Irradiance in Mixed Coherent/Incoherent Structures: An Analytical Approach

Abstract

We propose a new method for a light energy flux density (or irradiance) calculationin an arbitrary multilayer stack containing coherent and incoherent layers. Although the wellknown General Transfer-Matrix Method (GTMM) can be successfully used for the overall reflectanceand transmittance calculation, it does not allow us to obtain the corresponding irradiance depthprofile straightforwardly. We show in this paper that subsequent phase-shift integrations over theincoherent layers result in the reflectance and transmittance expressions identical to those of theGTMMformulation. However, the alternative mathematical approach allows us to derive an analyticalexpression for irradiance at an arbitrary depth of the multilayer stack, thus making it possible tocalculate the absorptance depth profile. In fact, the GTMM expressions for the overall reflectanceand transmittance turn out to be special cases of the irradiance calculation at the incident andemergent surface of the multilayer stack. Consequently, the proposed Phase-shift Integration Method(PIM) represents a continuous irradiance calculation model without any energy imbalances onlayer interfaces. In addition, since we are able to obtain analytical layer thickness derivatives,the PIM is suitable for use with gradient optimization methods. We verify the method on threecases of an encapsulated bifacial heterojunction silicon (HJ Si) solar cell, a perovskite solar cell,and a perovskite/silicon tandem solar cell, which all consist of thin and thick layers.