Using two alternative approaches to describing the defect structure of dislocation-free copper single crystals (the classical theory of the nucleation and growth of particles of the second phase in solids and Vlasov’s model for solids), we demonstrated that high-temperature precipitation of impurities occurs upon cooling of a growing crystal. High-temperature precipitation of impurities can lead to further development of a defective structure due to the formation of dislocation loops, microvoids (or micropores), dislocations, etc.
The basic principles of Vlasov’s physics are considered from a general point of view. The reliability of his judgments about the application of nonlocal statistical mechanics to real solids is shown. The possibilities of Vlasov’s physics for a reliable description of matter are discussed.
Using Vlasov’s model for solids, the diffusion model of defect formation in germanium was verified. The possibility of applying Vlasov’s model for solids to describe complexation in dislocation-free germanium single crystals is shown. Vlasov’s model for solids allows one to interpret the processes of defect formation in a crystal from a single viewpoint both at the stage of its growth and at the stage of heat treatment.
The basis for applying the model of high-temperature impurity precipitation is decay of a supersaturated solid solution of point defects near the crystallization front. A necessary condition for high-temperature precipitation is absence of recombination processes of intrinsic point defects (vacancies and intrinsic interstitial atoms, IPDs) at high temperatures. The recombination parameters for dislocation-free germanium single crystals were estimated using the terms and concepts of Voronkov’s recombination-diffusion model. It was shown that at high temperatures in germanium there is a barrier against the recombination of IPDs. It is assumed that the formation of structural imperfections, as well as in silicon, proceeds through the interaction “impurity + IPD”. The possibility of applying the mathematical apparatus the diffusion model of formation of structural imperfections to the formation of a defective structure in undoped dislocation-free germanium single crystals is considered.
The authors confirmed the validity of Vlasov’s model for solids using an example of real material. It is shown for the first time that Vlasov’s model for plasma and Vlasov’s model for solids give identical results and are, in fact, an analogue of the concept of the “large-scale structure of the Universe”. It is shown that in this aspect Vlasov confirmed the validity of the concept of Faraday-Thomson’s force lines. It is shown that since Vlasov developed his ideas on the basis of the mathematical apparatus of N.P. Kasterin, then adequate mathematical theories should emphasize the identity of the processes occurring at the macro and micro levels, which indicates the absence of any duality in nature.
It is shown that Vlasov’s model for solids describes the processes of complex formation during the growth of real crystals taking into account the thermal growth conditions. Allows in conjunction with the classical theory of nucleation and growth of second-phase particles in solids to calculate the defect structure of crystals, which was formed in the process of their growth. It has been established that the high-temperature precipitation of the impurity is directly related to the subsequent transformation of the defective structure during the production of silicon devices. A qualitative model of the formation of electrical centers has been proposed which directly links their origin with the initial silicon defect structure. It is shown that the concepts and principles of Vlasov’s physics are fully applicable to solid state physics.
The formation of silicon–carbon and silicon–oxygen complexes during cooling after the growth of dislocation-free silicon single crystals has been calculated using the Vlasov model of crystal formation. It has been confirmed that the complex formation begins in the vicinity of the crystallization front. It has been shown that the Vlasov model of a solid state can be used not only for the investigation of hypothetical ideal crystals, but also for the description of the formation of a defect structure of real crystals.
Theoretical studies of defect formation in semiconductor silicon play an important role in the creation of breakthrough ideas for next-generation technologies. A brief comparative analysis of modern theoretical approaches to the description of interaction of point defects and formation of the initial defect structure of dislocation-free silicon single crystals has been carried out. Foundations of the diffusion model of the formation of structural imperfections during the silicon growth have been presented. It has been shown that the diffusion model is based on high-temperature precipitation of impurities. The model of high-temperature precipitation of impurities describes processes of nucleation, growth, and coalescence of impurities during cooling of a crystal from 1683 to 300 K. It has been demonstrated that the diffusion model of defect formation provides a unified approach to the formation of a defect structure beginning with the crystal growth to the production of devices. The possibilities of using the diffusion model of defect formation for other semiconductor crystals and metals have been discussed. It has been shown that the diffusion model of defect formation is a platform for multifunctional solution of many key problems in modern solid state physics. Fundamentals of practical application of the diffusion model for engineering of defects in crystals with modern information technologies have been considered. An algorithm has been proposed for the calculation and analysis of a defect structure of crystals.
The adequacy of the model of high-temperature precipitation in dislocation-free silicon single crystals to the classical theory of nucleation and growth of second-phase particles in solids has been considered. It has been shown that the introduction and consideration of thermal conditions of crystal growth in the initial equations of the classical nucleation theory make it possible to explain the precipitation processes occurring in the high-temperature range and thus extend the theoretical basis of the application of the classical nucleation theory. According to the model of high-temperature precipitation, the smallest critical radius of oxygen and carbon precipitates is observed in the vicinity of the crystallization front. Cooling of the crystal is accompanied by the growth and coalescence of precipitates. During heat treatments, the nucleation of precipitates starts at low temperatures, whereas the growth and coalescence of precipitates occur with an increase in the temperature. It has been assumed that the high-temperature precipitation of impurities can determine the overall kinetics of defect formation in other dislocation-free single crystals of semiconductors and metals.
To describe the defective structure of semiconductor silicon, a triad is created: physical plus mathematical models — computational algorithm — program. This solution can be used both in studying the properties of crystals and in industrial production. Such a solution is the basic principle in the study of structural imperfections in any solid. A structural diagram of the diffusion model for the formation of structural imperfections in a crystal and a computational algorithm is presented.