The first part introduces the fundamental transport equations for electrons and holes, the continuity equations, and Poisson’s equation, which together form the basis for both analytical and numerical approaches. In addition, typical simulators such as PC1D, Sentaurus TCAD, and ASPIN3 are briefly presented, along with their main advantages and limitations.
The core of the work focuses on the simulation of three selected semiconductor devices: the pn-diode, the bipolar junction transistor (BJT), and the MOSFET. For each structure, the geometry, doping profile, boundary conditions, and recombination mechanisms were defined, and numerical simulations were performed. The results are presented in the form of energy band diagrams, carrier concentration distributions, electric fields, and current–voltage (I–V) characteristics. Numerical analysis allows us to observe the real shape of the graphs, including deviations from idealized models, which represents a significant advantage compared to classical analytical approaches.
Based on the analysis, it was found that numerical results provide a more accurate insight into device behaviour than idealized analytical models. Furthermore, a sensitivity analysis was carried out to demonstrate the influence of parameters such as doping, structural dimensions, and carrier lifetime on device performance. This identified the key factors affecting the characteristics of semiconductor devices and offered guidelines for their optimization.
The results confirm that the finite element method is an effective tool for the simulation and analysis of semiconductor structures and provides valuable support in the design and research of modern electronics.
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