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Optoelectronic performance of nano-/microscale porous and wired silver (Ag) and aluminum (Al) layers was theoretically studied. Within the nanoscale region, Ag porous and wired layers – possessing stronger surface plasmon response over the whole visible spectrum –demonstrate up to a 20% higher average transmittance in comparison to identic Al design. In the microscale region, difference in the average transmittance between the above mentioned metallic layers decreases to 5%. Moreover, the microscale Ag and Al layers exhibit up to a 5% higher average transmittance. The obtained results allow deeper analysis of the pattern scale of metallic transparent conductive layers for various optoelectronic applications, such as displays, solar cells, light-emitting diodes, touch screens and smart windows.
© 2016 Optical Society of America
1. Introduction
Patterned metallic layers gained interest as transparent electrodes for optoelectronic devices such as displays, solar cells, light emitting diodes, touch screens and smart windows in the last decade [1–8]. Variety of metallic patterns – pores, honeycombs, triangles and wires – were proposed and studied in details [9–12]. Multiple studies show that an open area dominates the transmittance of metallic patterned structures [13, 14]. For instance, the Al wired electrode reach around 90% transmittance, while the porous configuration exhibits only 80% at sheet resistance of 5 Ohm/sq [15]. Furthermore, materials with stronger plasmonic response show higher optoelectronic performance: as an example Ag nanoporous layers possess 8% higher average transmittance in visible wavelength range at sheet resistance of 3 Ohm/sq compared to identical Al layers [10, 15].
However, an impact of nano- and microscale patterns on the optoelectronic performance of metallic layers is poorly studied. Here we theoretically analyzed nano-/microscale porous and wired configurations for two materials – Ag and Al – possessing different plasmon response in visible wavelength range. We showed that Ag nanoporous/nanowired layers exhibit up to 20% higher transmittance due to stronger surface plasmon (SP) resonance, while within microscale the optoelectronic performance become comparable for both metallic layers and depends solely on its permittivity and conductivity. Moreover, the microscale Ag and Al layers exhibit up to 5% higher average transmittance.
2. Methodology
Figure 1 shows the geometrical models for the porous and wired metallic layers on the glass substrate. Pores and wires were arranged uniformly with interpore/interwire distance a and diameter of pore d. The simulation area was cut to unit cell, which size along X and Y axes was set to the distances a and a × for hexagonally arranged porous layers [Fig. 1(a)] and distance a for wired layers [Fig. 1(b)].
Fig. 1 Geometrical models for the porous (a) and wired (b) metallic layers on the glass substrate. Yellow dash rectangles are the unit simulation cells, which equal to a2 × and a2 for the pores and wired arrangements, respectively.
The optical properties were simulated using the finite-difference time-domain method which is commercially available within Lumerical software [16]. The incident light ranged in the visible spectrum was distributed along Z axis. The periodic boundary conditions and perfectly matched layers were applied perpendicular and parallel to Z axis, respectively. Mesh size was set to 10, 10 and 5 nm in X, Y, and Z directions, respectively.
The sheet resistance was calculated by the percolation model in accordance to [17–19], which is given by the following equation:
where σ0 is the conductivity of metal, ϕf is the volume fraction of patterned metal layer, ϕcrit is the volume fraction threshold when the patterned layer changes from insulator to conductor, h is the thickness of the metal layer and t is the critical exponent. Above mentioned models were successfully applied by our group in [10, 12, 15].3. Results and discussion
Metallic patterns possess SP response in specific wavelength range, which depends on material and geometrical parameters of patterns. We chose two metals with different SP response in the visible spectrum: Ag with strong SP resonance from 400 to 700 nm and Al with weak SP response from 400 to 500 nm [20]. Thickness of the layers was set to 60 nm in order to represent the common experimental studies [21–24]. We selected the interpore/interwire distances a from 200 nm to 30 μm aimed to investigate the optoelectronic properties of micro- and nanoscale configurations. Ratio of diameter d to distance a changed from 20% to 100%; i.e. from structure close to bulk configuration to structure with near zero conductivity.
Figure 2 shows the average transmittance in the visible spectrum for Ag and Al porous layers against the interpore distance a and ratio d/a. Two regions – one from 200 to 800 nm wavelength (nanoscale) and another from 800 nm to 5μm (microscale) – illustrate different behavior. Within the nanoscale region Ag porous layers demonstrate up to 20% higher average transmittance in comparison to Al layers; major difference takes place for the ratio d/a from 40 to 90%. In the microscale region the average transmittance between Ag and Al layers differs by less than 2%. Such behavior results from distinct impact of SP response on the transmittance, viz. that the energy of SPs decays exponentially over its propagation path [25]. SPs reach the bottom side of the nanoscale structure and then re-radiate into light enhancing the transmittance. In the microscale structure the energy of SPs reduces significantly at the bottom side due to long propagation path and negligibly influence on the transmittance.
Fig. 2 The average transmittance in the visible spectrum for Ag (a, c) and Al (b, d) porous layers against the interpore distance a and ratio d/a.
Figure 3 illustrates the calculated electric field distribution for nano- (a = 200 nm) and microscale (a = 2 µm) Ag and Al layers at 550 nm wavelength. The nanoscale Ag layer possesses strongest electric field along metal, while at a = 2 µm the electric filed decreases four times. Both nano- and microscale Al layers demonstrate negligible electric field along metal compared to Ag layers. Thus, in microscale layers the transmittance depends solely on material permittivity and conductivity.
Fig. 3 The calculated electric field distribution for nano- (a = 200 nm) and microscale (a = 2 µm) Ag (a, c) and Al (b, d) layers at 550 nm wavelength.
Ag and Al wired layers demonstrate similar effect as shown in Fig. 4: Ag outperforms Al up to 20% average transmittance in case of nanoscale layers, while within the microscale region the average transmittance differs by less than 2%.
Fig. 4 The average transmittance in the visible spectrum for Ag (a, c) and Al (b, d) wired layers against the interwire distance a and ratio d/a.
Figure 5 shows the average transmittance in visible spectrum against the sheet resistance for nano- (a = 200 nm) and microscale (a = 2 μm) porous Ag and Al layers. Ag nanoporous layers possess the average transmittance of 77% at the sheet resistance of 5 Ohm/sq, while Al layers obtain close average transmittance only at 50 Ohm/sq. This difference results from both higher transmittance of nanoscale Ag layer and bulk conductivity of Ag (σ0 = 6.3 × 107 S/m) compared to Al (σ0 = 3.5 × 107 S/m). At microscale range the average transmittance of Ag layers becomes 82% at the sheet resistance of 5 Ohm/sq, while Al layers obtain close average transmittance at the sheet resistance 12.5 Ohm/sq. This difference comes mainly from higher bulk conductivity of Ag compared to Al and slightly higher transmittance of microscale Ag layers. The microscale Ag and Al layers exhibit up to four times lower sheet resistance at given average transmittance. Moreover, microporous layers show 5% higher average transmittance due to larger open area of micropores.
Fig. 5 Average transmittance against sheet resistance for nano- (a) and microscale (b) porous Ag and Al layers. The interpore distance a = 200 nm and 2 μm for nano- and microscale configurations, respectively.
Figure 6 shows that Ag and Al wired layers demonstrate similar tendency: (i) Ag nanowired layers possess the average transmittance of 88% at the sheet resistance of 5 Ohm/sq, while Al layers obtain close average transmittance only at 35 Ohm/sq; (ii) at microscale range the average transmittance of Ag layers becomes 92% at the sheet resistance of 5 Ohm/sq, while Al layers obtain close average transmittance at the sheet resistance of 9 Ohm/sq; (iii) microwired layers show 4% higher average transmittance due to larger open area.
Fig. 6 Average transmittance against sheet resistance for nano- (a) and microscale (b) wired Ag and Al layers. The interpore distance a = 200 nm and 2 μm for nano- and microscale configurations, respectively.
Figure 7 shows the difference in average transmittance between Ag and Al layers against interpore/interwire distance a at fixed sheet resistance of 5 Ohm/sq. Ag layers exhibit from 20.2 to 6.5% higher transmittance at distance a from 200 to 600 nm, respectively. Further increment of the distance a affects the difference in the average transmittance between Ag and Al layers significantly less: Ag layers exhibit from 6.5 to 5% higher transmittance at the distance a from 600 nm to 30 μm. Close experimental results for nano- and microscale wired Ag and Al layers with distance were demonstrated in [26–28]. Large difference in transmittance – 20.2% at distance a = 200 nm – indicates that only Ag porous/wired layers can suit most optoelectronic aplications. Therefore, the metallic patterned layers with stronger SPs response possess higher optoelectronic performance at nanoscale patterns, while at microscale patterns their performance depends solely on permittivity and conductivity of micropatterned metallic layers.
Fig. 7 Difference in average transmittance between Ag and Al layers against interpore/interwire distance a at fixed sheet resistance of 5 Ohm/sq. Experimental results from [26–28].
4. Conclusion
We theoretically studied the optoelectronic properties of nano-/microscale porous and wired Ag and Al layers. Both nanoporous and nanowired Ag layers show up to 20% higher average transmittance due to stronger SP response over the whole visible spectrum. However, at the microscale patterns the difference in average transmittance between Ag and Al layers becomes less than 5%. Moreover, the microscale Ag and Al layers exhibit up to 5% higher average transmittance. The obtained results allow to estimate the impact of the pattern size of metallic transparent conductive layers on its optoelectronic performance for various optoelectronic applications, such as displays, solar cells, light-emitting diodes, smart windows, and other devices.
Acknowledgment
This project is supported by National Research Foundation of Singapore (No. NRF-CRP11-2012-01).
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