I. INTRODUCTION

To date, Sn-doped In$_{2}$O$_{3}$ (ITO) has been most widely used as a transparent electrode for the applications of flat panel displays, touch screen panels (TSPs), and Si-based solar cells ^(1-3). The reasons for this are its prominent properties of high optical transmittance and low resistivity. However, as the diagonal size of the screen increases, the requirements become more stringent. In addition, conductive oxide layers, such as ITO and AZO, are not sufficiently stable for use in flexible substrates. Organic light emitting diode (OLED) displays are currently used in many mobile devices, and some TVs and lighting fixtures. OLED displays also require more transparent and highly conductive electrode for better image quality ^(4,5). In particular, the anode electrode composing the OLED requires a resistance as low as possible, in order to avoid a deterioration of image uniformity due to a resistive voltage drop, besides the high transmittance. Recently, high-performance flexible OLEDs have been intensively developed for application to curved, rollable, or stretchable displays ⁽⁶⁾. Unfortunately, ITO is not a promising candidate for flexible substrates, owing to its brittleness when subjected to bending, and high sheet resistance when formed at room temperature (RT).

In order to replace the ITO, the use of multiple layers with a thin metal layer embedded between two TCO layers has been proposed as a possible alternative to the ITO ^(7,8). Of those multiple layers, ITO/Ag/ITO has been the most extensively examined structure by several researchers ^(9-11). However, even with the optimum combination for the thicknesses of both ITO and Ag, the continuous ITO/Ag/ITO multilayers show a limitation of the transmittance on shorter wavelengths below about 400 nm, and longer wavelengths above about 700 nm, compared to a single ITO layer ⁽¹²⁾.

In this study, in order to improve the transmittance, Ag layer was formed with mesh structure. The transmittance in the ITO/Mesh-Ag/ITO structure with a meshed Ag layer depends on several factors, such as Ag thickness, mesh space and width, in addition to the ITO thickness. Thus, experiments attempting to optimize the transmittance are time consuming. An alternative approach is to use a reliable simulation program that should allow for the computation of sub-micrometer structure. This work has focused on the analysis by simulations for the three dimensional (3D) structures of ITO/Mesh-Ag/ITO multilayer. The aim of this study is to theoretically analyze the transmission phenomena for the ITO/Mesh-Ag/ITO structure, and verify the effectiveness as a highly conductive transparent electrode. The simulated results were compared with the experimental ones for the same dimensions of the fabricated ITO/Mesh-Ag/ITO structures. In the experiments, the meshed Ag structures with optimum thickness were formed using a conventional photolithography method, which would be useful for commercialization of this technology in the transparent electrode industry. ITO and Ag layers are fabricated using an in-line sputtering method. Optimal thickness conditions have been investigated in terms of optical transmittance and electrical conductance.

II. Experimental Details

In our previous work ⁽¹²⁾, the ITO/Ag/ITO multilayers with continuous Ag film has some limitations in optical transmittance, having shown much lower transmittance over shorter wavelengths below about 400 nm, and over longer wavelengths above 700 nm, compared to a single ITO layer. For the purpose of improving the transmittance, the ITO layers embedded by an Ag film with mesh structure having a thickness of nanometer range were evaluated through the experiments and optical simulations. For the ITO/Mesh-Ag/ITO structure, the key issues would be an open ratio of the mesh-Ag layer, and the Ag thickness, in respect of the optical transmittance and electrical resistance. In this work, for experimental convenience, we have kept the Ag thickness fixed at about 10 nm, which was the proper thickness obtained in the previous experiments on the ITO/Ag/ITO multilayers.

For the experiments, ITO thin films were deposited on soda-lime glass substrates using an in-line pulsed DC magnetron sputtering system. The target was a ceramic alloy ITO (10 wt.% SnO$_{2}$-doped In$_{2}$O$_{3}$) with dimensions of 540 mm (L) ${\times}$ 165 mm (W) ${\times}$ 7 mm. The plasma was generated by applying 1.5 kW of pulsed DC power, which corresponds to a power density of 1.6 W/cm$^{2}$. Deposition was performed at a pressure of 6 mTorr, with an O$_{2}$/Ar flow rate of 1.5 sccm/50 sccm at RT. Ag thin films were also deposited using the in-line sputtering system, but the Ag target has a diagonal size of 4 inch with a purity of 99.99 %. In order to obtain the minimum possible thickness, RF power was applied with a minimum power of 30 W, which corresponds to a power density of 0.07 W/cm$^{2}$, and pressure was maintained at 4 mTorr using Ar gas only with a flow rate of 20 sccm.

To make the Ag mesh structure, a conventional photolithography method was used. The Ag film of about 10 nm thickness was patterned by the chemical etching process in SE-45T etchant for 10 s at RT with a positive photoresist (AE-HKT 501) mask pattern. For the various meshed Ag patterns, the sheet resistance and the transmittance were determined using a 4-point probe (Advanced Instrument Technology, CMT-SR 200n) and UV-vis spectrophotometry (Perkin Elmer-Lambda 35).

For more accurate and practical analysis, we performed the simulations based on wave optics, Full-wave simulation program provided by RSoft® company. This program uses the finite-difference time-domain (FDTD) method to solve the linear Maxwell equations. The FDTD method implements the spatial derivatives of the curl operators in Maxwell’s equations, by using finite differences on a regular Cartesian space mesh. In our simulations, the computation domain is set in the XZ-plane with 3D dimension, and a plane wave with variable wavelengths ranging from 250 to 850 nm is incident in the z-direction at normal incidence to the ITO/Mesh-Ag/ITO film that is surrounded by free-air space. In the optical simulations, to obtain the most accurate calculations possible, the indices of refraction that were measured using spectroscopic ellipsometry (Elli-SEU-R, Ellipso Tech.) for the ITO and Ag layers were used as the material properties in the simulations. The simulation results were provided to clarify the theoretical mechanism of the transmittance, and to utilize to search for the desirable conditions for the applications of this technology.

III. Results and Discussion

First, optical transmittances were simulated for the 3-dimensional structures of ITO/Mesh-Ag/ITO. In the simulations, the computation domains are (Lx, Lz) = (2*Xmax, 0.36 µm) in the XZ-plane, and (Ly, Lz) = (2*Ymax, 0.36 µm) in the YZ-plane, where Xmax = Ymax is given by (Mesh_space + Mesh_width)/2. Since the CW incidence wave is normal, periodic boundary conditions are applied in the x- and y-directions in order to simulate an infinite array of one mesh structure, repeated regularly at the intervals of Lx and Ly along the x- and y-axes, respectively. The perfectly-matched-layer (PML) boundary condition is applied in the z-direction to absorb the back-reflected, as well as the transmitted wave at the top and bottom boundaries of the domain. The launch source is placed 0.01 µm below the top PML.

Along the x- and y-axes, the grid is uniform at 0.2 µm. The grid along the z-axis is non-uniform, with different grid size depending on the layer. That is, the non-uniform grids in the z-direction are set at 0.0005 µm in the Ag layer, 0.005 µm in the ITO and glass layers, and 0.02 µm in the bulk air. Fig. 1 shows the cross-section and plane views for the 3D design of the ITO/Mesh-Ag/ITO structure. For convenience, the ITO thickness was fixed by 40 nm for both upper and lower layers. The thickness of the glass substrate was assumed to be 0.06 µm, because it would take too long a simulation time for the real thickness of 1 mm. Key parameters in the simulations were taken as the Mesh_space (S) and the Mesh_width (W), which are indicated in Fig. 1(b) with variable Ag thicknesses. The S and W values were set up in 5 cases : (I) S = 3.8 µm, W = 2.3 µm, (II) S = 6.7 µm, W = 2.7 µm, (III) S = 9.9 µm, W = 2.3 µm, (IV) S = 18.9~µm, W = 2.7 µm, and (V) S = 31.4 µm, W = 1.8 µm. All these set values correspond to those obtained in the experimental results in advance.

For the refractive indices of materials, the nk data measured using the spectroscopic ellipsometry were applied to the real (n) and complex (k) parts of the Ag, ITO films, and glass. Fig. 2 shows the real and complex indices of refractions for the ITO and Ag films as variations of the wavelength. In the Ag film, in the overall visible range, the real values (n) of indices are almost zero; and in contrast, as the wavelength increases from 330 to 800 nm, the imaginary values (k) increase monotonically from 0.8 to 5.3. The k values of the Ag film are much higher, compared with those of the ITO film.

Fig. 3 shows the simulated transmittances for the two ultimate cases (I) and (V) of the mesh space and width values with variable Ag thicknesses from 10 to 30 nm. In the case (I) of S = 3.8 µm and W = 2.3 µm, as the Ag thickness increased, the transmittances decreased considerably. Meanwhile, in the case (V) of S = 31.4 µm and W = 1.8 µm, as the Ag thickness increased, the transmittances did not decrease that much. Note that the main feature is an open ratio depending on the S and W values. Here, the open ratio was defined as the Ag-free area (A$_{\mathrm{O}}$) to the total mesh area (A$_{\mathrm{M}}$), i.e., S$^{2}$/(S+W)$^{2}$. Thus, the open ratios according to cases (I) and (V) become about 38 and 89 %, respectively. Therefore, it can be said that for a given Ag thickness, a larger open ratio results in higher transmittance. For two kinds of Ag thicknesses of 15 and 30 nm, the transmittances depending on the S and W values were simulated, as shown in Fig. 4, which figure shows that in the case of thicker Ag film, the transmittances were more dependent on the open ratio. In this simulation model, if the Ag thickness is less than 10 nm, the field in the visible wavelength range could not be correctly resolved. Thus, with respect to the analysis of the transmittance depending on the open ratio, it is inevitable to take the minimum Ag thickness as being around 15 nm.

Fig. 4 shows that the larger the open ratio, the higher the transmittance, and in the case of higher Ag thickness, the dependence on the open ratio was more prominent. This means that Ag film, even though it is very thin at less than 30 nm, will reduce the light propagation in the visible wavelength. The transmittance of conducting media, such as Ag, Au, and Cu, is usually affected by the absorption of the incoming flux as the incident electromagnetic waves penetrate the media. As the wave progresses into the conductor in the z-direction, its amplitude is exponentially attenuated. Because the irradiance is proportional to the square of the amplitude of the electric field, the irradiance can be written as:

$I\left(z\right)=I\left(0\right)e^{- 2\omega {n_{I}}z/c}=I_{0}e^{- \alpha z}$.

ere, I$_{0}$ = I(0) is the irradiance at the interface, Ω is the angular frequency, n$_{\mathrm{I}}$ is the imaginary part of the complex index, c is the velocity of light in air, and $\alpha =2\omega n_{\mathrm{I}}/c$s termed the absorption coefficient. At $z=1/\alpha$ the flux density will decrease by a factor of $e^{- 1}$and the distance $z=1/\alpha $ is therefore known as the penetration depth. Therefore, for a metal to be transparent, its thickness must be sufficiently thin, compared to the penetration depth. Fig. 4 shows the dependence of the transmittance on the open ratio for two cases of 15 nm and 30 nm in Ag thickness. The results showed that the transmittance was depended more prominently on the open ratio in the case of 30 nm. This indicates that the electromagnetic waves propagate through the Ag layer in the mesh structure and the transmission depend on the thickness and the index of refraction of Ag layer.

The phenomena responsible for the variation in the transmittance of Ag films with the wavelength may be related to the index of refraction. Fig. 2(b) shows that in the overall visible range, the real parts of the indices, n are almost zero; and in contrast, as the wavelength increases from 330 to 800 nm, the imaginary parts of the indices, k increase monotonically from 0.8 to 5.3. This effect is closely related to the decrease of the transmittance as the wavelength increases in the conducting media, such as Ag. The reduction effect of the transmittance due to the increased thickness of Ag film can also be seen from the spatial power distribution over one mesh area. For the ITO/Mesh-Ag/ITO structure with the mesh space of 9.9 µm and mesh width of 2.3 µm, the spatial power distributions of the transmitted electromagnetic waves were simulated for the Ag thicknesses of 15 and 30 nm, as shown in Fig. 5(a) and (b), respectively, where the wavelength of the incoming electromagnetic wave was given as 550 nm.

In the case of 15 nm thickness, the energy of the electromagnetic waves almost penetrated through the Ag layer. However, in the case of 30 nm thickness, only half of the energy penetrated through the Ag layer along the rim of the mesh, in comparison with that through the ITO layer only on the center area, without the Ag film. As a result, in order to minimize the absorption of the electromagnetic wave propagating through the Ag conducting media, to increase the transmission, it is necessary to make the open ratio as high as possible. However, due to the reduction of the area of highly conductive Ag film, too high an open ratio will increase the sheet resistance. Therefore, a tradeoff in the open ratio will be necessary with respect to the transmittance and the sheet resistance, which are the two main issues of the conductive transparent electrodes. These characteristics could be analyzed by experiments and comparisons with the simulation results. For this, ITO/Mesh-Ag/ITO multi-layer films were fabricated. ITO thin films were deposited on soda-lime glass substrates using an in-line pulsed DC magnetron sputtering system. ITO thickness was controlled by the scan numbers of the moving substrate with a speed of 120 cm/min. In these experiments, the measured thickness was about 40 nm via 2 scans by a pulsed DC power of 1.5 kW and working pressure of 6 mtorr in 50 sccm/1.5 sccm of Ar/O$_{2}$ gas flows. Ag thickness was also controlled by the scan numbers with a moving speed of 60 cm/min. About 10 nm was obtained via 2 scans by an RF power of 30 W and working pressure of 4 mtorr of Ar gas. In the experiments, the mesh structure of the Ag film was formed using a conventional photolithography method. In this case, the square pattern size was varied with different Ag film widths ranging from 0.26 to 2.7~µm, and different spaces ranging from 3.0 to 31 µm. Concerning the Ag thickness, the thickness values measured by a stylus profiler could not be correct, because Ag materials are very soft, and so are affected by the stylus pressure, and the surfaces of the sputtered Ag films are very rough. In our previous study, as the Ag thickness increases from 3.4 to 12.8 nm, the rms roughness increases from 0.77 to 2.05 nm. This trend of the roughness increasing with increasing Ag thickness is in accord with the results of many other reports ^(13,14). Therefore, the measured value of the Ag thickness may not be exact, and the references on the Ag thickness for investigating a certain phenomenon could be different between the simulation and the experiments.

We have analyzed the transmittance and the sheet resistance variances depending on the open ratio. Fig. 6 shows the transmittances measured in the spectral range from 250 to 850 nm for several different open ratios. These show that in the spectral ranges longer that 650 nm, as the open ratio increases, the transmittance increases. While, in the spectral ranges shorter than about 450 nm, the dependence on the open ratio is unclear, and as the open ratio increases, the transmittance randomly increases and decreases very slightly. This phenomenon seems to be related to the interference effects among the multiple layers. Incidentally, in the case of the open ratio of 38.8 %, the transmittance is reduced considerably over all of the visible spectral range.

A tradeoff will be necessary in terms of the transmittance and the sheet resistance, which can be reached at around 60 %. At this point, the averaged transmittance is about 82 %, and the sheet resistance is about 25 Ω/${\square}$. In comparison, in the case of the ITO single layer with a thickness of 106 nm, the averaged transmittance was about 85.7 % and the sheet resistance was about 88 Ω/${\square}$. Here, it should be remembered that the ITO films were sputtered at RT without post annealing. In general, the transmittances of ITO film could be increased by post annealing at a temperature higher than 300 $^{\circ}$C. Conclusively, the optimized ITO/Mesh-Ag/ITO multiple layers resulted in much smaller sheet resistance of about 25 Ω/${\square}$, compared to that of a single ITO layer, even with approximately the same transmittance spectrum as the single ITO layer. The sheet resistance of 25 Ω/${\square}$ obtained at this point should prove very successful as a transparent conductive electrode for large and flexible display applications.

IV. CONCLUSIONS

The ITO/Ag/ITO multiple layers used as an alternative to a highly conducting transparent electrode are limited in the transmittance in the visible wavelengths, especially in the range less than about 550 nm. In this study, we could obtain satisfying results in both the transmittance and the sheet resistance using the ITO/Mesh-Ag/ITO multiple layers. The effect of the meshed Ag structure on enhancing the optical transmittance was thoroughly analyzed using 3-dimensional wave simulations, and compared with the experimental results. The transmittance depended on several factors, such as Ag thickness and open ratio. In order to obtain a high transmittance and low sheet resistance, a tradeoff of the open ratio for a given Ag thickness should be required. With the Ag thickness of about 10 nm and the ITO thickness of 40 nm, the open ratio of about 60 % was most efficient for obtaining the sheet resistance of less than 25 Ω/${\square}$ while keeping the transmittance nearly similar to that in the case of a single ITO layer