Positron Annihilation Spectroscopy (PAS) is a powerful method for investigating questions in materials physics. In this process, the antiparticles of electrons, positrons, are used as highly sensitive probes to resolve material defects on an atomic scale. The non-destructive material characterization using positrons has developed into an established technique over the past decades and is now widely used in the study of metals, semiconductors, polymers, and porous materials.
When a positron encounters an electron, both particles annihilate, usually emitting two photons each with an energy of 511 keV, which are emitted in opposite directions. Various measurement techniques are based on the detection of these annihilation quanta. In the presence of disturbances in the crystal lattice, such as vacancies, both the energy and density distribution of the electrons change. Due to their positive charge, positrons are repelled by atomic nuclei and are preferentially captured (trapping) in (negative or neutral) vacancies, vacancy clusters, or nanoscale cavities. There they annihilate with electrons, whereby the positron lifetime and the momentum of the annihilation electron (Doppler broadening) serve as sensitive parameters for the identification and quantitative estimation of defect types and concentrations.

• Sensitivity: PAS can detect extremely low defect concentrations of up to 1 ppm (one defect per million atoms)
• Defect Characterization: PAS can determine defect types and concentrations via material-specific measured variables such as the positron lifetime τ_i and the S or W parameters
• Pore Sizes: Cavities and free volumes in the range of 0.3 to 100 nm can be measured for open and closed systems

The physical life cycle of a positron

• Generation: Positrons are created by β⁺ decay (e.g., from ²²Na) or pair production in accelerators
• Thermalization: After implantation, positrons lose their kinetic energy through collisions within a few picoseconds
• Diffusion: In thermal equilibrium, they diffuse approx. 100 nm through the lattice
• Trapping: Defects such as vacancies, vacancy clusters, or pores act as attractive potential wells and capture the positrons
• Annihilation: The positron annihilates with an electron, emitting mostly two 511 keV photons

What is PALS?

PALS is a highly sensitive, non-destructive method for investigating material defects and free volumes at the atomic level. The technique measures the time interval between the creation of a positron and the emission of the annihilation radiation. Since positrons are preferentially trapped in defects with lower electron density, their lifetime is extended there, allowing conclusions to be drawn about the type, size, and concentration of the defects. Basically: The larger a defect or a volume in the material, the longer the positron lifetime.

PALS Parameters

• Positron lifetime τ_i: Lifetime is defined as the time interval between the creation of the positron and its subsequent annihilation. The annihilation rate is directly proportional to the local electron density at the site of annihilation. Since lattice defects (such as vacancies or pores) have a lower electron density than the undisturbed lattice, positrons "live" longer there. The larger the free volume of a defect, the longer the measurable lifetime.
• Intensity I_i: Intensity describes the relative proportion of a specific lifetime component in the total number of measured events. It reflects the trapping probability of positrons in a specific defect type. A higher intensity of a defect-specific signal correlates directly with a higher concentration of these defects in the material.

Mathematically, the relationship can be represented as follows:

with the time resolution function R[t]:

Graphically represented, this results in the positron annihilation lifetime spectrum N[t], shown here using the example of the Metal-Organic Framework (MOF) CALF-20:

Application Examples of PALS

• Metals and Alloys: PALS is used to investigate vacancy complexes in the early stages of precipitation hardening – a process essential for mechanical integrity in aerospace applications. Additionally, neutron-induced defects (e.g., monovacancies and vacancy clusters) are identified, which cause the embrittlement of steels in fusion and nuclear reactors. The method enables the detection of ultra-fine defects in plastic zones long before macroscopic cracks are detectable with conventional methods.
• Semiconductors: In microelectronics, complexes of monovacancies and n-type dopants (e.g., phosphorus, arsenic) are analyzed, which limit the maximum doping concentration. For wide-bandgap semiconductors (ZnO, GaN, Ga₂O₃), cation and anion vacancies and their charge states are characterized to specifically control optoelectronic properties.
• Polymers and Free Volume: PALS determines the glass transition (T_g) via the thermal expansion of the free volume more precisely than many macroscopic methods. The technique monitors physical aging (relaxation) below T_g, which directly correlates with the increase in density and yield strength. Furthermore, aging processes under the influence of temperature changes or gas atmospheres can be followed in situ.
• Meso- and Microporous Materials: In Metal-Organic Frameworks (MOFs), the lifetime of ortho-positronium (o-Ps) via pick-off annihilation correlates directly with pore sizes in the range of 0.3 to 50 nm. PALS identifies bimodal structures consisting of crystalline micropores and irregular mesopores in various sample forms – from compact solids (bulk) and powders to thin membranes or coatings (50–5000 nm).

What is DBS?

Doppler Broadening Spectroscopy (DBS) is a non-destructive method of Positron Annihilation Spectroscopy (PAS) that measures the energy distribution of gamma quanta produced during the annihilation of positrons. When a positron annihilates with an electron in the material, two photons are usually produced, each with an energy of approximately 511 keV. Since the momentum of the electron prior to annihilation is transferred to these photons, a small energy shift occurs – the Doppler effect. This shift leads to a broadening of the 511 keV peak in the energy spectrum. Positrons are trapped in open volume defects (such as vacancies or clusters). There, they preferentially encounter slower valence electrons, which causes the measured peak to become narrower as the momentum distribution of the electrons at the site of annihilation changes.

Parameters of DBS

• S-parameter: The S-parameter (shape parameter) measures the central region of the peak. In defects, the positron preferentially annihilates with low-energy valence electrons. This leads to a narrowing of the 511 keV peak and thus to a higher S-value. A high S-parameter indicates an increased defect concentration, as more annihilations took place with slow electrons.

  $$S=\frac{A_S}{A}\text{ with }{A}_S=\underset{E_0-E_s}{\overset{E_0+E_s}{\int }}N[E]dE$$

• W-parameter: The W-parameter (wing parameter) measures the tails ("wings") of the peak. It is determined by annihilation with high-energy core electrons and provides information about the chemical environment of the defect. While the S-parameter primarily reflects the defect density, the W-parameter is particularly sensitive to the chemical environment of the defect. Since core electrons retain their elemental identity, the W-parameter (especially in Coincidence Doppler Broadening Spectroscopy, CDBS) enables the identification of foreign atoms or precipitates located in the immediate vicinity of a defect.

  $$W=\frac{A_W}{A}\text{ with }{A}_W=\underset{E_1}{\overset{E_2}{\int }}N[E]dE+\underset{E_3}{\overset{E_4}{\int }}N[E]dE$$

• S-W diagram: The correlation of both parameters is typically represented in an S-W diagram to identify changes in the defect structure. If the measurement points (S, W) for different sample states lie on a straight line passing through the bulk values (S_b, W_b), a single defect type dominates the trapping, with only its concentration varying. If the data points deviate from this line, it indicates a transition to a different defect species or the presence of multiple defect types (e.g., transition from simple vacancies to larger vacancy clusters). The slope of the line in the S-W plot is often referred to as the R-parameter. This value is characteristic of a specific defect type and remains independent of the defect concentration.

• Ps_3/2-parameter: The Ps_3/2 annihilation parameter describes the ratio between the frequency of three-photon annihilations and two-photon annihilations of a positron in a material. This parameter serves primarily as an indicator of the fraction of free ortho-positronium (o-Ps) decays. An increase in the 3γ / 2γ ratio suggests an increase in free o-Ps decays, typically caused by higher porosity, larger pores, or an increased Ps formation rate (e.g., near the sample surface).

  $${\mathrm{Ps}}_{3/2}=\frac{N_{3\gamma }}{N_{2\gamma }}=\frac{\underset{E_1}{\overset{E_2}{\int }}N[E]dE}{\underset{E_2}{\overset{E_3}{\int }}N[E]dE}\text{ with }{N}_{2\gamma }=A$$

Positron Annihilation Spectroscopy with variable implantation energy, often referred to as VEPAS (Variable Energy Positron Annihilation Spectroscopy), is a specialized method for depth-dependent investigation of surfaces, thin films, and membranes. In contrast to conventional source-based PAS, such as in the CoPS 1 and CoPS 2 systems, which use a broad energy spectrum and primarily measure bulk properties (up to 2 mm depth), VEPAS (like the MePS, SPONSOR, or AIDA systems) uses a monoenergetic positron beam. The kinetic energy of the positrons can be precisely adjusted, typically in the range of a few hundred eV up to 35 keV. By varying the energy, the mean implantation depth can be controlled from the first 10 nm to several micrometers.

The Implantation Profile – The Makhov Distribution

The depth distribution of the stopped positrons does not follow a point-like implantation, but rather a statistical distribution, the so-called Makhov distribution.

The mean penetration depth $\overline{z}$ is described by the following equation:

As energy increases, not only does the penetration depth increase, but the profile also broadens ("smearing"), which limits resolution at greater depths.

Measurement Methods at Variable Energy

• Variable Energy Doppler Broadening Spectroscopy (VE-DBS): This is the most common procedure. Here, the S, W, or Ps_3/2 parameter is measured as a function of energy to create defect or depth profiles. Since a continuous beam is sufficient for this, the technique is experimentally easier to implement. The SPONSOR and AIDA systems offer this technique.

• Variable Energy Positron Annihilation Lifetime Spectroscopy (VE-PALS): This method is technically more demanding as it requires a pulsed positron beam to generate a start signal for time measurement. It enables the determination of defect type and size (e.g., vacancy vs. cluster) as a function of depth. MePS is one of the few systems worldwide that offer such a measurement method.