Particularities of the interstitial atoms and vacancies clusters formation in a thin cadmium telluride foil during in situ electron irradiation in a TEM

The formation of interstitial atoms and vacancies, as well as their clusters in the form of dislocation loops and voids in CdTe is simulated. The sizes and features of the growth of dislocation loops and voids were determined depending on the irradiation time, taking into account the decrease in the number of nodes of the semiconductor crystal lattice with the irradiation time, since in experiments we studied a thin CdTe foil in a transmission electron microscope (TEM). The calculated and experimental data are compared.


Introduction
Cadmium telluride (CdTe) relating to compounds A 2 B 6 is one of the main materials of semiconductor microelectronics. This material is promising for the production of gamma and x-ray detector devices, new hard x-ray detection systems for space science, small pixel imaging detectors, ultra-highresolution SPECT with CdTe detectors [1][2][3][4][5]. However, upon irradiation of CdTe, in particular by electrons, the structural defects are formed in it [6,7], which affect the electrophysical properties of this material and devices made on its basis.
Computer simulation of the interstitial atoms and vacancies clusters formation in cadmium telluride upon irradiation with electrons was carried out in [7,8]. In real experiments on the analysis of defect formation upon electron irradiation in a TEM, a thin foil is studied and the formation of clusters of point defects in this foil over time tends to decompose the material [9]. This means that in a thin foil, when modeling the processes of defect formation in TEM, it is also necessary to take into account the change in the number of crystal lattice sites of the material under study, which decreases with the duration of irradiation.

Results and Discussion
In previous studies, it was found that the types of defects, their concentration and the rate of defect formation in semiconductors depend on the stacking fault energy (SFE) [6,10]. One of the options for the formation of dislocation loops is the presence of partial dislocation loops. TEM studies have shown that Frank and Shockley dislocations are involved in these processes [10]. The results made it possible to establish the "critical" radii of dislocation loops crit r , which determine the boundaries that separate processes with different qualitative and quantitative changes in the evolution of a defective To determine this parameter, the classical model describing the energy of the formation of Frank loops was upgraded, taking into account that the formation of this loop occurs from partial Shockley dislocations, which is more energy-efficient.
As a result, we get:  The results show a good correlation with the experimental data obtained previously [6,10]. However, the mechanisms of development and evolution of a defective network in various conditions require detailed study.
In this paper, as part of a theoretical study, the formation of interstitial atoms and vacancies, as well as their clusters in the form of dislocation loops and voids in CdTe under electron irradiation is modeled.
Using effective activation energy values and effective concentrations of interstitial  I  SI  bI  I  I  I  I  V  I   I   c  Taking into account the formula (2), it is possible to convert expressions (1) into a system of partial differential equations taking into account the decrease in the number of lattice nodes under irradiation as , 2    Figure 4 shows the change in the number of lattice nodes during irradiation. A model that takes this change into account is displayed in solid lines in the figures. A model with a constant number of lattice nodes is indicated by dashed lines in the figures. The difference between these models is noticeable in figures 1-3 only at long times.

Conclusion
The obtained data were compared with experimental data both for determining the "critical" radii of dislocation loops and for numerical simulation of the formation of point defects clusters of interstitial and vacancy types in cadmium telluride [6,9]. There is a good agreement between theory and experiment. It is particularly important that we were able to significantly improve the results by taking into account two important features in the process of defect formation in CdTe. First, a contribution from partial Shockley dislocations was added to the model describing the formation of Frank loops. Second, the simulation takes into account the decrease in the number of nodes of the semiconductor crystal lattice with the time of irradiation, which is an important physical point, since the crystal (foil) has a limited size when irradiated in situ in TEM.
Taking into account the foregoing, the obtained results quite adequately reflect the mechanisms of defect formation in cadmium telluride and can be applied to similar semiconductors taking into account their physicochemical properties and the value of the SFE.