The influence of silver core position on enhanced photon absorption of single nanowire α -Si solar cells Linxing Shi,1,∗ Zhen Zhou,1 and Zengguang Huang1,2 1 School
of Science, Huaihai Institute of Technology, Lianyungang, 222005, China of Condensed Matter Spectroscopy and Opto-Electronic Physics, and Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics, and Institute of Solar Energy, Shanghai Jiao Tong University, Shanghai, 200240, China ∗ [email protected] 2 Laboratory
Abstract: Photon absorption of single nanowire solar cells can be modulated by metallic core. Silver core was integrated into α -Si single nanowire solar cells (SNSCs), and the influence of silver core position on enhanced photon absorption efficiency and the short circuit current (Jsc ) was investigated. The finite-difference time domain (FDTD) method was used to rigorously solve Maxwell’s equations in two dimensions. The Jsc decreases when the silver core is integrated into the center of nanowire. However, the photon absorption efficiencies and Jsc could be enhanced by tuning the core position in the nanowire. Jsc enhancement of 21.4% is achieved when nanowire radius R is 190 nm, core radius r is 30 nm, the silver core is located in the negative Y-axis and the distance from the center of silver core to the origin d is 102 nm under realistic solar illumination. © 2013 Optical Society of America OCIS codes: (350.6050) Solar energy; (240.6680) Surface plasmons; (040.5350) Photovoltaic; (250.5403) Plasmonics; (310.6628) Subwavelength structures, nanostructures.
References and links 1. L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10(2), 439–445 (2010). 2. E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010). 3. L. Cao, J.-S. Park, J. S. White, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8, 643–647 (2009). 4. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010). 5. L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett. 91(23), 233117 (2007). 6. T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, “Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section,” Phys. Rev. Lett. 93(10), 103903 (2004). 7. R. Yan, D. Gargas, and P. Yang, “Nanowire photonics,” Nat. Photonics 3(10), 569–576 (2009). 8. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). 9. C. Lin and M. L. Povinelli, “The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays,” Appl. Phys. Lett. 97, 071110 (2010). 10. S. Brittman, H. Gao, E. C. Garnett, and P. Yang, “Absorption of light in a single-nanowire silicon solar cell decorated with an octahedral silver nanocrystal,” Nano Lett. 11(12), 5189–5195 (2011). 11. Y. H. Zhan, J. P. Zhao, C. H. Zhou, M. Alemayehu, Y. P. Li, and Y. Li, “Enhanced photon absorption of single nanowire α -Si solar cells modulated by silver core,” Opt. Express 20(10), 11506–11516 (2012).
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1007
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FDTD Solutions, from Lumerical Solutions Inc., http://www.lumerical.com. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985). ASTM, “Reference solar spectral irradiance: AM 1.5 Spectra,” http://rredc.nreal.gov/solar/spectra/am1.5. W. F. Liu, J. I. Oh, and W. Z. Shen, “Light trapping in single coaxial nanowires for photovoltaic applications,” IEEE Electron Device Lett. 32(1), 45–47 (2011). 16. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). 17. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A, Gen. Phys. 81(5), 053818 (2010). 18. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. v. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Stat. Sol. (a) 205(12), 2844–2861 (2008).
1.
Introduction
Single nanowire solar cells (SNSCs) using a silicon nanowire (SiNW) have received attention due to SiNWs’ unique optical and electrical characteristics, such as a superior ability for a high optical absorption and light trapping [1–4], a direct path for transport [5]. The high-refractiveindex SiNW forms a cavity in which light can circulate by multiple total internal reflections from the boundaries which often referred to as leaky mode resonances (LMRs) [6]. LMRs in the nanowires can be optimized for solar cells by tuning the size of single nanowires [3, 7]. To further enhance the absorption of sunlight, metallic nanostructures have been conceived to be combined into solar cells. Metallic nanoparticles can be used as subwavelength antennas in which the plasmonic near-field is coupled to the semiconductor, increasing its effective absorption cross-section [8]. Lin [9] found that gold, copper, and silver catalysts all decreased the integrated optical absorption across the solar spectrum in vertically aligned silicon nanowire arrays. Brittman [10] showed that increasement of photocurrent occurred at the wavelengths corresponding to the nanocrystal’s surface plasmon resonances, while decreases occurred at wavelengths corresponding to optical resonances of the nanowire in a single nanowire silicon solar cell decorating with an octahedral silver nanocrystal. Zhan [11] proposed and demonstrated numerically the possibility of metallic-cores that enable strong optical absorption in SNSCs. They showed that an enhancement of 16.6% in the photocurrent could be achieved by α -Si nanowire solar cells with the proper core size and filling-ratio compared to that without silver core. However, we found that α -Si SNSCs with centered silver core for whatever core size and filling-ratio all decrease the integrated optical absorption across the solar spectrum. In this letter, we proposed a circular cross-sectional single nanowire α -Si solar cells with embedded circular silver core as shown in Fig. 1. Using the finite-difference time domain method, we studied how the size and position of the silver core and the diameter of the nanowire affect the short circuit current density, Jsc , for both s- and p-polarized sunlight. We found that for a wide range of nanowire diameter, silver core located in the center of nanowire degraded the Jsc , in the photoactive region. However, an enhancement in the photocurrent could be achieved with off-center silver core compared to that without silver core. An enhancement of 54.9% in Jsc was produced by SNSCs with nanowire radius of 190 nm, silver core radius of 130 nm and distance upwardly offset from the center of silver core to that of nanowire of 54 nm for s-polarized. And an enhancement of 24% in Jsc was produced by SNSCs with nanowire radius of 200 nm, silver core radius of 20 nm and distance downwardly offset from the center of silver core to that of nanowire of 108 nm for p-polarized. 2.
Model and numerical method
The schematic diagram of SNSCs with silver core in this study is provided in Fig. 1. The single nanowire is treated as an infinitely long cylinder and characterized by the radius R. The silver core with radius r is embedded into the single α -Si nanowire. The d is the distance from the
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1008
Fig. 1. Schematic diagram of the simulation model.
center of silver core to the origin. The dimensionless parameter p=d/(R-r) is used to specify the radial position of the core center, where p, the ratio, varies between 0 and 1. When p is equal to 0, the silver core is at the center of the single α -Si nanowire. It is the same as [11]. The θ is the angle from the X-axis to d. It varies between - π2 and π2 . In the simulation, a commercial FDTD software package, FDTD Solutions, provided by Lumerical Solutions Inc. [12] was used. The total field scattered field (TFSF) plane wave source is used for non-periodic SNSCs. The incident light is along the Y-axis as shown in Figs. 1. The computational domain considered is terminated by perfectly matching layer (PML). The power absorption per unit volume (Pabs (x, y)) in the absorber (α -Si and Ag) can be calculated using the relation L = −0.5ω |E|2 ε (ω ), where ω is the angular frequency, |E|2 is normalized light intensity ar near field, ε is the imaginary part of dielectric function of the absorber. Dispersive dielectric functions of α -Si and Ag come from the experimental data of Palik [13]. When Pabs (x, y) is known, it is easy to calculate total absorption Pabs (λ ) in some volume by integrating the loss function over that volume. In this model, there are two dispersive materials (α -Si and Ag) in SNSCs, we are interested in the power absorbed by α -Si. Once the power absorbed as a function of space, ie, Pabs (x, y) is obtained, the total absorption in α -Si can be calculated by Pabs (x, y) · M(x, y)dxdy, where M is the filter factor. It is 1 if the (x,y) values are inside the α -Si and 0 if they are outside. Similarly, the total absorption in Ag core can also (λ ) , where Pin (λ ) is the be calculated. The absorption efficiency is calculated by Qabs (λ ) = PPabs in (λ ) power of the incident light. To investigate the potential benefit of the Ag core for SNSCs, the short circuit current density, Jsc , is calculated according to the following equation: Jsc =
800nm eλ 400nm
hc
Qabs (λ )ΦAM1.5 (λ )d λ
(1)
e where Qabs is the absorption efficiency, hc is the charge constant, ΦAM1.5 is the reference solar spectral irradiance (ASTM G-173) [14]. To match the solar spectrum to α -Si absorption, a wavelength range from 400 to 800 nm is considered.
3. 3.1.
Results and Discussion Influence of the core located in the center of nanowire on photon absorption for SNSCs
To determine whether the silver core located in the center of nanowire increase or decrease absorption inside the SNSCs, we study the Jsc enhancement (Jsc /Jscbare ) compared to that without silver core. Figure 2 shows the calculated contour map of Jsc enhancement in SNSCs with #195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1009
silver core located in the center of nanowire as a function of nanowire radius R and core radius r for p-polarized (a), s-polarized (b), and non-polarized (c) sunlight. In order to compare the results of [11], nanowire radius values from 100 nm to 190 nm are considered. We observe that the Jsc enhancement is always below 1 for both p-, s- and non-polarized. In other words, for a wide range of nanowire and silver core diameters, silver core located in the center of nanowire decreases the absorption in the nanowire. To understand why the silver core located in the center of nanowire degrades the Jsc enhancement, we compare absorptance spectra without and with silver core in the SNSCs. Figure 3 shows the influence of the silver core on the absorption in SNSCs with varying nanowire radius for both p- and s-polarized light. Figs. 3(a) and 3(d) describe the contour maps of Qabs in the SNSCs without silver core as a function of illumination wavelength and nanowire radius R for p- and s-polarized, while Figs. 3(b) and 3(e) describe that of α -Si nanowire in SNSCs with silver core. To study the effect of silver core on photon absorption in SNSCs, Figs. 3(c) and 3(f) describe that of silver core in SNSCs. The core radius is chosen as 36 nm, and the nanowire radius, R, is changing from 100 to 190 nm. To illustrate more clearly, the absorption efficiency Qabs of α -Si nanowire without core, α -Si nanowire with core and silver core in the SNSCs for p- and s-polarized are extracted from Figs. 3(a)-(f) and plotted in Figs. 3(g) and 3(h). The nanowire radius, R, is 130 nm and the silver core radius, r, is 36 nm. They correspond to the parameters for maximum absorption enhancement in the SNSCs of [11]. It can be concluded from Figs. 3(a) and 3(d) that LMRs actually exist in the SNSCs without core [15]. Note here that there are common characteristics between p- and s-polarized light. The number of resonant peaks is augmented with increasing R, and these resonant peaks clearly tend to show substantial red shifts with increasing R. These resonant peaks can be understood by means of the Fano effect [16] that has been observed in spherical core/shell nanoparticles [17]. The lower the field intensity, the weaker the LMRs. For strong LMRs (longer wavelength region), the LMRs arise from whispering gallery mode which exists in microdisk resonators. For weak LMRs (short wavelength region), the incident light appears to be localized via constructive interference with the reemitted light. The LMRs are similar to the Fabry-perot resonance (FP modes). The fields of these LMRs will be shown in Figs. 4. Figure. 3(b) and 3(e) show the effect of the silver core on absorptance spectrum of nanowire for p- and s-polarized. From Figs. 3(b), we can find that the number of resonant peaks is reduced. Meanwhile, the number of LMRs peaks is reduced with decreasing R. And there is only one LMR peak when the radius of nanowire is ∼100 nm. As a result, the Jsc enhancement is much lower than 1 [Figs. 2(a)]. In contrast with that under s-polarized illumination [Figs. 3(e)], the number of LMRs peaks is almost no change. But the positions of some peaks are slightly (a) p−polarized 90
1
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Fig. 2. Contour map of Jsc enhancement in SNSCs with silver core located in the center of nanowire as a function of nanowire radius R and core radius r for (a) p-polarized, (b) s-polarized and (c) non-polarized sunlight.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1010
Fig. 3. Contour maps of Qabs in the SNSCs as a function of illumination wavelength and nanowire radius R. The silver core radius, r, is 36 nm. (a) without silver core, (b) Qabs in the α -Si nanowire and (c) Qabs in the silver core for p-polarized light. (d) without silver core, (e) Qabs in the α -Si nanowire and (f) Qabs in the silver core for s-polarized light. The absorption efficiency Qabs in the SNSCs (g) p-polarized and (h) s-polarized. The nanowire radius, R, is 130 nm and the silver core radius, r, is 36 nm. They correspond to the parameters for maximum absorption enhancement in the SNSCs of [11].
shifted. So the integrated absorption efficiency is proportionally lower than the bare SNSCs [Figs. 2(b)]. To understand the effect of silver core on photon absorption in SNSCs, we calculate the Qabs in the silver core. Figure. 3(c) and 3(f) show the maps of Qabs in the silver core as a function of illumination wavelength and nanowire radius R under p- and s-polarized. From Figs. 3(c), we can find that the number of resonant absorption peaks of silver core is augmented with increasing R. There are nearly 50% resonant absorption efficiency at the wavelengths from 550 to 700 nm, when the nanowire radius is between 120 and 160 nm. Under p-polarized illumination, there is a localized plasmon plariton (LPPs) [18] in the silver core. We observed a largely enhanced scattering as well as absorption cross section [not shown] and a significantly enlarged near-field amplitude in close vicinity to the silver core [Figs. 4(7-9)]. From Figs. 3(f), some resonant absorption peaks of silver core are also observed. But, those peaks are not LPPs because the light is s-polarized. Note here that there are common characteristics between Figs. 3(c) and 3(f). But the role of resonance from silver core is thoroughly different [see Figs. 3(g, h) and Figs. 4]. From Figs. 3(g) and 3(h), we can find that there are many LMRs in bare SNSCs under both p- and s-polarized light. So, the integrated absorption performance has been good. But, when the silver core is embedded into the single nanowire, it will damage the formation of LMRs which exist in bare SNSCs. However, due to the existence of silver core, forming some localized surface plasmon resonance peaks (p-polarized), located in 440 nm, 543 nm, 593 nm, and 763 nm. In the corresponding resonance, the absorption in α -Si nanowire at these wavelength regions has been enhanced. The corresponding field distributions are demonstrated in Figs. 4(7-9). Through careful observation, we found that, in addition to the resonance region, the absorption in SNSCs at other parts is obviously reduced. As a result, the integrated absorption performance decreased instead. However, when the illumination is s-polarized, there is no formation of LPPs. The absorption of silver core is also very low. The presence of silver core did not affect the formation of LMRs in SNSCs [Figs. 4(16-21)]. Obviously, because of the
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1011
423 nm p-polarized
w/o core
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resonance resonance deletion deletion
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Fig. 4. H-field distribution in SNSCs. The nanowire radius, R, is 130 nm. The core radius, r, is 36 nm. The color is not in scale, which is just to show the steady mode. Sub-graph 1-6 for without core and 7-9 for with core under p-polarized illumination; sub-graph 1015 for without core and 16-21 for with core under s-polarized illumination. The resonant wavelength marked on the top of each sub-graph.
existence of silver core, the volume of α -Si nanowire is decreased, so the overall absorption in SNSCs is also reduced. 3.2.
Influence of silver core position on photon absorption for SNSCs
Figure 5 shows the influence of the silver core with varying radius on Jsc enhancement in SNSCs, note here that the core moves from the lower positive along the Y-axis. We used these positions, selected from optimal regions that will be clarified in Figs. 9. The nanowire radius, R, is 190 nm. That’s because this value corresponds to the maximum Jsc enhancement for nonpolarized sunlight as shown in Figs. 8. The core radius, r, is changing from 10 to 160 nm. The point A in Figs. 5(a) is corresponding to the maximum Jsc enhancement (22.8%) under p-polarized illumination. Here, the core radius, r, is 20 nm, and the ratio, p, is -0.6. According the formula, d=(R-r)·p, the distance from the center of silver core to the origin is 102 nm. Moreover, the core is located in the negative Y-axis. As can be seen in Figs. 5(a), there are two Jsc enhancement regions. The stronger enhancement region is that r∈[20, 80] nm and p∈[-1, -0.5]. The other region is that r∈[50, 70] nm and p∈[0.4, 0.6]. It also can be seen, in addition to that the core located near the center of the nanowire, the Jsc enhancement is almost all larger than 1 for core radius r less than 80 nm. The point B in Figs. 5(b) is corresponding to the maximum Jsc enhancement (54.9%) under s-polarized illumination. Here, the core radius, r, is 130 nm, and the ratio, p, is 0.9. Likewise, the core is located in the positive Y-axis, and the distance from the center of silver core to the origin is 54 nm. Similarly, there are three Jsc enhancement regions. One is r∈[30, 160] nm and p∈[0.9, 1]. The second is r∈[20, 60] nm and p∈[-1, -0.6]. And the third is r∈[30, 50] nm and p∈[0.5, 0.7]. By comparing Figs. 5(a) and
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1012
Fig. 5. Contour maps of Jsc enhancement in SNSCs as a function of core radius r and the ratio p, here p varies from -1 to 1, corresponding to the core moves from bottom to up along the Y-axis. (a) p-polarized, (b) s-polarized and (c) non-polarized. The nanowire radius, R, is 190 nm.
5(b), we can see that the maximum Jsc enhancement under s-polarized is larger than that under p-polarized. But what’s even more crucial is that silver core size and position of maximum Jsc enhancement under p- and s-polarized illumination are not consistent. That is not suitable for practical application. Therefore, the averaged Jsc enhancement (i.e., p-/2+s-/2) is plotted in Figs. 5(c) to show the device performance under realistic solar illumination. From Figs. 5(c), we can see that an enhancement of 21.4% in the Jsc could be achieved by SNSCs with core radius, r, 30 nm, and ratio, p, -0.7 (i.e., the center of the silver core is located at coordinates (0, -112) nm. Labeled C). At the same time, the region I (r∈[20, 50] nm, p∈[-1, -0.6]) is acceptable, the Jsc enhancement are all above 18%. In addition to region I, the region II (r∈[20, 130] nm, p∈[0.9, 1]) and region III (r∈[30, 70] nm, p∈[0.4, 0.6]) are also acceptable. In Figs. 6(a), we show the wavelength dependence of Qabs in SNSCs with Si nanowire of radius R=190 nm, silver core located in the negative Y-axis of radius r=20 nm and the distance from the center of silver core to the origin d=102 nm under p-polarized illumination. Without-core Qabs is shown for comparison. Meanwhile, Ag-core Qabs is also shown to determine whether the resonant peaks in nanowire come from the LPPs excited in silver core. The Qabs spectra for the two structures with and without core are almost overlapping together when λ < λc ∼ 490nm (see the dashed line at 490 nm). This is because the incoming photon energy is fully absorbed at the surface before reaching the silver core. Moreover, the absorption in silver core is near 0 at this short wavelength region according to the Qabs spectra of silver core. But the absorption in SNSCs is clearly enhanced at both resonance and off-resonance region for long λ > λc ∼ 490nm. Note here that λc is a characteristic wavelength, up which the light absorption enhancement always occurs due to the silver core. From Figs. 6(a), we can see that there are 5 resonant peaks at the absorption enhancement region. According to the absorption peaks of silver core labeled from AE1 and AE5 . we can draw the conclusion that these peaks originate in part from LPPs excited in silver core. In order to clarify the role of silver core, H-field distribution in SNSCs at the resonant peak labeled from T E1 to T E5 is plotted in Figs. 6(b) to 6(f). From Figs. 6(b), we can see that the silver core can be regarded as a high reflector. There is no strong localization of light around the silver core. But the Fabry-perot resonance
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1013
(a)
(b) TE1
(c) TE2
(d) TE3
(e) TE4
(f) TE5
Fig. 6. (a) The absorption efficiency Qabs in the SNSCs under p-polarized illumination. The nanowire radius, R, is 190 nm, the silver core radius, r, is 20 nm, and the ratio, p, is -0.6. (i. e., silver core located in the negative Y-axis and the distance from the center of silver core to the origin d=102 nm.) (b)-(f) H-field distribution in SNSCs at the resonant peak labeled from TE1 to TE5 , respectively. The color is not in scale, which is just to show the steady mode.
mode is generated between silver core and the inner edge of the nanowire. From Figs. 6(c) to 6(e), we can see that strong LMRs (whispering gallery modes here) and LPPs are coexist in the SNSNc. That caused a strong absorption enhancement from the widespread field enhancement because the light absorption is proportional to the product of the field intensity and the imaginary part of the silicon refractive index. Similarly, the weak LMRs (FP mode here) and LPPs are also coexist in the SNSCs as shown in Figs. 6(f). In Figs. 7(a), we show the wavelength dependence of Qabs in SNSCs with Si nanowire of radius R=190 nm, silver core located in the positive Y-axis of radius r=130 nm and the distance from the center of silver core to the origin d=54 nm under s-polarized illumination. Withoutcore and Ag-core Qabs are also shown for comparison. From Figs. 7(a), it can be seen that the
(a)
(b) TM1
(c) TM2
(d) TM3
(e) TM4
(f) TM5
(g) TM6
Fig. 7. (a) The absorption efficiency Qabs in the SNSCs under s-polarized illumination. The nanowire radius, R, is 190 nm, the silver core radius, r, is 130 nm, and the ratio, p, is 0.9. (i. e., silver core located in the positive Y-axis and the distance from the center of silver core to the origin d=54 nm.) (b)-(g) E-field distribution in SNSCs at the resonant peak labeled from TM1 to TM6 , respectively. The color is not in scale, which is just to show the steady mode.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1014
absorption enhancement emerged in almost the whole spectrum except λ < λc ∼ 420nm (see the dashed line at 420 nm). The Qabs decreases a little at the region of λ < λc because the effective absorption volume of the SNSCs with silver core reduced greatly. With increasing the wavelength of incident light, the influence of volumetric reduction is won over by emergence of the LMRs (whispering gallery modes here). The silver core works as a reflector. Then, a resonator cavity can be formed between silver core and the inner edge of the nanowire. The incident light circles around the cavity, supported by continuous total internal reflection of the cavity surface, that meet the resonance condition. In order to explain the resonant absorption peaks labeled from T M1 to T M6 , E-field distribution in SNSCs at each resonant peak is plotted in Figs. 7(b) to 7(g). From the E-field distribution, according to the wave theory of whispering gallery modes, we can use multi-index (mode numbers) to label the eigenmodes. Then the resonant mode labeled from T M1 to T M6 shown in Figs. 7(a) can be lebeled as (15,1), (13,1), (11,1), (9,1), (7,1) and (5,1), respectively. These whispering gallery modes result in a substantial improvement of Qabs in SNSCs. On the other hand, the short the characteristic wavelength and the more the number of resonant modes, the larger the absorption enhancement. It is noticed that the LPPs can not be excited under the s-polarized illumination. The silver core just serves as a reflector. Under such conditions, we can use the dielectric core to replace silver core. As one of the most simple example, we used air to replace silver core and obtained the similar absorption enhancement (not shown here). We’ll dig into these issues in our next post. 3.3.
Optimization and tolerance evaluation
To further investigate the optimal combination of nanowire radius (R), silver core radius (r) and the position of the core (p, i.e., d), the Jsc enhancement was calculated by sweeping those
(a)
(b)
Fig. 8. Maximum of Jsc enhancement as a function of radius of SNSCs (circle points in blue). (a) p-polarized, (b) s-polarized. The left inset is the optimum core radius (diamond points in red) and the right inset is the optimum ratio (square points in green), respectively. The light dotted line in the inset is the linear fitting for the relationship between r and R.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1015
parameters. The geometrical parameters are swept within R∈[100, 220] nm; r∈[10, 200] nm; p∈[-1, 1]. The Jsc enhancement cannot be represented by graph because there are too many parameters. However, the optimal parameters can be extracted from the multidimensional matrix. Figure. 8 shows the maximum of Jsc enhancement as a function of radius of SNSCs under p-polarized (a) and s-polarized (b) illumination. The left inset is the optimum core radius and the right inset is the optimum ratio, respectively. As shown in Figs. 8(a), with increasing R, the maximum Jsc enhancement rises first and then falls slightly. The summit with 24% enhancement is corresponding to the nanowire radius of 200 nm. From the insets of Figs. 8(a), with increasing R, the optimum core radius r and ratio p remain constant, that is to say r=20 nm, and p=-0.6. Therefore the optimum combination under p-polarized illumination for R, r and d is that R=200 nm, r=20 nm and d=108 nm. In contrast, as shown in Figs. 8(b), with increasing R, the maximum Jsc enhancement periodic changes in about 50%, and the ratio remains constant. But, different R correspond to different core radius r, and that when the R become greater the optimal core radius r is increasing linearly, as given by r=k·R+b, where k is the slope coefficient, b is the intercept of fitting-line, which both can be calculated by numerical fitting from the left inset in Figs. 8(b). If R is in units of nanometers, the k=0.86 and b=-26. As a result under s-polarized illumination, the optimum combination for R, r and d is that R=190 nm, r=130 nm and d=54 nm. Up to now, we have already discussed the influence of silver core with different radius located in Y-axis on photon absorption for SNSCs with different radius R. Assuming the silver core deviate from the Y-axis, then how the silver core would affect on light absorption in SNSCs. Given that, the influence of position deviation of silver core, namely the SNSCs with silver core is tilted, on Jsc enhancement in SNSCs is discussed. Figure 9 shows the maps of Jsc enhancement in SNSCs as a function of d and θ , expressed in polar coordinates. Here, d is the distance from the center of silver core to the origin, d=(R-r)·p, p varies from 0 to 1. The θ is the angle from the x-axis to d. It varies from −π /2 to π /2. Because the structure of SNSCs and light source are symmetric about Y-axis, we only need to compute the structure that the silver core is located at the right/left side of the Y-axis. The nanowire radius, R, is 190 nm. Under p-polarized illumination, the silver core radius, r, is 20 nm. So the d varies from 0 to 170 nm. Under s-polarized illumination, the silver core radius, r, is 130 nm. And d varies from 0 to 60 nm. Under non-polarized illumination, the silver core radius, r, is 30 nm. And d varies from 0 to
Fig. 9. Contour maps of Jsc enhancement in SNSCs as a function of d and θ , expressed in polar coordinates. The points on the graph represent the positions of the center of silver core. The nanowire radius, R, is 190 nm. d=(R-r)·p, p varies from 0 to 1. The θ is the angle from the x-axis to d. It varies from −π /2 to π /2. (We only need to compute a half because the structure of SNSCs and light source are symmetric about the Y-axis.) (a) p-polarized, the silver core radius, r, is 20 nm, d varies from 0 to 170 nm; (b) s-polarized, the silver radius, r, is 130 nm. d varies from 0 to 60 nm; (c) non-polarized, the silver radius, r, is 30 nm. d varies from 0 to 160 nm.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1016
160 nm. From Figs. 9(a), we can see that the Jsc enhancement appears below the X-axis. With increasing θ , the Jsc enhancement falls gradually. For the maximal Jsc enhancement region, i.e., d is about 60 nm, it is acceptable when θ ∈ [−90o , −50o ]. In other words, the silver core can be placed in the Y-axis on both sides of the 40o range. From Figs. 9(b), we can see that the Jsc enhancement appears above the X-axis. With increasing θ , the Jsc enhancement rises gradually. For the maximal Jsc enhancement region, i.e., d is about 54 nm, it is acceptable when θ ∈ [40o , 90o ]. That is to say, the SNSCs could be placed within 50 degree reclining. From Figs. 9(c), we can see that the Jsc enhancement appears both above and below the X-axis. With increasing θ , the Jsc enhancement falls first and then rises slightly. For two maximal Jsc enhancement regions, i.e., d is about 112 nm and 160 nm, it is acceptable when θ ∈ [−90o , −60o ] and θ ∈ [70o , 90o ]. 4.
Conclusion
In conclusion, we proposed a circular cross-sectional single nanowire α -Si solar cells with a circular silver core is embedded and, using the finite-difference time domain method, investigated numerically how the size and position of the silver core and the diameter of the nanowire affect the short circuit current density, Jsc , for both s- and p-polarized sunlight. Firstly, we investigated the influence of silver core located in the center of the nanowire on the Jsc enhancement, and found that for a wide range of nanowire diameter, the silver core degraded the Jsc . Next, the silver core was deviated from the center of nanowire and the influence of silver core size and position on photon absorption for SNSCs was studied. The results suggested that an enhancement in the Jsc could be achieved in SNSCs with off-center silver core compared to that without silver core. An enhancement of 54.9% in Jsc was produced by SNSCs with nanowire radius of 190 nm, silver core radius of 130 nm and distance upwardly offset from the center of silver core to that of nanowire of 54 nm for s-polarized. And an enhancement of 24% in Jsc was produced by SNSCs with nanowire radius of 200 nm, silver core radius of 20 nm and distance downwardly offset from the center of silver core to that of nanowire of 108 nm for p-polarized. For practically useful device, an enhancement 0f 21.4% in the Jsc could be achieved by SNSCs which nanowire radius R is 190 nm with core radius, r, 30 nm and it is located at coordinates (0, -112) nm under really sunlight illumination. Finally, the optimal combination of nanowire radius (R), silver core radius (r) and the position of core (d) was calculated for each polarized light. The influence of position deviation of silver core on Jsc enhancement in SNSCs was also discussed. Acknowledgment This work is financially supported by Huaihai Institute of Technology (Grant No.KQ08027, KX08039).
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1017
of Science, Huaihai Institute of Technology, Lianyungang, 222005, China of Condensed Matter Spectroscopy and Opto-Electronic Physics, and Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics, and Institute of Solar Energy, Shanghai Jiao Tong University, Shanghai, 200240, China ∗ [email protected] 2 Laboratory
Abstract: Photon absorption of single nanowire solar cells can be modulated by metallic core. Silver core was integrated into α -Si single nanowire solar cells (SNSCs), and the influence of silver core position on enhanced photon absorption efficiency and the short circuit current (Jsc ) was investigated. The finite-difference time domain (FDTD) method was used to rigorously solve Maxwell’s equations in two dimensions. The Jsc decreases when the silver core is integrated into the center of nanowire. However, the photon absorption efficiencies and Jsc could be enhanced by tuning the core position in the nanowire. Jsc enhancement of 21.4% is achieved when nanowire radius R is 190 nm, core radius r is 30 nm, the silver core is located in the negative Y-axis and the distance from the center of silver core to the origin d is 102 nm under realistic solar illumination. © 2013 Optical Society of America OCIS codes: (350.6050) Solar energy; (240.6680) Surface plasmons; (040.5350) Photovoltaic; (250.5403) Plasmonics; (310.6628) Subwavelength structures, nanostructures.
References and links 1. L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10(2), 439–445 (2010). 2. E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010). 3. L. Cao, J.-S. Park, J. S. White, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8, 643–647 (2009). 4. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010). 5. L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett. 91(23), 233117 (2007). 6. T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, “Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section,” Phys. Rev. Lett. 93(10), 103903 (2004). 7. R. Yan, D. Gargas, and P. Yang, “Nanowire photonics,” Nat. Photonics 3(10), 569–576 (2009). 8. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). 9. C. Lin and M. L. Povinelli, “The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays,” Appl. Phys. Lett. 97, 071110 (2010). 10. S. Brittman, H. Gao, E. C. Garnett, and P. Yang, “Absorption of light in a single-nanowire silicon solar cell decorated with an octahedral silver nanocrystal,” Nano Lett. 11(12), 5189–5195 (2011). 11. Y. H. Zhan, J. P. Zhao, C. H. Zhou, M. Alemayehu, Y. P. Li, and Y. Li, “Enhanced photon absorption of single nanowire α -Si solar cells modulated by silver core,” Opt. Express 20(10), 11506–11516 (2012).
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1007
12. 13. 14. 15.
FDTD Solutions, from Lumerical Solutions Inc., http://www.lumerical.com. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985). ASTM, “Reference solar spectral irradiance: AM 1.5 Spectra,” http://rredc.nreal.gov/solar/spectra/am1.5. W. F. Liu, J. I. Oh, and W. Z. Shen, “Light trapping in single coaxial nanowires for photovoltaic applications,” IEEE Electron Device Lett. 32(1), 45–47 (2011). 16. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). 17. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A, Gen. Phys. 81(5), 053818 (2010). 18. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. v. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Stat. Sol. (a) 205(12), 2844–2861 (2008).
1.
Introduction
Single nanowire solar cells (SNSCs) using a silicon nanowire (SiNW) have received attention due to SiNWs’ unique optical and electrical characteristics, such as a superior ability for a high optical absorption and light trapping [1–4], a direct path for transport [5]. The high-refractiveindex SiNW forms a cavity in which light can circulate by multiple total internal reflections from the boundaries which often referred to as leaky mode resonances (LMRs) [6]. LMRs in the nanowires can be optimized for solar cells by tuning the size of single nanowires [3, 7]. To further enhance the absorption of sunlight, metallic nanostructures have been conceived to be combined into solar cells. Metallic nanoparticles can be used as subwavelength antennas in which the plasmonic near-field is coupled to the semiconductor, increasing its effective absorption cross-section [8]. Lin [9] found that gold, copper, and silver catalysts all decreased the integrated optical absorption across the solar spectrum in vertically aligned silicon nanowire arrays. Brittman [10] showed that increasement of photocurrent occurred at the wavelengths corresponding to the nanocrystal’s surface plasmon resonances, while decreases occurred at wavelengths corresponding to optical resonances of the nanowire in a single nanowire silicon solar cell decorating with an octahedral silver nanocrystal. Zhan [11] proposed and demonstrated numerically the possibility of metallic-cores that enable strong optical absorption in SNSCs. They showed that an enhancement of 16.6% in the photocurrent could be achieved by α -Si nanowire solar cells with the proper core size and filling-ratio compared to that without silver core. However, we found that α -Si SNSCs with centered silver core for whatever core size and filling-ratio all decrease the integrated optical absorption across the solar spectrum. In this letter, we proposed a circular cross-sectional single nanowire α -Si solar cells with embedded circular silver core as shown in Fig. 1. Using the finite-difference time domain method, we studied how the size and position of the silver core and the diameter of the nanowire affect the short circuit current density, Jsc , for both s- and p-polarized sunlight. We found that for a wide range of nanowire diameter, silver core located in the center of nanowire degraded the Jsc , in the photoactive region. However, an enhancement in the photocurrent could be achieved with off-center silver core compared to that without silver core. An enhancement of 54.9% in Jsc was produced by SNSCs with nanowire radius of 190 nm, silver core radius of 130 nm and distance upwardly offset from the center of silver core to that of nanowire of 54 nm for s-polarized. And an enhancement of 24% in Jsc was produced by SNSCs with nanowire radius of 200 nm, silver core radius of 20 nm and distance downwardly offset from the center of silver core to that of nanowire of 108 nm for p-polarized. 2.
Model and numerical method
The schematic diagram of SNSCs with silver core in this study is provided in Fig. 1. The single nanowire is treated as an infinitely long cylinder and characterized by the radius R. The silver core with radius r is embedded into the single α -Si nanowire. The d is the distance from the
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1008
Fig. 1. Schematic diagram of the simulation model.
center of silver core to the origin. The dimensionless parameter p=d/(R-r) is used to specify the radial position of the core center, where p, the ratio, varies between 0 and 1. When p is equal to 0, the silver core is at the center of the single α -Si nanowire. It is the same as [11]. The θ is the angle from the X-axis to d. It varies between - π2 and π2 . In the simulation, a commercial FDTD software package, FDTD Solutions, provided by Lumerical Solutions Inc. [12] was used. The total field scattered field (TFSF) plane wave source is used for non-periodic SNSCs. The incident light is along the Y-axis as shown in Figs. 1. The computational domain considered is terminated by perfectly matching layer (PML). The power absorption per unit volume (Pabs (x, y)) in the absorber (α -Si and Ag) can be calculated using the relation L = −0.5ω |E|2 ε (ω ), where ω is the angular frequency, |E|2 is normalized light intensity ar near field, ε is the imaginary part of dielectric function of the absorber. Dispersive dielectric functions of α -Si and Ag come from the experimental data of Palik [13]. When Pabs (x, y) is known, it is easy to calculate total absorption Pabs (λ ) in some volume by integrating the loss function over that volume. In this model, there are two dispersive materials (α -Si and Ag) in SNSCs, we are interested in the power absorbed by α -Si. Once the power absorbed as a function of space, ie, Pabs (x, y) is obtained, the total absorption in α -Si can be calculated by Pabs (x, y) · M(x, y)dxdy, where M is the filter factor. It is 1 if the (x,y) values are inside the α -Si and 0 if they are outside. Similarly, the total absorption in Ag core can also (λ ) , where Pin (λ ) is the be calculated. The absorption efficiency is calculated by Qabs (λ ) = PPabs in (λ ) power of the incident light. To investigate the potential benefit of the Ag core for SNSCs, the short circuit current density, Jsc , is calculated according to the following equation: Jsc =
800nm eλ 400nm
hc
Qabs (λ )ΦAM1.5 (λ )d λ
(1)
e where Qabs is the absorption efficiency, hc is the charge constant, ΦAM1.5 is the reference solar spectral irradiance (ASTM G-173) [14]. To match the solar spectrum to α -Si absorption, a wavelength range from 400 to 800 nm is considered.
3. 3.1.
Results and Discussion Influence of the core located in the center of nanowire on photon absorption for SNSCs
To determine whether the silver core located in the center of nanowire increase or decrease absorption inside the SNSCs, we study the Jsc enhancement (Jsc /Jscbare ) compared to that without silver core. Figure 2 shows the calculated contour map of Jsc enhancement in SNSCs with #195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1009
silver core located in the center of nanowire as a function of nanowire radius R and core radius r for p-polarized (a), s-polarized (b), and non-polarized (c) sunlight. In order to compare the results of [11], nanowire radius values from 100 nm to 190 nm are considered. We observe that the Jsc enhancement is always below 1 for both p-, s- and non-polarized. In other words, for a wide range of nanowire and silver core diameters, silver core located in the center of nanowire decreases the absorption in the nanowire. To understand why the silver core located in the center of nanowire degrades the Jsc enhancement, we compare absorptance spectra without and with silver core in the SNSCs. Figure 3 shows the influence of the silver core on the absorption in SNSCs with varying nanowire radius for both p- and s-polarized light. Figs. 3(a) and 3(d) describe the contour maps of Qabs in the SNSCs without silver core as a function of illumination wavelength and nanowire radius R for p- and s-polarized, while Figs. 3(b) and 3(e) describe that of α -Si nanowire in SNSCs with silver core. To study the effect of silver core on photon absorption in SNSCs, Figs. 3(c) and 3(f) describe that of silver core in SNSCs. The core radius is chosen as 36 nm, and the nanowire radius, R, is changing from 100 to 190 nm. To illustrate more clearly, the absorption efficiency Qabs of α -Si nanowire without core, α -Si nanowire with core and silver core in the SNSCs for p- and s-polarized are extracted from Figs. 3(a)-(f) and plotted in Figs. 3(g) and 3(h). The nanowire radius, R, is 130 nm and the silver core radius, r, is 36 nm. They correspond to the parameters for maximum absorption enhancement in the SNSCs of [11]. It can be concluded from Figs. 3(a) and 3(d) that LMRs actually exist in the SNSCs without core [15]. Note here that there are common characteristics between p- and s-polarized light. The number of resonant peaks is augmented with increasing R, and these resonant peaks clearly tend to show substantial red shifts with increasing R. These resonant peaks can be understood by means of the Fano effect [16] that has been observed in spherical core/shell nanoparticles [17]. The lower the field intensity, the weaker the LMRs. For strong LMRs (longer wavelength region), the LMRs arise from whispering gallery mode which exists in microdisk resonators. For weak LMRs (short wavelength region), the incident light appears to be localized via constructive interference with the reemitted light. The LMRs are similar to the Fabry-perot resonance (FP modes). The fields of these LMRs will be shown in Figs. 4. Figure. 3(b) and 3(e) show the effect of the silver core on absorptance spectrum of nanowire for p- and s-polarized. From Figs. 3(b), we can find that the number of resonant peaks is reduced. Meanwhile, the number of LMRs peaks is reduced with decreasing R. And there is only one LMR peak when the radius of nanowire is ∼100 nm. As a result, the Jsc enhancement is much lower than 1 [Figs. 2(a)]. In contrast with that under s-polarized illumination [Figs. 3(e)], the number of LMRs peaks is almost no change. But the positions of some peaks are slightly (a) p−polarized 90
1
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Fig. 2. Contour map of Jsc enhancement in SNSCs with silver core located in the center of nanowire as a function of nanowire radius R and core radius r for (a) p-polarized, (b) s-polarized and (c) non-polarized sunlight.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1010
Fig. 3. Contour maps of Qabs in the SNSCs as a function of illumination wavelength and nanowire radius R. The silver core radius, r, is 36 nm. (a) without silver core, (b) Qabs in the α -Si nanowire and (c) Qabs in the silver core for p-polarized light. (d) without silver core, (e) Qabs in the α -Si nanowire and (f) Qabs in the silver core for s-polarized light. The absorption efficiency Qabs in the SNSCs (g) p-polarized and (h) s-polarized. The nanowire radius, R, is 130 nm and the silver core radius, r, is 36 nm. They correspond to the parameters for maximum absorption enhancement in the SNSCs of [11].
shifted. So the integrated absorption efficiency is proportionally lower than the bare SNSCs [Figs. 2(b)]. To understand the effect of silver core on photon absorption in SNSCs, we calculate the Qabs in the silver core. Figure. 3(c) and 3(f) show the maps of Qabs in the silver core as a function of illumination wavelength and nanowire radius R under p- and s-polarized. From Figs. 3(c), we can find that the number of resonant absorption peaks of silver core is augmented with increasing R. There are nearly 50% resonant absorption efficiency at the wavelengths from 550 to 700 nm, when the nanowire radius is between 120 and 160 nm. Under p-polarized illumination, there is a localized plasmon plariton (LPPs) [18] in the silver core. We observed a largely enhanced scattering as well as absorption cross section [not shown] and a significantly enlarged near-field amplitude in close vicinity to the silver core [Figs. 4(7-9)]. From Figs. 3(f), some resonant absorption peaks of silver core are also observed. But, those peaks are not LPPs because the light is s-polarized. Note here that there are common characteristics between Figs. 3(c) and 3(f). But the role of resonance from silver core is thoroughly different [see Figs. 3(g, h) and Figs. 4]. From Figs. 3(g) and 3(h), we can find that there are many LMRs in bare SNSCs under both p- and s-polarized light. So, the integrated absorption performance has been good. But, when the silver core is embedded into the single nanowire, it will damage the formation of LMRs which exist in bare SNSCs. However, due to the existence of silver core, forming some localized surface plasmon resonance peaks (p-polarized), located in 440 nm, 543 nm, 593 nm, and 763 nm. In the corresponding resonance, the absorption in α -Si nanowire at these wavelength regions has been enhanced. The corresponding field distributions are demonstrated in Figs. 4(7-9). Through careful observation, we found that, in addition to the resonance region, the absorption in SNSCs at other parts is obviously reduced. As a result, the integrated absorption performance decreased instead. However, when the illumination is s-polarized, there is no formation of LPPs. The absorption of silver core is also very low. The presence of silver core did not affect the formation of LMRs in SNSCs [Figs. 4(16-21)]. Obviously, because of the
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1011
423 nm p-polarized
w/o core
1
433 nm w core
7 423 nm
s-polarized
w/o core
10 430 nm
w core
16
460 nm
2
510 nm
3
resonance resonance deletion deletion
457 nm
11 460 nm
17
513 nm
12
550 nm
603 nm
4
5
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9
547 nm
603 nm
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6 resonance deletion
647 nm
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Fig. 4. H-field distribution in SNSCs. The nanowire radius, R, is 130 nm. The core radius, r, is 36 nm. The color is not in scale, which is just to show the steady mode. Sub-graph 1-6 for without core and 7-9 for with core under p-polarized illumination; sub-graph 1015 for without core and 16-21 for with core under s-polarized illumination. The resonant wavelength marked on the top of each sub-graph.
existence of silver core, the volume of α -Si nanowire is decreased, so the overall absorption in SNSCs is also reduced. 3.2.
Influence of silver core position on photon absorption for SNSCs
Figure 5 shows the influence of the silver core with varying radius on Jsc enhancement in SNSCs, note here that the core moves from the lower positive along the Y-axis. We used these positions, selected from optimal regions that will be clarified in Figs. 9. The nanowire radius, R, is 190 nm. That’s because this value corresponds to the maximum Jsc enhancement for nonpolarized sunlight as shown in Figs. 8. The core radius, r, is changing from 10 to 160 nm. The point A in Figs. 5(a) is corresponding to the maximum Jsc enhancement (22.8%) under p-polarized illumination. Here, the core radius, r, is 20 nm, and the ratio, p, is -0.6. According the formula, d=(R-r)·p, the distance from the center of silver core to the origin is 102 nm. Moreover, the core is located in the negative Y-axis. As can be seen in Figs. 5(a), there are two Jsc enhancement regions. The stronger enhancement region is that r∈[20, 80] nm and p∈[-1, -0.5]. The other region is that r∈[50, 70] nm and p∈[0.4, 0.6]. It also can be seen, in addition to that the core located near the center of the nanowire, the Jsc enhancement is almost all larger than 1 for core radius r less than 80 nm. The point B in Figs. 5(b) is corresponding to the maximum Jsc enhancement (54.9%) under s-polarized illumination. Here, the core radius, r, is 130 nm, and the ratio, p, is 0.9. Likewise, the core is located in the positive Y-axis, and the distance from the center of silver core to the origin is 54 nm. Similarly, there are three Jsc enhancement regions. One is r∈[30, 160] nm and p∈[0.9, 1]. The second is r∈[20, 60] nm and p∈[-1, -0.6]. And the third is r∈[30, 50] nm and p∈[0.5, 0.7]. By comparing Figs. 5(a) and
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1012
Fig. 5. Contour maps of Jsc enhancement in SNSCs as a function of core radius r and the ratio p, here p varies from -1 to 1, corresponding to the core moves from bottom to up along the Y-axis. (a) p-polarized, (b) s-polarized and (c) non-polarized. The nanowire radius, R, is 190 nm.
5(b), we can see that the maximum Jsc enhancement under s-polarized is larger than that under p-polarized. But what’s even more crucial is that silver core size and position of maximum Jsc enhancement under p- and s-polarized illumination are not consistent. That is not suitable for practical application. Therefore, the averaged Jsc enhancement (i.e., p-/2+s-/2) is plotted in Figs. 5(c) to show the device performance under realistic solar illumination. From Figs. 5(c), we can see that an enhancement of 21.4% in the Jsc could be achieved by SNSCs with core radius, r, 30 nm, and ratio, p, -0.7 (i.e., the center of the silver core is located at coordinates (0, -112) nm. Labeled C). At the same time, the region I (r∈[20, 50] nm, p∈[-1, -0.6]) is acceptable, the Jsc enhancement are all above 18%. In addition to region I, the region II (r∈[20, 130] nm, p∈[0.9, 1]) and region III (r∈[30, 70] nm, p∈[0.4, 0.6]) are also acceptable. In Figs. 6(a), we show the wavelength dependence of Qabs in SNSCs with Si nanowire of radius R=190 nm, silver core located in the negative Y-axis of radius r=20 nm and the distance from the center of silver core to the origin d=102 nm under p-polarized illumination. Without-core Qabs is shown for comparison. Meanwhile, Ag-core Qabs is also shown to determine whether the resonant peaks in nanowire come from the LPPs excited in silver core. The Qabs spectra for the two structures with and without core are almost overlapping together when λ < λc ∼ 490nm (see the dashed line at 490 nm). This is because the incoming photon energy is fully absorbed at the surface before reaching the silver core. Moreover, the absorption in silver core is near 0 at this short wavelength region according to the Qabs spectra of silver core. But the absorption in SNSCs is clearly enhanced at both resonance and off-resonance region for long λ > λc ∼ 490nm. Note here that λc is a characteristic wavelength, up which the light absorption enhancement always occurs due to the silver core. From Figs. 6(a), we can see that there are 5 resonant peaks at the absorption enhancement region. According to the absorption peaks of silver core labeled from AE1 and AE5 . we can draw the conclusion that these peaks originate in part from LPPs excited in silver core. In order to clarify the role of silver core, H-field distribution in SNSCs at the resonant peak labeled from T E1 to T E5 is plotted in Figs. 6(b) to 6(f). From Figs. 6(b), we can see that the silver core can be regarded as a high reflector. There is no strong localization of light around the silver core. But the Fabry-perot resonance
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1013
(a)
(b) TE1
(c) TE2
(d) TE3
(e) TE4
(f) TE5
Fig. 6. (a) The absorption efficiency Qabs in the SNSCs under p-polarized illumination. The nanowire radius, R, is 190 nm, the silver core radius, r, is 20 nm, and the ratio, p, is -0.6. (i. e., silver core located in the negative Y-axis and the distance from the center of silver core to the origin d=102 nm.) (b)-(f) H-field distribution in SNSCs at the resonant peak labeled from TE1 to TE5 , respectively. The color is not in scale, which is just to show the steady mode.
mode is generated between silver core and the inner edge of the nanowire. From Figs. 6(c) to 6(e), we can see that strong LMRs (whispering gallery modes here) and LPPs are coexist in the SNSNc. That caused a strong absorption enhancement from the widespread field enhancement because the light absorption is proportional to the product of the field intensity and the imaginary part of the silicon refractive index. Similarly, the weak LMRs (FP mode here) and LPPs are also coexist in the SNSCs as shown in Figs. 6(f). In Figs. 7(a), we show the wavelength dependence of Qabs in SNSCs with Si nanowire of radius R=190 nm, silver core located in the positive Y-axis of radius r=130 nm and the distance from the center of silver core to the origin d=54 nm under s-polarized illumination. Withoutcore and Ag-core Qabs are also shown for comparison. From Figs. 7(a), it can be seen that the
(a)
(b) TM1
(c) TM2
(d) TM3
(e) TM4
(f) TM5
(g) TM6
Fig. 7. (a) The absorption efficiency Qabs in the SNSCs under s-polarized illumination. The nanowire radius, R, is 190 nm, the silver core radius, r, is 130 nm, and the ratio, p, is 0.9. (i. e., silver core located in the positive Y-axis and the distance from the center of silver core to the origin d=54 nm.) (b)-(g) E-field distribution in SNSCs at the resonant peak labeled from TM1 to TM6 , respectively. The color is not in scale, which is just to show the steady mode.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1014
absorption enhancement emerged in almost the whole spectrum except λ < λc ∼ 420nm (see the dashed line at 420 nm). The Qabs decreases a little at the region of λ < λc because the effective absorption volume of the SNSCs with silver core reduced greatly. With increasing the wavelength of incident light, the influence of volumetric reduction is won over by emergence of the LMRs (whispering gallery modes here). The silver core works as a reflector. Then, a resonator cavity can be formed between silver core and the inner edge of the nanowire. The incident light circles around the cavity, supported by continuous total internal reflection of the cavity surface, that meet the resonance condition. In order to explain the resonant absorption peaks labeled from T M1 to T M6 , E-field distribution in SNSCs at each resonant peak is plotted in Figs. 7(b) to 7(g). From the E-field distribution, according to the wave theory of whispering gallery modes, we can use multi-index (mode numbers) to label the eigenmodes. Then the resonant mode labeled from T M1 to T M6 shown in Figs. 7(a) can be lebeled as (15,1), (13,1), (11,1), (9,1), (7,1) and (5,1), respectively. These whispering gallery modes result in a substantial improvement of Qabs in SNSCs. On the other hand, the short the characteristic wavelength and the more the number of resonant modes, the larger the absorption enhancement. It is noticed that the LPPs can not be excited under the s-polarized illumination. The silver core just serves as a reflector. Under such conditions, we can use the dielectric core to replace silver core. As one of the most simple example, we used air to replace silver core and obtained the similar absorption enhancement (not shown here). We’ll dig into these issues in our next post. 3.3.
Optimization and tolerance evaluation
To further investigate the optimal combination of nanowire radius (R), silver core radius (r) and the position of the core (p, i.e., d), the Jsc enhancement was calculated by sweeping those
(a)
(b)
Fig. 8. Maximum of Jsc enhancement as a function of radius of SNSCs (circle points in blue). (a) p-polarized, (b) s-polarized. The left inset is the optimum core radius (diamond points in red) and the right inset is the optimum ratio (square points in green), respectively. The light dotted line in the inset is the linear fitting for the relationship between r and R.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1015
parameters. The geometrical parameters are swept within R∈[100, 220] nm; r∈[10, 200] nm; p∈[-1, 1]. The Jsc enhancement cannot be represented by graph because there are too many parameters. However, the optimal parameters can be extracted from the multidimensional matrix. Figure. 8 shows the maximum of Jsc enhancement as a function of radius of SNSCs under p-polarized (a) and s-polarized (b) illumination. The left inset is the optimum core radius and the right inset is the optimum ratio, respectively. As shown in Figs. 8(a), with increasing R, the maximum Jsc enhancement rises first and then falls slightly. The summit with 24% enhancement is corresponding to the nanowire radius of 200 nm. From the insets of Figs. 8(a), with increasing R, the optimum core radius r and ratio p remain constant, that is to say r=20 nm, and p=-0.6. Therefore the optimum combination under p-polarized illumination for R, r and d is that R=200 nm, r=20 nm and d=108 nm. In contrast, as shown in Figs. 8(b), with increasing R, the maximum Jsc enhancement periodic changes in about 50%, and the ratio remains constant. But, different R correspond to different core radius r, and that when the R become greater the optimal core radius r is increasing linearly, as given by r=k·R+b, where k is the slope coefficient, b is the intercept of fitting-line, which both can be calculated by numerical fitting from the left inset in Figs. 8(b). If R is in units of nanometers, the k=0.86 and b=-26. As a result under s-polarized illumination, the optimum combination for R, r and d is that R=190 nm, r=130 nm and d=54 nm. Up to now, we have already discussed the influence of silver core with different radius located in Y-axis on photon absorption for SNSCs with different radius R. Assuming the silver core deviate from the Y-axis, then how the silver core would affect on light absorption in SNSCs. Given that, the influence of position deviation of silver core, namely the SNSCs with silver core is tilted, on Jsc enhancement in SNSCs is discussed. Figure 9 shows the maps of Jsc enhancement in SNSCs as a function of d and θ , expressed in polar coordinates. Here, d is the distance from the center of silver core to the origin, d=(R-r)·p, p varies from 0 to 1. The θ is the angle from the x-axis to d. It varies from −π /2 to π /2. Because the structure of SNSCs and light source are symmetric about Y-axis, we only need to compute the structure that the silver core is located at the right/left side of the Y-axis. The nanowire radius, R, is 190 nm. Under p-polarized illumination, the silver core radius, r, is 20 nm. So the d varies from 0 to 170 nm. Under s-polarized illumination, the silver core radius, r, is 130 nm. And d varies from 0 to 60 nm. Under non-polarized illumination, the silver core radius, r, is 30 nm. And d varies from 0 to
Fig. 9. Contour maps of Jsc enhancement in SNSCs as a function of d and θ , expressed in polar coordinates. The points on the graph represent the positions of the center of silver core. The nanowire radius, R, is 190 nm. d=(R-r)·p, p varies from 0 to 1. The θ is the angle from the x-axis to d. It varies from −π /2 to π /2. (We only need to compute a half because the structure of SNSCs and light source are symmetric about the Y-axis.) (a) p-polarized, the silver core radius, r, is 20 nm, d varies from 0 to 170 nm; (b) s-polarized, the silver radius, r, is 130 nm. d varies from 0 to 60 nm; (c) non-polarized, the silver radius, r, is 30 nm. d varies from 0 to 160 nm.
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1016
160 nm. From Figs. 9(a), we can see that the Jsc enhancement appears below the X-axis. With increasing θ , the Jsc enhancement falls gradually. For the maximal Jsc enhancement region, i.e., d is about 60 nm, it is acceptable when θ ∈ [−90o , −50o ]. In other words, the silver core can be placed in the Y-axis on both sides of the 40o range. From Figs. 9(b), we can see that the Jsc enhancement appears above the X-axis. With increasing θ , the Jsc enhancement rises gradually. For the maximal Jsc enhancement region, i.e., d is about 54 nm, it is acceptable when θ ∈ [40o , 90o ]. That is to say, the SNSCs could be placed within 50 degree reclining. From Figs. 9(c), we can see that the Jsc enhancement appears both above and below the X-axis. With increasing θ , the Jsc enhancement falls first and then rises slightly. For two maximal Jsc enhancement regions, i.e., d is about 112 nm and 160 nm, it is acceptable when θ ∈ [−90o , −60o ] and θ ∈ [70o , 90o ]. 4.
Conclusion
In conclusion, we proposed a circular cross-sectional single nanowire α -Si solar cells with a circular silver core is embedded and, using the finite-difference time domain method, investigated numerically how the size and position of the silver core and the diameter of the nanowire affect the short circuit current density, Jsc , for both s- and p-polarized sunlight. Firstly, we investigated the influence of silver core located in the center of the nanowire on the Jsc enhancement, and found that for a wide range of nanowire diameter, the silver core degraded the Jsc . Next, the silver core was deviated from the center of nanowire and the influence of silver core size and position on photon absorption for SNSCs was studied. The results suggested that an enhancement in the Jsc could be achieved in SNSCs with off-center silver core compared to that without silver core. An enhancement of 54.9% in Jsc was produced by SNSCs with nanowire radius of 190 nm, silver core radius of 130 nm and distance upwardly offset from the center of silver core to that of nanowire of 54 nm for s-polarized. And an enhancement of 24% in Jsc was produced by SNSCs with nanowire radius of 200 nm, silver core radius of 20 nm and distance downwardly offset from the center of silver core to that of nanowire of 108 nm for p-polarized. For practically useful device, an enhancement 0f 21.4% in the Jsc could be achieved by SNSCs which nanowire radius R is 190 nm with core radius, r, 30 nm and it is located at coordinates (0, -112) nm under really sunlight illumination. Finally, the optimal combination of nanowire radius (R), silver core radius (r) and the position of core (d) was calculated for each polarized light. The influence of position deviation of silver core on Jsc enhancement in SNSCs was also discussed. Acknowledgment This work is financially supported by Huaihai Institute of Technology (Grant No.KQ08027, KX08039).
#195638 - $15.00 USD Received 12 Aug 2013; revised 21 Sep 2013; accepted 24 Sep 2013; published 11 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.0A1007 | OPTICS EXPRESS A1017
