An Accurate Representation of Incoherent Layers Within One-Dimensional Thin-Film Multilayer Structures With Equivalent Propagation Matrices

摘要

Working with electric fields (not their squares) in the presence of one or more incoherent layers requires averaging by varying their phase additions or layer thicknesses in random or equidistant steps. Our approach allows equivalent layers to be used in a single coherent calculation instead of variation and averaging. We believe that the idea has quite a strong potential for advances in the thin-film simulation field.We propose a novel approach of including incoherent layers into an arbitrary multilayer stack and treating them using the conventional matrix methods in the wave-optics regime. The proposed “Equivalent Matrix Method” (EMM) calculates two phase-shift additions that totally cancel out the interference terms in front of, and behind the incoherent layer. The additions are merged into an equivalent incoherent layer propagation matrix that can be used in the standard coherent calculation. The mathematical model that we describe in the paper has three important advantages. First, the exact calculation of the phase-shift additions efficiently replaces various phase-averaging approaches normally used to deal with incoherency. Second, instead of an incoherent layer, we can use an equivalent coherent layer in a rigorous simulation using the phase-matching. Last, there is no energy imbalance error caused by wave coupling in lossy incoherent layers. We verify the proposed EMM against the general transfer-matrix method (GTMM) and the combined ray optics/wave optics model (CROWM) using two cases: an arbitrary multilayer structure with four incoherent glass layers, and a thin-film hydrogenated amorphous silicon solar cell. In both cases, the EMM yielded the same results as the GTMM and CROWM, thus confirming its regularity.