrogen was not readily available in quantities sufficient for our needs. With these upgrades, Ayrault [47] was able to obtain quantitative data for the self-diffusion of rhodium atoms on many different planes of rhodium - (1111, (311), (1101, (331) and (100). Quite early in this work it became evident that diffusion parameters differed when only a single Rh atom was present on a Rh(l10) plane, and when observations were made on a plane with several atoms on it. All further experiments were therefore done with only a single atom per plane, an improvement possible because of the rapid imaging achieved with channel plates. Ayrault’s studies, which established the first diffusion parameters for isolated single atoms, yielded surprisingly simple results. The highly directional nature of diffusion, first found on tung-

sten, was preserved on this fee metal: on the channeled (11(l), (3311, and (311) planes, with structures reminiscent of WfZll> and (3211, atom motion was observed to occur along the channels in the substrate. Quite different from tungsten was the relation between surface roughness and the activation energy of diffusion - the barrier to the diffusion of rhodium atoms increased as the structure of the surface became rougher on the atomic scale. Behavior on the atomically smooth (111) plane was especially surprising. On the smoothest plane of tungsten, that is on W(llO), diffusion occurred in the same general temperature range as for W(3211, which is quite a rough surface. On Rh(lll), however, atom motion already set in at cryogenic temperatures, in the vicinity of - 50 K. On rougher surfaces, Rh(100) for example, diffusion only began at room temperature. In fact, the progression of activation barriers from planes of one structure to another was in good agreement with calculations based on pairwise interactions represented by a Morse potential. Prefactors were generally - 1OV” cm*/s, as expected for atomic jumps between nearest neighbors. At the end of roughly the first decade of diffusion studies on single atoms, considerable quantitative information had been obtained. Diffusion parameters had been determined on different planes of both a bee and an fee metal, and it was clear that atom motion already set in at rather low temperatures. Movement of atoms seemed quite simple, except on the (211) plane of tungsten: diffusion occurred by random transitions between nearest-neighbor sites. The atomic geometry of the substrate provided an excellent guide to directional preferences. On rhodium, an fee metal, simple bonding schemes even afforded semi-quantitative predictions for the energetics of diffusion. Activation energies on tungsten, a bee metal, were not in accord with this simple scheme, but that was not surprising; the pair bonding approximation should not work for metals in any event. The correlation between the barrier to diffusion and the apparent binding energy of atoms (derived from field evaporation studies) gave hope that a better understanding of atomic behavior would emerge for bee surfaces as well.

4. Later developments

- the second decade

Actual developments in surface diffusion did not follow the trends that had emerged from the early diffusion studies. For one thing, the focus of a considerable part of the overall effort shifted away from single atoms to examining interactions between atoms and to the behavior of clusters formed by association of several atoms. Stimulated by conversations with A.J.W. Moore from CSIRO, we had at GE briefly looked for, but not detected, the nucleation of clusters when there were several atoms present on a surface ]17]. David Bassett at Imperial College. however, was able to observe the formation of small clusters of different adatoms on several planes of tungsten 1481. His work opened up a new field of activity. devoted to understanding the diffusion of clusters, as well as to characterizing the interactions between adatoms on a surface. Much effort has gone into such studies [49]. Pursuing these devclopments here would take us too far afield, especially since the effort devoted to single-atom motion had expanded as well, as groups at Penn State, under T.T. Tsong, at the University of Pennsylvania, under W.R. Graham, and at Osaka University, under S. Nakamura, undertook such work. Initially, these studies served to amptify the existing picture. Considerable improvements were made in the techniques for controlling and calibrating the temperature; at Illinois, this happened largely through the efforts of David Reed [.50]. With the improved equipment, W.R. Graham while at Illinois [51] made observations on a single W atom diffusing on W(211>. In contrast to the initial studies, where there had been many atoms present on a piane, these obse~ations revealed quite ordinary behavior - a prefactor D,, of - 1O-1 cm’,/s, and an activation energy of - 18 kcal/moi, rather similar to what had been found on W(321). The mystery of anomalous diffusion on W(211) was solved. In collaboration with Kaj Stolt [52], measurements were also done for a single Re adatom on W(211). The diffusion characteristics did not differ significantly from the earlier values obtained at Imperial College [44]. However, the distribu-

G. Ehrlich / Diffusion of indicidual adatoms

tion of distances covered in diffusion on W(211) was also measured and compared with values predicted for a model in which jumps always occurred between nearest-neighbor sites, for which eq. (7) should be appropriate. Within the large statistical scatter inevitable for a small data base, agreement was found to be reasonable, and it was concluded that on this plane, diffusion of Re involved primarily single jumps. Similar comparisons were also done by Coulman at Illinois for W atoms diffusing on W(211) [53]. The distribution of displacements expected if adatoms can jump between nearest neighbors at the rate CX, and between second-nearest neighbors at the rate p, had been derived by Mark Twigg [.54] as pX = exp[ -2(a

+P)tl C zj(2Pt)z.r-2,(2at)’ j= -_m (8)

Comparison of eq. (8) with the admittedly limited data again suggested that the predominant mechanism of diffusion involved transitions between adjacent binding sites. Tsong and Casanova [55] at Penn State later carried out this type of analysis for W on W(llO), and for this plane as well came to the same conclusion: atomic motion occurred predominantly between adjacent sites. It should be noted that primarily because of the tediousness of recording data and then properly analyzing it, the number of observations in all these studies was quite small. These experiments were useful, however, in demonstrating that diffusion did not occur by a series of long jumps over the surface. For deducing reliable jump rates from the displacement distribution, an order of magnitude more data would have been required. During the 1970s there also accumulated quite a number of incidental measurements of atom diffusivities on planes of tungsten previously studied. These have been reviewed by Bassett [56], and did not significantly change the overall picture apparent from earlier measurements. Diffusion studies were brought to a new level of refinement through the work of Flahive and Graham at the University of Pennsylvania [57,581. In their studies on W(lll), (211) and (3211, they identified the geometry of the sites at which atoms

635

were bound. Having done this, they also succeeded in deriving diffusion parameters for Ni on W(lll), as well as for W on W(211); the extensive measurements for the latter, for a well-defined geometry, were in reasonable agreement with earlier (and less detailed) results. At roughly the same time, Crewe and his group at Chicago [59] developed an entirely new way of looking at the motion of atoms on surfaces. They were able to detect single atoms of heavy metals such as silver, gold, or uranium on graphite by using a high resolution scanning transmission electron microscope; they also observed the occasional movement of these atoms over the surface [60]. These were heroic experiments, under very difficult conditions, and yielded some quantitative estimates for atomic hopping rates [61]. Although a tremendous technical triumph, these observations were not continued and have not provided significant quantitative information about diffusion on surfaces. By far the most interesting and important results came about from what seemed, at the start, a routine extension of diffusion studies to another fee metal. Rhodium had been examined early in the 70s Bassett and Coulson [62] briefly looked at diffusion on iridium, and later in the 70s Bassett and Webber [63] decided to examine platinum, another catalytically important metal amenable to study in the FIM. Although their work was somewhat restricted by the high temperature (77 K) at which the surface was imaged, Bassett and Webber carried out an extensive examination in which they observed diffusion of platinum atoms on the (1131, (1101, and (133) planes of platinum; in addition, more limited experiments were done with Ir and Au atoms. The pattern of behavior observed for the platinum atoms was similar to what had previously been noted for rhodium atoms on rhodium, but with one truly startling exception. On Pt(llO), diffusion of platinum as well as iridium atoms, but not gold atoms, was two-dimensional - that is, atoms were not confined to moving along the surface channels formed by lattice atoms closepacked along [liO]. Bassett and Webber [63] offered two possible explanations for this surprising effect. At the

636

G. Ehrlich

/ Diffusion qf individual adatoms

diffusion temperature, chance fluctuations occur in the lateral positions of the atoms in the channel walls. During an especially large fluctuation, a gap could open in the wall, allowing the adatom to slip through. In another, likelier scenario, a lattice atom was assumed to jump out of the wall and into the adjacent channel; the vacancy so created in the wall can then be filled by the adatom. Bassett and Webber also speculated that the cross-channel diffusion observed could in some way be related to the reconstruction of the Pt(ll0) plane. Although the mechanism of diffusion on Pt(ll0) was not revealed by this study, Bassett and Webber had discovered a new, unexpected, and exciting phenomenon. While these studies were under way, John Wrigley had started on his PhD research at Illinois, in which he was going to examine cluster motion on an fee metal [64]. For ease of observation he picked iridium in preference to rhodium, for which diffusion of single atoms had already been studied. In exploratory experiments with iridium atoms deposited on lr(llO), he found that the atoms did not move along the [liO] channels - instead, transitions always appeared to take place into the adjacent channel. This, of course, was quite contrary to expectation. I for one suspected some artifact, so John Wrigley refocussed his work to understanding how cross-channel diffusion occurred. Soon thereafter, Bassett and Webber’s exciting results appeared [63], and John Wrigley devised a clever way of testing the mechanism at work, by observing cross-channel motion for adatoms chemically different from the substrate. If cross-channel diffusion takes place by the adatom jumping, either over the channel walls, or through a gap opened up by a large fluctuation, it is the adatom that appears in the adjacent channel. On the other hand, if in diffusion the adatom changes place with a lattice atom that has moved into the adjacent channel, then the chemical identity of the adatom appearing in the neighboring channel will have undergone a change. Wrigley [65] deposited tungsten atoms on Ir(llO), and in a series of experiments in the atom probe was able to establish that after a cross-channel event it was an iridium atom that was sitting on the surface, not a tungsten atom.

That, of course, demonstrates that diffusion occurred by an exchange mechanism, and this conclusion was buttressed by a further observation. After diffusion, the adatom can be removed by field evaporation, and the composition of the surface layer can then be tested atom-by-atom in a time-of-flight analysis. When this was done following a cross-channel event, tungsten was usually found present in the first surface layer. just as expected if the adatom had changed place with a lattice atom. Tungsten was never found in the surface if cross-channel motion had not taken place. In experiments on exchange diffusion using a foreign adatom, the adatom moves into the lattice, and it is a lattice atom that continues the diffusion. That implies that the conditions necessary to initiate the diffusion of tungsten on Irt 110) should be different from those required to continue diffusion, which occurs via iridium atoms. Even prior to establishing the exchange mechanism by atom probe analysis, Wrigley [64] found that self-diffusion of iridium atoms occurred at temperatures T > 330 K. However, when a tungsten atom was deposited on Ir(1 lo), cross-channel motion was already observed at T > 270 K. To continue atom motion thereafter required temperatures T > 350 K. These later transitions were always between the channel into which tungsten had originally been deposited, and its neighbor, into which the first transition had occurred. Only at much higher temperatures, - 400 K, was diffusion to other parts of the plane observed. After the atom probe experiments, the significance of the observations was clear: the iridium atom continuing the motion obviously was in some way bound to the buried tungsten atom. The generality of cross-channel diffusion on fcc(l10) planes, presumably by an exchange mechanism, was soon demonstrated in very impressive experiments by Tung and Graham at the University of Pennsylvania [66]. Up to that time, diffusion had been explored on reasonably refractory metals, for which experiments were easy to do. Tung and Graham set out to characterize atom motion on nickel and also aluminum; they selected these materials, despite the fact they are hard to work with, in the hope that theoretical

G. Ehrlich / Diffusion of indiuidual adatoms

calculations would in the near future be feasible. Despite considerable difficulties, they were able to determine diffusion parameters on Ni(311), (3311, and (1101, and to estimate the diffusion barrier on Ni(100) and (111). The measured values were found to be in rather poor agreement with calculations based on Morse potentials. What was most interesting, however, was that on Nit1 lo), and apparently also on AK1 lo), diffusion was two-dimensional. This was surprising, as in previous studies of diffusion on fee (110) planes the correlation between cross-channel diffusive motion and the restructuring of the (110) plane had been emphasized. Neither Ni(ll0) nor Al(110) are known to reconstruct [67]. It also appeared from these measurements that it is one-dimensional diffusion on Rh(ll0) 1471 that is unusual - cross-channel motion is rather a more widespread phenomenon. Observation of cross-channel diffusion created considerable interest, and for the first time attracted significant theoretical effort. Halicioglu [68] at Stanford did statics calculations for atom motion on the (110) plane of a Lennard-Jones crystal. He concluded that the transition state for diffusion differed from that envisioned by Bassett and Webber [631. The adatom, together with a lattice atom slightly displaced into the adjacent channel, formed a symmetrical, dumbbell-shaped structure. That such entities actually played a role in self-diffusion was almost immediately demonstrated in molecular dynamics simulations, by DeLorenzi, Jacucci, and Pontikis at Trento [69,70] and by Mruzik and Pound at Stanford [71]. The former studies also extensively compared vacancy and adatom movement on different fee planes, and suggested that especially at higher temperatures, adatom hopping between nearestneighbor sites would give way to longer jumps over the surface. In this second decade of studies on the migration of individual adatoms, it became clear that atomic diffusion was a much more complicated phenomenon than thought earlier: it involved a variety of different mechanisms, about which even qualitatively reliable predictions were difficult to make. One hopeful development took place almost unnoticed at the end of this period: more

637

modern equipment, allowing automatic control of diffusion experiments, became accessible [72], raising hopes for an expansion of the quantitative data available on diffusion phenomena at surfaces.

5. The third decade The first experiments taking advantage of improved instrumentation to accumulate statistically significant data on diffusion of individual atoms were aimed at an old subject - diffusion on W(211). Previous experiments on chemically different atoms on this plane suggested that there were large variations in the prefactor D, as well as in the barrier to diffusion from one system to the next. This could possibly be indicative of different diffusion mechanisms, and so S.C. Wang at Illinois [73] undertook a reexamination of the diffusion of Re, W, MO, Ir and Rh on W(211). A rather surprising result emerged from what is at present the most extensive study of the diffusion of single atoms: there were no significant differences in the dynamics of atom motion, that is in the prefactor, for chemically different atoms on W(211). To a rather good approximation, the prefactor for all the atoms tested was close to lo-” cm*/s. Furthermore, the barrier to surface diffusion could be related quite simply to the heat of vaporization of the atoms from their parent metal. The startling differences in D, in the literature had to be attributed to problems in the early experiments, not to any real physical effects. With improved capabilities for gathering data, Wang et al. 1741 also carried out analyses of the distance distribution of diffusing atoms, the first in which statistically significant amounts of data were accumulated. Experiments were done with most of the adatoms for which diffusion had been studied on W(211). These demonstrated what had earlier only been surmised, namely that jumps to nearest-neighbor sites completely dominated diffusion on that plane. It appears from these studies that at least on W(211), diffusion occurs in a very simple way, by the random motion of adatoms between nearest-

h38

G. Ehrlich

/ Diffusion

neighbor sites, over a barrier related to the energy of vaporization of the parent metal. This simple picture is deceptive, however. That became evident from the work of DeLorenzi at Illinois, who in 1989 created a video from molecular dynamics simulations of atom motion on a bee (211) plane. This revealed very clearly how complicated the diffusion process really is even when atoms jump just between nearest-neighbor sites. The early idea, that the surface channels on this plane might widen out in a fluctuation to permit easy passage of an adatom [40], appears dose to the mark: in the molecular dynamics simulations, a successful diffusion event involves the concerted movement of several lattice atoms together with the adatom. It must also be noted parenthetically that detailed diffusion experiments, on W(211) as well as on other surfaces, have been done over only a narrow temperature interval; such experiments do not preclude more unusual behavior at higher temperatures, for example [751. That the results available on W(211) cannot serve as a guide even to behavior on other planes of tungsten has recently been shown by M.F. Lovisa at Illinois [761, who carefully characterized the distribution of displacements observed in the diffusion of iridium and also tungsten atoms on W(llO>. These measurements demonstrate that at lower temperatures, diffusion occurs by single jumps along the close-packed directions. At higher temperatures, T r 340 K for tungsten atoms, double jumps along the close-packed directions make quite a significant contribution on W(110). For diffusion on macroscopic crystals, where transport over distances larger than those studied in the FIM are important, a much more varied behavior can be expected. Another interesting development has been the renewed interest in diffusion by an exchange mechanism. The stage for this was set in 1985, when DeLorenzi and Jacucci [77] reported new molecular dynamics simulations of surface diffusion; they had extended their work to bee surfaces, using a metallic potential. The simulations revealed an unexpected effect - on the bee (100) plane, DeLorenzi and Jacucci found that “in addition to conventional nearest-neighbor jumps

of indiriduul

adatoms

between surface sites, the adatom undergoes migration events reminiscent of exchange processes . . “. Jumps over the surface, along (001). occasionally alternated with transitions in which the adatom displaced a lattice atom from its site, and the former then continued the diffusion process. In these transitions, the net displacement was along (011). Diffusion by an atom exchange mechanism was not limited to a channellcd plane like the fee (110) surface; it was rather a general phenomenon, also “contributing to atomic diffusion on isotropic crystal surfaces”. Five years later, the importance of atomic exchange in diffusion was confirmed by Feibelman at Sandia [78]. He concluded from ab initio calculations on Al(100) that a transition state would be favored in which the adatom and a slightly displaced lattice atom form a dumbbell structure. When this decomposes, an atom may appear in a unit cell diagonal to the original position of the adatom. A plot of the sites occupied by atoms during diffusion on fee (100) should, according to this mechanism, give a c(2 X 2) mesh. Such a c(2 X 2) mesh has indeed been observed in very nice studies on Ir(1001 by Chen and Tsong at Penn State [791, and also in experiments on Pt(100) by Kellogg at Sandia [SO]. Fried1 et al at Erlangen [Sl] have pointed out that a c(2 X 2) mesh for the sites observed in diffusion on an fee (100) plane does not by itself establish that diffusion occurs by an exchange mechanism. Much the same mesh could bc obtained as a consequence of a c(2 x 21 rearrangement of the (100) surface in the vicinity of the adatom, without invoking atomic exchange for diffusion. Recently, however, experiments have been done with chemically different adatoms on Ni(100) at Sandia [82], and on Ir(l00) at Penn State [83]; these do demonstrate exchange between the adatom and a lattice atom. It is a reasonable assumption that in self-diffusion also this is the likely mechanism. The interest in diffusion on fee (100) has generated new studies on fee (110) planes as well. In work with Pt atoms on Ni(llO), Kellogg [84] verified what had previously only been an assumption, namely that cross-channel motion on this plane occurred by an exchange mechanism. Most

G. Ehrlich / Diffksioionof indiLl~ua1 adatoms

interesting, however, is a study of the distribution of displacements for Ir on Ir(llO), by Tsong and Chen [85]. The results are clearly not in agreement with the idea of a dumbbell intermediate made up of adatom and lattice atom, as proposed in various simulations of diffusion on fee (110). How exchange diffusion actually occurs is still not clear. Energy estimates [861 using the embedded atom method indicate, however, that the balance between ordinary hopping diffusion and exchange processes can be quite close, making it difficult to predict in advance how an unexplored material will behave. The old suggestion that reconstruction and exchange diffusion are connected has been revived repeatedly, but is not in agreement with the fact that exchange occurs on Ni and also Al(1101, which do not reconstruct. The best guide at the moment appears to be that if cross-channel diffusion is observed on the (110) plane of an fee metal, diffusion wilI also occur by an exchange mechanism on the (100) plane. A new area of investigation to open in the third decade of single-atom studies is the detailed exploration of atomic behavior on fee (111) planes. Diffusion on such surfaces is of special interest, as on the atomic level this is the smoothest plane known for a metal. It is compiicated by the fact that on (111) planes at least two very similar sites, labelled fee and hcp, respectively, are available for occupation. A prerequisite to detailed studies on fee (111) pIanes is the ability to ascertain the sites at which metal atoms are actually held on the surface. By mapping the positions occupied after diffusion of iridium atoms on Ir(llI), Wang at Illinois [87] was able to establish that self-adsorption of single iridium atoms occurs preferentially at hcp sites, but that occasionally fee sites were filled as well. In the course of these studies it also became clear that atoms held at different sites could be readily distinguished just by observing the image spot produced in the FIM. An Ir adatom at an hcp site has a triangular image with its apex pointed aIong [2ii]; at an fee site, the orientation is reversed [88,89]. With these capabilities it has become possible to quantitativeIy examine the detailed jump processes contributing to diffusion on Ir(l11). Even though the (111) plane is very smooth, Wang [88]

639

showed that atoms still migrate in a sequence of jumps from hcp to fee site and then again on to hcp. At low temperatures at least these are the only events important, and quantitative values for the barrier height, and also frequency factors, have been measured for Ir, as well as W and Re adatoms [90]. The activation energy for motion of Ir, for example, is unusually low, amounting to less than l/20 the binding energy of an atom on Irflll). Perhaps the most interesting result concerns the magnitude of the prefactors in the diffusivity. There appear to be significant differences in D, for different metal atoms on the same plane, and the prefactors consistently are below the magic value of 11Y3 cm’/s. To finish this survey of developments in the third decade of atomic diffusion studies, it may be appropriate to note that the work on Ir(ll1) provides an excellent example of the importance of luck in research. The detaiIed studies at Illinois were made possible because Ir adatoms prefer hcp sites, but occasionally do occupy fee positions. This led to an assignment of the favored sites, and everything else followed quite simply. Had the first studies been done on other adatoms, such as W or Re, which now are known to occupy hcp sites on Ir(ll1) under almost all conditions, the work would have come to an end. The group at Erlangen [91] had the bad luck to start their explorations of the Ir(ll1) face with tungsten atoms. Although they did excellent work, their attempts at site identification were frustrated.

6. Reprise Tnis survey of some highlights in 30 years research on the diffusion of individual atoms on metals should make it clear that, even though the field has developed fairly randomly, we know infinitely more now than at the beginning of the 1960s. After three decades of work, the atomic events in the migration of atoms over surfaces are probably better understood than in any other process important on surfaces. One central theme to emerge from this effort is that atomic motion in surface diffusion is complex, and can occur in

different ways. which were not anticipated at the beginning of this era. Another obvious conclusion, however, is that the ability to see individLlal atoms confers tremendous powers for characterizing atomic events, the full potential of which has not yet been explored. One of the tangible consequences of past work is that we now have available quantitative tabulations of diffusion parameters for different systems [92]. Values of prefactors and activation energies are very important, both for quantitative predictions of atom transport on crystals and to reveal qualitative trends that may allow extrapolation to materials not yet studied. In this regard, the state of the Literature is rrot satisfactory, however. Only a very limited number of materials has been examined. Worse than that, even though instrumentation has constantly improved. and in some instances excellent agreement has been achieved between studies in different laboratories hy different investigators, such agreement is far from general. In fact, rather little effort has been devoted during the last decade to building up a reliable data base for diffusion phenomena by taking advantage of modern techniques. Much remains to be done to characterize the diffusion of atoms on crystals, and the hope is that in the future this will he done not just on metals, but also on other materials, using a larger variety of techniques. Almost all the quantitative data presently available has been gathered by field ion microscopy. Some information about atom motion, on semiconductors [Y3,94], has been obtained indirectly from studies with the STM and, as already noted, observations have been made of diffusion on graphite, using high resolution scanning eIectron microscopy [5Y]. Further devei~)pment of methods to provide reliable direct data on atom motion on solids would ccrtainly be desirable, and is certain to yield important information. Finally it should bc noted that early studies of single adatoms were strongly intluenced by a desire to better understand the growth of crystals. During the last decades, work on atomic diffusion has progressed to such an extent that this initial goal is gradually being realized - observations on single atoms are beginning to provide new in-

sights into how atoms crystals 1951.

actually

incorporate

into

This account was made possible through support from the National Science Foundation under Grant DMR 91 01429. It is a pleasure to acknowledge the contributions, both in the past and in the preparation of this manuscript, from the many people that have been involved in diffusion studies on adatoms.

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