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information is wanted and is practicable to obtain. Some of the examples given in this section are close to the current technical limits. Rather than laboring the virtues of STM, STS, AFM, etc., in this and other respects, speci®c results are used to illustrate points being made as they arise in the text. To get started in this area, one can consult the references given in section 3.1.3 and the web-based resources listed in Appendix D.
Further reading for chapter 3
Briggs, D. & M.P. Seah (1990) Practical Surface Analysis, vols. I and II (John Wiley). Buseck, P., J.M. Cowley & L. Eyring (Eds.) (1988) High Resolution Transmission Electron Microscopy and Associated Techniques (Oxford University Press) especially
chapter 13: Surfaces by K. Yagi.
Chen, C.J. (1993) Introduction to Scanning Tunneling Microscopy (Oxford University Press), especially chapter 1 and the photographic plates which precede this chapter.
Clarke, L.J. (1985) Surface Crystallography: an Introduction to Low Energy Electron DiVraction (John Wiley).
Feldman, L.C. & J.W. Mayer (1986) Fundamentals of Surface and Thin Film Analysis
(North-Holland).
Lüth, H. (1993/5) Surfaces and Interfaces of Solid Materials (2nd/3rd Edns, Springer), panels 2, 3 9 and 11, and chapter 6.
Moore, J.H., C.C. Davis & M.A. Coplan (1989) Building Scienti®c Apparatus (2nd Edn, Addison-Wesley) chapter 5.
Prutton, M. (1994) Introduction to Surface Physics (Oxford University Press), chapters 2 and 3.
Rivière, J.C. (1990) Surface Analytical Techniques (Oxford University Press). Stroscio, J. & E. Kaiser (Eds.) (1993) Scanning Tunneling Microscopy (Methods of
Experimental Physics, Academic), volume 27.
Smith, G.C. (1994) Surface Analysis by Electron Spectroscopy (Plenum).
Walls, J.M. (Ed.) (1990) Methods of Surface Analysis (Cambridge University Press). Wiesendanger, R. (1994) Scanning Probe Microscopy and Spectroscopy (Cambridge University Press) especially chapters 4 and 5.
WoodruV, D.P. & T.A. Delchar (1986, 1994) Modern Techniques of Surface Science (Cambridge University Press) especially chapters 2 and 3.
Problems, talks and projects for chapter 3
These problems, talks and projects are to test and explore ideas about surface techniques and surface electronics.
Problem 3.1. Some questions on surface techniques
Give a short description of the following points in relation to surface techniques, including some examples.
1063 Electron-based techniques
(a)Explain why we say that we have conservation of k//, but not of k', in surface scattering experiments.
(b)Explain why surface X-ray diVraction can be understood quantitatively in terms of `kinematic' scattering, whereas the various forms of electron diVraction require a `dynamic' theory.
(c)Explain why the lineshape in UPS is said to re¯ect the `valence band density of states' whereas the AES lineshape may depend on a `self-convolution of the VB DOS'.
(d)Explain the experimental setup, and energy resolution, needed to observe surface phonons. Comment on the relative energy resolution required for inelastic photon (Raman), electron (HREELS) and helium atom scattering.
Problem 3.2. The role of inelastic scattering in LEED
A quasi-kinematic model of LEED is possible based on the following assumptions. The inner potential of the crystal, is V0,10V, which increases the wavevector in the crystal over that in free space and refracts the beam at the surface. The attenuation of the incident beam amplitude (and the back-diVracted beams) is exponential with a short mean free path l, which is inversely proportional to the imaginary potential V0i ,3±5V. A single backscattering event happens at a given atom at depth z, and has scattering factor f (or equivalently t, the t-matrix) which is a function of the beam energy E and the scattering angle u.
Assuming that the surface plane is (001), do the following.
(a)Draw the LEED geometry and Ewald sphere, with a plane wave input beam not necessarily perpendicular to the surface.
(b)Write down an expression for the scattered amplitude from a crystal into the (hk) reciprocal lattice rod, where the spacings between layers parallel to the surface are not necessarily equal to the bulk spacing.
(c)Work out the scattered intensity distribution I(V) along the (hk) rod for the case of normal incidence, where the spacings are equal to the bulk spacing, and draw the intensity pro®le.
(d)Show that the peak positions and spacings can be used to calculate the c-plane
spacing, and V0 if f is real. Show that the width of the peaks is inversely related to l, and hence directly to V0i.
Problem 3.3. The importance of a high SNR in AES
One of the main problems in Auger electron spectroscopy is that the signal rides on a non-negligible background, and that the signal to noise ratio (SNR) and the peak/background ratio (P/B or PBR) can be small. This leads to long data collection times and/or noisy signals, which are especially troublesome for imaging. The schemes discussed in section 3.5 are attempts to approximate the desired ratio signal with a simple algorithm which can be implemented using digital data collection and process-
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ing. Assuming that the energy channels A, B and C are equally spaced, with A over the peak, B just above the peak and C an equal distance to higher energy:
(a)Show that (A22B1C)/(2B2C) is the simplest linear measure of the P/B ratio, and that this reduces to (A2B)/B if the background spectrum has zero slope.
(b)Assuming that the measured counts are limited by electron shot noise, ®nd the SNR of the peak height (A22B1C) and of the peak to background ratio, explaining your reasons carefully.
(c)Compare the SNR of the logarithmic measure (A2B)/(A1B) with that of the linear measure, and convince yourself that it is typically higher for comparable values of the numbers of counts.
Student talks related to chapter 3 have included the following
In each case a page of suggestions for narrowing the topic, and suggested references have been given out. The aim is to give the main features of the techniques clearly, with adequate visual aids, in about 20 minutes, taking questions from the class.
1.A comparison of XPS (X-ray photoelectron spectroscopy) and AES.
2.Angular resolved AES and/or X-ray Photoelectron diVraction (XPD).
3.ARUPS and inverse photoemission.
4.Electron stimulated desorption (ESD) and the angular distribution of ions (ESDIAD).
5.High energy ion, or Rutherford back scattering (HEIS-RBS) or medium energy (MEIS).
6.Low energy ion scattering and ICISS.
7.Scanning tuneling spectroscopy (STS) and microscopy (STM) in UHV.
8.STM in solution.
9.Field ion microscopy (FIM) studies of atomic mobility on surfaces.
10.SIMS and SNMS (sputtered neutral mass spectroscopy).
11.Secondary electron spectroscopy and microscopy in UHV.
12.Low energy and photo-electron microscopy (LEEM/PEEM).
13.RHEED and REM.
14.Optical techniques for monitoring semiconductor crystal growth.
15.Surface magneto-optic Kerr eVect (SMOKE).
16.SEM with polarization analysis (SEMPA).
17.Film thickness measurements.
18.Nanoindentation.
19.Reactive ion etching.
4 Surface processes in adsorption
4.1Chemiand physisorption
A qualitative distinction is usually made between chemisorption and physisorption, in terms of the relative binding strengths and mechanisms. In chemisorption, a strong `chemical bond' is formed between the adsorbate atom or molecule and the substrate.
In this case, the adsorption energy, Ea, of the adatom is likely to be a good fraction of the sublimation energy of the substrate, and it could be more. For example, in chapter
1, problem 1.2(a), we found that in a nearest neighbor pair bond model, Ea52 eV for an adatom on an f.c.c. (100) surface when the sublimation energy L053 eV. In that case the atoms of the substrate and the `adsorbate' were the same, but the calculation of the
adsorption stay time, ta, would have been valid if they had been diVerent. Energies of 1±10 eV/atom are typical of chemisorption.
Physisorption is weaker, and no chemical interaction in the usual sense is present. But if there were no attractive interaction, then the atom would not stay on the surface for any measurable time ± it would simply bounce back into the vapor. In physisorption, the energy of interaction is largely due to the (physical) van der Waals force. This force arises from ¯uctuating dipole (and higher order) moments on the interacting adsorbate and substrate, and is present between closed-shell systems. Typical systems
are rare gases or small molecules on layer compounds or metals, with experiments performed below room temperature. Physisorption energies are ,50±500 meV/atom; as they are small, they can be expressed in kelvin per atom, via 1 eV; 11604 K, omitting
Boltzmann's constant in the corresponding equations. These energies are comparable to the sublimation energies of rare gas solids, as given in section 1.3, table 1.1.
Adsorption of reactive molecules may proceed in two stages, acting either in series or as alternatives. A ®rst, precursor, stage has all the characteristics of physisorption, but the resulting state is metastable. In this state the molecule may reevaporate, or it may stay on the surface long enough to transform irreversibly into a chemisorbed state. This second stage is rather dramatic, usually resulting in splitting the molecule and adsorbing the individual atoms: dissociative chemisorption. The adsorption energies for the precursor phase are similar to physisorption of rare gases, but may contain additional contributions from the dipole, quadrupole, and higher moments, and from the anisotropic shape and polarizability of the molecules. The dissociation stage can be explosive
± literally. The heat of adsorption is given up suddenly, and can be imparted to the
resulting adatoms. Examples are O2/Al(111) and O2/Pt(111), which will be discussed brie¯y in section 4.5. O2 and N2 can be condensed at low temperatures as (long-lived)
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