**7. Conclusion**

636 Advances in Crystallization Processes

The program complex is the first experience of a virtual experimental device for research the real structure of dislocation-free silicon single crystals. Currently, it can be used for the analysis and calculation of the defect structure of undoped single-crystal silicon. Depending on the thermal conditions of crystal growth can determine crucial parameters such as size and concentration of grown-in microdefects. Approach to the analysis and calculation of formation grown-in microdefects has an important advantage in simplicity, accessibility and sufficient adequacy of mathematical modeling in comparison with other methods. For its implementation does not require supercomputers, and can effectively use the experimental data, experience and intuition of physicists, materials scientists and technologists for the analytical calculation and design of the defect structure. The program complex is easy to

Disadvantages software system is determined deficiencies of the diffusion model of formation grown-in microdefects. These include: (i) one-dimensional model; (ii) failure to account for the width of the V-shaped distribution of precipitates; (iii) uncertainty in determining of thermal conditions of growth; (iv) the error of approximate numerical methods. Elimination of these deficiencies will increase the accuracy of the calculations.

The influence of other impurities (e.g., dopants, nitrogen, hydrogen, iron, and others) on the formation of the defect structure of silicon can be taken into account by using two approaches: a rigorous approach and a simplified approach. A rigorous approach requires accurate accounting of all the components in equations (1) mass balance of point defects in the crystal. In this case, the solution of the corresponding system of coupled equations of the

A simplified approach assumes the separation of impurities in the two groups. The first group contains impurities, which interact with vacancies. The second group contains impurities, which interact with self-interstitial atoms. This interaction for the first group of impurities is similar to the interaction of oxygen atoms with vacancies. This interaction for the second group of impurities is similar to carbon atoms interaction with self-interstitial atoms.. Therefore, in equations (1) the sum of the concentrations of the components of the first group of impurities is equivalent to the impurity concentration of oxygen, and oxygen diffusion coefficient is the sum of the diffusion coefficients of the system components. Are defined analogously the components of interaction in the second group of impurities. Then the system of equations reduced to the system of equations (1), followed by the task of

The task of construction the defect structure of dislocation-free silicon single crystal is an inverse problem the analysis and calculation of grown-in microdefects. In this case, you must first specify the type, size and concentration of grown-in microdefects. Parameters of grown-in microdefects are selected based on the requirements for defect structure of devices and integrated circuits. In the next stage are calculated parameters of crystal growth (the growth rate for a certain diameter of the crystal and temperature gradients), which provide presence of given defects of structure. We get that the defect structure determines thermal conditions of crystal growth. To automate the process of crystal growth need to carry out the development of software products based on the diffusion model in combination with

implement on a personal computer in technology and research practices.

Fokker-Planck equation can be considerably more difficult.

determining the chemical nature of precipitates.

known software products for modelling crystal growth.

The diffusion model of the formation grown-in microdefects provides the unity and adequacy of physical and mathematical modeling. This model simulates of the defect structure of dislocation-free silicon single crystals of any diameters. The model of point defects dynamics can be considered as component of the diffusion model for formation grown-in microdefects. The diffusion model allowed to create software for personal computer. With the help of software can be conducted analytical researches which replace the expensive experimental researches.

Further development and modification of the software will lead to the development of information system of formation grown-in microdefects in dislocation-free silicon single crystals. The combinations of an information system with software for control the crystal growth will allow construct the defect structure of crystals during their growth. In turn, application a diffusion model of formation grown-in microdefects in the calculation of the formation of postgrowth microdefects allow to calculate the defect structure of silicon-based devices. In this case, it is possible to adequately construction the defect structure of silicon devices. We believe that the proposed in an article algorithm for the engineering of the defect structure of silicon can be used for other materials.
