1 Rutherford Back Scattering (RBS)

Dr. Ajit K. Mahapatro

Learning Objectives:

From this module students may get to know about the following:

i. Surface Characterizations Techniques

ii. Introduction to Rutherford Back Scattering

iii. Scattering Geometry and Kinematics

1. Introduction

Surface analysis is an important part of materials characterizations and is important in many ways to know about its properties including its chemical reactivity, electrical properties of interfaces, corrosive properties, defects and dislocations on the surface. Moreover surface of the materials can be modified selectively and can be functionalized for specific purpose.

There are many important techniques for characterizing the surface of a sample including Auger electron spectroscopy (AES), X-ray fluorescence spectroscopy (XRFS), X-ray photoelectron spectroscopy (XPS), secondary ion mass spectrometry (SIMS) and Rutherford back scattering (RBS) techniques.

Auger electron spectroscopy (AES): The principle of Auger electron Spectroscopy is governed by allowing a high-energy electron from the incident beam to eject an electron from its inner orbit creating a vacant space or a hole in the orbit. Due to this another electron from the higher orbital jumps into and occupies the vacant state. As there is a transition of electron from higher orbit to lower orbit, energy is released. This energy might eject another electron from its orbit instead of emitting a photon. This electron is called Auger electron. These transitions are characteristic transitions and are used to identify the elements by measuring the energy of the emitted Auger electrons. These transitions depend on initial energy of the incident beam and their interaction with the atom. These interactions include the coupling between spin and orbital angular momentum of electron and accordingly the energy spectra in each case is analyzed with greater details.

X-ray fluorescence spectroscopy (XRFS): When the surface of a material is exposed to high energy radiations, e.g. X-rays, they become ionized. If the incident radiation is high enough to dislodge a tightly bound inner electron then an outer electron makes a transition from outer orbital to the inner orbital and replaces it. When this happens, energy is released due to the decreased binding energy of the inner electron orbital compared with an outer one. The emitted radiation is of lower energy than the primary incident X-rays and is termed fluorescent radiation. As the energy of the emitted photon is a characteristic of that particular element, this can be used to detect the element present in the sample. The analysis of major and trace elements in geological materials by x-ray fluorescence is made possible by the behavior of atoms when they interact with radiation.

X-ray photoelectron spectroscopy (XPS): X-ray photoelectron spectroscopy (XPS) is used in analyzing the surface chemistry of a material. XPS can measure the chemical, electronic state and composition of the materials. XPS spectra are obtained by irradiating a solid surface with a beam of X-rays while simultaneously measuring the kinetic energy and electrons that are emitted from the surface of the material within few nanometer of depth. An XPS spectrum is recorded by counting the number of ejected electrons over a range of electron kinetic energies. The peaks in the spectrum are the characteristic energy of that particular element. The energies and intensities of the photoelectron peaks are essential for the identification and quantification of all surface elements.

Secondary ion mass spectrometry SIMS: In this technique abundance of materials on the surface are probed by sputtering it with a focused primary ion beam and the ejected secondary ions are collected and analyzed. The mass to charge ratios of these secondary ions are measured with a mass spectrometer and the elemental, isotopic, or molecular composition of the surface is analyzed. Due to the large variation in ionization probabilities among different materials, SIMS is considered to be a qualitative technique. SIMS is the most sensitive surface analysis technique, with elemental detection limits ranging from parts per million to parts per billion.

All the spectroscopic techniques described above are having both the advantages and limitations, and are described in a tabular form below.

Technique	Advantages	Limitations
AES (Auger Electron Spectroscopy)	High Resolution	Destructive
XRF (X-ray fluorescence)	Non-destructive, liquid samples	Low resolution for light elements
XPS (X-ray photoelectron spectroscopy)	10% accuracy with standards	Destructive
SIMS (Secondary ion mass spectroscopy)	Detects H atom isotopes	Complex
RBS (Rutherford backscattering spectroscopy)	Non-destructive Less than 5% accuracy	Expensive, Accelerator needed

Table 1: Different Surface Characterizations Techniques

2. Rutherford Back Scattering: An Overview

Rutherford Backscattering Spectrometry (RBS) is a technique used for the surface analysis of solid samples. In this techniques, ion energy in the range of 0.5–4 MeV is used to bombard the target and the resulting back scattered ion is analyzed by solid state detectors placed near the target. Both quantitative analysis of the composition of a material and depth profiling of individual elements are possible by RBS techniques. It is non-destructive and does not require any reference sample for the quantitative analysis. RBS has a depth resolution of the order of several nm, and is sensitive to the detection of heavy elements of the order of parts-per-million (ppm). The analyzed depth is typically about 2 μm and 20 μm for incident He-ions and incident protons respectively. One of the limitations of RBS is its low sensitivity for light elements, which often requires the combination of other nuclear based methods like nuclear reaction analysis (NRA) or elastic recoil detection analysis (ERDA). The projectile ions used in RBS include protons, 4He, and lithium ions at backscattering angles of typically 150⁰–170⁰.

3. Rutherford Back Scattering (RBS)

The underlying principle in RBS is governed by the kinematics for binary collisions. A beam of particles (projectiles) with mass M₁ and energy E₀ is bombarded on to the sample of mass M2 (Target) as shown in Figure 1.

Figure 1. An elastic collision between two –positively charged- particles before and after the collision. Momentum and energy is conserved.

The energy E₁ and the scattering angle Θ of the particle M₁ are detected after the collision. As the collision is elastic, mass of the target particles M₂ can be estimated using the law of conservation of energy and momentum. Furthermore, since the probability of scattering in a certain angle is known by Rutherford cross section, it is also possible to estimate the abundance of M₂ particles in the sample by counting the yield of scattered particles M₁ in a certain solid angle covered by the detector.

4. Schematics of RBS Experimental Set Up

A schematic diagram of Rutherford backscattering setup is shown in Figure 2 above. The setup has a tandem particle accelerator which can produce beams of low-mass ions in the MeV range. It generates negative ions which are subsequently accelerated towards positive potential. All the measurements are done in a vacuum system and at the high voltage terminal electrons are stripped off and the particle becomes positively charged. Then they are repelled by the high positive voltage and increase their energy further. The beam is then analyzed and directed to the target chamber. The spot size of the beam is about a millimeter in diameter at the target.

Figure 3: Schematics of Rutherford back scattering set up.

When the positively charged ions reach near the target, they experience the columbic repulsion due to the nuclei of the target atoms and are deflected from their original path. During this process some of the projectiles will also be backscattered and would be collected by the detector mounted at an angle of 170° from the incident beam. Note that the number of back scattered ions would depend on the Rutherford scattering cross-section which would be discussed later. During the process of collisions, there are other inelastic collisions as well and the incident energy E0 lose energy during the process. A proper knowledge of the incident energy, (E0) of the projectile and nature of target would enable us to analyze depth profile of the specimen under study. RBS technique can be used to analyze several micrometer deep profiles for different targets. The back scattered electrons generate electron signal which is amplified and processed by digital electronics. The output is displayed as a spectrum on the computer screen and hence is called backscattering spectrometry.

5. Basic Physical Concepts

RBS involves the scattering of two different particles having different energies associated with them. Accordingly, four different physical phenomena during the scattering need to be taken into consideration. These factors fundamentally influence the outcome of the results which are given below.

1. Energy transfer in the process of scattering between the projectile and target nucleus under study in an elastic two body collision. This process determines an important factor called the kinematic-factor.

2. Likelihood of occurrence of the event, viz. two-body collision. It leads to the concept of scattering cross section and to the capability of quantitative analysis of atomic composition.

3. Energy loss of ion passing through a dense medium. This process leads to the concept of stopping cross section and to the capability of depth perception.

4. Statistical fluctuations in the energy loss of an atom moving through a dense medium. This process determines the resolution of depth profile analysis in backscattering spectrometry.

5.1. Limiting Conditions for designing the Experiment

In RBS a projectile with certain energy collides elastically with a target atom having different mass and energy than the projectile. During the process of collision there is an energy transfer between the projectile and target atom under study. By carefully analyzing the energy of incident beam and the final beam of projectile and the target atom, one can estimate the mass concentration and do depth profile analysis of the target atom. In order to achieve this one needs to consider the following two limiting cases which need to be taken into consideration while designing the experiment.

(1) The initial energy of the incident beam E₀ must be greater than the binding energy of the target atom which is typically of the order of 10 eV. This will enable the scattering process to start effectively.

(2) Nuclear reactions and resonances must be absent. This puts an upper limit to the energy of the incident beam. Nuclear reactions generally occur in the MeV range of energy and is dependent on the atoms under study. For example nuclear effect appears in 1MeV range of energy for H+  ions while it is 2-3 MeV for He+ ions.

6. Scattering geometry and Kinematic Factor ‘K’

The simple elastic collisions of the two body problems can be solved by equating the energy of the incident and target particle before and after the collision while applying the law of conservation of energy and momentum.  Let v₀  and E₀  = ½ M1v01² be the velocity and the kinetic energy of the incident particle before collision and target particle M₂ is at rest. ½ M1v2² the projectile and target ion respectively, after the collision.

Figure 4: Scattering geometry in RBS

Conservation of energy and momentum in the parallel and perpendicular directions require that

Summary

• Rutherford Back scattering is a non-destructive surface characterization technique.
• It involves the elastic collision of two species, viz. projectile and target and the energy of the incident and back scattered beam of ions are taken into account to calculate the concentration and make depth profile analysis of the target.
• Kinematic factor ‘K’ is important in the quantitative estimation of concentration and depends on the energy of the incident ion beams.

References:

• Quantum Mechanics, Volume 1-2,1st Editionby Claude Cohen-Tannoudji (Author),Bernard Diu (Author),Frank Laloe (Author)Brice, D. K. (1973). Thin Solid Films 19, 121