Chapter 1

Introduction

The properties of semiconductor interfaces are currently of great interest [1].   These interfaces have physical and chemical characteristics which are important for both their practical and theoretical significance.   A coherent understanding of these properties requires knowledge of the interface's crystal structure.   Structural surface-science studies seek this knowledge for a broad range of semiconductor surfaces.  

One interface type of particular note is that which is formed from near-monolayer coverages of metal atoms adsorbed on or in Si{111} surfaces. The presence of these foreign atoms can cause the surface to change its two-dimensional periodicity, vary the spacing between atoms, and change electronic properties.   Therefore, the surface may no longer have bulk-like properties or have a unit cell which is the projection of the bulk three-dimensional unit-cell onto the surface.   The Si{111}√3x√3-30-X is one common such surface, where X is a metallic element, and is also referred to as X/Si-√3, X-√3, √3-X, or rt.   The lattice vectors of the √3 surface unit-cell are larger than the bulk-like surface lattice-vectors by a factor of √3.   Hence, the √3-X unit-cell is three times larger and rotated by 30 degrees as compared to the bulk-like surface unit-cell.   The coordination and spacing between adsorbate (X) and Si atoms in the rt unit-cell is the surface structure.  

Several experimental techniques, see Glossary A, are being used to unravel the surface atomic and electronic structure of Si{111}√3x√3-30-X systems.   This thesis focuses on one technique (LEED) used for determining surface structure, on the importance of these systems in surface science, and on several √3-X systems which have been examined by dynamical LEED analysis and other surface probes.   In particular, the remainder of this chapter is devoted to the basic structural phenomena that occur on surfaces, Si surfaces, and Si{111}√3x√3-30-X surfaces. Chapter 2 will begin with the basic physics behind LEED, its application, and surface structure-analysis.   Chapter 2 continues with a description of the salient features of AES and sample preparation, as used in this study.   Chapters 3, 4, 5, and 6 then present overviews, details, and discussion of four particular Si{111}√3x√3-30-X surface systems, with X representing B, Mg, Au, and Ce. These chapters are followed by discussion.   Appendices are also provided with a literature survey of results for additional √3 systems.   Additionally, owing to the complexity and wealth of information, many figures are provided for the aid of the reader, and two glossaries are provided to detail various acronyms.  

1.1 Surfaces

Society has benefitted greatly from scientific studies of the solid state.   The imposition of infinite three-dimensional periodicity on matter has allowed for experimental and theoretical simplicity when choosing to describe common materials.   A surface is, like defects and grain boundaries, a transgression from this ideal situation.   Hence, halving an infinite bulk to expose a surface creates a new interface, with often unique physical and chemical properties.   These new properties are exploited for their technological uses in metastable materials, magnetic multilayers, catalytic systems, corrosion studies, and semiconductor fabrication.   Several of the unique surface-phenomena are reconstruction, relaxation, adsorption, and epitaxy.   These phenomena are briefly described in the following.  

Reconstruction is the result of a process by which the surface periodicity becomes different from the bulk.   The changed periodicity of the surface is detectable by examining the LEED patterns of reconstructed surfaces, which will contain ``integral-order'' spots arising from the periodicity of the parallel bulk-planes and ``fractional-order'' spots arising from the different periodicity of the surface.   This phenomenon is best described by defining the relationship between the bulk-like and surface periodicity; there is a set of bulk-like surface unit-cell vectors projected on to the surface planes (a_b,b_b) and a set of surface unit-cell vectors (a_s,b_s) which define the two-dimensional periodicity of the surface.   If the two sets of vectors are the same then the surface is unreconstructed.   If they differ, however, so that a_s=Ma_b and b_s=Nb_b, then the surface is reconstructed and termed MxN.   When the surface unit-cell is rotated by angle phi from the bulk net, the reconstruction is called MxN-phi, see Figure 1.1.   For example, the clean Si{111} surface has a 7x7 reconstruction, with an area 49 times larger than the bulk-like surface unit-cell and the notation commonly used is Si{111}7x7.   Other reconstructions are, e.g., Au{110}2x1, InSb{111}2x2, and Ge{111}c(2x8) (where c means ``centered'').   There are many such reconstructions on both metal and semiconductor surfaces; it is possible for a surface to have several reconstructions existing simultaneously.   As an example, the surface of Si{111} can have concurrent 7x7, 5x5, 9x9, and √3x√3-30 reconstructions.  

Relaxation consists of rigid translations of the surface planes with respect to parallel bulk-layers.   The translations can be perpendicular and parallel to the plane of the surface, but within each atomic layer the translational symmetry of the bulk is maintained, see Figure 1.2. &nbps; Thus, the geometry of the LEED pattern produced by a relaxed surface is the same as that which would be produced by unrelaxed bulk-termination, a 1x1 pattern.   Relaxation can extend several layers into the crystal (hence the term multilayer relaxation) and can be very complex.   For example, Ag{001} shows no relaxation [2]; Pd{001} has a 3% expansion in the first interlayer-spacing and a 1% contraction in the second [3]; Tb(0001) has a relaxation of -3.9% and +1.4% in the first and second interlayer-spacings, respectively [4]; and Pb{110} has relaxations of -16.3%, +3.4%, and -4.0% in the first, second, and third interlayer-spacings, respectively [5].   In general, more-open surfaces display larger relaxations and close-packed surfaces barely relax [6].   LEED has been very successful in determining such relaxations.  

Adsorption is the binding of foreign atoms on a surface, whereupon changes can occur to the surface's physical, chemical, and electronic properties.   Adsorbed atoms can form a superstructure on top of the surface with a unit cell different from that of the clean surface.   The adsorption process can also induce the substrate atoms themselves to reconstruct or to relax.   For example, oxygen atoms adsorb on the Fe{001} surface and form a 1x1 unit-cell.   The adsorbate is in the four-fold symmetric hollow created by the Fe atoms.   Additionally, the first Fe interlayer-spacing is expanded by 8% as compared to a 2% contraction on the clean Fe{001} surface [7].   Hence, in order to understand these systems we must determine the amount of adsorbate (coverage), the adsorption site (model), and the locations of the adsorbate and substrate atoms in the surface region (structure) [8].

Epitaxial growth is the oriented growth of a crystalline material over another crystalline material [9].   For example, films of fcc Au{001} can be grown by the deposition of gold on fcc Ag{001} surfaces; the silver lattice-parameter (4.08 Ang.) is very close to the gold lattice-parameter (4.09 Ang.).   In some case the meshes may not match, e.g., Tb(0001) grown on W{110}, but incommensurate growth is still possible.   In other cases, the meshes may match by the expansion, dilation, and rotation of the meshes, as Pb{111} grown on Si{111}.   The success or failure of epitaxial growth depends highly upon the chosen material's chemical and physical properties, as well as the surface structure of the substrate.  

It has been known for some time that the bulk or surface doping of semiconductors alters the electronic properties of metal-semiconductor interfaces.   Metal atoms typically alter the semiconductor's intrinsic surface-states, pin the Fermi level, and cause adatom or vacancy surface-defects.   Hence, the structure of Si √3-X's and other superstructures on semiconductor surfaces are technologically important.   Schottky barriers, thin-film growth, and surface doping are three areas where surface structure is important.  

When a metal is placed upon a semiconductor a potential step, Schottky barrier, forms which allows for current to flow in only one direction [10].   The height of the barrier was thought to depend only upon the difference between the metal's work function and the semiconductor's electron affinity.   Studies show, however, that this linear behavior for barrier heights fails for most elements, and the barrier heights are relatively material independent.   The question is, `What pins the Fermi-level, thus fixing the barrier height?' Recent studies suggest two opposing explanations.   In one description, the band structure of the interface has gap states induced by the presence of the metal atoms, which pin the Fermi-level.   In the other description, the interface has defects (vacancies, adatoms, etc.... which, as evidenced in numerous STM experiments, are strongly localized, distort the topography, and create energetic states within the gap.   Hence, both explanations of Schottky barrier-heights rely on structural information.   The first explanation requires structural information to describe the band structure and the resultant states.   The second explanation requires structural information to describe the order and the possible types of disorder.   Therefore, the formation of Schottky barriers at these interfaces is strongly related to the detailed mechanism of submonolayer to multilayer metal-overlayer growth.  

1.2 Silicon Surfaces

Silicon crystallizes in the diamond structure, as do carbon and germanium, in which all atoms are tetrahedrally bonded to four other atoms.   The {111} planes of Si consist of double layers which are attached by bonds, one per atom, perpendicular to the layers.   Within the double layer a mesh of tetrahedral bonds, the remaining three per atom, rigidly connect atoms in 3-fold symmetric coordination.   A {111} surface is formed by breaking the bonds that connect two double-layers, see Figure 1.3.   There is one broken (unsatisfied or dangling) bond per atom, i.e., per bulk-like surface unit-cell in the top double-layer.   These dangling bonds are highly energetic and the clean surface seeks to rearrange in such a way as to reduce their number.  

Cleaved Si{111} surfaces display a 2x1 reconstruction, whose structure has been determined by a LEED intensity-analysis [11].   The reconstruction involves rearranging atoms from the hexagonal rings (normally six per ring) to form alternating rings with five and seven atoms.   This arrangement buckles the surface, and does not reduce the number of dangling bonds, but chains the top-layer atoms near to each other allowing a pi-bonding interaction.   Thus, the surface energy is lowered, but the number of atoms is conserved.  

Anneal of a Si{111}2x1 surface transforms it into a new and stable 7x7 phase [12].   The large number of atoms per cell, nominally 200, in the top two double-layers has made the determination of the 7x7 structure a daunting problem.   The Si{111}7x7 phase has been attacked by every surface tool, primarily because of silicon's significance technologically. LEED was the principal tool in revealing the existence of this superstructure before other probes tried to analyze it.   LEED could not be fully utilized, however, until enough model parameters were known or restricted so that a fully dynamical analysis [13] became computationally feasible.   This analysis relied on the in-plane structure given by TED [14], then both the optimal in-plane and out-plane atomic coordinates were determined.   It can not be overstated that while all surface science techniques tried to ``solve'' the 7x7, it was necessary for each probe to combine with dynamical LEED analysis to determine the full structure, described next.  

The Si{111}7x7 structure primarily involves removing 49 dangling-bonds by using dimers, adatoms, and stacking faults [15].   There are 18 adatoms, inside the unit-cell, which remove 36 dangling-bonds in the first layer, but add 12 into the adatom layer.   Thus, a net reduction of 24 is garnered.   A stacking fault (in one half of the 7x7 unit-cell) allows for the reduction of dangling bonds by grouping atoms close enough for dimerization to occur along the edges of the 7x7 unit-cell and across the short unit-cell diagonal.   Hence, dimerization further reduces the dangling-bond count by six.   The final structure has only 19 (49-24-6) dangling bonds which reduces the surface energy and stabilizes the surface more than the cleaved Si{111}2x1 surface.   Of course, the imposition of a stacking fault is highly energetic, which is why the surface can only be produced by high-temperature anneal.  

1.3 Si{111}√3x√3-30-X Surfaces

The Si{111} dangling-bonds may be satisfied by the addition or removal of bonding electrons in the surface region.   This is most easily accomplished by adsorbing foreign elements on a 2x1 or 7x7 surface, to which the unsatisfied Si atoms can bond.   The simplest such arrangement might give a Si{111}1x1-X surface unit-cell, if there is only one additional adsorbate atom (X) per bulk-like surface unit-cell.   However, most metals adsorbed on Si{111} and Ge{111}, at less than or approximately 1 monolayer (ml), will form some superstructure.   A clear example of this is demonstrated by Pedersen et.al.[16] with surface X-ray diffraction, SXD.   Submonolayer coverages of Sn on clean Ge{111}c(2x8) surfaces can induce 5x5, 7x7, or √3x√3-30 phases, which involve substantial rearrangements caused by electronic effects.   Such rearrangements are strongly dependent on adsorbate type, substrate temperature, coverage, anneal, and contamination parameters.  

The most common reconstruction or superstructure is the √3x√3-30 formed with one-third of an atomic layer (sometimes more) of metal atoms.   Atoms of group-III (B,Al,Ga,In), group-IV (Si,Ge,Sn,Pb), group-V (Sb,Bi), noble metals (Ag,Au), alkali metals (Li,Cs) and others (Ce,Mg) have been reported to form √3x√3-30-X structures on Si{111}, see Figure 1.4.   This list is not exclusive, most systems require heat treatments during or after deposition to form the √3's, and some of the same elements form √3's on Ge{111}.   The structures of these surfaces are not all known; some (B, Al, Ga, Sn, Sb, Bi, and Au) have been solved reliably by LEED and SXD, with the aid of other probes.  

Some elements (Pd, Fe, Y) form silicides when deposited upon Si{111} and heated [17,18,19].   These silicides can display √3x√3-30 structure, but such silicide structures are extended in depth and only coincidentally display ``√3x√3-30-like'' diffraction patterns.   In reality, these silicides may have a bulk-like surface unit-cell that is just larger and rotated.   Hence, silicide √3x√3-30's are quite different from adsorbed Si{111}√3x√3-30-X superstructures.  

The first goal in understanding Si{111}√3x√3-30-X adsorbed superstructures is to determine the adsorbate coverage.   Coverage, the amount of adsorbate atoms per substrate first-layer atoms, is usually referred to in terms of monolayers (ml).   Note, the Si{111}1x1 top-layer has a surface density of 7.83E+14 atoms/cm².   In the case of Si{111}√3-X structures, the surface unit-mesh is three times larger than the bulk-like unit-mesh.   The ideal surface may contain one, two, three, or four adsorbate atoms per √3x√3-30 unit-cell.   However, surface techniques for measuring coverage have never proven to be very accurate and are a source of controversy.   Additionally, superstructures may appear at coverages much less and much more than ideal, because they may not uniformly cover the surface.   In general we may feel safe in assuming one adsorbate per √3x√3-30 unit-cell if experimental studies indicate that the adsorbate coverage is between 0.1 and 0.5~ml.   Higher-coverage systems often are more difficult to understand and plausible structures may need 2/3, 1, 4/3 ml of adsorbates.   Higher coverages are implausible owing to close-packing constraints and number of available adsorption sites.  

The second goal in understanding Si{111}√3x√3-30-X systems is to determine the adsorbate's location.   The surface layer of Si{111} has several high-symmetry locations (sites) for atoms to chemisorb.   There are four primary-sites: T₁, T₄, H₃, and B₅; a definition of structure acronyms is provided in Glossary B.   The T₁ site is a 1-fold coordinated site on top of a first-layer atom, see Figure 1.5.   The H₃ site is a 3-fold coordinated site in the hollow created by first-, second-, and third-layer atoms above a fourth-layer atom, see Figure 1.6.   The T₄ site is a 4-fold coordinated site on top of a second-layer atom, see Figure 1.7.   The B₅ is a 5-fold coordinated site wherein the second-layer Si atom and the adsorbate are reversed with respect to the normal T₄-geometry, see Figure 1.8, i.e., the adsorbate is below the surface.   Only one site need be occupied per √3x√3-30 unit-cell to fulfill 1/3 ml coverage.   Modifications are allowable if symmetry and coverage restrictions are not violated.   The most common modifications are the use of several sites simultaneously and the trimerization of adsorbate atoms.   Trimerization is the symmetric distortion of three adsorbate surface-bonds which brings the triad closer together; trimerized-atom models are also called ``milk-stool'' models, because of the obvious resultant structure.   Such models will be discussed further in Chapters 4 and 5, concerning the Si{111}√3x√3-30-Mg and -Au surfaces.  

The third goal, in any structural study of Si{111}√3x√3-30-X systems, is to know what substrate reconstruction or relaxation appears as a result of the adsorption, because the change in substrate-atom locations relieves stresses produced by the new environment of the surface.   However, no single surface-technique can directly determine all of the structural changes induced by the adsorbate.   SEXAFS may be able to determine particular surface bond-lengths. STM may be able to determine the general model required, on the top layer.   LEED, SXD, and ion scattering may determine the structure by the comparison of experimental data with calculated spectra for proposed models.   Additionally, energy calculations may be made to determine which models contain the least stress, for which the three important factors in the creation or removal of stress in metal/semiconductor surfaces are: 1) adsorbate atomic-size, 2) adsorbate chemistry, i.e., bonding capabilities, and 3) adsorbate bonding-site [20].   As an example, a Keating-energy analysis (see Chapter 3) [21,22] may be used to show how the surface stabilizes by competition between the energy cost of bond compression or expansion and the ease of bond bending, with the introduction of either adsorbate or adatom rearrangements.   Total-energy calculations may also provide insight into how charge transfers between adsorbate and substrate atoms, inducing substrate relaxations and stability.   Hence, all of the above information and techniques are desirable in order to positively determine a particular Si{111}√3x√3-30-X surface structure.  

A final characteristic of most surface structures is simplicity.   There is usually a sensible chemical reason for a particular bonding configuration.   For example, all of the commonly accepted determinations of Si{111}√3x√3-30-X structures saturate the Si dangling-bonds, have 3-fold rotational symmetry, and keep mirror-plane symmetry.   Model structures that do not saturate all of the Si dangling-bonds have been proposed, but have not been proven.   Model structures that require five or six bonds per Si atom have been proposed, but have not been proven.   Model structures that rotate (twist) surface unit-meshes have been proposed, but they break mirror-symmetry and have not been proven. Models structures which place two or more adsorbates in different positions (with different coordinations) have been proposed, but only those producing close-packed overlayers have been proven.   Finally, Pauling's rules on bonding are very important for semiconductor surfaces.   We cannot expect two atoms with a sum of tetrahedral covalent-radii equal to 2.5 Ang. to have a bond length of 1.5 Ang.   Common sense, physical properties, chemical properties, and various surface techniques need to be coalesced in the determination of Si{111}√3x√3-30-X and other surface structures.