Appl. Phys.A26,93-100 (1981) Applied Physics 9 Springer-Verlag 1981 Positron Detrapping from Defects" A Thermodynamic Approach M. Manninen NORDITA, Blegdamsvej 17, DK-2100 Copenhagen, Denmark R. M. Nieminen Department of Physics, University of Jyv~iskyl~i, SF-40720 Jyv~iskyl~i 72, Finland Received 19 May 1981/Accepted 2 June 1981 Abstract. 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. PACS: 71.60 + Z, 78.70B The detrapping of positrons (e+) from lattice defects can affect experimental results in three different ways. First, thermally activated detrapping may be seen directly as a change in the annihilation parameters, as is most clearly observed in the emission of positronium (Ps) from a metallic surface [1-3]. Secondly, strong trapping into one kind of a trap prevents the positron from trapping into any other defect. If the binding energy in the primary traps is small ("shallow traps") and if the annihilation characteristics in them differ only slightly from those in the bulk material, thermally activated detrapping from these defects increases the relative importance of trapping into other (deeper) defect states. This is experimentally seen as an ap- parent strong temperature dependent trapping rate into those defects, where the annihilation characteris- tics are clearly different from those of the bulk [4]. Finally, the trapped state from which the detrapping takes place can act as a precursor state to a deeper trap. In this case the detrapping decreases drastically the trapping rate into these deeper traps. An example of this is the model studied by Smedskjaer et al. [5], where the dilatation field of a dislocation forms an extended defect with a small positron binding energy and provides an effective trapping channel to jogs or other point defects in the vicinity of the dislocation line. Experimental evidence for detrapping seems to be unquestionable only in the case of thermal desorption of Ps from a positron surface state [1-3]. Maier et al. [6] have explained the anomalous temperature de- pendence of Doppler broadening of the 27 annihilation line of Ta by direct detrapping of positrons from monovacancies. Similar measurements have also been carried out for other refractory metals [7]. However, this interpretation has not been accepted by Gupta and Siegel [8] who estimated the positron-vacancy binding energies to be too high to allow any sub- stantial detrapping. Smedskjaer et al. [5, 9, 10] have explained low-temperature anomalies found in lifetime spectra, for example, in Cd and Au in terms of detrapping from dislocations, but there the tempera- ture dependence of the trapping process (perhaps diffusion limited) is not completely ruled out as anoth- er explanation. Similarly, the apparent strong tempera- ture dependence of positron trapping into voids in Mo has been explained by detrapping from some other shallow traps by Schultz et al. [4], whereas Nieminen et al. [11] were able to explain related behaviour for voids in A1 solely by temperature dependent trapping 0340-3793/81/0026/0093/$01.60