Elastic recoil detection

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. 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. 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. 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. 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: 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°. Eq. 7 models the recoil kinematical factor that occurs during the ion bombardment. or a light element (H, He, Li, C, O, Mg, K) profiling with an absorber foil in front of the energy detector for beam suppression. Atoms must be electrically charged (ionized) before they can be accelerated. Since the motion is always circular, cyclotron frequency-ω in radians/second-can be described by the following equation:

Now that the vapor of the desired has been ionized, they must be removed from the magnetic bottle. To do this, a high voltage is between the hexapoles applied to pull out the ions from the magnetic field. There are advantages when using absorber films:

1. The large beam Z₁ gives rise to a large Rutherford cross section and because of the kinematics of heavy-on-light collisions that cross section is nearly independent of the target, if M₁>> M₂ and M ~2Z; this helps in reducing the background. and the intrinsic indistinguishability of the signals for the various different recoiled target elements. These types of detectors usually implement small solid angles for higher depth resolution. Hi mass bipolar (high mass ion detection), Gen 2 Ultra Fast (twice as fast as traditional detectors), and High temperature (operated up to 150 °C) TOF are just a few of the commercially available detectors integrated with time-of-flight instruments. These detectors have also been implemented in heavy-ion rutherford backscattering spectrometry.

The energy resolution obtained from this detector is better than a silicon detector when using ion beams heavier than helium ions. There are various designs of ionization detectors but a general schematic of the detector consists of a transversal field ionization chamber with a Frisch grid positioned between anode and cathode electrodes. The anode is subdivided into two plates separated by a specific distance. From the anode, signals ∆E(energy lost), E_rest(residual energy after loss), and E_tot (the total energy E_tot= ΔΕ+E_rest) as well as the atomic number Z can be deduced.

Main assumptions in physical concepts of Back scattering spectrometry

• Elastic collision between two bodies is the energy transfer from a projectile to a target molecule. This process depends on the concept of kinematics and mass perceptibility.
• Probability of occurrence of collision provides information about scattering cross section.
• Average loss of energy of an atom moving through a dense medium gives idea on stopping cross section and capability of depth perception.
• Statistical fluctuations caused by the energy loss of an atom while moving through a dense medium. This process leads to the concept of energy straggling and a limitation to the ultimate depth and mass resolution in back scattering spectroscopy.

<math>\Delta x = \frac{\Delta E_{total{(dE_{det}/dx)}</math>where defines as the energy width of a channel in a multichannel analyzer, and is the effective stopping power of the recoiled particles.

Consider an Incoming and outgoing ion beams that are calculated as a function of collisional depth, by considering two trajectories are in a plane perpendicular to target surface, and incoming and outgoing paths are the shortest possible ones for a given collision depth and given scattering and recoil angles .

Impinging ions reach the surface, making an angle θ₁, with the inward-pointing normal to the surface. After collision their velocity makes an angle θ₁, with the outward surface normal; and the atom initially at rest recoils, making an angle θ₁, with this normal. Detection is possible at one of these angles as such that the particle crosses the target surface.

Paths of particles are related to collisional depth x, measured along a normal to the surface.

Practical importance of depth resolution

The concept of depth resolution represents the ability of Recoil spectrometry to separate the energies of scattered particles that occurred at slightly different depths δR_x is interpreted as an absolute limit for determining the concentration profile. From this point of view, a concentration profile separated by a depth interval of the order of magnitude of δR_x would be undistinguishable in the spectrum, and obviously it is impossible to gain accuracy better than δR_x to assign depth profile. In particular the fact that the signals corresponding to features of the concentration profile separated by less than δR_x strongly overlap in the spectrum.

A finite final depth resolution resulting from both theoretical and experimental limitations has deviation from exact result when consider an ideal situation. Final resolution is not coincide with theoretical evaluation such as the classical depth resolution δR_x precisely because it results from three terms that escape from theoretical estimations:

The energy distribution of straggling is divided into three domains depending on the ratio of ΔE i.e., ΔE /E where ΔE is the mean energy loss and E is the average energy of the particle along the trajectory.

:2. Medium fraction of energy loss: for regions where 0.01< ΔE/E ≤ 0.2. Bohr’s model based on electronic interactions is useful for estimating energy straggling for this case, and this model includes the amount of energy straggling in terms of the areal density of electrons traversed by the beam.

The standard deviation Ω²B of the energy distribution is<math>\Omega^2 B = 4\pi ((Z_1 e^2)^2 NZ_2 \Delta x

</math>, where NZ₂Δx is the number of electrons per unit area over the path length increment Δx.

:3. Large fraction of energy loss: for fractional energy loss in the region of 0.2 < ΔE/E ≤ 0.8, the energy dependence of stopping power causes the energy loss distribution to differ from Bohr’s straggling function. This case can not be described by the Bohr theory,

An expression of energy for straggling was proposed by Symon in the region of 0.2 < ΔE/E ≤ 0.5.

Tschalar et al. derived a straggling function <math>\Omega^2 T = (S^2[E(x)] \sigma^2(E) dE)/(S^3(E))

</math>, where σ²(E) represents energy straggling per unit length (or) variance of energy loss distribution per unit length for particles of energy E, and E(x) is the mean energy at depth x. The Tschalar's expression is valid for nearly symmetrical energy loss spectra.

Mass resolution

In a similar way mass resolution is a parameter that characterizes the capability of recoil spectrometry to separate two signals arising from two neighboring elements in the target. The difference in the energy δE₂ of recoil atoms after collision when two types of atoms differ in their masses by a quantity δM₂ is: These two parameters are discussed below. Hence, path length will be increased than expected causing fluctuations in ion beam. This process is called multiple scattering, and it is statistical in nature due to the large number of collisions. Lateral displacement perpendicular to the beam direction is ρ(y,z), and α is the total angular deviation after the penetrated depth x]]

thumb|upright=1.5|Propagation of multiple scattering angular distribution through matter. The half-width of the angular distribution is α_1/2. There is a considerable difference between the shape of Gaussian peak (ideal condition) and angularly deviated peak.

Theory and experiment of multiple scattering phenomena

In the study of multiple scattering phenomenon angular distribution of a beam is important quantity for consideration. The lateral distribution is closely related to the angular one but secondary to it, since lateral displacement is a consequence of angular divergence. Lateral distribution represents the beam profile in the matter. both lateral and angular Multiple scattering distributions are interdependent.

The analysis of multiple scattering was started by Walther Bothe and Gregor Wentzel in the early 1920s using well-known approximation of small angles. The physics of energy straggling and multiple scattering was developed by Williams in 1929–1945. Williams devised a theory, which consists of fitting the multiple scattering distribution as a Gaussian-like portion due to small scattering angles and the single collision tail due to the large angles. William, E.J., studied beta particle straggling, Multiple scattering of fast electrons and alpha particles, and cloud curvature tracks due to scattering to explain Multiple scattering in different scenario and he proposed a mean projection deflection occurrence due to scattering. His theory later extended to multiple scattering of alpha particles.

Goudsmit and Saunderson provided a more complete treatment of multiple scattering, including large angles. For large angles Goudsmit considered series of Legendre polynomials which are numerically evaluated for distribution of scattering. The angular distribution from Coulomb scattering has been studied in by Molière in the 1940s and then by Marion and coworkers, who tabulated energy loss of charged particles in matter, multiple scattering of charged particles, range straggling of protons, deuterons and alpha particles, and equilibrium charge states of ions in solids and energies of elastically scattered particles. Scott presents a complete review of basic theory, mathematical methods, as well as results and applications. Sigmund and Winterbon extended the Meyer's calculation to a more general case. Marwick and Sigmund carried out development on lateral spreading by multiple scattering, which resulted in a simple scaling relation with the angular distribution.

Applications

ERDA has applications in the areas of polymer science, semiconductor materials, electronics, and thin film characterization. ERDA is widely used in polymer science. This is because polymers are hydrogen-rich materials which can be easily studied by LI-ERDA. One can examine surface properties of polymers, polymer blends and evolution of polymer composition induced by irradiation. HI-ERDA can also be used in the field of new materials processed for microelectronics and opto-electronic applications. Moreover, elemental analysis and depth profiling in thin film can also be performed using ERDA.

ERDA is also used to characterize hydrogen transport near interfaces induced by corrosion and wear.

Electronic devices are usually composed of sequential thin layers made up of oxides, nitrides, silicides, metals, polymers, or doped semiconductor–based media coated on a single-crystalline substrate (Si, Ge or GaAs). Moreover, this technique offers an opportunity to study the density profiles of hydrogen, carbon and oxygen in various materials, as well as the absolute hydrogen, carbon and oxygen content.

References