Accuracy-control techniques applied to stable transfer-matrix computations

The transfer-matrix methodology is frequently used to deal with elastic scattering problems that require a solution of the Schrödinger or homogeneous Maxwell equations in the continuous part of their spectra. The numerical stability of the transfer-matrix algorithm can be dramatically improved by a subdivision of the diffusive part of the system into several adjacent layers. However, until now, no accurate recommendation on the number of layers to use was given. This paper presents the transfer-matrix technique and the layer addition algorithm. A model is developed to analyze the accuracy of these techniques and enable a quantitative control. As a result of the model, an expression for the minimum number of layers to consider in order to achieve a given accuracy on the transfer-matrix computation is derived. The theory is illustrated by a simulation of electronic field emission.