Chapter 2 Photoemission
2.8 Low Energy Electron Diffraction
Low energy electron diffraction (LEED) is a standard technique to check the crys-tallography quality of a surface, prepared either as a clean surface, or in connection with the ordered adsorbate overlayers. The LEED pattern exhibits sharp spots with high contrast on low background intensity. Defects or crystallographic imperfections will broaden the spots and increase the background. Electrons with energy between 10 and 200 eV incident on the surface and the elastically backscattered electrons give rise to diffraction spots that are imaged on a phosphorous screen. According to the de Broglie relation, the wavelength of electrons with kinetic energy E is given by
λ = h
p = h
√2mE, (2.22)
typically in the range of angstroms, where h is Planck’s constant. For electrons with kinetic energy 20 eV the wavelength is about 2.7 ˚A. The low electron energy is suited for surface studies since the mean free path in the solid is short enough to give good surface sensitivity.
Figure 2.11: Schematic of a LEED optics for electron diffraction experiments [2].
The set up for LEED consists of an electron gun to produce an electron beam and the display system. A typical LEED system is exhibited in Fig. 2.11. Electrons emitted from a heated filament of the electron gun unit are accelerated by an elec-trostatic lens with apertures and incident normally on the sample. The low energy electrons are strongly backscattered by the electrons of the surface atoms.
Consider a one-dimensional chain of atoms with an electron beam incident nor-mally into it. The interference maxima are in the direction given by
a sin θ = nλ (2.23)
where a is the distance between the periodically arranged atoms, θ is the angle between normal and scattered electrons, and n is an integer number denoting the order of diffraction. This is a simple model for scattering of electrons by the atoms in the topmost layer of solid.
In the two-dimensional case, the condition for the occurrence of an elastic Bragg spot is given by
Kk = kk0 − kk = Gk (2.24)
where K is the scattering vector, k and k0 are the wave vector before and after
scattering, and Gk = hg1+ kg2 is the 2D surface reciprocal lattice. The wave vec-tor before scattering is zero since the the electron beam hits the surface at normal incidence. This simplifies the analysis because the diffraction maxima can be di-rectly associated with the reciprocal lattice and the diffraction pattern represents the symmetry of the surface. The diffraction pattern will be an image of the surface reciprocal lattice. The position of the intensity maxima on the fluorescent screen is described as
dh,k = Rsinθh,k = R
|k0|kk0 = R r
~2
2mE(hg1 + kg2), (2.25) where R is the distance from the screen to the surface. The distance between recip-rocal lattice points decreases with the increasing electron beam energy.
((a) 35eV)
(c) 55eV
(d) 75eV
(f) 105eV (b) 45eV (e) 90eV
Figure 2.12: LEED patterns for clean Ge(111) surface with different electron energy.
Chapter 3
Surface Systems and Thin Films
3.1 Crystal Lattices and Surface Lattices
Pb and Ag have a face-centered cubic (f cc) lattice. The spacing between crys-tal plane depends on both the plane orientation and the particular cryscrys-tal basis.
For the simple fcc crystal with the lattice constant a, the cube diagonal spans four evenly-spaced planes and so adjacent (111) planes are separated by a/√
3. The lat-tice constant of Pb and Ag are 4.95 ˚A and 4.09 ˚A, respectively. As it pertains to (111) film thickness, the spacing atomic planes between two adjacent is a/√
3. As for Ag(111) film, one monolayer is equal to 2.36 ˚A; for Pb(111) film, it is equal to 2.86 ˚A.
A basis is the configuration of the individual constituents within a unit cell.
The diamond structure is regarded as a face-centered cubic lattice with a two-point basis with one atom at the origin and the other located at the vector position R = (ˆx + ˆy + ˆz)/4. The semiconductor Ge has a diamond structure crystal with lattice constant a = 5.658 ˚A. Successive planes are unevenly spaced along the cube diagonal with alternate separations of √
3a/12 and √
3a/3 as shown as Fig. 3.1.
3.1.1 Reciprocal Space
The real fcc lattices transform into body-centered cubic (bcc) lattices in k-space.
The primitive unit cell about a reciprocal lattice point composed of a region of k-space that is closer to that point than to any other lattice point is termed the first
Figure 3.1: (a) The structure of diamond structure [8]. (b) Successive planes which are unevenly spaced along the cube diagonal produces a series of bilayer in the (111) orientation with alternate separations of√
3a/12 and√ 3a/4.
Brillouin zone. The First Brillouin zone for a bulk fcc crystal is shown in Fig. 3.2, with high symmetry points and directions labeled by letters.
The electronic structure of a periodic solid can be described with band structure.
The band calculation for Pb, Ag, and Ge are performed using the STATIC tight-binding code which is publicity available from the Naval Research laboratory and are presented in Fig. 3.3, where the electron energies as a function of wave vectors as are traversed along the high symmetry directions of the crystal Brillouin zone with the zero energy setting to the Fermi level.
3.1.2 Crystal Surfaces
In a real system, a crystal does not extend to infinity but rather possess a surface.
The surface of a crystal depends on the particular plane that terminates the bulk lattice. For the (111) surface, the surface exhibits six-fold symmetry, as the set of
< 2¯1¯1 > directions repeats at 60◦ intervals with the < 1¯11 > directions offset by 30◦.
The bulk termination of a crystal surfaces often produces an arrangement of atoms and bonds. To minimize the energy, the surface atoms configure into a stabi-lized reconstruction. The reconstruction is expressed in coordinates related to the periodicity of the underlying bulk terminated plane, specifically in reference to the
Figure 3.2: First Brillouin zone for a bulk f cc crystal [9].
1 × 1 unit surface cell. According to Wood there is a simple notation for reconstruc-tions in terms of the ratio of the length of the primitive translation vectors of the reconstruction and the unit cell. The notation N (n × m)Rθ◦ denotes a reconstruc-tion which has a periodicity of n bulk units by m bulk units rotated by θ degrees relative to the surface unit cell, where N = p or c for primitive or centrad cells, respectively. One example of reconstruction is the Ge(111)-c(2 × 8) surface.
The interruption of a crystal lattice by finite boundary condition also alters its reciprocal lattice and the related electronic structure. The termination produces a 2D surface Brillouin zone (SBZ). The relation between the surface Brillouin zone and the bulk Brillouin zone for the fcc lattices is illustrated in Fig. 3.4, where the (111) surface Brillouin zone is the projection of the bulk Brillouin zone in the direc-tion from Γ to L. The SBZ is a hexagon with the zone center denoted by ¯Γ, the zone boundary corner by ¯K, and the zone boundary edge by ¯M and ¯M0. Γ ¯K is parallel to < 1¯10 > and ¯Γ ¯M is parallel to < 2¯1¯1 >.
Reconstruction can also be formed by depositing a small amount of atoms to surface, e.g. Pb on Ge. The Pb atoms on Ge substrates can form different (√
3 ×
Figure 3.3: Band structures for Ag, Pb, and Ge.
Figure 3.4: Bulk and surface Brillouin zone for a fcc crystal [1].
√3)R30◦ reconstructions in the submonolayer regime. Early studies by M´etois and Le Lay using low energy electron diffraction, Auger electron spectroscopy, and scan-ning electron microscopy found that the system exhibited the Stranski-Krastanov growth mode at room temperature [10, 11]. This is confirmed by Ichikawa using reflection high-energy diffraction [12, 13]. M´etois and Le Lay found two different reconstructions with completion coverage of 1/3 and 1 monolayer (ML) in substrate units which were labeled by α and β phase, respectively. The coverage units used are referred to the Ge(111) unreconstructed substrate: 1 ML = 7.21 × 1014atom/cm2 = one-half of a Ge(111) double layer. Ichikawa found completion coverage of 2/3 and 4/3 ML for these phase. Later, more x-ray diffraction work and dynamical LEED I-V analysis found a completion coverage of 4/3 ML for β phase [14, 15]. In addition to the α and β phases, a completion coverage of 1/6 ML, labeled the γ phase, were found by T.-C. Chiang’s group [16].
The general consensus is that the α phase is composed of 1/3 ML Pb atoms occupying the T4 sites, as shown in Fig. 3.5 (a). T4 sites are threefold-symmetric sites located directly above an atom in the second layer. In the 4/3 ML β phase, 1/3 Pb atoms are in H3 sites and the remaining 1 ML Pb atoms are in bridge
T
1Figure 3.5: Structure models for the Pb/Ge(111) system. (a) α phase. (b) β phase [17].
sites, between T1 and T4 sites, as shown in Fig. 3.5 (b). This phase consists of a 1 percent compressed, close-packed Pb(111) layer rotated 30◦ with respect to the Ge substrate, namely, Pb< 11¯2 > k Ge< ¯110 >. The occupied bridge sites between T4 and T1 sites with a small displacement to the T1 sites are called off-centered (OC) T1 sites [18]. Based on the previous photoemission and STM studies [19], the γ phase consists of an equal number of Pb and Ge adatoms on the surface, forming a mosaic phase. The structure model is similar to α phase but half Pb atoms are replaced by Ge atoms.
3.2 Surface Preparation
3.2.1 Clean Substrate
Sputtering of noble gas ion with subsequent annealing is the most general cleaning technique for metal surfaces and elemental semiconductors like Si and Ge. Contam-inants are removed by bombardment with noble gas ions, and subsequent annealing can remove embedded and adsorbed noble gas so as to recover the surface crystal-lography. The ion current is produced by electron impact on noble gas atoms and accelerated by a voltage of few kilovolts towards the sample. The ion current, beam voltage, times of cycles, sputtering and annealing temperature all depend on the material and the thickness of the layer to remove. Sample heating can be done by
Figure 3.6: Photoemission spectroscopy of the clean Ge(111)-c(2 × 8) surface at normal emission.
resistance heating or electron bombardment heating (EBH).
A clean Ge(111)-c(2 × 8) surface was prepared by sputtering at a substrate tem-perature of 500◦C followed by annealing at 600◦C. This procedure generally yields very sharp c(2×8) LEED pattern. Another way to check the cleanness of the surface is by the photoemission spectrum. As shown in Fig. 3.6, two sharp surface states labeled by SS and SS0 are the indicator that the sample is clean [20, 21].
3.2.2 Film Growth
The deposited material can be developed into a film through layering or island coalescence. There are three growth modes: layer-by-layer, island, and layer-plus-island. The layer-by-layer (Frank-van der Merwe) growth mode occurs when the atoms of the evaporant are attracted strongly to the substrate than themselves.
When the atoms are bound to each other strongly, islands will be formed. The layer- plus-island ( Stranski-Krastanov ) mode arises when the formation of a wet-ting layer is subsequently followed by island growth.
Recently a two-step growth method for thin film was widely used : a film is in growth at very low temperature and then anneal to suitable temperature [22]. At
low temperature the atoms are randomly distributed on the substrate to form dis-order clusters. On annealing to a suitable temperature, the film will transform into an ordered, and atomically flat film.
Molecular beam epitaxy (MBE) is a standard technique for depositing a material onto a substrate. UHV EFM3 evaporator and K-cell evaporator are used in our chamber and beamline, respectively. In the EFM3, the evaporant is either evapo-rated from a rod or a crucible. This is achieved by electron bombardment heating.
The bombarding electron beam induces a temperature rise of the evaporant and causes evaporation. The evaporation cell is enclosed in a water-cooled copper cylin-der so that just a restricted region of the evaporant is heated. K-cell evaporator is equipped with a big crucible surrounded by a resistance heater.
The comparisons from two kinds of evaporators are described as following.
• The size of crucible for K-cell is larger than EFM3.
• The beam size of EFM3 is smaller.
• The depositing flux is more stable for EFM3.
• The preheating time for EFM3 is short.
3.2.3 Thickness of Thin Film
For higher coverage, one monolayer is defined as the spacing between crystal planes which depends on the plane orientation. For the simple f cc the adjacent (111) planes are separated by a/√
3, where a is the lattice constant. When considering surface coverage under one monolayer, the conversion factor depends on both the substrate and the adsorbed materials and is given by
Θ = ρ NA
WMδS t = C t (3.1)
where Θ is the thickness in monolayer, t is the thickness in angstrom, NA is Avo-gadro’s number, ρ and WM are the density and molecular weight of the evaporant, δS is the site density of the substrate surface, and C is the surface factor.
The deposition rate can be determined by using a quartz-crystal thickness moni-tor. Usually, there is 10 ∼ 20 percents error of calibrating the thickness by thickness monitor. The quantum well electronic structure is sensitive to the thickness to the degree of one atomic layer. Thus the quantum well states can be used to monitor the roughness of the film and determine the thickness [23].
3.3 Surface States
Surface is the termination of a bulk crystal. Surface atoms have fewer neighbors than bulk atoms and some of the bonds are broken at surface. Therefore, the elec-tric structure near the surface differs from bulk. Solving the Schrodinger equation for electrons roaming in the potential field which is periodic inside the crystal and constant in the vacuum region, the wave vector is then determined. When a crystal is limited by a surface, the restriction that k is real to ensure the wave function remains finite for an infinite crystal is no longer necessary. Bulk states are Bloch waves which oscillate in the solid and have a small tail into the vacuum. Addi-tional surface solutions become possible if the wave vectors are complex. The wave function is localized near the surface and the energy falls into the forbidden gap of the projection of the bulk band and this is known as surface state, as shown in Fig. 3.7. The energy and parallel momentum of the surface state lie in a gap in the projection of the bulk band structure onto the SBZ. However surface states can penetrate into a part of the surface Brillouin zone, where propagating bulk states exist. Those states degenerated with bulk states and mixed with them are known as surface resonances and will propagate deep into the bulk.
The existence of the surface states can be easily explained by the picture of tightly bound electrons. For the top most atoms, they have fewer neighbors and their wave functions have less overlap with wave functions of neighboring atoms. The splitting and shifting of their energy levels are smaller than those in the bulk, as shown in Fig. 3.8.
(a)
(b)
Figure 3.7: Wave function for (a) a standing Bloch wave and (b) a surface state [2].
Figure 3.8: Surface states have acceptor-type or donor-type charging character [2].
The higher lying surface state has conduction band character whereas the lower level which is split off from the valence band of the semiconductor is more valence band like. The charging character of the surface states also reflects the correspond-ing bulk states. A semiconductor is neutral if all conduction band states are empty and all valence states are occupied. So the conduction band states carry a neg-ative charge if they are occupied by an electron; the valence band states carry a positive charge when they are unoccupied. Surface states derived from the conduc-tion band have the same characteristics , called acceptor-type states; surface states derived from the valence band have the same characteristic, called donor-type states.
Surface states can also be produced by adsorbed atoms which cause changes in the chemical bonds near the surface and affect the distribution of the intrinsic sur-face states. In addition, a new sursur-face state can be formed by the bonding and antibonding orbitals between the adsorbed atoms and the surface. They form 2D lattices with translational symmetry along the surface and thus form the 2D band structures.
3.4 Quantum Well States
When electron states within the film overlap with the state in the substrate, no confinement will occur. However, if the electrons in film fall into the a band gap of the substrate, the electrons will be confined like particles-in-a-box, called quantum well states.. The width of the box is the thickness of the film. The electrons are confined between the film-vacuum and the film-substrate potential barriers. Con-finement can be found in both metal-on-metal or metal-on-semiconductor system.
For the (111) thin films, the relevant direction in real space is the [111] direction, which is the surface normal for both the substrate and the film, corresponding to the ΓL direction in the k -space. Pb is a metal that displays a Fermi level band crossing.
Ge is a semiconductor with a band gap in which the Fermi level falls. A comparison of the two band structures in Fig. 3.9 shows that the electrons with energy near
Figure 3.9: Comparison of the ΓL band structures in the [111] direction.
the Fermi level in Pb have no corresponding states in Ge above the valence band maximum (VBM) to which they can transit and thus they are confined in the film.
Electrons in Pb with energy larger than VBM have corresponding states in Ge and they are not totally confined in the thin film. This is called quantum well resonance (QWR). For Ag/Ge(111) system, the metal electrons are not totally confined. All the states we observed at the zone center are quantum well resonance.
The electron state are only quantized in the direction perpendicular to the film, while the lateral expanse of the film is not restricted. As a confined electron traverses in the film, its wave function accumulates phase not only in the transit but also when it is reflected from the vacuum and substrate interface. The total phase accumulates to an integer multiple of 2π after the quantum well electrons make a round trip between two interfaces to form a standing wave like wave function. The quantum
well state energy level can be thus determined by the Bohr-Sommerfeld quantization rule, or phase accumulation model:
2k⊥(E)N t + φi(E) + φs(E) = 2nπ (3.2) where k⊥ is the electron wave vector perpendicular to the interface, E is the energy of the state, N is the number of the monolayer, t is the monolayer thickness, φi and φs are the energy dependent phase shift at the surface and interface, respectively;
and n is a quantum number.
3.4.1 Quantum Number
In (3.2), one can choose to measure k⊥ from the zone center (Γ point) or the zone boundary at the L point. The quantum numbers depend on where the origin is chosen. Conventionally the zone boundary is chosen as the origin. At the normal emission the wave vector is limited in the direction perpendicular to the surface while the parallel component of the wave vector is zero. The total phase in a round trip perpendicular to the surface is equal to an integer times 2π. The value of k⊥
which satisfies (3.2) can be rewritten as k⊥= nπ
N t − φ
2N t (3.3)
where φ = φs+ φi is the total phase shift.
A film is invariant under a translation of t in the direction perpendicular to the surface, where t is the monolayer thickness. In the reciprocal lattice, the distance between the zone center and the zone boundary is equal to half of the reciprocal vector ~G = 2πt = ∆kΓLΓ. The distance from the zone center to the zone boundary at L is π/t. When the phase shift is zero, the wave vectors satisfied (3.3) divide the region between the Γ and L point into N parts. For this simple case the allowed k⊥
values are the integer times π/N t. Thus the quantum number is labeled from 0 to N for N monolayers thin film. The wave vector corresponding to state n = 0 is at the zone center and the state n = N is at the zone boundary. This should be the
values are the integer times π/N t. Thus the quantum number is labeled from 0 to N for N monolayers thin film. The wave vector corresponding to state n = 0 is at the zone center and the state n = N is at the zone boundary. This should be the