An analytical model is presented to determine the potential and electric field distribution along the semiconductor surface of new silicon-on-insulator (SOI) reduced surface field (RESURF) device. The SOI structure is characterized by a semi-insulating polycrystalline silicon (SIPOS) layer inserted between a silicon layer and a buried oxide. An improvement in the breakdown voltage due to the presence of the SIPOS shielding layer is demonstrated. Numerical simulations using medici are shown to support the analytical model.
SUMMARYThe Kronig-Penney model is quite useful for illustrating many important features of the quantum behaviour of electrons in periodic lattice. Although the Kronig-Penney model is well-known and has been discussed in solid state textbooks, we try to use a simple and accessible way without the extremely laborious and tedious algebra evaluation to solve Kronig-Penney model. This paper presents a simple method without solving the difficult eigen-problem to solve the Kronig-Penney model, and the important energy band characteristics can be easily obtained with circuit concepts. The simulation results are presented to demonstrate the accuracy and superiority of the model.
The Kronig-Penney model consists of a periodic potential function, which is used to derive the concepts of allowed and forbidden energy bands. Here, to circumvent the tedious evolution, it is helpful to use computer methods to derive the textbook equation of the analytic Kronig-Penney model. The hierarchical methodology with the shorter symbols can effectively reduce the complication in the expression of the 4 × 4 matrix. By defining the symbol sequence, we can easily reduce terms by cancellation. With these methods and computer-aided evolution, we can derive the Kronig-Penney model from the matrix expression to the textbook form without the extremely laborious evolution.
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