Elemental composition and two-body collision model

Due to the energy range typically used in ion scattering experiments (> 500 eV), effects of thermal vibrations, phonon oscillations, and interatomic binding are ignored since they are far below this range (~a few eV), and the interaction of particle and surface may be thought of as a classical two-body elastic collision problem. Measuring the energy of ions scattered in this type of interaction can be used to determine the elemental composition of a surface, as is shown in the following:

Two-body elastic collisions are governed by the concepts of energy and momentum conservation. Consider a particle with mass m_x, velocity v₀, and energy given as ${\displaystyle E_{0}={\tfrac {1}{2}}m_{x}v_{0}^{2}\,\!}$ impacting another particle at rest with mass m_y. The energies of the particles after collision are ${\displaystyle E_{1}={\tfrac {1}{2}}m_{x}v_{1}^{2}\,\!}$ and ${\displaystyle E_{2}={\tfrac {1}{2}}m_{y}v_{2}^{2}\,\!}$ where ${\displaystyle E_{0}=E_{1}+E_{2}\,\!}$ and thus ${\displaystyle {\tfrac {1}{2}}m_{x}v_{0}^{2}={\tfrac {1}{2}}m_{x}v_{1}^{2}+{\tfrac {1}{2}}m_{y}v_{2}^{2}\,\!}$. Additionally, we know ${\displaystyle m_{x}v_{0}=m_{x}v_{1}\cos \theta _{1}+m_{y}v_{2}\cos \theta _{2}\,\!}$. Using trigonometry we are able to determine

${\displaystyle E_{1}=E_{0}\left({\frac {m_{x}\cos \theta _{1}\pm {\sqrt {m_{y}^{2}-m_{x}^{2}\sin ^{2}\theta _{1}}}}{m_{x}+m_{y}}}\right)^{2}}$

Similarly, we know

${\displaystyle E_{2}=E_{0}\left({\frac {4m_{x}m_{y}cos^{2}(\theta _{1})}{(m_{x}+m_{y})^{2}}}\right)}$

In a well-controlled experiment the energy and mass of the primary ions (E₀ and m_x, respectively) and the scattering or recoiling geometries are all known, so determination of surface elemental composition is given by the correlation between E₁ or E₂ and m_y. Higher energy scattering peaks correspond to heavier atoms and lower energy peaks correspond to lighter atoms.

Getting quantitative

While obtaining qualitative information about the elemental composition of a surface is relatively straightforward, it is necessary to understand the statistical cross-section of interaction between ion and surface atoms in order to obtain quantitative information. Stated another way, it is easy to find out if a particular species is present, but much more difficult to determine how much of this species is there.

The two-body collision model fails to give quantitative results as it ignores the contributions of coulomb repulsion as well as the more complicated effects of charge screening by electrons. This is generally less of a problem in MEIS and RBS experiments but presents issues in LEIS. Coulomb repulsion occurs between positively charged primary ions and the nuclei of surface atoms. The interaction potential is given as:

${\displaystyle V(r)={\frac {Z_{1}Z_{2}e^{2}}{r}}\phi (r)\qquad (1)}$

Where ${\displaystyle Z_{1}\,\!}$ and ${\displaystyle Z_{2}\,\!}$ are the atomic numbers of the primary ion and surface atom, respectively, ${\displaystyle e\,\!}$ is the elementary charge, ${\displaystyle r\,\!}$ is the interatomic distance, and ${\displaystyle \phi (r)\,\!}$ is the screening function. ${\displaystyle \phi (r)\,\!}$ accounts for the interference of the electrons orbiting each nucleus. In the case of MEIS and RBS, this potential can be used to calculate the Rutherford scattering cross section (see Rutherford scattering) ${\displaystyle {\tfrac {d\sigma }{d\Omega }}}$:

Repulsive scattering by a point particle.

${\displaystyle {\frac {d\sigma }{d\Omega }}=\left({\frac {Z_{1}Z_{2}e^{2}}{4E_{0}}}\right)^{2}{\frac {1}{\sin ^{4}\left({\frac {\theta }{2}}\right)}}\qquad (2)}$

As shown at right, ${\displaystyle d\sigma \,\!}$ represents a finite region for an incoming particle, while ${\displaystyle d\Omega \,\!}$ represents the solid scattering angle after the scattering event. However, for LEIS ${\displaystyle \phi (r)\,\!}$ is typically unknown which prevents such a clean analysis. Additionally, when using noble gas ion beams there is a high probability of neutralization on impact (which has strong angular dependence) due to the strong desire of these ions to be in a neutral, closed shell state. This results in poor secondary ion flux. See AISS and TOF-SARS below for approaches to avoiding this problem.

Shadowing and blocking

Shadowing and blocking effects in two dimensions. No ions will be detected at angles below ${\displaystyle \alpha _{crit}.\,\!}$ Primary ions are approaching from the upper left.

Shadowing and blocking are important concepts in almost all types of ion-surface interactions and result from the repulsive nature of the ion-nucleus interaction. As shown at right, when a flux of ions flows in parallel towards a scattering center (nucleus), they are each scattered according to the force of the Coulomb repulsion. This effect is known as shadowing. In a simple Coulomb repulsion model, the resulting region of “forbidden” space behind the scattering center takes the form of a paraboloid with radius ${\displaystyle r=2{\sqrt {\tfrac {Z_{1}Z_{2}e^{2}L}{E_{0}}}}}$ at a distance L from the scattering center. The flux density is increased near the edge of the paraboloid.

Blocking is closely related to shadowing, and involves the interaction between scattered ions and a neighboring scattering center (as such it inherently requires the presence of at least two scattering centers). As shown, ions scattered from the first nucleus are now on diverging paths as they undergo interaction with the second nucleus. This interaction results in another “shadowing cone” now called a blocking cone where ions scattered from the first nucleus are blocked from exiting at angles below ${\displaystyle \alpha _{crit}\,\!}$. Focusing effects again result in an increased flux density near ${\displaystyle \alpha _{crit}\,\!}$.

In both shadowing and blocking, the "forbidden" regions are actually accessible to trajectories when the mass of incoming ions is greater than that of the surface atoms (e.g. Ar⁺ impacting Si or Al). In this case the region will have a finite but depleted flux density.

For higher energy ions such as those used in MEIS and RBS the concepts of shadowing and blocking are relatively straightforward since ion-nucleus interactions dominate and electron screening effects are insignificant. However, in the case of LEIS these screening effects do interfere with ion-nucleus interactions and the repulsive potential becomes more complicated. Also, multiple scattering events are very likely which complicates analysis. Importantly, due to the lower energy ions used LEIS is typically characterized by large interaction cross-sections and shadow cone radii. For this reason penetration depth is low and the method has much higher first-layer sensitivity than MEIS or RBS. Overall, these concepts are essential for data analysis in impact collision LEIS experiments (see below).

Diffraction does not play a major role

The de Broglie wavelength of ions used in LEIS experiments is given as ${\displaystyle \lambda ={\tfrac {h}{mv}}}$. Using a worst-case value of 500 eV for an ⁴He⁺ ion, we see λ is still only 0.006 Å, still well below the typical interatomic spacing of 2-3 Å. Because of this, the effects of diffraction are not significant in a normal LEIS experiment.

ICISS geometry and its relevance to structural characterization of surfaces. The direction and length of the surface-subsurface bond may be determined from an intensity vs. ${\displaystyle \alpha \,\!}$ plot. Red: determining the shape of the shadow cone; Green: determining surface-subsurface spacing and direction with a known shadow cone shape.

Variations of technique

Depending on the particular experimental setup, LEIS may be used to obtain a variety of information about a sample. The following includes several of these methods.

• Alkali ion scattering spectroscopy (AISS) uses alkali ions in place of noble gas ions to give a distinctly different type of interaction. The primary difference between AISS and normal ISS is the increase in ion survival probability when using alkali ions. This is due to the relative stability of alkali (+1) ions as opposed to noble gas ions which have a much stronger energetic incentive for abstracting electrons from the sample. Increasing the ion survival probability results in an increase in ion flux and an improvement in sensitivity, which in turn allows for a reduction in primary ion flux to a point where the method is almost non-destructive. A disadvantage of using alkali ions in place of noble gas ions is the increased likelihood of adsorption or deposition to the sample surface.
• Impact-collision ion scattering spectroscopy (ICISS) takes advantage of shadowing and blocking in order to make precise determinations about interatomic spacing of the first 1-2 layers in a surface. The specific scattering geometry (180 degrees) ensures detection of only those particles which have undergone head-on collisions with surface atoms (thereby avoiding the complications of multiple scattering events). Starting sampling at a relatively high angle of incidence and scanning over varying incidence angles, the intensity of one particular energy peak is monitored. Scattered ions form shadow cones (see above) behind each atom, which prevents any backscattering at low incidence angles. A peak in scattering intensity is observed when the cones line up such that each passes over the adjacent atom. Performing such an analysis on a sample with known interatomic spacing enables determination of the shape of the shadow cone, where as shown at right, ${\displaystyle r=d\sin \alpha _{crit}\,\!}$ and ${\displaystyle L=d\cos \alpha _{crit}\,\!}$.
  

  A graph of intensity versus angle of incidence for scattering from a subsurface atom in the ICISS geometry. The directionality of the surface-subsurface bond (see diagram above) may be deduced from ${\displaystyle \alpha _{0}\,\!}$. The length of this bond may be deduced from ${\displaystyle \alpha _{1}\,\!}$ and ${\displaystyle \alpha _{2}\,\!}$ when the shape of the shadow cone is known.
  If the shape of the shadow cone is known, the interatomic spacing between surface atoms as well as the spacing and directionality between surface and subsurface atoms can then be calculated from the resulting peak-and-valley structure in a graph of intensity versus scattering angle. In the graph at right showing scattering intensity from a subsurface (second layer) atom, ${\displaystyle \alpha _{0}\,\!}$ corresponds to the middle of the "valley" where the atom is being blocked by a surface atom. ${\displaystyle \alpha _{1}\,\!}$ and ${\displaystyle \alpha _{2}\,\!}$ correspond to the peaks due to intersection of the shadow cone with the subsurface atom. Interatomic spacing can be directly calculated from these values if the shape of the shadow cone is known.
• Neutral Impact-collision ion scattering spectroscopy (NICISS) uses detection of backscattered projectiles to determine concentration depth profiles of the elements. The NICISS technique uses noble gas ions (usually He⁺) of energy 1-5 keV. When the projectile ions are within a few angstrom of the surface they are neutralised, and proceed to penetrate into the surface. The projectiles may be backscattered (at an angle of up to 180°) upon collision with a target atom. This backscattering causes the projectiles to lose energy proportional to the mass of the target and is of the order of a few hundred eV. The final energy of the projectiles is determined via time-of-flight (TOF). Hence by knowing the initial and final energies of the projectile, it is possible to determine the identity of the target atom. The projectiles also experience an additional energy loss while penetrating through the bulk, of the order of a few eV per angstrom. Hence the depth that each target atom was hit can also be determined. From the TOF spectrum it is then possible to gain the concentration depth profiles of the elements present in the sample. NICISS is able to probe to a depth of approximately 20 nm with a resolution of only a few angstrom.
• Reactive ion scattering (RIS) utilizes a stream of very low-energy (1-100 eV) Cs⁺ ions to probe molecules adsorbed at the surface of a sample. Upon impact the ions may interact with and chemically bind to species present at the surface. These interactions take place on a rapid (picosecond) timescale and can be used to analyze for the presence of different molecules or molecular fragments by observing spectra of Cs-X⁺ coming from the surface.
• Time-of-flight scattering and recoiling spectroscopy (TOF-SARS) uses the TOF analysis setup. Elemental analysis may be performed via observation of in-plane scattering, while structural information may be obtained by following certain spectral peaks while shifting either sample incident or azimuthal angle.
• Scattering and recoiling imaging spectroscopy (SARIS) takes advantage of blocking cone geometries to focus ions in a manner similar to conventional optics. This gives very large magnifications (~10⁹) when projected onto a 2-d detector and may be used to give element-specific images of the sample surface. The use of a wide 2-d MCP detector greatly reduces sample analysis time as opposed to the TOF geometry with an inherently narrow-angle detector (see drift tube above). J. Wayne Rabalais at the University of Houston is one of the pioneers of this method, and a fine image of the output of a SARIS experiment can be found here.