Nanometer-scale electric field analysis by sub-window zooming-in technique

Recently, various micro- or nanometer-scale electromagnetic systems have been being developed. For analysis and design of those systems, precise calculation of electromagnetic field distribution is required especially on some minute local region. When the interesting parts in the system are extremely small compared to the whole region, its geometrical modeling and physical evaluation become a serious problem. In this paper, to resolve this problem, we present a numerical technique of electromagnetic field analysis for minute and fine structures. That is a sequential sub-window technique for closing up local electric field in the small region. The sub-window technique is on the basis of the finite element method and the outer boundary condition. To show the usefulness of the proposed algorithm, we tested it through two numerical models with exact analytic solutions. Their results showed the validity of the sub-window zooming-in technique. It was also applied to a real model of ferroelectric thin film recording by scanning probe microscopy.