Mathematical model of static and quasi-static electric fields of ultra-low power under a polyelectrode cylindrical transducer
Abstract
The article has established that the simulation of static and quasi-static electric fields of ultralow power on the surfaces of materials of different conductivity of microelectronic devices with the possibility of integration into the hardware base of the information and measurement equipment created on the basis of such mathematical software modeling is an actual issue. Therefore, the main goal of this article is to carry out analytical and computer modeling of static and quasi-static electric fields of ultra-low power on the surfaces of materials of different conductivity under a polyelectrode cylindrical transducer. The results of mathematical modeling of static and quasi-static electric fields of ultra-low power, which is carried out by solving a system of analytical equations based on Laplace's differential equations, are presented. The peculiarity of this model is that it takes into account the dynamics of changes in the electric field and its dimensions in the process of scanning the latter by a polyelectrode cylindrical transducer, as well as the influence of external climatic (temperature, relative humidity) factors and electromechanical influence on the part of the investigated surface. On the basis of the performed analytical modeling, a computer model has been created based on the finite element method, and the model software has been created using the Python 3.10 object-oriented programming language. The developed model allows with high accuracy (the difference between the data of mathematical and analytical models does not exceed 2.15%, and with the experimentally obtained data - does not exceed 7.15%), as well as in real time, to build the distribution graphs of the intensity of electric field and electric charge, as well as to determine the parameter ranges of these fields, compliance with which does not lead to an electric breakdown. The scientific novelty of the article is that, for the first time, as a result of mathematical modeling, mathematical regularities of the influence of changes in the parameters of static and quasi-static electric fields of microelectronic devices (speed of changes in the shape and position of such fields in time and space), as well as changes in external factors on the power and energy characteristics of these fields are obtained. This makes it possible to determine with high accuracy and adequacy the critical values of such parameters, the excess of which leads to electrical breakdown and destruction of components of micro-electronic devices. The practical significance of the capabilities of the developed model, as well as the software tool for its implementation, lies in the experimentally confirmed results of calculating the main force and energy parameters of the electric field. In further research, it is planned to simulate and investigate the process of emergence and spatio-temporal changes of dynamic electric fields over surfaces of different electrical conductivity under a polyelectrode cylindrical transducer
Keywords
mathematical model; analytical equation; polyelectrode cylindrical transducer; electric field; electric tension; electric charge
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