Chapter 2 Photoemission
2.5 Ultra High Vacuum
L(E0, Γ)G(E − E0, σ)dE0 (2.17)
2.5 Ultra High Vacuum
From the experimental viewpoint, the preparation of a well-defined and clean surface, on which surface studies are usually performed, became possible only after the development of ultra high vacuum (UHV) techniques. UHV conditions are those with pressures below 10−9 torr. With a sticking coefficient S = 1, which means that every molecule or atom impinging on a surface sticks there, one needs an exposure of approximately 10−6 torr for one second to obtain a coverage of 1 monolayer on a surface. At a pressure of 10−10 torr it takes about 10000 seconds until a coverage of one monolayer is achieved. Fortunately, for many materials the sticking coefficients are much smaller than one. The preparation of well-defined surfaces with negligible contamination requires ambient pressures lower than 10−10 torr so that samples re-main uncontaminated for several hours.
The process of lowering the pressure of a chamber from atmospheric pressure, 760 torr, down to the UHV regime requires different pumping mechanisms. A turbo-molecular pump starting in the 10−3 torr range which are established by a roughing pump is used to lower the pressure in the chamber down to 10−7 torr. Then a ion pump is turn on to pump down the the pressure to 10−9 torr. The pressure could not be lower since some molecules, mainly water molecules, adsorbed in the inner wall of the chamber would desorb slowly. To remove the molecules the process of bake is necessary.
The chamber is warned by several heating tapes and then covered with aluminum foils to achieve uniform temperature. When the current is applied to the heating tapes, the chamber will be heated. Note that the baking temperature should be
achieved within half a day and each component has different limited baking tem-perature: 200◦ for ion pump, 180◦ for energy analyzer, and 150◦ for evaporator.
The baking temperature of the main chamber is keep at 150◦ and other component are keep at different temperatures to avoid possible damage to the accessories and instruments. Usually it takes two days to bake in our chamber to achieve a UHV condition. The degassing procedure should be carried out after bakeout. The cham-ber will be cooled after half a day and the pressure will be down to 5 × 10−10 torr or better.
2.6 Sources of Photons
Photoemission requires a high-intensity and monochromatic photon source. He-lium lamps, laser system, X-ray tubes or synchrotron are usually used today, while helium lamps and laser systems are both lab-based source. The energy emitted by Helium lamp are at 21.2 and 40.8 eV. A number of groups are developing laser sys-tems for low photon energy either tunable or not [4]. Yet X-ray tubes produce high energy photons , on the order of 1500 eV, which are used for core level spectroscopy for determining the composition of a material. They are not well suited to valence band studies. Synchrotron source is bright and photon energy is tunable, but the disadvantage is the limited beamtime. In our experiment, the sources are basically provided by Helium lamps and synchrotron radiations which are introduced by the following sections.
2.6.1 Helium Lamp
The operation of the high intensity VUV Source HIS 13 lamp is based on the principle of a cold cathode capillary discharge. When the potential applied between the ends of an insulating tube filled with gas is large enough, spontaneous breaking through occurs leading to a continuous discharge. The ignition potential is larger than the operating potential to maintain a continuous discharge.
The nature and intensity are strongly dependent on gas pressure and discharge current [3]. The optimum operational pressure of the lamps for the desired
reso-Figure 2.5: Comparing to the photon energy of He I α, the photoemission intensity induced by photon energy He II is weak. Choosing the region that no electron state induced by He I, as shown in the bottom picture, the electron excited by He II is observed at 18.83 eV..
nance line has to be determined experimentally. Studies by G. Sch¨onhense and U.
Heinzmann showed that the photon flux of the windowless lamp, which is differen-tially pumped, is dependent on the discharge current and operation pressure. For the resonance lines of the neutral atoms, such as He I, Ne I, Ar I, Kr I, Xe I, the optimum operation pressure shows a flat maximum. The photon flux vs. discharge current shows a saturation characteristic. For the resonance lines of the ionized gases, such as He II, Ne II, Ar II, Kr II, Xe II, the photon flux is proportional to the discharge current. Photons yield strongly increases with decreasing pressure.
In this experiment, the He gas is used to provide two different photon energies, He I and He II. The photon energy provide by He gases is shown in table 2.1. The main photon energy provided by He is 21.22 eV, He I α. Other photon energies exist but have weak intensity.
The photon energy of He II is also adopted in many experiments. As shown in
Table 2.1: Positions and intensities of He cold cathode discharge lines.
Fig. 2.5, the intensity of the kinetic energy below 17.3eV caused by the He I α is stronger. Crossing the Fermi edge, some signals emerge. At the kinetic energy 18.83 eV, a small peak appears which is corresponding to one of the Pb 5d5/2 core level. The work function of Pb(111) were measured to be 3.8 eV [5]. By (2.6), the kinetic energy of electron emission from 5d5/2 core level, with binding energies 17.9 and 20.6 eV [5], is equal to 40.81 − 3.8 − 17.9 = 19.11 and 40.81 − 3.8 − 20.6 = 16.41 eV , respectively. Which is consistent with our experiment data, a peak position at 18.83 eV. Yet another core level with binding energy 20.6 eV is not observed since its intensity is covered by the signal caused by He I. If the observed kinetic energy is lager than the Fermi energy corresponding to He I, the photon energy of He II is also another choice to use.
2.6.2 Synchrotron Radiation
Some of our data were taken at BL21B1 in National Synchrotron Radiation Re-search Center (NSRRC). This beamline is an undulator beamline with high flux and high resolution. Synchrotron radiation is light emitted by the electrons undergoing centripetal acceleration according to EM mechanics. Synchrotron facilities feature a storage ring where the electrons is bent into a quasi-circular trajectory by magnetic fields. When electrons are accelerated to travel a nonlinear course, they emit elec-tromagnetic radiation. Under non-relativistic conditions, the radiation will adhere to a dipole distribution around the electron, as shown in Fig. 2.6. Whenever elec-trons moving close to the speed of light, β ∼ 1, are deflected by a magnetic field, the radiation converges into a thin beam of radiation tangentially from their path
Figure 2.6: The angular distribution of the produced by electrons undergoing synchrotron radiation emission for non-relativistic and relativistic case. The radiation will adhere to a dipole distribution around the electron in the non-relativistic case; the photon is peaked sharply in the direction tangent to the circular path of the electrons in the relativistic case [1].
due to Lorentz transformation (effect).
In NSRRC, the electrons are first accelerated in the linear accelerator (LINAC) that boosts the electrons up to an energy of 50 MeV, and the booster ring then ac-celerates the electrons to an energy of 1.5 GeV. The electrons traveling at 99.999995 percent of the speed of light are then guided through a 70-meter-long transport line and into the storage ring, where electrons with an energy of 1.5 GeV circulate in an ultra-high-vacuum chamber for several hours. A series of magnets situated around the ring steer the electrons along circular arcs, and synchrotron radiation is contin-uously emitted tangentially from the arcs. The emitted light is channeled by the insertion devices through beamlines to the experimental stations where experiments are conducted [6].
Insertion devices (wigglers and undulators) comprising rows of magnets with al-ternating polarity produce brighter synchrotron radiation by causing the beam to oscillate rapidly. Wigglers cause multiple direction changes in the electron beam that generate extremely bright white light with short wavelengths; undulators cause periodic changes in the electron beam’s direction that produce ultra-brilliant,
single-wavelength radiation from the resulting interference patterns.
2.7 Energy Analyzer
2.7.1 Electron Detector
SCIENTA 200 is equipped at BL21B1 and SCIENTA R3000 is equipped in our chamber. The main difference is the energy resolution due to the radius of the hemi-spherical analyzer and the function of them is the same. Only SCIENTA R3000 is introduced since it is similar to SCIENTA 200 and the energy resolution is test in our chamber.
SCIENTA R3000 is a high-resolution energy analyzer for photoemission spec-troscopy [7]. The schematic overview of the system parts are shown in Fig. 2.7.
The electrical potentials applied to the SCIENTA R3000 may reach up to 1.5 kV by the high voltage unit. The personal computer provides instrument control, read-out and data management. The electron spectrometer consists of three major parts:
electron lens, hemispherical analyzer and detector assembly with a CCD camera.
The multi-element electron lens act as a focusing lens, which were used to collect and transfer electrons from sample to the slit of the hemispherical analyzer; that matches the initial kinetic energy (Ekinectic) of the emission electrons to the fixed pass energy (Epass) as the electrons start to enter the hemispherical analyzer. That is,
Epass = Ekinetic− eVretarding (2.18)
where Vretarding is the retarding potential provided by the electric lens to slow down the electron. Electron trajectories are bent in a 180◦ radial electrostatic field in the analyzer with positive charged inner sphere and negative charged outer sphere, as shown as Fig. 2.8.
The pass energy is the kinetic energy of the electron at the center of the detected energy band when it passes through the hemispherical analyzer which also relies on the voltage difference between the inner and outer spheres. The relationship can
Figure 2.7: The schematic overview of the SCIENTA R3000 system parts [7].
Figure 2.8: The schematic overview of the hemispherical analyzer [7].
describe as
While the analyzer electric field ends at a field termination mesh, the Mulit-Channel Plates (MCP) pair multiplies each incoming electron about a million times.
This electron pulse is accelerated to the phosphorous screen producing a light flash detectable by the FireWire CCD camera. The detector area registered by the CCD camera is a square of over 600 simultaneous energy channels and over 400 channels in the spatial or angular direction; that is, the MCP/CCD camera detection system is a 2-D detection system with energy in one direction and spatial or angular infor-mation in the other direction. It can determine their energy as well as the sample image or the electron emission angle simultaneously when the lens system were op-erated in transmission or angular multiplexing imaging modes.
In the transmission mode, the detector records the energy of all the electrons in a large angular range emitted from each location at a continuous range of positions on sample. Angular multiplexing mode is used for ARPES measurements, which efficiently probe the band structure of solids. In the angular mode, electrons emit-ted at identical angles are bind together, regardless of the position on the sample of emission, and the angular resolution will vary with the angular mode chosen.
The energy resolution of the electron spectrometer varies by the entrance slit size, shape, and the pass energy. Curved slits normally improve the energy resolution and straight slits achieve a higher count rate. The theoretical energy resolution is approximated with
∆E ≈ sEpass
2R (2.20)
where s is the slit width and R is the analyzer radius. To achieve the best resolution a narrow curved slit, small pass energy and large analyzer radius should be used, whereas they give a lower intensity. With the MCP/CCD camera detection system the intensity scales approximately aspEpass. As a rule of thumb high pass energy and small slit gives the best count rate.
Sample Analyzer
Figure 2.9: The sample and analyzer are grounded to ensure the kinetic energy Ekin measured in analyzer is the same as measured in sample.
The actual photoemission measurement is performed in an energy analyzer in-stead of vacuum. The kinetic energy E measured in vacuum and Ekin measured in an analyzer are not equal for the work function of sample and analyzer are different.
In experiments, sample and analyzer are grounded to align their Fermi level to en-sure that the binding energy ~w − (Ekin+ φ0) in analyzer is the same as ~w − (E + φ) in sample, shown in Fig. 2.9.
2.7.2 Resolution
The total energy resolution derives from the energy resolutions of the energy analyzer and of the incident photon beam, given by
∆E = q
∆Ephotons2 + ∆Eanalyzer2 . (2.21) The energy resolution of analyzer is related to the pass energy and slit setting. As shown in (2.20), lower pass energy and narrow slit increase the energy resolution.
SCIENTA R3000 is equipped with six slits, three curves and three straight slits.
The table 2.2 shows the six different sets of slit-aperture pairs.
The resolution function can be measured at low temperatures. Fig. 2.10 gives a photoemission spectrum for the energy region around the Fermi energy. This figure depicts the spectrum measured for Mo and gives an analysis of the data by a Fermi
Table 2.2: Six modes of slit.
Mode Width (mm) Length (mm) Shape
1 0.2 20 Straight
Table 2.3: The energy resolution with different modes of slit and pass energy.
Mode Pass energy (eV) ∆E (meV)
1 2 95.6
function convoluted with a Gaussian function. The solid line is the Fermi function at 120 K. The dashed line convoluted the Fermi function with a Gaussian of width 95.6 meV (FWHM), with pass energy 5 and slit mode 1. The full width at half max-imum (FWHM) of the Gaussian function gives the energy resolution. For different pass energies and slits, ∆E are shown in table 2.3. It is not obvious that the lower pass energy and narrow slit increase the energy resolution. This may be caused by the large beam size.
Figure 2.10: Energy distribution around Fermi level in photoemission spectrum from Mo at 120 K with photon energy 21.2 eV. The energy resolution is obtained by convoluting Fermi function (dashed line) with a Gaussian function of width 95.6 meV
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
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