Elastic recoil detection analysis (ERDA), also referred to as forward recoil scattering or spectrometry, is an ion beam analysis technique, in materials science, to obtain elemental concentration depth profiles in thin films. This technique can be achieved using many processes.

In the technique of ERDA, an energetic ion beam is directed at a sample to be characterized and (as in Rutherford backscattering) there is an elastic nuclear interaction between the ions of the beam and the atoms of the target sample. Such interactions are commonly of Coulomb nature. Depending on the kinetics of the ions, cross section area, and the loss of energy of the ions in the matter, ERDA helps determine the quantification of the elemental analysis. It also provides information about the depth profile of the sample.

The energy of incident energetic ions can vary from 2 MeV to 200 MeV, depending on the studied sample. The energy of the beam should be enough to kick out ("recoil") the atoms of the sample. Thus, ERDA usually employs appropriate source and detectors to detect recoiled atoms.

ERDA setup is large, expensive and difficult to operate. Therefore, although it is commercially available, it is relatively uncommon in materials characterization. The angle of incidence that an ion beam makes with the sample must also be taken into account for correct analysis of the sample. This is because, depending on this angle, the recoiled atoms will be collected.

ERDA has been used since 1974. It has similar theory to Rutherford backscattering spectrometry (RBS), but there are minor differences in the set-up of the experiment. In case of RBS, the detector is placed in the back of the sample whereas in ERDA, the detector is placed in the front.

Characteristics of ERDA The main characteristics of ERDA are listed below. A variety of elements can be analyzed simultaneously as long as the atomic number of recoiled ion is smaller than the atomic number of the primary ion. The sensitivity of this technique primarily depends upon scattering cross-section area, and the method has almost equal sensitivity to all light elements. Depth resolution depends upon stopping power of heavy ions after interactions with sample, and the detection of scattered primary ions is reduced due to the narrow scattering cone of heavy ions scattering from light elements. Gaseous ionization detectors provides efficient recoil detection, minimizing the exposure of sample to the ion beam and making this a non-destructive technique. This is important for accurate measurement of hydrogen, which is unstable under the beam and is often removed from the sample.

History

ERDA was first demonstrated by L'Ecuyer et al. in 1976. They used 25–40 MeV 35Cl ions to detect the recoils in the sample. Later, ERDA has been divided into two main groups. First is the light incident ion ERDA (LI-ERDA) and the second is the heavy incident ion ERDA (HI-ERDA). These techniques provide similar information and differ only in the type of ion beam used as a source.

LI-ERDA uses low voltage single-ended accelerators, whereas the HI-ERDA uses large tandem accelerators. These techniques were mainly developed after heavy ion accelerators were introduced in the materials research. LI-ERDA is also often performed using a relatively low energy (2 MeV) helium beam for measuring the depth profile of hydrogen. In this technique, multiple detectors are used: backscattering detector for heavier elements and forward (recoil) detector to simultaneously detect the recoiled hydrogen. The recoil detector for LI-ERDA typically has a "range foil". It is usually a Mylar foil placed in front of the detector, which blocks scattered incident ions, but allows lighter recoiling target atoms to pass through to the detector. Usually a 10 μm thick Mylar foil completely stops 2.6 MeV helium ions but allows the recoiled protons to go through with a low energy loss.

HI-ERDA is more widely used compared to LI-ERDA because it can probe more elements. It is used to detect recoiled target atoms and scattered beam ions using several detectors, such as silicon diode detector, time-of-flight detector, Gaseous ionization detector etc. The main advantage of HI-ERDA is its ability to obtain quantitative depth profiling information of all the sample elements in one measurement. Depth resolution less than 1nm can be obtained with good quantitative accuracy thus giving these techniques significant advantages over other surface analysis methods. Additionally, a depth of 300 nm can be accessed using this technique. A wide range of ion beams including 35Cl, 63Cu, 127I, and 197Au, with different energies can be used in this technique.

The setup and the experimental conditions affect the performances of both of these techniques. Factors such as multiple scattering and ion beam induced damage must be taken into account before obtaining the data because these processes can affect the data interpretation, quantification, and accuracy of the study. Additionally, the incident angle and the scattered angle help determine the sample surface topography.

Prominent features of ERDA ERDA is very similar to RBS, but instead of detecting the projectile at the back angle, the recoils are detected in the forward direction. Doyle and Peercey in 1979 established the use of this technique for hydrogen depth profiling. Some of the prominent features of ERDA with high energy heavy ions are: Large recoil cross-section with heavy ions provides good sensitivity. Moreover, all chemical elements, including hydrogen, can be detected simultaneously with similar sensitivity and depth resolution. Concentrations of 0.1 atomic percent can be easily detected. The sampling depth depends on the sample material and is of the order of 1.5–2.5 μm. For the surface region, a depth resolution of 10 nm can be achieved. The resolution deteriorates with increasing depth due to several physical processes, mainly the energy straggling and multiple scattering of the ions in the sample. Same recoil cross-section for a wide mass range of target atoms. The unique characteristic of this technique is depth-profiling of a wide range of elements from hydrogen to rare earth elements.

ERDA can overcome some of the limitations of RBS. ERDA has enabled depth profiling of elements from lightest elements like hydrogen up to heavy elements with high resolution in the light mass region as discussed above. Also, this technique has been highly sensitive because of the use of large area position sensitive telescope detectors. Such detectors are used especially when the elements in the sample have similar masses.

Principles of ERDA

The calculations that model this process are relatively simple, assuming projectile energy is in the range corresponding to Rutherford scattering. Projectile energy range for light incident ions is in 0.5–3.0 MeV range. For heavier projectile ions such as 127I the energy range is usually between 60 and 120 MeV; and for medium heavy ion beams, 36Cl is a common ion beam used with an energy of approximately 30 MeV. For the instrumentation section, the focus will be on heavy ion bombardment. The E2 transferred by projectile ions of mass m1 and energy E1 to sample atoms of mass m2 recoiling at an angle ϕ, with respect to the incidence direction is given by the following equation.

(1)

Eq. 1 models the energy transfer from the incident ions striking the sample atoms and the recoiling effect of the target atoms with an angle of ϕ. For heavier ions in elastic recoil detection analysis, if m2/m1 <<1, all recoiling ions have similar velocities. It can be deduced from the previous equation the maximum scattering angle, θ'max, as Eq. 2 describes:

(2)

Using these parameters, absorber foils do not need to be incorporated into the instrument design. When using heavy ion beams and the parameters above, the geometry can be estimated as to allow for incident particle collision and scattering at an angle deflected away from the detector. This will prevent degradation of the detector from the more intense beam energies.

The differential elastic recoil cross-section σERD is given by:

(3)

where Z1 and Z2 are the atomic numbers of projectile and sample atoms, respectively. For m2/m1 <<1 and with approximation m=2Z; Z being the atomic number of Z1 and Z2. In Eq. 3 two essential consequences can be seen, first the sensitivity is roughly the same for all elements and second it has a Z14 dependence on the projector of the ion. This allows for the use of low energy beam currents in HI-ERDA preventing sample degradation and excessive heating of the specimen.

When using heavy ion beams, care must be taken for beam-induced damage in sample such as sputtering or amorphization. If only nuclear interaction is taken into account, it has been shown that the ratio of recoiling to displaced atoms is independent of Z1 and only weakly dependent on the projectile mass of the incident ion. With heavy ion bombardment, it has been shown that the sputter yield by the ion beam on the sample increases for nonmetallic samples and enhanced radiation damage in superconductors. In any case, the acceptance angle of the detector system should be as large as possible to minimize the radiation damage. However, it may reduce the depth profiling and elemental analysis due to the ion beam not being able to penetrate the sample.

This demand of a large acceptance angle, however, is in conflict with the requirement of optimum depth resolution dependency on the detection geometry. In the surface approximation and assuming constant energy loss the depth resolution δx can be written:

(4)

where Srel is the relative energy loss factor defined by:

(5)

here, α and β are the incidence angles of the beam and exit angle of the recoiling ion respectively, connected to the scattering angle ϕ by ϕ=α+β. It should be noticed here that the depth resolution depends on the relative energy resolution only, as well as the relative stopping power of incoming and outgoing ions. The detector resolution and energy broadening associated with the measuring geometry contribute to the energy spread, . The detector acceptance angle and the finite beam spot size define a scattering angle range causing a kinematic energy spread according to Eq. 6:

(6)

A detailed analysis of the different contributions to depth resolution shows that this kinematic effect is the predominant term near the surface, severely limiting the permitted detector acceptance angle, whereas energy straggling dominates the resolution at larger depth. For example, if one estimates for a scattering angle of 37.5° causing a kinematic energy shift comparable to typical detector energy resolutions of 1%, the angular spread δψ must be less than 0.4°. The angular spread can be maintained within this range by contributions from the beam spot size; however, the solid angle geometry of the detector is only 0.04 msr. Therefore, a detector system with large solid angle as well as high depth resolution may enable corrections for the kinematic energy shift.

In an elastic scattering event, the kinematics requires that the target atom is recoiled with significant energy. Eq. 7 models the recoil kinematical factor that occurs during the ion bombardment.

(7)

(8)

(9)

(10)