Figure 1: Positron Annihilation Technique (PAT), a relatively new nuclear physics technology, which utilizes the annihilation radiation of positrons in condensed matter to bring out information on the internal microstructure of the matter, electron momentum distribution and defect states, thus providing a non-destructive means of research, and it has become a new technology and means of researching the microstructure of the matter, defects, fatigue and so on.

Positronic Science

Development of positronic science

In 1928, the British physicist Dirac first put forward the concept of "anti-electron"; in 1930, the Chinese physicist Zhao Zhongyao first discovered the anomalous absorption of hard γ-rays and special radiation on heavy elements; positron was discovered by Anderson and his mentor, Milligan, in 1932; and by O. Klemperer and others in 1932, the phenomenon of positive and negative electron annihilation was discovered, thus beginning the development of positron annihilation technology, the important history of the development of positron is shown in Table 1. 1932 found the phenomenon of positive and negative electron annihilation, thus beginning the development of positron annihilation technology; the important history of the development of positron is shown in Table 1.

Table 1 Important history of the development of positrons

Fundamentals of positron annihilation spectroscopy

Positron annihilation spectroscopy (PES) is the detection of localized electron density and atomic structure information through the interaction of positrons with the material's surroundings. The commonly used positron source is the positron produced by the decay of 22Na radioactive source. 22Na decay produces two energies of positron (90% of the positron energy of 0.545MeV and 10% of 1.82MeV) and at the same time, it will also emit γ-photons of 1.275MeV.

In addition, another method of obtaining a source of positrons experimentally can be generated by high-energy electron acceleration impact target γ photons, when the γ photon energy exceeds the sum of the rest mass of the two electrons (i.e., 1.02 MeV), in the nucleus of the Coulomb field, the γ photon is converted into a pair of positron and negative electrons.

After entering the interior of the material, the positron generally undergoes several processes of annihilation, including the processes of superthermalization, thermalization, diffusion, capture, and finally annihilation, as shown in Figure 2. Positron in the superthermalization process time relative to the annihilation lifetime of positron is very short, the annihilation lifetime of positron experiment basically has no effect, can be ignored.

Figure 2: Schematic of annihilation of positron after thermalization, diffusion and trapping in a material

When the energy of the positron drops to 20 eV, the inelastic scattering of electrons begins to weaken, and the main energy loss of the positron comes from the lattice scattering, i.e., the phonon scattering mechanism, until finally the positron is completely thermalized and the material itself reaches thermal equilibrium, a process that is the thermalization process of positrons.

When the positron is completely thermalized and the material itself reaches thermal equilibrium, diffusion occurs in the material, due to the low rate of the diffusion process, relative to the injection depth of the thermalization process, the diffusion length is only about 100 nm. Therefore the injection depth of positron inside the material is mainly determined by the thermalization process of positron. The distribution of injection profiles of positrons in Si with different energies is shown in Fig 3.

Figure 3: Distribution of injection profiles of positrons in silicon for different energies in the range of 1.5-10 keV

Positrons encountering negatively charged vacancies or doping-type defects during diffusion are likely to be trapped, resulting in a longer lifetime of the positron. The ability of defects to trap positrons can be expressed in terms of the capture rate κ:

where $\mu$ is the positron trapping coefficient and Cd is the defect concentration of the crystal. The positron capture rate is affected by the nature of the material defects as well as the defect concentration. Figure 4 shows the relationship between the capture coefficients of positrons by Si vacancies of different charge states with temperature. At the same temperature, the larger the absolute value of the negative charge state is, the higher the capture rate of positrons is; with the increase of temperature, the capture rate of positrons by defects in the negative charge state gradually decreases, and the capture rate of positrons by neutrally-charged defective states gradually increases.

Figure 4: Capture coefficients of positron by Si vacancies of different charge states as a function of temperature

The type and concentration of defects in a material can be determined by measuring the lifetime of positrons, i.e., positron lifetime spectroscopy. In addition, the electron momentum distribution in a material can be determined by measuring the energy information of the photons produced by annihilation, i.e., Doppler spreading spectroscopy, etc.

Advantages of Positron Annihilation Technology for the Study of Materials

Positron annihilation technology can combine nuclear physics and nuclear technology and be applied to research in the field of solid state physics and materials, including positron experimental detection technology and positron theoretical calculation technology. Its most important feature is that it is extremely sensitive to structural phase transitions and atomic scale defects, and has become a non-destructive means of detecting and analyzing the microstructure and electronic structure of materials. As a new microanalytical technique, the research scope of positron annihilation technology is mainly aimed at atomic-size microstructures and defects. Figure 5 below shows the comparison between positron spectroscopy and other methods. By comparison, it is easy to see that positron spectroscopy shows its unique properties in areas of research that are very active today, such as surfaces and interfaces of semiconductor materials, polymers, condensed matter physics, and so on. Compared with the usual microstructure analysis such as STM, SEM, TEM and other techniques, positron annihilation technology can not only provide information on the size of the defects, phase transition information, but also provide information on the distribution of the defects with the depth, and be able to deeply analyze the electronic structure of the material as well as the chemical environment at the positron annihilation, which can make up for the deficiencies of the other microscopic detection techniques, and has irreplaceable characteristics.

Figure 5: Comparison of micro-scale and defect concentration analyzed by various probes

Positron Annihilation Lifetime Spectrum (PALS)

Positron Annihilation Spectroscopy, also known as Positron Annihilation Lifetime Spectroscopy (PALS), is a cutting-edge non-destructive material testing technique designed to provide insight into the atomic level properties of materials. This technique is mainly applied to the detection of defects and vacancies in solid materials. The principle is based on the annihilation process induced by positron-electron interactions, which is realized by detecting the relaxation time of the gamma rays released during annihilation. The length of this relaxation time directly reflects the size of the atomic level holes, i.e. the size of the vacancies, in the material. By indirectly measuring the relaxation time of annihilation, the amount of defects in a material can be accurately determined, which plays an extremely important role especially in the field of defect design and characterization of energy storage materials. This technique provides us with a means to explore the internal structure of materials in depth, bringing unprecedented opportunities for research and applications in materials science and engineering.

Principle

Positron lifetime is the time from the generation of positrons to the annihilation of the disappearance of positrons, that is, positrons from the radioactive source to enter the material and the total time of electron annihilation. The starting signal of positron generation can be replaced by the 1.28 MeV γ-photon emitted by22 Na, and the signal of annihilation disappearance can be replaced by the 0.511 MeV γ-photon produced by the annihilation of positron and negative electrons. The positron lifetime is measured by measuring the time difference between the 1.28 MeV γ-photon signal and the 0.511 MeV γ-photon signal. The positron lifetime can reflect information about the microstructure of many materials.

Figure 6: Schematic diagram of positron annihilation lifetime spectrum measurement

Application Examples

Figure 7: Example for PALS

Doppler broadening spectroscopy (DBS)

The magnitude of the energy change is related to the momentum of the electron before the annihilation, so the Doppler broadening spectrum can be measured to obtain the information of the division of the electron momentum. A high energy resolution detector is often used to detect the γ-photons after the annihilation in the experimental process. Through the detection of a large number of annihilation events produced by γ photons can be obtained to 0.511MeV as the center of the symmetric distribution of the annihilation photon energy distribution curve, and the Doppler broadening spectrum, the shape of the spectrum has the momentum of the electrons before the annihilation of the electron to determine the shape of the peaks in the spectrum, you can obtain the momentum distribution of annihilated electrons in the sample.

Principle

For measurements, the source and sample form a "sandwich" structure and are placed in front of the HPGe detector. Positron annihilation of the γ-photons is processed by the HPGe detector, amplifier and multi-channel analyzer to obtain a Doppler broadening spectrum.

Figure 8: Positron Annihilation Radiation Doppler Broadening Measurement Setup

Parametric analysis is commonly used in Doppler broadening spectroscopy, where the S-parameter is defined as the ratio of the area in the 510.24-511.76 keV energy range to the total area in the 501.00-521.00 keV energy range, and the W-parameter is defined as the ratio of the sum of the areas in the 513.6-516.9 keV and 505.10-508.40 keV energy ranges to the total area in the 501.00-521.00 keV range. The W parameter is defined as the ratio of the area in the energy ranges of 513.6-516.9 keV and 505.10-508.40 keV to the total area in the energy range of 501.00-521.00 keV. The S parameter reflects the annihilation information of the positronic electrons and the low-momentum electrons (conduction electrons) in the material. The probability of low-momentum electrons at vacancy defects is much higher than that of core electrons, which increases the annihilation probability of positrons and low-momentum electrons, leading to an increase in the S-parameter, which is manifested as higher and narrower peaks in the Doppler broadening spectrum.

The W parameter reflects the annihilation information of positrons and high-momentum electrons (core electrons). When there is a precipitation phase inside the material, the positrons are easily captured by the precipitation phase and annihilate with the inner-shell electrons of the atoms in the precipitation phase, resulting in a larger W parameter and a lower and wider peak on the Doppler broadening spectrum. When the defects in the material increase, the probability of the positrons being captured by the defects increases, leading to an increase in the S-parameter, which in turn reflects the information about the defects in the material.

Figure 9: Schematic definition of Doppler spread spectrum parameters

Application Examples

Figure 10: Example for DBS