Transparent conductive films (TCF) are transparent and conductive thin layers. They are an essential component in various optoelectronic components such as liquid crystal displays, OLEDs, touch screens, and photovoltaics [1, 2]. For TCF, a metal oxide layer using indium tin oxide (ITO), fluorine-doped tin oxide (FTO), and doped zinc oxide is usually used . Although these are widely used, alternative competitors are also introduced. Other conductive oxides with a broader transparent spectrum, dielectric/metal/dielectric multilayer structure instead of monolayer structure, conductive polymers, metal grid, and random metal grid. Carbon nanotubes, graphene, nanowire mesh, and ultra-thin metal films have also been proposed [1-4]. To date, one of the most practical TCFs is ITO. The sheet resistance and optical transition of ITO depend on its thickness and fabrication method [1, 5]. For an ITO layer at a thickness of 200 nm, specifications such as sheet resistance of the order 11 * 10-2 Ω-1 and the optical transition of ~ 86% at 550 nm wavelength has been reported . But the main problem with ITOs is that they are expensive (restricted source) and have limited mechanical flexibility . Among the various other TCF options, the dielectric/metal/dielectric thin film (or D/M/D multilayer arrangements) has proven its worth [5, 6]. Moreover, various dielectrics using metal oxides (like MoO3, V2O5, ZnO, and WO3) and ZnS have been investigated as dielectric layers [1, 7, 8]. In general, to use D/M/Ds as transparent conductive electrodes, a load carrier density of 1020 cm-3 is required to achieve low resistance. Also, the bandgap of the structure should be larger than 3 eV to prevent light absorption. Such structures can also have excellent flexibility, high conductivity, and good transmission. They can also be placed on the substrates, usually at room temperature, by different chemical or physical methods [9, 10]. Also, the D/M/D work function can be controlled by the dielectric selection, allowing them to be used as a cathode-anode or even as an intermediate electrode in tandem solar cells. To theoretical study and simulation, 3D modeling is the first step. In simple modeling, the only optical difference in depth is to be considered. After selecting the type of material, the theoretical optimization of this structure involves determining the thickness of these three layers. Hence, reflection and transmission can be calculated such as the Transfer Matrix Method (TMM) [11-13]. Moreover, the refractive index of the layers is typically assumed to be constant, but the dispersion of the refractive index can also be considered in this method. Determining the thickness of the metal layer is one of the significant design challenges of this structure. This thickness should be large enough to ensure the conductivity of the layer and at the same time, be as small as possible so as not to impede the required transparency. In D/M/D structures, Ag is usually chosen as the metal layer due to its high conductivity and reasonable price . If the thickness of the metal layer (Ag) is less than ~8 nm, discontinuities will occur on its surface, which will increase the sheet resistance. Also, its thickness should not be more than 20 nm because it increases the reflection in the visible section. Depending on the nominal thickness at this very thin domain of metal, thin-film growth can occur in three ways Volmer-Webber (island growth), Frank-Van der Merwe (layer by layer growth), and Stranski-Krastanov (an intermediate case) . The Volmer-Weber happens with low wettability materials forms isolated islands. This method is the typical growth accessible by soft metals (like Ag) onto insulators . Hence, one of the design challenges of these ِD/M/D structures shows itself. In other words, at least the metal layer cannot have a homogeneous shape (uniform thin film). Therefore, the last optimized thickness, which is calculated based on the assumption of a uniform and homogeneous layer, seems to need more investigation. Certainly, if the righter morphology of the metal layer is considered, more details will be apparent in the D/M/D design. In contrast to TMM, there is a finite-difference time-domain (FDTD) simulation method that allows different 3D aspects of structure to be considered . In a few studies for designing the D/M/D, the FDTD method has been used, but the assumption of uniform layers has remained. Therefore, those results can be achieved with TMM, too [18, 19].
In this study, first, the nanostructured D/M/D was modeled appropriately. Then, by selecting the typical materials, the near and far-field results were obtained by the FDTD method. The results obtained by 3D-FDTD modeling were analyzed and compared with TMM results. Moreover, the details that were not considered by the TMM method were highlighted and studied. Also, the change of metal material from Ag to Al and the effect of adding surface roughness to the nano-based modeling were investigated.