Abstract
The purpose of the article is the study of convective flows and their influence on the growth of single crystals of silicon by the Czochralsky method from a large melt, which contributes to the emergence of non-stationary convection. Therefore, simulation of convection for the growth of silicon single crystals is an important step in the development of conditions for the growth of perfect single crystals. Silicon substrates are used to manufacture more than 90% of semiconductor devices and solar cells. A special role in the development of electronics is played by monocrystalline silicon, which is used for the manufacture of semiconductor devices and integrated microcircuits. The main requirements for the development of technology for the production of silicon substrates is an increase in quality at a decrease in cost. Promising technologies of 10-nm size and 3D-transistor structures significantly increase the requirements for uniformity of distribution of components, including layering in silicon single crystals. For the mathematical modeling of convective flows, melt flows were considered for a cylindrical crucible with a radius of 150 mm at a melt height of up to 40 mm. Such parameters ensure stationary convection in molten silicon. Methods of reducing stratification have been studied and developed for more than 50 years, but have not yet found a definitive solution. This method of single crystal growth is the most controlled and allows to influence the convective flows in the silicon melt below the phase interface with ultrasonic waves in the megahertz range. The effectiveness of using ultrasound in the extraction of semiconductor single crystals depends on the creation of special conditions for introducing them into the melt. 
 Reducing the influence of oxygen on the electrophysical properties of silicon single crystals is an intractable problem of silicon technology. One of the ways to solve this problem is alloying with an isomorphic impurity, for example, tin. The development of a method of doping single crystals of silicon with tin requires determination of its concentration in the liquid and solid phases
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