Elastic recoil detection

LI-ERDA is also often performed using a relatively low energy (2 MeV) helium beam for measuring the depth profile of hydrogen.

[6] 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.

[3] 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.

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.

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.

This demand of a large acceptance angle, however, is in conflict with the requirement of optimum depth resolution dependency on the detection geometry.

[1] 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.

Depth resolution and element profiling of thin films has been greatly advanced using elastic recoil detection analysis.

[19] Since the motion is always circular, cyclotron frequency-ω in radians/second-can be described by the following equation:[19] where m is the mass of the particle, its charge is q, and the velocity is v. Ionization is a step-by-step process from collisions of the accelerated electrons with the desired vapor atoms.

[16] Aside from the listed disadvantages, ERDA range foils with silicon detectors is still a powerful method and is relatively simple to work with.

[16] Nuclear experiments with large area ionization chambers increase the particle and position resolution have been used for many years and can easily be assimilated to any specific geometry.

[1] The limiting factor on energy resolution using this type of detector is the entrance window, which needs to be strong enough to withstand the atmospheric pressure of the gas, 20–90 mbar.

[1] ERDA in transmission geometry, where only the energy of the recoiling sample atoms is measured, was extensively used for contamination analysis of target foils for nuclear physics experiments.

With ERDA and heavy ion projectiles, valuable information can be obtained on the light element content of thin foils even if only the energy of the recoils is measured.

To prevent pileup of signals from these recoiled ions, a limit of 500 Hz needed to be set on the count rate of ΔΕ pulses.

[28] Physical concepts of two-body elastic scattering are the basis of several nuclear methods for elemental material characterization.

The Fundamental aspects in dealing with recoil spectroscopy involves electron back scattering process of matter such as thin films and solid materials.

[29] Physical concepts that are highly important in interpretation of forward recoil spectrum are depth profile, energy straggling, and multiple scattering.

This parameter is defined as the ability of an analytical technique to measure a variation in atomic distribution as a function of depth in a sample layer.

In terms of low energy forward recoil spectrometry, hydrogen and deuterium depth profiling can be expressed in the following mathematical notation:[30]

where δEdet defines as the energy width of a channel in a multichannel analyzer, and dEdet/dx is the effective stopping power of the recoiled particles.

Here, δET is the total energy resolution of the system, and the expression in the denominator is the sum of the path integrals of initial, scattered and recoil ion beams.

Final resolution is not coincide with theoretical evaluation such as the classical depth resolution δRx precisely because it results from three terms that escape from theoretical estimations:[28] Straggling is energy loss of particle in a dense medium is statistical in nature due to a large number of individual collisions between the particle and sample.

[37] 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.

[41] The analysis of multiple scattering was started by Walther Bothe and Gregor Wentzel in the early 1920s using well-known approximation of small angles.

[38] A comparative development of multiple scattering at small angles was presented by Meyer, based on a classical calculation of single cross section.

Marwick and Sigmund carried out development on lateral spreading by multiple scattering, which resulted in a simple scaling relation with the angular distribution.

[48] 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).

Schematic of ERDA. ϕ, α and β are recoil angle, incident angle, and exit angle, respectively. x is the probing depth.
Van de Graaff generator coupled with a particle accelerator
Gas ionization chamber, in which positive charges are migrating toward the cathode and the negatively charged ions are migrating toward the sub divided anode through a Frisch Grid.
Planar representation of scattered projectile path of an ion beam. This figure is plane representation of a scattered projectile on the target surface, when both incoming and outgoing paths are perpendicular to target surface. [ 28 ]
Planar representation of recoiled path of an ion beam. This figure is plane representation of a recoiled ion path on the target surface, when both incoming and outgoing paths are perpendicular to target surface. [ 28 ]
Typical geometrical configuration of recoil spectrometry [ 28 ]
Propagation of the energy straggling distribution through an Al foil for protons of 19.6 MeV with different distribution functions f B :Bohr,f S :Symon,f T :Tschalar
Multiple scattering scheme where the ion beam is directed in the x direction. [ 39 ] Lateral displacement perpendicular to the beam direction is ρ(y,z), and α is the total angular deviation after the penetrated depth x
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. [ 40 ]