Software system for mathematical modeling the influence of effective potentials on electron states in quantum wells
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This work presents a detailed review and analysis of mathematical models and development software solutions applicable to the field of electronics of low-dimensional structures. Based on this, the architecture and components of a comprehensive software system were developed, intended for mathematical modeling of the spectral characteristics of electronic states in quantum wells using various effective potentials. A wide range of effective potentials is considered, including: the harmonic oscillator, anharmonic oscillator, Pöschl–Teller potential, modified Pöschl–Teller potential, as well as Morse and Lennard-Jones potentials. Each component of the software system allows users to modify the input physical and geometrical parameters according to the developed mathematical models and the types of functional materials used. In addition, the software enables convenient and efficient visualization of the effective potentials applied to potential wells, performs calculations of electronic spectra dependencies on input parameters, and generates their graphical representations. Based on the developed software modules, a software suite was designed and subsequently constructed in this work for direct application in the fields of nano- and microelectronics, addressing both engineering and purely scientific purposes.
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