Handbook of Modern Coating Technologies

Measurement of Doppler broadening of the annihilation peak

• Experimental setup

The aforementioned energy broadening of the annihilation line was estimated using an energy-dispersive system of high-resolution detectors (Fig. 5—13C). High resolution (~20%) was provided by pure Ge crystals cooled by liquid nitrogen. An electric pulse in the pre­amplifier is formed by separation of the charge when a high voltage is applied due to posi­trons with an energy of several kiloelectron-volts. After the main amplification in the multi­channel analyzer, the amplitude of the electric pulse can be detected and corresponds to the photon energy. Long-term collection of several million samples is carried out by a digital peak stabilization system. The collection time characterizing the spectrum of the positron lifetime corresponds to the measurement time. In this way, the total life span of the positrons can be measured. The Ge detector should be sufficiently separated from the sample so that there are no accumulation effects in the detector system, both methods can be implemented simultaneously.

• Data treatment

Fig. 5—13D shows the effect on the Doppler broadening spectrum of the positrons capture in defects N_d = f(E). With certain parameters of the line shape, a quantitative assessment is car­ried out. After subtracting the background, the parameter S is calculated as the ratio of the central part area of the spectrum with a low momentum (A_s) to the area under the entire curve (A₀):

Fig. 5—13D shows that the parameter W is calculated far from the center of the line, in the high-momentum region. It is calculated as the ratio of the area under the curve A_w in a fixed range of energies to the area under the entire curve A₀

To calculate the S parameter and E₀ ± E_s at an equal distance from the energy E = 511 keV, the integration limits are determined. For parameter W, the energy limits E₁ and E₂ are selected, taking into account the absence of correlation effects with the S parame­ter. For all compared spectra, the integration limits remain unchanged. The S parameter is determined for curves from samples free of positron traps and samples with a high defect content are normalized to an equal area and plotted in Fig. 5—13D. To get the maximum sensitivity to changes in the line shape due to defects, the intersection points of both curves are selected by the limits of the parameter S. For defect-free material, these limits are used to determine the parameter S 0.5 often. The value of W is calculated for a limit far from the points where the curves intersect. In Fig. 5—13D, for determining S, the limits are selected at the point 511 ± 0.8 keV and for determining W at the points 511 ± 2.76 and 511 ± 4 keV. For GaAs reference samples for plastically deformed, the ratio between S parameters is 0.935. For the parameters W, the corresponding ratio was 1.294.

The background is adjusted by subtracting the straight line from the spectrum. Because the Doppler broadening spectrum of gamma-quantum annihilation radiation is symmetric with respect to 0 degree, peak tail intensities will be identical. A realistic background distri­bution modeled by a nonlinear function is a more complex processing method. At a given energy, the Y-ray background is proportional to the sum of high-energy annihilation events, which is taken into account by such a nonlinear function. The Doppler broadening curve remains slightly asymmetric, despite such a background decrease. Based on this W parame­ter is often calculated only in part of the high-energy Doppler curve. Using a setup with 2 Ge detectors, one can obtain high-quality Doppler broadening spectra by the coincidence method. The parameters W can be calculated on either side of the spectrum curve.

• Positron beam guidance systems

Before starting the study of the surface, it is necessary to separate the positrons leaving the moderator depending on their energy. Using an energy filter located in the beam guidance system, the beam of positrons is separated into unmoderated (fast) particles and a small fraction of monoenergetic positrons. This can be accomplished in a magnetic guidance sys­tem with the use of external electrodes in an E X B filter (crossed magnetic and electrical fields [133,135]) or in the external magnetic fields applied perpendicularly to the beam direc­tion (see references cited in the article [133]). A different method is based on the use of curved solenoids. Unmoderated positrons in this case are stopped by a shield. The study of positrons near the surface of the sample and the operation of the guidance system is
provided by a high vacuum (10^_5 Pa) inside the setup. Ultrahigh vacuum is required to study the surface. Here, the differential pumping station should be far from the sample chamber.

Fig. 5—13E shows a positron-beam system with magnetic guidance implemented at Martin Luther University, Halle-Wittenberg, Germany. Drifting tubes are placed behind the source-moderator system. At the ends of the drift tubes, positrons enter the E X B filter. In a linear accelerator, a maximum energy that can be received by the monoenergetic positron beam directed to the axis of the system is 50 keV. The collimator stops fast positrons. The angle of the emission of positron is several degrees relative to the normal to the decelerating foil [144]. Positrons move in a spiral because of the longitudinal magnetic field in the entire system of beams. All emitted positrons reach the target due to the magnetic field. The longi­tudinal field is generated by a guide coil system (Fig. 5—13E). Using a system of electrostatic lenses, beam directions are corrected ([133,135]). As the positron beam has wide range of energies, the design of lenses is very complex, but its advantage is the ability to focus the positron beam.