Nano-viewpoint in Modeling and Investigation of the D/M/D Transparent-Conductive Layer

A transparent-conductive film (TCF) is widely used in various electro-optical devices. The dielectric/metal/dielectric (D/M/D) as one type of TCF has been highly considered due to more advantages, such as the possibility of selecting different materials and engineering other properties. For pre-fabrication design, it is often modeled with a 1D photonic crystal. This model needs to be improved due to the low thickness of the metal layer since a very thin metallic layer leads to a nanostructure instead of a uniform layer. In this study, after proper nanostructure modeling, the 3D-FDTD method was used to simulate different optical properties of the structure. The first aspect of the importance of the nanostructured model is to address the serious plasmonic losses. They are associated with the complicated metallic form in D/M/D that is not considered in conventional modeling. The simulation results showed that for Ag, plasmonic loss peaks demonstrate a wide distribution over the visible spectrum. These peaks show a more significant distribution near the UV–visible border for Al nanostructure. In both, the behavior of optical plasmonic loss tends to redshift compared to their bulk plasmonic peaks. Concerning optical transmission, Al does not offer a notable advantage over Ag. Due to the intense excitation of plasmonic modes when the metal layer has pores, a layer of entirely connected nanoparticles with the least possible thickness can have the desired optical properties. The increased rough surface of the dielectric layer due to the nanostructured metallic layer was also modeled.


Introduction
Transparent-conductive films (TCFs) are an essential component in various optoelectronic components such as liquid crystal displays, OLEDs, touch screens, and photovoltaics [1,2]. For TCF, the metal oxide layer using indium tin oxide (ITO), fluorine-doped tin oxide (FTO), and doped zinc oxide is usually used [2]. Alternative competitors have also been introduced, such as new conductive oxides with a broader transparent spectrum, dielectric/metal/dielectric multilayer structure instead of monolayer structure, conductive polymers, uniform-random metal grid, carbon nanotubes, graphene, nanowires-nanorods mesh, and ultra-thin metal film with or without periodic holes [1][2][3][4][5][6]. To date, one of the most practical TCFs is ITO. The sheet resistance and optical transmission of ITO depend on its thickness and fabrication method [1,7]. For an ITO layer at a thickness of ~ 200 nm, the sheet resistance of order 11 × 10 −3 Ω −1 and the optical transmission of ~ 86% at 550 nm wavelength have been reported [8]. But the main problem with ITOs is that they are expensive (restricted source) and have limited mechanical flexibility [1]. Among different types of TCF, the dielectric/metal/dielectric thin film (D/M/D) has proven its worth [7,8]. In the D/M/D arrangements, various dielectrics using metal oxides (like MoO3, V2O5, ZnO, and WO3) and ZnS have been investigated as dielectric layers [1,9,10]. In general, to use D/M/Ds as transparent-conductive electrodes, a load carrier density of 10 20 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 optical transmission. They can also be placed on the substrates, usually at room temperature, by different chemical or physical methods [11,12]. 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. For theoretical study and simulation of TCF, 3D modeling can be the first step. In simple structure modeling of the D/M/D, the only optical difference in depth is to be considered. On the other hand, after selecting the type of material, the design involves determining the thickness of these three layers. Hence, reflection and transmission can be calculated by techniques, such as the transfer matrix method (TMM) [13][14][15]. Moreover, the refractive index of the layers is typically assumed to be constant, but the dispersion of the refractive index should be considered in the transmission spectrum. Determining the thickness of the metal layer can be one of the design challenges of this D/M/D arrangement. 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 selected as the metal layer due to its high conductivity and reasonable price [16]. If the nominal thickness of the metal layer (Ag) is less than ~ 8 nm, discontinuities will occur on its surface, which will increase the sheet resistance. Also, the thickness should not be more than ~ 20 nm because it increases the reflection in the visible section. Depending on the thickness, thin film growth can occur in three ways, that they are Volmer-Webber (island growth), Frank-Van der Merwe (layer by layer growth), and Stranski-Krastanov (an intermediate case) [17]. 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 [18]. Hence, the metal layer in ِ D/M/D structures cannot usually have a homogeneous shape (uniform thin film). Therefore, the designing process, which is calculated based on a uniform and homogeneous metal layer, needs more investigation. Indeed, if the righter morphology of the metal layer can be considered, more details will be apparent in the D/M/D design. In contrast to the TMM method, the finite-difference time-domain (FDTD) simulation method allows 3D aspects of structure can be considered [19]. In one optoelectrical study of TCF based on randomly arranged Ag nanorods, the FDTD was used for simulation [5]. In another study, this method was used to investigate the optical transmission through square hole arrays in thin metal films [6].
Moreover, in a few studies for designing the D/M/D, the FDTD method was used, but the assumption of a uniform layer has remained [20,21].
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. Then, the results were analyzed and compared with TMM ones. Moreover, the details that cannot be considered by the TMM method were highlighted. Also, the change of metal material from Ag to Al and adding surface roughness to the nano-based modeling were investigated.

1D Photonic Structure
In this study, the TiO 2 /Ag/In 2 O 3 was selected for considering the nano aspect with 3D-FDTD simulation against the commonly TMM design. The Lumerical simulator is used for FDTD simulation. In choosing this typical D/M/D, both more flexible and less amount of In 2 O 3 has been considered. Simultaneously, it has the advantage that the top layer is similar to ITO, that its various effects have been widely used in optoelectronic applications [22,23]. Different aspects of introducing the simulation are given in Fig. 1a-f. Firstly, an initial value for the thickness of the three layers was estimated by the FDTD method. This was based on the approximation of a homogeneous and uniform layer with a sharp interface on the semi-infinite glass substrate (1D photonic structure introduced in Fig. 1a). The following describes the steps for calculating thicknesses by this TMM model: the a, b, and c in TiO 2 (a nm)/Ag(b nm)/In 2 O 3 (c nm) refer to layer thicknesses. At first, a and b were assumed to be equal to 25 nm, and the total reflectance of the ِ D/M/D was calculated at wavelength 550 nm for different thicknesses of Ag (Fig. 2, curve M). According to this curve, for the next step, 10 nm was selected for the Ag layer. Then, the total reflectance was calculated for the selected b = 10 nm and c = 25 nm, and different values of a-parameter (Fig. 2, curve N). In this section, the a = 33 nm was chosen for TiO 2 . Finally, the total reflectance was calculated for a = 33 nm and b = 10 nm and different values of c-parameter. In this section, the c = 33 nm was selected for In 2 O 3 (Fig. 2, curve O). Lastly, the D/M/D becomes the TiO 2 (33 nm)/Ag(10 nm)/In 2 O 3 (33 nm). Figure 3 shows the spectral reflectance and transmittance of the final D/M/D design by both TMM and FDTD methods. In Fig. 3, there is a good match between them. The mesh size of the FDTD method was 2 nm for the D/M/D structure.

Nanostructure Viewpoint
As mentioned in the introduction and thin films grow epitaxially at an interface, the nucleation mechanism of thin film development has been divided into three main types. It depends on the interaction between the deposited atoms of the target and the substrate surface [24]. The metal creates the nanostructure form since the thickness (< ~30 nm) is not thick sufficient to make a continuous film [25]. Therefore, to modeling the ~ 10 nm Ag thin layer in the D/M/D structure, oblate nanoparticles with a relatively large distribution in their size can be used. For this, the half elliptical nanoparticles were utilized from a somewhat random combination of size, position, and angle to each other. The average length of elliptical Ag particles and their standard deviation (estimated close to experimental one [26]) are given in Table 1. The modeling procedure was performed in the form of three samples with three different surface coverages (SCs) or SC 1 , SC 2 , and SC 3 (Fig. 4). These SCs of samples were selected qualitatively so that due to the lateral contact of particles with each other, they can characterize samples in the form of very high sheet resistance (SR), acceptable SR, and very low SR, respectively. On the other hand, the metal nanostructure in these samples consists of particles separated from each other (SC 1 ), somewhat separated from each other (SC 2 ), and the nanoparticles stick entirely to each other (SC 3 ). These XY cross-sections are shown in Fig. 4 (Fig. 1e refers to the location of these cross-sections in the structure).
In experimental studies, a figure of merit is usually used, which is defined based on optical transmittance (reflectance) and sheet resistance [27]. In this study, modeling is specified so that three limit states to SR (low, suitable, high) can be created qualitatively. Then their optical behaviors are determined in detail. For far-field (like reflection, transmission, and absorption), the results were presented after averaging on the data of ten simulations. In these ten simulations for each case, the random   Table 1 The particles size distribution for modeling Ag nanostructured layer (the average and its deviation along different axes) Z-standard deviation (nm) 35 10 36 8 18 5 distribution of nanostructure was different from each other. But the mean values determining the distribution characteristic of metallic nanostructure remained the same. The near-field results are comparative and are based on the maximum amount of field intensity (E 2 max (λ)) recorded in a typical vertical-plane section with the same geometric details for all samples.
In this study, the D/M/D layers are embedded on a semiinfinite glass substrate (moreover the Fig. 1c, the FDTD simulation design is also shown in the inset of Fig. 2). The light source is located in this glass substrate instead of outside. This setup leads to an appropriate reduction of the simulation time since the space in the FDTD method must be meshed.

Result and Discussion
The interaction of light with ِ D/M/D for three samples (SC 1 , SC 2 , and SC 3 ) in the form of reflectance, transmittance, and absorption curves are shown in Fig. 5. In the first comparison between Figs. 3 and 5, the difference between the conventional D/M/D design and the nano-viewpoint is quite apparent. In the TMM method, due to the assumption of a homogeneous and uniform layer (10 nm) and according to the Beer-Lambert rule, the absorption is relatively small. However, due to the nanostructure of the Ag layer in D/M/D, the plasmonic resonance absorption losses are more essential. Plasmonic resonances are a function of the shape, the material, the surrounding medium of nanoparticles, and the form they are placed relative to each other. Thus, contrary to Mie theory [28], which is commonly used for the optical study of single ~ spherical nanoparticle, 3D-FDTD simulation is one of the main steps for the plasmonic study of these kinds of nanostructures. The simulation results show that this distribution of Ag nanoparticles in the D/M/D structure leads to a wide range of plasmonic resonance wavelengths from 400 nm. In simple regard to D/M/D design (SC 1 , SC 2 , and SC 3 ), it may seem that an appropriate strategy would be consisting of nanoparticles that, while interconnected, still have enough empty space (pinholes structure). In other words, the connected nanoparticles ensure reduced SR, and enough open space provides proper light transmission. This form is well modeled in the SC 2 sample. Nevertheless, what is observed by the simulated results is that plasmonic losses in this structure are significant and appropriate transparency cannot be attributed to it. These samples were used to introduce three limit cases (i.e., style with high, acceptable, and very low SR). The surface coating of the Ag nanostructure is specified inside the figures It may then appear that the use of a metal whose plasmonic wavelengths are not within this range, can reduce these plasmonic losses. Therefore, Al shows its bulk plasmonic wavelength in the UV region, which may seem like a good alternative (instead of Ag) in the SC 2 sample. The simulated absorptance spectra for the three samples (SC 1 , SC 2 , and SC 3 -metallic layer Ag or Al) are shown in Fig. 6. The simulated results show that the nanostructured plasmonic peaks tend to redshift in both cases, compared to their bulk plasmonic peaks. For the Ag sample, the plasmonic peaks of the nanostructure are seen more in 600 nm to 800 nm. But they have more shifted to the beginning of the UV/visible spectrum for Al. Therefore, these plasmonic resonances of Al nanostructure can also harm the application of D/M/D, as a transparent layer.
The shape of nanoparticles in this study is part of a spheroid and can be formed by methods such as thermal evaporation. In another study that was performed on Ag nanorods on a glass substrate (random or uniform), the results showed that in addition to good SR (~ 5 Ohm/sq), the optical transmittance also resulted in ~ 80% [5]. This optical characteristic can be related to the lack of excitation of different plasmonic modes (less optical loss). This property can be the result of good nanostructure geometry that with a surface coverage of 35% can result in good optical transmission and low SR. In addition, this reference [6] is the study of square hole arrays in the thin metal film as a TCF with the extraordinary optical transmission. The coupling of light with short and long-range surface plasmons polariton has been introduced as an essential factor in enhanced light transmission. On the other hand, the tunneling through surface plasmons formed on each metal-dielectric interface plays an important role [29]. Although this structure seems to have complicated production steps than the D/M/D structure, it does not show a better optical transmittance. Moreover, especially SC 2 sample in this study can be considered an example of a thin metal layer with irregular holes. However, due to the strong localization of plasmonic modes (if any) due to irregularity [30,31], these modes do not seem very effective in optical transmission.
The imaginary part of the refractive index is directly related to losses inside the metal. The imaginary index value for Al is significantly higher than Ag. In contrast, the effects of plasmonic scattering for Ag can be significant. For showing this, a typical XZ cross-section was selected for monitoring the near-field. The maximum amount of field intensity (E 2 max ) on this surface was recorded at each wavelength. This quantity is a function of the details of nanostructured D/M/D and can be used to compare near-field effects between different modeled samples (Fig. 7). The results of Fig. 7 show that the near-field effect of Ag is more substantial than those of Al. Therefore, according to Figs. 6 and 7, Al would not offer a significant advantage over Ag in the D/M/D structure.
In this modeling, the SC 3 sample compared to others is more similar to the TMM model. On the other hand, the SC 3 represents the nanostructure with the least porosity. This sample shows absorption behavior that may be explained by the coherence interference and the Beer-Lambert relationship.
The decrease in the absorption behavior, especially compared to the SC 2 sample, can confirm that the plasmonic effects are attenuated by the orientation of the nanostructure Fig. 6 Absorptance of SC 1 , SC 2 , and SC 3 for the case in which the material Ag and Al are selected for TiO 2 /M/In 2 O 3 Fig. 7 The maximum field intensity simulated at each wavelength on the selected XZ cross-section for the three samples and different materials Ag and Al towards the continuous layer. In contrast, the SC 1 sample, which describes a state with wholly separated particles, shows broad plasmonic peaks that are somewhat similar to the extinction curve of a single particle with medium size. In SC 2 , which is more similar to the mean of the other samples, the absorption is relatively high, especially from 500 nm onwards. This behavior may be related to the presence of the near-field coupling effect, in addition to the loss of plasmonic resonances associated with the nanostructure themselves [32].
Finally, to add another aspect to the nano-viewpoint in D/M/D design, the optical effect of Ag nanostructure on the surface roughness of the second layer was modeled (this part of the simulation was performed for SC 2 sample, i.e., SC 2 -rough). The presence of metallic nanostructure on the first layer may lead to an increase in the surface roughness of the second layer [33]. Figure 8 shows this model for the SC 2 sample considering surface roughness. In this section of the modeling, roughness with dimensions commensurate with the metal Ag nanoparticles and aligned to them have been added to the surface of the second dielectric layer (In 2 O 3 ). The optical response curves of SC 2 and SC 2 -rough samples are also shown in Fig. 9. As can be seen, the addition of roughness to the model has not made a considerable change in far and near-field effects.

Conclusion
Paying attention to the nanostructured properties of D/M/D as a TCF during design can have particular importance. In most thin film fabrication methods, a continuous metallic layer with 10-nm nominal thickness is not formed. Prefabrication designs are usually based on the 1D photonic crystal that this selected model does not conform to the experimental fabrication characteristics. In this research, 3D-FDTD modeling was performed based on the nanotechnology viewpoint of the metallic layer. Due to metal nanostructure, complex plasmonic behaviors occur that cannot be investigated by conventional modeling. Therefore, three metal nanostructures that can represent cases with high (SC 1 ), suitable (SC 2 ), and low (SC 3 ) sheet resistance were modeled for the simulation. SC 2 sample refers to a metal nanostructure, where the particles have good continuity (low sheet resistance) and at the same time should be optically suitable due to the presence of sufficient porosity. The simulation results show that all three samples, especially sample SC 2 , do not have appropriate optical transmission due to complex resonant plasmonic losses. This negative plasmonic effect is also effective for metals such as Al, even in the visible range. As an idea for proper designing, the simulation results emphasize that the fabrication methods should be engineered so that the particles are wholly adhered to and with a minimum height to form a metal nanostructure. In other words, with the relative approach of the nanostructure to the uniform layer, the complexity and diversity of plasmonic peaks are reduced and move to bulk plasmonic ones. Of course, in this case, it is better to pay Fig. 8 Demonstration of a cross-section of the SC 2 sample, that the typical surface roughness has also added to the surface of the second dielectric layer Fig. 9 The maximum field intensity (a) and absorption curve (b) for two models Ag-SC2 and Ag-SC2-rough attention to surface plasmonic polariton (SPP) as well. The effect of the rough surface caused by Ag nanostructure was modeled. This roughness did not make much change in near and far-field results (in this size of spatial meshing).