Theoretical studies of physical processes and phenomena in the zone of physical interaction of nanoinstruments with the surfaces of elements of microsystem technology are carried out in work. Based on the conducted research, mathematical models of energy heat exchange in the zone of physical contact of nanometric dimensions were compiled, and their analytical solution was obtained using the Fourier method of separation of variables and Goodman's integral method. Simultaneously, the energy components of the processes in the nanocontact zone were considered. The numerical solution of the mathematical model of energy heat exchange in the zone of physical nanocontact was carried out using a software application based on the finite element method. The results were checked according to the equivalent thermal scheme to confirm the adequacy and accuracy of the obtained models. As a result, the mechanisms of energetic interaction of the nanoinstrument with the surfaces of the elements of microsystem technology devices were clarified. It is shown that the use of the proposed method of equivalent thermal circuits for the evaluation of mathematical models of the energy interaction of nanoinstruments with the surfaces of microsystem technology device elements, as well as the further study of the distribution of thermal fields in the nanocontact zone, differs from other numerical and analytical methods in terms of sufficient accuracy and speed of calculations. At the same time, it was established that the discrepancy between the results of mathematical modeling and the results obtained according to the equivalent thermal scheme does not exceed 5 - 8 %.

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• Бондаренко Марина Олександрівна (технічні науки)

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