Surface Green's functions for semi-infinite systems play an important role in the design of nano-scale electronic devices. In particular, functions in multilayered periodic structures are useful for practical applications. This paper describes numerical issues associated with the computation of these functions and offers an approach to addressing these issues. The proposed approach is based on the observation that numerical errors, which can occur in the existing algorithm to compute the functions, are caused by inaccurate computation of eigenpairs. We consider an alternative approach to eigenpairs to derive an algorithm to compute the functions. Numerical experiments show that the proposed algorithm can compute functions that satisfy physical requirements.
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