1. Basics of Ion Beam Analysis
Srdjan Petrović
Laboratory of Physics, Vinča Institute of Nuclear Sciences, University of Belgrade, Serbia

2. INTRODUCTION
Ion Beam Analysis (IBA) of the target material is based on the information obtained from the ion beam – target interaction.
In general, IBA provides the depth profiling of the material - the material atoms concentration dependence on the target depth and/or the elemental analysis - material atoms composition (stoichiometry).
Rutherford Backscattering Spectrometry (RBS) - depth profiling and elemental analysis
Elastic Backscattering Spectrometry (EBS) – depth profiling and elemental analysis
Elastic Recoil Detection Analysis (ERDA) – depth profiling and elemental analysis
Nuclear Reaction Analysis (NRA) – depth profiling and/or elemental analysis
Particle-Induced X-Ray Emission Analysis (PIXE) – elemental analysis
Particle-Induced -Ray Emission Analysis (PIGE) – elemental analysis and/or depth profiling
Ion Channeling – RBS/C, EBS/C, ERDA/C and impurity/crystal characterization

3. Rutherford backscattering spectrometry (RBS)
Rutherford scattering – scattering by the pure Coulomb interaction:
V r = Z 1 Z 2 e 2 r , α = Z 1 Z 2 e 2
Schematic figure of the Rutherford experiment

4. Rutherford Backscattering Spectrometry (RBS)
Diagrammatic view of the internal configuration of the alpha-scattering sensor head deployed on the surface of the moon, Surveyor V, September 9, 1967 (from Turkevich et al. (1968). This experiment was the first widely publicized application of the Rutherford scattering introduced some 50 years earlier.

5. Experimental set up for RBS
Schematic diagram of a typical backscattering spectrometry in use today

6. Rutherford Backscattering Spectrometry (RBS)
RBS is an analytical method, which provides depth profiling and stoichiometry
It is suitable for heavier elements in lighter matrix material
Typical depth profiling accuracy is 10 – 30 nm
Detection limit range from about a few parts per million for heavy elements to a few percent for light elements
RBS is nondestructive method, which is insensitive to the sample chemical bonding
From the practical point of view, it is quick and easy experiment, with data acquisition times of a few tens of minutes

7. Kinematics of elastic particle collisions

8. Backscattering geometry ( 𝐌 𝟏 ≤ 𝐌 𝟐 )
x = M 1 M mass ratio
K = 𝐸 1 𝐸 projectile kinematic factor
𝐊 𝐌 𝟐 = (𝟏− 𝐱 𝟐 𝐬𝐢𝐧 𝟐 ) 𝟏/𝟐 +𝐱𝐜𝐨𝐬 𝟏+𝐱 𝟐

9. dσ(θ C ) dΩ = α 4E c 2 1 sin 4 (θ c /2)
Rutherford differential scattering cross section (the center of mass frame):
dσ(θ C ) dΩ = α 4E c sin 4 (θ c /2)
Rutherford differential cross section (the laboratory frame):
𝐝𝛔(𝛉) 𝐝𝛀 = 𝜶 𝟒𝐄 𝟐 𝟒 𝐬𝐢𝐧 𝟒 (𝛉) 𝟏− (𝐱𝐬𝐢𝐧 (𝛉)) 𝟐 𝟏/𝟐 + 𝐜𝐨𝐬⁡(𝛉) 𝟐 𝟏− (𝐱𝐬𝐢𝐧 (𝛉)) 𝟐 𝟏/𝟐 , 𝐱= 𝐌 𝟏 𝐌 𝟐

10. Energy loss and depth scale (depth profiling) - single element target
E 0 - the energy of the incident particle
Δ E in - the energy loss of particle from the surface at thickness t
Δ E out - the energy loss of particle after the collision from the thickness t to the surface
E t - energy of the incident particle just prior to the collision
E 1 - energy of particle measured at the detector
E 1 = K E t - Δ E out - the dependence of the measured energy on the depth!

11. RBS spectrum – homogeneous thick one element sample
Backscattering spectrum for 1.4 MeV He ions incident on thick Au sample
Υ t = σ θ ΩQNΔt −the experimental yield
σ θ - the scattering cross section at the measured angle θ
Ω – the detector solid angle
Q - the measured number of incident particles
N – atomic density
NΔt − the number of target atoms per unit area in the layer Δt thick

12. Compound target – thin film
Depth profiling
E 1 (A) = K A E t 𝐴 𝑚 𝐵 𝑛 - Δ E out 𝐴 𝑚 𝐵 𝑛
E 1 (B) = K B E t 𝐴 𝑚 𝐵 𝑛 - Δ E out 𝐴 𝑚 𝐵 𝑛
Surface area approximation
𝜎 ( 𝐸 𝑡 , 𝜃) ≅ 𝜎 ( 𝐸 0 , 𝜃)
Stoichiometry (thin film)
m n ≡ N A N B = A A A B σ B ( E 0 ) σ A ( E 0 )
A A - the area of compound A
A B - the area of compound B
A schematic representation of the backscattering process from a free-standing compound film with composition A m B n and thickness t (a) Energy loss relation, and (b) predicted backscattering spectrum.

13. Energy loss in compounds – Bragg’s rule
Δ𝐸(𝑡)= 0 𝑡 𝑆 𝑥 𝑑𝑥 , 𝑆 𝑥 ≡ 𝑑𝐸 𝑑𝑥 - stopping power
𝜀(𝑥)= 𝑆(𝑥) 𝑁 - stopping cross section
Bragg’s rule
𝜀 𝐴 𝑚 𝐵 𝑛 = m 𝜀 𝐴 + n 𝜀 𝐵
Stopping cross sections for He ions on Si, O, and Si O 2 . The Si O 2 stopping cross section ε Si O 2 was determined on the molecular basic with 2.3  molecules/ cm 3 .

14. 𝑚 𝑛 = 𝐻 𝑁𝑖,0 𝜎 𝑆𝑖 ( 𝐸 0 ) 𝜎 𝑁𝑖 𝑁𝑖𝑆𝑖 𝐻 𝑆𝑖,0 𝜎 𝑁𝑖 ( 𝐸 0 ) 𝜎 𝑆𝑖 𝑁𝑖𝑆𝑖
Compound target – thin film + thick substrate
Stoichiometry from the surface height
K Ni - kinematic factor of Ni (0.7624, θ= )
K Si - kinematic factor of Si (0.5657, θ= )
H Ni,0 - the surface height of Ni
H Si,0 - the surface height of Si
𝑚 𝑛 = 𝐻 𝑁𝑖,0 𝜎 𝑆𝑖 ( 𝐸 0 ) 𝜎 𝑁𝑖 𝑁𝑖𝑆𝑖 𝐻 𝑆𝑖,0 𝜎 𝑁𝑖 ( 𝐸 0 ) 𝜎 𝑆𝑖 𝑁𝑖𝑆𝑖
Scematic backscattering spectra for MeV 4 He ions incident on 100 nm Ni film on Si (a) Before reaction, and (b) after reaction to form Ni 2 Si.

15. Examples
RBS data at 2 MeV He ions from two reference film standards that were used to measure the relative cross section of Cu, Y, and O relative to to Ba as a function of He energy

16. Examples
The 1.9 MeV He backscattering spectrum of a three-layered film on a carbon substrate. The backscattering signals from the three layers are clearly separated. The Ni and Fe peaks are not resolved.

17. Examples
The 1.9 MeV backscattering spectrum of a ceramic glass. The indicated stoichiometry was determined from the step heights.

18. Examples
RBS spectrum from the optical glass filter consisting of layers of WO 3 layers interspersed with MgF 2 . Non-uniformity is clearly visible on the height of the peaks (W content).

19. Examples
Energy spectrum of 2 MeV He ions backscattered from a silicon wafer implanted with 250 keV As ions to a nominal fluence of 1.2  ions/ cm 2 . The vertical arrows indicate the energies of He backscattered from the surface atoms of 28 Si and 75 As .

20. Non- Rutherford backscattering – homogeneous thick one element sample (a clear need for the use of a special computational programs, e.g., SIMNRA)
Backscattering spectrum of 1 MeV protons in the random orientation (scattering angle of 170 degre) from a thick diamond (just recently obtained results from the experiment performed in the Rudjer Bošković Institute, Zagreb, Croatia).

21. Elastic Recoil Detection Analysis (ERDA)
ERDA is an analytical method, which provides depth profiling and stoichiometry
It is complementary with RBS and suitable for lighter elements in heavier matrix material
Depending on the way how the recoil ion(s) are detected, there are for example: a conventional range-foil ERDA, Time of Flight (TOF) ERDA and E-E ERDA
Depth profiling accuracy and detection limit range depend on the way recoil ion(s) are measured.
ERDA is nondestructive method, which is insensitive to the sample chemical bonding
From the practical point of view, it is quick and easy experiment, with data acquisition times of a few tens of minutes

22. Kinematics of recoil elastic particle collisions
Recoil kinematic factor:
𝐾 ′ = E 2 E 0 = 4 M 1 M M 1 + M cos 2 ϕ
Recoil cross section:
dσ(ϕ) dΩ = 𝛂 𝟒𝐄 𝟐 [ M 1 + M 2 M 2 ] 𝟐 𝟏 cos 3 ϕ
Dependence of the kinematic on the recoil angle and mass ratio.

23. Schematic presentation of the standard range-foil ERDA

24. Ideal versus realistic recoil energy spectrum
Converting a measured energy spectrum, i.e. counts versus recoil energy into a desired depth profile requires a lot of analytical efforts that in many cases cannot produce an accurate result.
In the computational programs, like SIMNRA, one can include the reflection geometry (ERDA) and a foil, as well as, the energy loss straggling, multiple scattering energy spread due to specific ERDA geometry and the non-Rutherford cross sections. Practically, the only computational programs are used for the ERDA depth profiling.
Sensitivity of a standard foil ERDA for hydrogen is around 0.1%, for 1 – 3 MeV He projectile beams.

25. Examples of standard range-foil ERDA – thin layers
Energy spectra of 7 Li recoils observed when targets containing 7 Li F are bombarded by a 35-MeV 35 Cl beam. Each target was made of two thin layers of 7 Li F separated by a copper layer of thickness ∆x; 7 Li 0 corresponds to the first layer and 7 Li 1 to the second layer. In (a) and (b) the target surface was perpendicular to the beam direction; in (c) it was tilted at with the beam direction.

26. Examples of standard range-foil ERDA – homogenous thick target
The ERDA spectrum of 1 H by using the Kapton polyimide foil [ H 10 C 22 N 2 O 5 ]. It was collected with 1.3 MeV 4 He beam under the measurement geometry of the target tilt, Θ 1 = , and the detector tilt, Θ 2 =

27. Example of a transmission ERDA experiment
Schematic of a transmission ERDA experiment for hydrogen profiling with an helium beam, with the zero detection angle and a target thick enough to stop completely incident particles.

28. Example of a range-foil ERDA implanted depth profiling of hydrogen
Typical range-foil ERDA hydrogen profiling with an helium beam in the case of the hydrogen implantation a target. (The thin peak is due to hydrogen adsorbed on the surface.)

29. Time-of-flight ERDA (TOF-ERDA)
Simultaneous measurements of both the velocity (via time-of-flight) and energy of recoiled ions.
Energy measurement – standard solid state detector.
TOF measurement – a telescope with the start (T1) and stop (T2) detectors (two ultra thin carbon foils producing secondary electrons, not disturbing the ion path).
Example of the TOF-ERDA experimental set-up.

30. Example
The TOF-ERDA coincidence spectrum for a polyimide sample ( C 22 H 10 N 2 O 6 ) measured with a 84 MeV I beam. Each recorded data point corresponds to the measured energy, E (abscissa) and the delayed flight time, t 0 − t f (ordinate).

31. E–E ERDA (solid-state telescope)
Simultaneous measurements of both the energy loss and energy of recoiled ions with a E–E telescope.
Energy loss measurement – very thin solid state detector
Energy measurement – standard solid state detector
Schematic view of a solid-state telescope
Variation of energy loss in a 10 m thick solid state detector for protons, deuterons and alpha particles

32. Example
(a) Three-dimensional plot of hydrogen, deuterium, and tritium distributions in a titanium hydride sample bombarded with 4 MeV He ions. (b) Two-dimensional plot in the interval keV.