Aarhus University Seal / Aarhus Universitets segl

Ion scattering

Ion Scattering for surface analysis

Ion scattering is concerned with accelerating ions, causing them to impinge on a sample, and analysing the angle and energy distributions of the scattered ions. Ion scattering distinguishes itself by being a relatively simple, almost non-destructive, real-space technique, which can be applied for the analysis of sample composition and sample structure. The technique was developed for structural analysis in the late 1960’es and has matured to become an important research and analysis tool in many laboratories.

Traditionally, scientist have distinguished between three different energy regimes for ion scattering:

  • High-energy ion scattering (HEIS)
  • Medium-energy scattering (MEIS)
  • Low-energy ion scattering (LEIS)

HEIS, which also comprises RBS (Rutherford backscattering spectrometry), is normally carried out with H or He ions with energies from about 200 keV to 2 MeV. MEIS is based on scattering of protons of 50 – 200 keV. There is hardly any difference in the basic physics governing HEIS and MEIS. The scattering process is determined by the Coulomb potential, the yield is determined by the Rutherford cross-section, and the scattered particles suffer little neutralization along the exit path. On the other hand, LEIS or ion-scattering spectroscopy (ISS), is based on scattering of either inert-gas ions (He or Ne) or alkali ions (Li, Na or K) with energies of the order of 1 –10 keV. At this energy, there are strong screening effects on the Coulomb potential, and a significant neutralization of the scattered particles is observed. This neutralization is frequently dependent on both the path and matrix.

There are two major differences between MEIS/MEIS and LEIS - quantitative measurements of composition are easier in the high-energy regime than in the low-energy regime. HEIS and MEIS determine the position of surface atoms relative to the bulk-atom positions, while LEIS measurements reveal relative positions between surface atoms.

Composition analysis

Ion beam techniques are well suited for a quantitative analysis of the surface and near-surface composition of a sample because the energy spectrum of scattered particles shows mass dispersion, and the scattering process has a well-defined cross-section at high energies.

When scattered from a surface layer, the energy of the scattered particle E1 is proportional to the incident energy E0: E1 = K E0, where K (the kinematic factor) is determined by energy and momentum conservation and depends on the mass of the incoming particle, M1, the mass of the target atom, M2, and the scattering angle q. This leads to mass dispersion as illustrated in Figure1, which shows a backscattering spectrum from a Si sample covered with very thin layers of Cr and Au. The continuum below the Si edge is due to ions backscattered after penetration into the Si sample. The energy of such ions can be related to the scattering depth z.

Figure1. Rutherford backscattering spectrum (2 MeV He ions scattered 140 deg.) from a Si sample with thin surface layers of Cr (3 * 10^15 atoms/ cm^2) and Au (8 * 10^14 atoms/cm^2).

In the high-energy regime the scattering takes place on the unscreened Coulomb potential of the nucleus. Hence, the probability of scattering (expressed as a scattering cross section) is the well-known Rutherford cross section. The scattering yield is proportional to the number of incident ions (the cross section). The solid angle of the detector and the areal density of the relevant target atoms. The measured yields can, therefore, be converted into absolute densities of the different elements present at the surface.

In the low-energy regime, quantitative surface composition analysis is less straightforward. Screening of the Coulomb potential, path dependent neutralization and shadowing effects may complicate the analysis significantly. However, LEIS offers one advantage: an extreme surface sensitivity can be obtained with He+ ions because ions scattered subsurface will neutralize on their exit path. If only scattered ions are detected, the signal will originate exclusively from the surface monolayer of atoms.

Structure analysis

Suppose that a beam of ions is incident on a crystal along a major crystallographic axis. The closer the incidence is to the first atom, the larger the deflection will be, as illustrated in Figure2. This will result in a formation of a shadow cone behind the first atom. The radius of the shadow cone depends on the atomic numbers of the projectile and target atoms. It decreases roughly with the square root of the energy, i.e., low energies correspond to wide shadow cones.

Figure2. Formation of a shadow cone behind a surface atom for beam incidence along a row of atoms. Additional, deflections at the second atom have been neglected.

In a static representation the flux (inside the shadow cone) is zero. Finite vibrations of the crystal atoms tend to smear out the shadow cone, and the backscattering probability form the second and following atoms along the axis of incidence must be taken into account. By adding the backscattering probabilities from the outermost atom to a depth at which this probability becomes negligible, the total effective number of atoms, which contribute to backscattering from the surface region, can be determined.

Figure3. Backscattering spectrum for incidence of a 500 keV. He+ ion beam along a <100> direction in a W crystal.

Experimentally the high-energy end of the backscattering spectrum will exhibit a peak, which corresponds to backscattering from the surface atoms as outlined above, see Figure3. Information about surface structure is derived from an analysis of the energy and/or angular dependence of this surface peak.


There are numerous applications of ion scattering for surface structure analysis. Reconstructions and relaxations of surfaces involve displacements of the surface atoms away from their bulk-like, high symmetry positions. For a suitable choice of direction of ion incidence, the shadowing of deeper-lying atoms by the surface atoms becomes less effective. This leads to a measurable increase in surface peak yield and may induce an asymmetry in the surface peak yield versus tilt angle away from a high-symmetry direction.

See the example below for an illustration of how surface reconstruction may be detected.

Other applications include the determination of chemisorption positions of adsorbed atoms, studies of the initial stages of epitaxial growth, and investigations of the dynamic properties of surfaces, including enhanced surface vibrations and surface melting.


This example is concerned with detection of a surface reconstruction on the W(100) surface. Figure4 shows the experimental surface peak yield as a function of temperature for normal incidence, measured with 1 MeV He+ ions. Yields for the clean surface are shown as green circles. The red circles indicate measured surface peak yields when the surface has been exposed to hydrogen. It is evident that the adsorption of hydrogen below »320 K causes the surface peak yields to drop to a level consistent with the solid line, which is the result of a computer simulation for an unreconstructed surface (inset (a)). The increased yields measured for the clean surface, and at high temperature, are consistent with a model in which the surface atoms have adopted a zigzag structure with lateral displacements of 0.15 Å (inset (b) – the displacements are exaggerated). The lateral displacement causes a less effective shadowing along the direction of incidence and hence an increased surface peak yield. The reconstructed surface phase is denoted (Ö2 Ö2)R45o.

Figure4. Experimental and calculated surface peak yields for 1 MeV He+ ion scattering from a W(100) surface at normal incidence.


M. Aono and R. Souda, Quantitative surface atomic structure analysis by low-energy ion scattering spectroscopy (ISS). Japanese Journal of Applied Physics 24 (1985) 1249-1262.

L.C. Feldman and S.T. Picraux, In: Ion Beam Handbook for Materials Analysis, eds. J.W. Mayer and E. Rimini, Academic Press, New York (1977).

L.C. Feldman and J.W. Mayer, Fundamentals of Surface and Thin Film Analysis. North Holland, New York, (1986).

H. Niehus, W. Heiland and E. TagIauer, Low-energy ion scattering at surfaces. Surface Science Reports 17 (1993) 213-303.

I. Stensgaard, Surface studies with high-energy ion beams. Reports on Progress in Physics 55 (1992) 989-1033.

J.F. van der Veen, Ion beam crystallography of surfaces and interfaces. Surface Science Reports 5 (1985) 199-288.

J.F. van der Veen, B. Pluis B, A.W. Denier van der Gon, Surface melting. In: R. Vanselow and R. Howe, Chemistry and Physics of Solid Surfaces VII, Springer Series on Surface Science, chap. 16, p. 455 (1988). Springer-Verlag, Heidelberg.

D.P. Woodruff and T.A. Delchar, Modern techniques of surface science, Cambridge University Press, 1986.

John C. Vickerman, ed., Surface Analysis: The Principle Techniques, John Wiley & Sons, 1997.