Theoretical foundation and extension of the trapping model

The trapping model frequently used for analyzing experiments on positron annihilation in solids is put on a firm theoretical basis by deriving it from Waite's theory of diffusion-limited reactions. The conventional version of the trapping model turns out to be correct only if the trapping process is not diffusion-limited and if the escape probability of positrons from traps is negligibly small. The present paper treats both detrapping and the effects of positron diffusion for an arbitrary number of different types of traps, and develops a perturbation-theory solution for the general case.     

A study of mono and divacancies in Cu and Au by positron annihilation

The peak counting rate of the angular correlation curve was measured for Cu and Au in the temperature range between ?196°C and 1200°C. The experimental data were analysed by means of the trapping model under consideration of positron trapping by mono-and divacancies and detrapping of positrons from monovacancies. Such an analysis leads to acceptable results for both monovacancy and divacancy parameters.     

Positron trapping at grain boundaries

A simple model is developed for the trapping of positrons at grain boundaries. It is shown that there is a linear relationship between any linear annihilation parameter and the inverse grain size. An effective grain boundary width is defined, which depends on the positron diffusion length and on the strength of the grain boundary for positrons. The effect of detrapping on this effective width is also considered. The model is tested by using the experimental results available in the literature.     

Trapping of positrons at vacancies in magnesium

Trapping of positrons at vacancy-type defects in magnesium was studied by positron lifetime and Doppler-broadening measurements. Vacancy defects were produced by quenching, electron irradiation and deformation at low temperatures as well as by thermal agitation at elevated temperatures. In the first three cases we observed trapping at multiple vacancies, which anneal out between 77...400 K. Thermal equilibrium measurements show S-shape behaviour originating from positron trapping at magnesium monovacancies. However, changes in the positron parameters were very small, which is due to the weakness of the positron-vacancy interaction. A detrapping analysis yielded a positron-vacancy binding energy of the order of 0.3...0.4 eV.     

On the trapping rate of positrons in deformed lead over the temperature range 4–100 K

The trapping of positrons in annealed and plastically deformed samples of lead has been studied over the temperature range 4–100 K. The rate of trapping by defects has been found to be independent of temperature — a finding that supports the golden rule positron trapping model.     

Temperature dependence of positron parameters in voids and loops in Mo

The temperature dependence of positron lifetime parameters has been measured in the temperature interval from ?196°C to 300°C for two Mo samples containing voids? and loops. Both samples show an increased intensity of positrons annihilating in voids with increasing temperature. Strongly temperature dependent trapping into a loop bound defect is consistent with the experimental observations. It is shown that this trapping rate then decreases by approximately a factor 3 in the temperature range from ?196°C to 300°C. On basis of experimental data it can be ruled out that detrapping takes place from this defect.     

Positron lifetimes and annihilation lineshape in Cd and au from 4.2 K to the melting points

By means of an integrated source-specimen technique the temperature dependence of positron lifetimes and annihilation lineshapes has been measured, on the same specimens of gold and cadmium from 4.2K to the melting points, and also in electronirradiated and quenched gold. The anomalous temperature dependence of positron annihilation at intermediate temperatures (200 to 350 K in Cd, 270 to 750 K in Au) discovered by Lichtenberger, Schulte, and MacKenzie is confirmed. The data are incompatible with the idea that the intermediate temperature dependence is due to thermal expansion. They are well explained by an extension of the trapping model which includes the formation of metastable self-trapped positrons. From lineshape measurements after electron irradiation at 180 K and after quenching it is deduced that the trapping rate of positrons at vacancy-type defects in Au is temperature independent below room temperature.     

Positron trapping in electron-irradiated silicon crystals

The positron lifetime in electron-irradiated undoped and doped silicon crystals is studied as a function of temperature between 90 and 300 K. We show that the temperature dependence of the two lifetime components does not arise from the escape, but from the trapping rate at defects. The temperature dependences of the capture cross sections are deduced. It is concluded that in undoped crystals the positrons interact with negatively charged and neutral defects, probably divacancies and vacancy-oxygen complexes, respectively. In strongly P-doped crystals positron trapping occurs preferably in negatively charged centers.     

The temperature dependence of the diffusion coefficient and of the trapping rate of positrons in metals

The paper explores the consequences of metastable self-trapping of positrons for the temperature variation of positron diffusion coefficients and trapping rates. It is shown that the diffusion coefficient is expected to decrease with increasing temperatures from a value determined by the scattering of positron Bloch waves by acoustic phonons to a much lower one governed by a hopping process. The temperature variation of the rate of trapping by small defects such as vacancies is more complicated since only at high temperatures can we expect it to be limited by the positron diffusion coefficient. At low temperatures the observed magnitude of the rate of trapping at monovacancies can only be understood if the trapping rate is controlled by the rate of capture of positrons that have arrived at the trap.     

Positron detrapping from defects: A thermodynamic approach

The rate of positron detrapping in thermal equilibrium from lattice defects has been calculated by relating it to the specific trapping rate. The results for vacancies, dislocations and surfaces each show a different temperature dependence for the escape rate. For vacancies a measure of the importance of the detrapping can be obtained from the ratio of the vacancy formation energy to the positron binding energy in the defect. The positronium desorption rate from a surface is also calculated and agreement with experimental results is found.     

Positron annihilation studies of vacancy-type defects

The annihilation radiation of low energy positrons gives information on the electronic and defect structure of solids. There are three conventionally measurable quantities: the positron lifetime, the angular correlation of 2 annihilation radiation and the Doppler-broadened annihilation line shape. In the presence of lattice defects the annihilation characteristics show considerable changes. This is due to positron trapping at defects like vacancies and their agglomerates, voids, dislocations and grain boundaries. The concentration of defects can be deduced from the ratio of trapped and free positrons.The annihilation characteristics are different for different defect configurations. Positrons reveal vacancy agglomeration and the lifetime of trapped positrons gives estimates on the size of microvoids in the range of 2–10 Å. Various examples on the study of equilibrium and non-equilibrium defects, radiation damage and defect annealing are presented. Special emphasis is given to vacancy recovery and vacancy-impurity interactions in electron and neutron irradiated bcc transition metals like Fe, Mo, Nb, Ta.     

A model allowing pre thermalization trapping of positrons

A simple trapping model is developed incorporating the assumption that positrons may trap in defects prior to complete thermalization and is shown to explain recent lifetime data on Pb.     

New design of the CDB-spectrometer at NEPOMUC for T-dependent defect spectroscopy in Mg

Crystal defects in magnesium and magnesium-based alloys like AZ31 are of major interest for the understanding of their macroscopic properties. Coincident Doppler broadening spectroscopy with positrons (CDBS) is a well-established technique to investigate lattice defects and their chemical surrounding in solids. However, Mg and its alloys are demanding materials for positron spectroscopy, since the trapping rate in Mg is low and the trapping sites are shallow. In order to increase the trapping rate, the CDBS-facility at the high intense positron beam NEPOMUC is currently redesigned and improved with a cryostat for sample cooling. Furthermore, the recently installed remoderator provides a beam energy between 20 and 200 eV. On the contrary to the previous beam energy of 1 keV, the beam is therefore no longer non-adiabatically released from the magnetic field at the grounded field termination. Hence it is necessary to construct an insulated field termination where voltages up to 5 kV can be applied.     

Temperature dependence of positron annihilation parameters in neutron irradiated molybdenum

Positron lifetime measurements have been performed for molybdenum samples containing different densities of voids and dislocation loops. The samples consisted of single crystal molybdenum exposed to 2.7×10¹⁸ fast neutrons/cm₂ at 60°C, and subsequently annealed at 650°, 725°, 800°, and 875°C in vacuum (p<10^–7 Torr). After each annealing, where the densities of voids and loops were changed, positron lifetime measurements were performed in the temperature interval [–194°, 285°C]. In two-term fits of the measured spectra the longer lifetime, _e2-460 ps corresponds to an intensityI _e2 increasing with sample temperature. The shorter lifetime _e1 decreases with increasing temperature. A three-state trapping model with and without detrapping is discussed, and appears to be incapable of explaining the observed temperature dependences. A four-state positron trapping model including detrapping is necessary and satisfactory. It describes positron trapping to voids and trapping to dislocation loops, which is followed by a competition between detrapping and positron transition to jogs or other dislocation-bound defects. Mathematical expressions of the four-state trapping model including detrapping are worked out and calculations of the intensityI _e2 are compared with the experimental values ofI _e2. By use of special models for the temperature dependence of trapping rates, numerical values can be determined for the positron-dislocation-binding energy and for specific positron trapping rates.     

Isothermal annealing of oxygen decorated defects in silver

The dynamics of trapping and detrapping processes of oxygen decorated radiation defects in silver were investigated by the TDPAC technique. Three defect clusters containing In, oxygen and vacancies were studied by isothermal annelaing experiments between 250°C and 450°C. For the desintegration respective formation of two of these complexes, activation energies of E_a=1.02±0.08 eV and E_a=0.94±0.12 eV were found.     

Temperature dependence of positron lifetime in GaAs crystals with defects

Positron lifetime has been measured as a function of temperature in Sidoped GaAs single crystals subjected to various heat treatments. Defects produced by these heat treatments trap positrons. In all the GaAs samples containing defects positron lifetime was found to decrease with temperature in the range from 375 K to 16 K. The decrease is explained as due to the decrease in the trapping rate. The trapping rate is mainly controlled by the diffusion of the positron to the trap. The diffusion constant is determined mainly by the scattering from charged Si impurities.     

Positron escape from annihilation centers in electron-irradiated Si crystals

The mean positron lifetime in irradiated Si diminishes with increasing temperature between 77°K and 300°K. Isochronal high-temperature crystal anneals reduce the effect. Analysis suggests that thermally activated positrons escape after trapping in radiation-induced defects.     

Determination of trapping–detrapping events,recombination processes and gap-state parameters by modulated photocurrent measurements on amorphous silicon

Analysis of the out-of-phase modulated photocurrent (MPC) signal, the so-called Y signal, is proposed for determining the trapping–detrapping events, recombination processes and gap-state parameters in amorphous silicon. This is demonstrated by analysing experimental Y spectra obtained on this material from different laboratories including our own. Model simulations are also employed in which the amphoteric nature of the dangling bonds and their distribution according to the defect-pool model are taken into account. From the reconstruction of the Y signal, phase shift and MPC amplitude spectra, several contributions resolved from the frequency dependence of the experimental Y spectra are identified. Two electron trapping–detrapping processes are resolved. These are attributed to hydrogen-related positive defects and to transitions involving the D^+/0 level of the normal dangling bonds from the defect-pool distribution. At lower frequencies a residual contribution is resolved that is attributed to a term related to recombination through the D^+/0 and D^0/? levels. Between 300 and 150?K the above recombination contribution is essentially from the D^0/? and dominates the Y signal at lower frequencies. In this region a characteristic phase lead appears, which is attributed to the existence of safe hole traps in the valence band tail. Around 150?K, trapping–detrapping events in the conduction band tail dominate.     

Chemical analysis using coincidence Doppler broadening and supporting first-principles theory: Applications to vacancy defects in compound semiconductors

The Doppler broadening of the positron annihilation radiation contains information on the chemical environment of vacancy defects trapping positrons in solids. The measured signal can, for instance, reveal impurity atoms situated next to vacancies. As compared to integrated quantities such as the positron annihilation rate or the annihilation line shape parameters, the full Doppler spectrum measured in the coincidence mode contains much more useful information for defect identification. This information, however, is indirect and complementary understanding is needed to fully interpret the results. First-principles calculations are a valuable tool in the analysis of measured spectra. One can construct an atomic-scale model for a given candidate defect, calculate from first principles the corresponding Doppler spectrum, and directly compare results between experiment and theory. In this paper we discuss recent examples of successful combinations of coincidence Doppler broadening measurements and supporting first-principles calculations. These demonstrate the predictive power of state-of-the-art calculations and the usefulness of such an approach in the chemical analysis of vacancy defects.     

Subsurface-channeling-like energy loss structure of the skipping motion on an ionic crystal

The skipping motion of Ne+ ions in grazing scattering from the LiF(001) surface is studied for velocity below 0.1 a.u. with a time-of-flight technique. It is demonstrated that suppression of electronic excitation and dominance of optical phonon excitation in the projectile stopping results in an odd 1,3,5,... progression of the energy loss peaks, a feature usually ascribed to subsurface channeling. The experimental findings are well reproduced by parameter-free model calculations where thermal vibrations are the dominant cause for the ion trapping and detrapping.