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The amazing story of semiconductor surface structures
Progressin Surface Science, Vol. 50, Nos 1-4, pp. 31-36.1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved. 0079-6816/95$29.00
Pergamon
0079-6816(95)00042-9
THE AMAZING STORY OF SEMICONDUCTOR SURFACE STRUCTURES C. B. Duke Xerox Wilson Center for Research and Technology, 800 Phillips Road, 0114-38D Webster, NY 14580, U.S.A.
Abstract A brief indication of the history of the determination and prediction of the structure of semiconductor surfaces is given. Only clean surfaces are considered, although adsorbate structures exhibit analogous features. Many of these surfaces are reconstructed, i.e., the symmetry of their surface structure is lower than that of the corresponding bulk lattice plane. During the 1980s and 199Os, the detailed atomic geometries of many of these structures were determined. They exhibit a wide variety of atomic motifs, many of which are not familiar from either small molecule geometries or solid state structures. Theoretical predictions exist for a few of the most heavily studied structures, but even in these cases not all the details of the structures are accepted. The enormous literature on this topic can be comprehended by recognizing that the surface regions of semiconductors constitute a new class of two dimensional chemical compounds, restricted by the requirement that they fit epitaxically on the bulk crystalline substrate. Five principles govern the formation of these compounds for clean tetrahedrally coordinated semiconductors, guiding even a novice to a rudimentary understanding of the origin of the observed rich variety of surface structures. In the case of the cleavage surfaces additional scaling laws are satisfied which further buttress the concept that these surfaces are two dimensional compounds governed by coordination chemistry considerations which are distinct from those appropriate for either molecules or bulk solids.
1. Introduction The purpose of this article is to provide a brief indication of the amazing progress that has been made in the determination, prediction and understanding of the structure of semiconductor surfaces during the past twenty five years. The occasion for this report is the silver anniversary of the journal Progress in Surface Science which is commemorated by the program of Surface Canada ‘95. During this period semiconductor surface structures have gone from unknown to widely determined if 31
32
C. B. Duke
not always well understood [l-5]. This report is an overview of the evolution and current status of the determination and understanding of the structures of clean semiconductor surfaces for the proceedings of Surface Canada ‘95. Its intended audience is individuals who desire a quick snapshot of this topic together with suitable entrees into the literature. The review rather than the original literature is cited. Details are left for the reader to discover from that literature, of which there is a generous supply during the past decade[l-131.
2. Evolution of Semiconductor Surface Structure Determination The first task in determining the structure of a semiconductor surface is to prepare a clean surface. In the early days (the 195Os), this was not a simple task but was eventually accomplished by Farnsworth’s group at Brown University and a group at the Bell Telephone Laboratories, as described in an overview of this period by Gatos [14]. Shortly thereafter, using low-energy electron diffraction (LEED), Schlier and Farnsworth1151 recognized that the low index surfaces of silicon were reconstructed, i.e., they exhibited lower symmetry than the corresponding bulk planes. A flurry of activity attempting to determine the structure of both these and compound semiconductor surfaces ensued [16, 171, but due to difficulties encountered in constructing a suitable theory of LEED 1181, these structures were still unknown in the early 1970s [l, 191. A sea change occurred in the late 1970s and 1980s. As discussed and documented by Duke [l], “Surface structure determination in the early 1990s is about as similar to that in the early 1970s as modern jet aircraft with their supporting terminal and air traffic control infrastructure are to the bi-wing propeller aircraft and farm-field aerodomes of the World War I era. Routine tasks in 1993 (e.g., one day commercial transport between any to major cities on the globe) were almost inconceivable in the earlier era.” The technology for fabricating devices has become in situ growth by molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD). The quantitative characterization of surface structures is performed by a variety of diffraction spectroscopies including LEED, X-ray standing wave spectroscopy, photoelectron diffraction, and high resolution transmission electron Direct images of surfaces species are now routinely obtained by microscopy. scanning tunneling microscopy (STM) with the attendant local electronic structure obtained by scanning tunneling spectroscopy , including dynamic studies of atomic motions during growth an processing. A typical modern research project described, e.g., in the proceedings of recent conferences on the Physics and Chemistry of Semiconductor
Interfaces[l],
could hardly
have been conceived
ago. This remarkable story is described by the individuals commemorative volume Surface Science: The First Thirty
twenty
five years
who created it in a recent Years [20]. Case histories
Semiconductor Surface Structures for individual semiconductor surfaces have been described by Duke 111. Thus, we now possess an abundance of information on the atomic geometries and atomic dynamics of semiconductor surfaces in specific individual cases. The question that now confronts us is how to make sense of this wealth of data.
3. Surface Structure Motifs Surface structural studies on the low index faces of clean elemental and binary semiconductors have revealed a variety of unexpected atomic motifs out of which the structures are composed. A brief compendium of the major ones has been published by Dukeill, who also has prepared a more extensive, but not as yet in print, description of the structures of the low index faces of most elemental and binary III-V semiconductor surfaces[211. For elemental semiconductors these motifs include tilted dimers [(2x1) structures on Si(100) and Ge(lOO)l, pi-bonded zigzag chains [Si(lll)-(2x1)1, adatom structures [Ge(lll)--(2x8)], and a complex structure for Si(lll)-(7x7) which includes adatoms, they include aniondimers and stacking faults. For compound semiconductors cation chains, dimers and trimers in a wide variety of configurations. Most of these motifs were unexpected. Many are not known in detail. Each individual surface has its own story associated with the determination and interpretation of its structure. These tales often contain conflicting claims and an evolution of the “accepted” structure in time as more experimental results are obtained. Accounts of these evolutions may be found in the review literaturell, 2, 6131. Therefore it is appropriate to inquire into how to organize and interpret this massive body of results for individual
surfaces.
4. Principles of Semiconductor Surface Reconstruction One approach to bringing order from this diversity is to search the literature for general features of these structures and their interpretation which can be abstracted as “principles” which describe their construction. This sort of activity has a long history, indicated to varying degrees in several of the reviews cited[1,5,8,10,121. Building on earlier work, Duke[5, 211 recently proposed a set of five principles suitable to describe the clean low index faces of tetrahedrally coordinated elemental These principles are built on two important and compound semiconductors. foundations: the concepts of two-dimensional (2D) chemical bonding and the charge neutrality of surfaces. Simply put, the surface layers of a semiconductor are regarded as a new 2D chemical compound, constrained to be epitaxically bonded to its substrate, which carries precisely enough charge to cancel out the space charge in the surface region of the semiconductor[5, 211. In the simple cases that we consider, no
33
34
C. B. Duke
space charge occurs so the surface compounds are electrically uncharged, i.e., autocompensated. To indicate the nature of these principles, we articulate them explicitly. Principle (2): Reconstructions tend either to saturate surface “dangling” bonds via rehybridization or to convert them into non-bonding electronic states. Principle (2): In many cases (and in all quasi one dimensional ones) surfaces can lower their energies by atomic relaxations leading to semiconducting (as opposed to metallic) surface state eigenvalue spectra. Principle (3): The surface structure observed will be the lowest energy structure kinetically accessible under the preparation conditions. Although these are the only principles which we require for space-charge-free elemental semiconductors, for compound semiconductors the surface atomic composition may be ifferent from that of the bulk, requiring two additional principles to guide the determination of the surface stoichiometry and atomic geometry, respectively. These are: Principle (4): Surfaces tend to be autocompensated. Principle (5): For a given surface stoichiometry, the surface atomic geometry is determined primarily by a rehybridization-induced lowering of the (delocalized) surface state energy bands associated with either surface bonds or (filled) anion dangling bond states. Principle (5) is a restatement of principle (1) appropriate for compound semiconductors. It is an important extension of principle (1) because it describes the result that local bonding considerations, which seem appropriate for group IV and III-V semiconductors, fail when applied to the surfaces of II-VI and I-VII materials[ll, 221. In these cases the nature of the saturation of the valencies of surface species must be re-expressed in terms of the delocalized electronic surface states characteristic of the two-dimensional surface compound as a whole. Only when this is done are the results for all the III-V through I-VII compounds expressible in a common language. Moreover, the predicted energies of the surface state bands are directly observable by photoemission spectroscopy[ll]. Thus, this principle encapsulates the distinction between local coordination chemistry, familiar from molecular chemistry, and the unique two-dimensional nature of the chemical bonding in these surface compounds. Together with principles (2) and (3), it captures the extensions of local coordination chemistry concepts required to describe the structure of the epitaxically constrained[ll, 221 two dimensional compounds which occur at the clean surfaces of tetrahedrally coordinated semiconductors. Deriving an understanding of these principles requires applying them to a variety of cases to see how they work. Descriptions of such applications may be found in several of the references cited[2, 5, 10, 211. The important
point here is that such
35
Semiconductor Surface Structures principles exist, and are enormously useful in selecting promising trial structures for consideration in new situations and in rationalizing the results of numerous diverse detailed structural studies and predictions.
5. Scaling and Universality In one special case, the cleavage surfaces of tetrahedrally coordinated compound semiconductors, we can say more: I.e., that the surface structures of all different materials appear to be the same when measured in a suitable (dimensionless) coordinate system[2,5,11, 121. Moreover there is some evidence that the potential energy surface from which the surface structures are derived also is a universal (i.e., materials independent, in suitable units) function [51. Thus, the surface atomic vibrations as well as atomic geometries exhibit universal properties. These sorts of scaling laws are important because they yield clues to the dominant physical phenomena governing the surface reconstructions as well as provide useful predictions of the properties of new materials from the behavior of those whose properties already have been measured. In particular, they reveal the important role of the symmetry of the substrate in determining the properties of the 2D epitaxically constrained surface compounds.
6. Synopsis Amazing advances in technique and in computer power during the past twenty five years have rendered the structure of almost any surface obtainable, for a price. This explosion in capability has produced a bewildering variety of results individual systems, which make it difficult to discern general patterns exhibited
on by
Progress in Surface Science is a review journal initiated, the wealth of detail. among other purposes, to bring order to advances in the field by commissioning articles which organize and relate the results of many individual systems into a coherent whole. This brief overview, presented on the occasion of the silver anniversary of Progress in Surface Science, is designed to further that purpose by indicating the nature of general principles and scaling laws which permit general concepts to be extracted from the details of the structures of the low index surfaces of clean tetrahedrally
coordinated
semiconductors.
Acknowledgement I am indebted to the organizers of Surface Canada ‘95 for inviting
me to deliver a
plenary lecture on “Semiconductor surface structures: Results, general principles and scaling laws” of which this article is a brief summary.
36
C.B.Duke
References 1. 2.
3. 4. 5. 6. 7 8. 9.
10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
C. B. Duke, J. Vat. Sci. Technol. B 11, 1336 (1993). A. Kahn, Surf Sci. 299/300, 469 (1994). M. B. Webb, Surf Sci. 299/300,454 (1994). E. D. Williams, Surf Sci. 299/300, 502 (1994). C. 8. Duke, Appl. Surf. Sci. 65166, 543 (1993). A. Kahn, Surf. Sci. Rep. 3, 193 (1983). D. Hanneman, Rep. Prog. Phys. SO,1045 (1987). M. Schliiter, in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, D. A. King and D. I’. Woodruff (Eds.), Elsevier, Amsterdam (1988), vol. 5, pp. 37-68. C. 8. Duke, in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, D. A. King and D. I’. Woodruff (Eds.), Elsevier, Amsterdam (1988), vol. 5, pp. 64-118. D. J. Chadi, Ultramicroscopy 31, 1 (1989). C. B. Duke, J. Vat. Sci. Technol. A 10, 2032 (1992). J. I’. LaFemina, Surf. Sci. Reps. 16, 133 (1992). C. B. Duke, in Festkbperprobleme/Adv. Solid State Phys., R. Helbig fed.), Vieweg, Breunschweiglwiesbaden (1994), pp. l-36. H. C. Gatos, Surf Sci. 299/300, 1 (1994). R. E. Schlier and H. E. Farnsworth, J. Chem. Phys. 30,917 (1959). A. U. McRae and G. B. Gobeli, J. Appl. Phys. 35,1269 (1964) J. J. Lander, Prog. Solid State Phys. 2, 26 (1965). C. B. Duke, Surf Sci. 299/300, 24 (1994). P. Mark, S. C. Chang, W. F. Creighton and 8. W. Lee, Crit. Rev. Solid State Mater Sci. 5, 189 (1975). C. B. Duke, (Ed. ), Surface Science: The First Thirty Years, Surf. Sci 299/300 (1994). C. B. Duke, in Handbook of Surface Science, S. Holloway and N. V. Richardson (Eds), Elsevier, Amsterdam (1995), vol 2, chpt. 10. C. 8. Duke, in Atomic and Molecular Processing of Electronic and Ceramic Materials, I. A. Aksay, G. L. McVay, T. G. Stroebe, and J. F. Wagner, (Eds.), Materials Research Society, Pittsburgh (1987), pp. 3-10.
Pergamon
0079-6816(95)00042-9
THE AMAZING STORY OF SEMICONDUCTOR SURFACE STRUCTURES C. B. Duke Xerox Wilson Center for Research and Technology, 800 Phillips Road, 0114-38D Webster, NY 14580, U.S.A.
Abstract A brief indication of the history of the determination and prediction of the structure of semiconductor surfaces is given. Only clean surfaces are considered, although adsorbate structures exhibit analogous features. Many of these surfaces are reconstructed, i.e., the symmetry of their surface structure is lower than that of the corresponding bulk lattice plane. During the 1980s and 199Os, the detailed atomic geometries of many of these structures were determined. They exhibit a wide variety of atomic motifs, many of which are not familiar from either small molecule geometries or solid state structures. Theoretical predictions exist for a few of the most heavily studied structures, but even in these cases not all the details of the structures are accepted. The enormous literature on this topic can be comprehended by recognizing that the surface regions of semiconductors constitute a new class of two dimensional chemical compounds, restricted by the requirement that they fit epitaxically on the bulk crystalline substrate. Five principles govern the formation of these compounds for clean tetrahedrally coordinated semiconductors, guiding even a novice to a rudimentary understanding of the origin of the observed rich variety of surface structures. In the case of the cleavage surfaces additional scaling laws are satisfied which further buttress the concept that these surfaces are two dimensional compounds governed by coordination chemistry considerations which are distinct from those appropriate for either molecules or bulk solids.
1. Introduction The purpose of this article is to provide a brief indication of the amazing progress that has been made in the determination, prediction and understanding of the structure of semiconductor surfaces during the past twenty five years. The occasion for this report is the silver anniversary of the journal Progress in Surface Science which is commemorated by the program of Surface Canada ‘95. During this period semiconductor surface structures have gone from unknown to widely determined if 31
32
C. B. Duke
not always well understood [l-5]. This report is an overview of the evolution and current status of the determination and understanding of the structures of clean semiconductor surfaces for the proceedings of Surface Canada ‘95. Its intended audience is individuals who desire a quick snapshot of this topic together with suitable entrees into the literature. The review rather than the original literature is cited. Details are left for the reader to discover from that literature, of which there is a generous supply during the past decade[l-131.
2. Evolution of Semiconductor Surface Structure Determination The first task in determining the structure of a semiconductor surface is to prepare a clean surface. In the early days (the 195Os), this was not a simple task but was eventually accomplished by Farnsworth’s group at Brown University and a group at the Bell Telephone Laboratories, as described in an overview of this period by Gatos [14]. Shortly thereafter, using low-energy electron diffraction (LEED), Schlier and Farnsworth1151 recognized that the low index surfaces of silicon were reconstructed, i.e., they exhibited lower symmetry than the corresponding bulk planes. A flurry of activity attempting to determine the structure of both these and compound semiconductor surfaces ensued [16, 171, but due to difficulties encountered in constructing a suitable theory of LEED 1181, these structures were still unknown in the early 1970s [l, 191. A sea change occurred in the late 1970s and 1980s. As discussed and documented by Duke [l], “Surface structure determination in the early 1990s is about as similar to that in the early 1970s as modern jet aircraft with their supporting terminal and air traffic control infrastructure are to the bi-wing propeller aircraft and farm-field aerodomes of the World War I era. Routine tasks in 1993 (e.g., one day commercial transport between any to major cities on the globe) were almost inconceivable in the earlier era.” The technology for fabricating devices has become in situ growth by molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD). The quantitative characterization of surface structures is performed by a variety of diffraction spectroscopies including LEED, X-ray standing wave spectroscopy, photoelectron diffraction, and high resolution transmission electron Direct images of surfaces species are now routinely obtained by microscopy. scanning tunneling microscopy (STM) with the attendant local electronic structure obtained by scanning tunneling spectroscopy , including dynamic studies of atomic motions during growth an processing. A typical modern research project described, e.g., in the proceedings of recent conferences on the Physics and Chemistry of Semiconductor
Interfaces[l],
could hardly
have been conceived
ago. This remarkable story is described by the individuals commemorative volume Surface Science: The First Thirty
twenty
five years
who created it in a recent Years [20]. Case histories
Semiconductor Surface Structures for individual semiconductor surfaces have been described by Duke 111. Thus, we now possess an abundance of information on the atomic geometries and atomic dynamics of semiconductor surfaces in specific individual cases. The question that now confronts us is how to make sense of this wealth of data.
3. Surface Structure Motifs Surface structural studies on the low index faces of clean elemental and binary semiconductors have revealed a variety of unexpected atomic motifs out of which the structures are composed. A brief compendium of the major ones has been published by Dukeill, who also has prepared a more extensive, but not as yet in print, description of the structures of the low index faces of most elemental and binary III-V semiconductor surfaces[211. For elemental semiconductors these motifs include tilted dimers [(2x1) structures on Si(100) and Ge(lOO)l, pi-bonded zigzag chains [Si(lll)-(2x1)1, adatom structures [Ge(lll)--(2x8)], and a complex structure for Si(lll)-(7x7) which includes adatoms, they include aniondimers and stacking faults. For compound semiconductors cation chains, dimers and trimers in a wide variety of configurations. Most of these motifs were unexpected. Many are not known in detail. Each individual surface has its own story associated with the determination and interpretation of its structure. These tales often contain conflicting claims and an evolution of the “accepted” structure in time as more experimental results are obtained. Accounts of these evolutions may be found in the review literaturell, 2, 6131. Therefore it is appropriate to inquire into how to organize and interpret this massive body of results for individual
surfaces.
4. Principles of Semiconductor Surface Reconstruction One approach to bringing order from this diversity is to search the literature for general features of these structures and their interpretation which can be abstracted as “principles” which describe their construction. This sort of activity has a long history, indicated to varying degrees in several of the reviews cited[1,5,8,10,121. Building on earlier work, Duke[5, 211 recently proposed a set of five principles suitable to describe the clean low index faces of tetrahedrally coordinated elemental These principles are built on two important and compound semiconductors. foundations: the concepts of two-dimensional (2D) chemical bonding and the charge neutrality of surfaces. Simply put, the surface layers of a semiconductor are regarded as a new 2D chemical compound, constrained to be epitaxically bonded to its substrate, which carries precisely enough charge to cancel out the space charge in the surface region of the semiconductor[5, 211. In the simple cases that we consider, no
33
34
C. B. Duke
space charge occurs so the surface compounds are electrically uncharged, i.e., autocompensated. To indicate the nature of these principles, we articulate them explicitly. Principle (2): Reconstructions tend either to saturate surface “dangling” bonds via rehybridization or to convert them into non-bonding electronic states. Principle (2): In many cases (and in all quasi one dimensional ones) surfaces can lower their energies by atomic relaxations leading to semiconducting (as opposed to metallic) surface state eigenvalue spectra. Principle (3): The surface structure observed will be the lowest energy structure kinetically accessible under the preparation conditions. Although these are the only principles which we require for space-charge-free elemental semiconductors, for compound semiconductors the surface atomic composition may be ifferent from that of the bulk, requiring two additional principles to guide the determination of the surface stoichiometry and atomic geometry, respectively. These are: Principle (4): Surfaces tend to be autocompensated. Principle (5): For a given surface stoichiometry, the surface atomic geometry is determined primarily by a rehybridization-induced lowering of the (delocalized) surface state energy bands associated with either surface bonds or (filled) anion dangling bond states. Principle (5) is a restatement of principle (1) appropriate for compound semiconductors. It is an important extension of principle (1) because it describes the result that local bonding considerations, which seem appropriate for group IV and III-V semiconductors, fail when applied to the surfaces of II-VI and I-VII materials[ll, 221. In these cases the nature of the saturation of the valencies of surface species must be re-expressed in terms of the delocalized electronic surface states characteristic of the two-dimensional surface compound as a whole. Only when this is done are the results for all the III-V through I-VII compounds expressible in a common language. Moreover, the predicted energies of the surface state bands are directly observable by photoemission spectroscopy[ll]. Thus, this principle encapsulates the distinction between local coordination chemistry, familiar from molecular chemistry, and the unique two-dimensional nature of the chemical bonding in these surface compounds. Together with principles (2) and (3), it captures the extensions of local coordination chemistry concepts required to describe the structure of the epitaxically constrained[ll, 221 two dimensional compounds which occur at the clean surfaces of tetrahedrally coordinated semiconductors. Deriving an understanding of these principles requires applying them to a variety of cases to see how they work. Descriptions of such applications may be found in several of the references cited[2, 5, 10, 211. The important
point here is that such
35
Semiconductor Surface Structures principles exist, and are enormously useful in selecting promising trial structures for consideration in new situations and in rationalizing the results of numerous diverse detailed structural studies and predictions.
5. Scaling and Universality In one special case, the cleavage surfaces of tetrahedrally coordinated compound semiconductors, we can say more: I.e., that the surface structures of all different materials appear to be the same when measured in a suitable (dimensionless) coordinate system[2,5,11, 121. Moreover there is some evidence that the potential energy surface from which the surface structures are derived also is a universal (i.e., materials independent, in suitable units) function [51. Thus, the surface atomic vibrations as well as atomic geometries exhibit universal properties. These sorts of scaling laws are important because they yield clues to the dominant physical phenomena governing the surface reconstructions as well as provide useful predictions of the properties of new materials from the behavior of those whose properties already have been measured. In particular, they reveal the important role of the symmetry of the substrate in determining the properties of the 2D epitaxically constrained surface compounds.
6. Synopsis Amazing advances in technique and in computer power during the past twenty five years have rendered the structure of almost any surface obtainable, for a price. This explosion in capability has produced a bewildering variety of results individual systems, which make it difficult to discern general patterns exhibited
on by
Progress in Surface Science is a review journal initiated, the wealth of detail. among other purposes, to bring order to advances in the field by commissioning articles which organize and relate the results of many individual systems into a coherent whole. This brief overview, presented on the occasion of the silver anniversary of Progress in Surface Science, is designed to further that purpose by indicating the nature of general principles and scaling laws which permit general concepts to be extracted from the details of the structures of the low index surfaces of clean tetrahedrally
coordinated
semiconductors.
Acknowledgement I am indebted to the organizers of Surface Canada ‘95 for inviting
me to deliver a
plenary lecture on “Semiconductor surface structures: Results, general principles and scaling laws” of which this article is a brief summary.
36
C.B.Duke
References 1. 2.
3. 4. 5. 6. 7 8. 9.
10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
C. B. Duke, J. Vat. Sci. Technol. B 11, 1336 (1993). A. Kahn, Surf Sci. 299/300, 469 (1994). M. B. Webb, Surf Sci. 299/300,454 (1994). E. D. Williams, Surf Sci. 299/300, 502 (1994). C. 8. Duke, Appl. Surf. Sci. 65166, 543 (1993). A. Kahn, Surf. Sci. Rep. 3, 193 (1983). D. Hanneman, Rep. Prog. Phys. SO,1045 (1987). M. Schliiter, in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, D. A. King and D. I’. Woodruff (Eds.), Elsevier, Amsterdam (1988), vol. 5, pp. 37-68. C. 8. Duke, in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, D. A. King and D. I’. Woodruff (Eds.), Elsevier, Amsterdam (1988), vol. 5, pp. 64-118. D. J. Chadi, Ultramicroscopy 31, 1 (1989). C. B. Duke, J. Vat. Sci. Technol. A 10, 2032 (1992). J. I’. LaFemina, Surf. Sci. Reps. 16, 133 (1992). C. B. Duke, in Festkbperprobleme/Adv. Solid State Phys., R. Helbig fed.), Vieweg, Breunschweiglwiesbaden (1994), pp. l-36. H. C. Gatos, Surf Sci. 299/300, 1 (1994). R. E. Schlier and H. E. Farnsworth, J. Chem. Phys. 30,917 (1959). A. U. McRae and G. B. Gobeli, J. Appl. Phys. 35,1269 (1964) J. J. Lander, Prog. Solid State Phys. 2, 26 (1965). C. B. Duke, Surf Sci. 299/300, 24 (1994). P. Mark, S. C. Chang, W. F. Creighton and 8. W. Lee, Crit. Rev. Solid State Mater Sci. 5, 189 (1975). C. B. Duke, (Ed. ), Surface Science: The First Thirty Years, Surf. Sci 299/300 (1994). C. B. Duke, in Handbook of Surface Science, S. Holloway and N. V. Richardson (Eds), Elsevier, Amsterdam (1995), vol 2, chpt. 10. C. 8. Duke, in Atomic and Molecular Processing of Electronic and Ceramic Materials, I. A. Aksay, G. L. McVay, T. G. Stroebe, and J. F. Wagner, (Eds.), Materials Research Society, Pittsburgh (1987), pp. 3-10.