Improved Silver Optical Constants for Photovoltaic

28th European Photovoltaic Solar Energy Conference and Exhibition

IMPROVED SILVER OPTICAL CONSTANTS FOR PHOTOVOLTAIC PLASMONICS Yajie Jiang, Martin A. Green, Hamid Mehrvarz, Supriya Pillai, Henner Kampwerth, Robert J. Patterson, Australian Centre for Advanced Photovoltaics University of New South Wales, Sydney NSW 2052, Australia

ABSTRACT: Plasmonics open up new ways to construct optically thick but physically very thin photovoltaic absorbers. Silver is the most favored plasmonic material, and has demonstrated the lowest parasitic absorption losses among other noble metals. However, the presence of many different sets of optical constants for silver in literature makes it difficult to conduct reliable theoretical analysis. Realistic predictions necessitate optical constant data sets that are more accurate, considering that even small variations can influence calculation of Surface Plasmon effectiveness. Surface tarnish layers form quickly when silver is exposed to air making it challenging to determine the optical constants from air exposed samples. Our work aims to determine a reliable set of values that can be used with confidence in predicting experimental outcomes. We measured the optical data of silver using a novel method avoiding the air exposed side that might be contaminated. Our work seeks to pinpoint accurate values by using a range of different measurement approaches. Keywords: Optical Properties, Grain, Light Trapping, Plasmonic, Silver

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derived from J&C [2], which did not take the formation of Ag2S into account when extracting their values. Nash and Sambles (hence forth referred to as N&S) reviewed the published silver optical constants comprehensively [14]. They questioned all data sets derived from air exposed samples. Furthermore, an obvious difference in the optical constants derived in ultra-high vacuum and in air for a thin film of silver is attributed to the film properties being altered by air [15]. Realistic predictions necessitate optical constant data sets that are more accurate, considering that even small variations can influence calculation of Surface Plasmon effectiveness [16]

Introduction

Surface plasmons are longitudinal oscillation of conduction electrons at a metal dielectric interface bound to an electromagnetic wave. Plasmonics open up new ways to construct optically thick but physically very thin photovoltaic absorbers. Many modeling techniques are being developed to precisely predict the performance of plasmonic systems and associated components for light trapping applications, highlighting the importance of the accuracy of optical constants used. Noble metals support plasmons because of their high density of free electrons. Silver is known to be the most favored plasmonic material due to its large relaxation time, low absorption and high radiative efficiency. Simulation studies for plasmonics for light trapping applications in photovoltaics show Palik [1] and Johnson and Christy [2] (henceforth referred to as J&C)’s data being the more favored ones. Dionne [3], Beck [4], Dunbar [5] etc. cite J&C’s data, and some researchers have opted Palik’s data [6, 7] Ferry cites Rakic’s modeled data [8] using LorentzDrude model fit to Palik’s data.. The accuracy of existing data may affect most of theoretical work in plasmonic research. Surface tarnish layers form quickly when silver is exposed to air making it challenging to determine the optical constants from air exposed samples. Many researchers detected that silver sulphide (Ag2S) is the main component of the surface tarnish layer for silver. Different Ag2S growth rates have been reported in the literature. Bennett’s group conducted a series of experiments to study the growth of silver sulphide tarnish films [9-11]. They adopted an ellipsometry technique and electron microscopy to determine the average thickness of the tarnish film. They showed that the initial growth rate is 0.1nm per hour in normal air, while a rate of 10nm/s is recorded in the atmosphere containing 10% H2S. This quickly growing tarnish layer has a large enough effect on any measurements that use reflectance to obtain the optical constants, since silver sulphide is strongly absorbing especially in the visible spectrum. The optical constants for Ag2S tarnish film were also measured for further study [12]. Kovacs recorded the value of 0.5 nm per week by comparing the resonance shifts of surface plasma wave from an evaporated single Ag film on glass prism substrate [13]. However, the silver optical constants they used in the calculation was

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Comparative Studies of Most Cited Values

The optical constants of silver ( n and k) have been measured by many research groups, while the most widely accepted are those from Palik’s handbook and J&C’s data. We choose these two sets of data together with N&S’s data for comparison in this paper. 2.1 Optical constants Palik’s handbook [1] of optical constants is one of the most cited references. However, this data set for silver combines the work of four research groups using different sample preparation method, and includes data from samples exposed to air. This definitely causes inconsistencies in their values. The most heavily cited source for the optical constants of evaporated silver films in plasmonic photovoltaics is J&C [2], probably because their data produce the best theoretical results. However, this set of values is not considered to be reliable since their samples were exposed to air when conducting the measurements, and the errors stated in their paper are almost half or even larger than their silver n values in visible and infra-red region. N&S [14] claim that they obtained the best data for silver because they avoided measurement on the surface exposed to air. However, their results are limited to the 450-900nm range. We are interested in the visible and near infra-red for solar cell applications, while N&S’s data not cover the infra-red. Big differences can be seen in the visible region among the three set of data as shown in Fig.1. Optical constant here is denoted as refractive index n and extinction coefficient k however the use of permittivity ε is more

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commonly associated with plasmonic work. The dielectric function is related to the complex refractive index as by the equation ( n + ik )2 = εr + εi.

was off by an order of magnitude. Similarly, silver nanoparticle plasmon relaxation time calculated by Maier [19] based on J&C’s data exhibits a marked difference between Palik’s data and the optical constants published for silver clusters [20]. These discrepancies were not explained and could be attributed to the inconsistencies in these data sets.

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Experimental Procedures

In order to avoid the air exposed side that might be contaminated, we conduct the measurement from substrate side and measure the silver property at the interface. A specific substrate is adopted since the substrate should be treated as a film as well if the measurement is taken from the substrate side. We choose a 75nm thick silicon nitride membrane as the substrate. The 5x5mm membrane is held by a 10x10mm silicon frame. The structure is shown in Fig. 3. A thin layer of optically opaque silver is thermally evaporated at the rate of 20Å/s on our substrates. Ellipsometry and reflection measurements are adopted to determine the optical constants. The measurements are done from the substrate side to avoid the influence of any tarnished surface layer. The experimental results are evaluated by a fitting process using W-VASE software to extract optical constants.

Figure 1: Comparison of the optical constants of silver by Palik [1] (chopped to region of interest), J&C [2] and N&S [14]. 2.2 Plasmonic Effectiveness Analysis Quality factors or figures–of–merit can be adopted as criteria for a materials’ plasmonic performance [17]. Quality factor for spherical nanoparticle supporting a localized Surface Plasmons (LSP) is given by QLSP = -εr / εi. Small difference in the optical constants can result in significant difference in plasmonic performance. Up to 6 fold discrepancy can be seen in the quality factors using the three most popular sets of optical constants in the literature as in Fig. 2.

Figure 3: Schematic of the SiN membrane structure used in the experiment. The figure, which is not to scale, shows the silicon frame, the silicon nitride membrane and the silver layer. The optical property of the silicon nitride is measured before the silver measurement. An unetched 200 μm silicon wafer with 100nm silicon nitride on both sides is measured to extract the optical constants of silicon nitride. Literature shows that reflectance data is more commonly used to extract the optical constants, while this alone might not be sufficient to extract accurate values. In this work we adopt both ellipsometry and reflectance measurements. After the deposition of silver film, the measurements were conducted from the silicon nitride side. A preliminary set of optical constants of silver film measured at the silver/substrate interface is extracted. This value is derived from the W-VASE software by fitting ellipsometry and optical reflection data to a Lorentz-Drude model The optical constants are affected by silver grain structures, especially grain boundary. The grain size at silver/SiN interface is measured by multiple methods. Electron backscatter diffraction (EBSD) and X-Ray Diffraction (XRD) are used to define grain boundaries and determine the grain sizes in relation to different growth techniques. EBSD gives the crystal orientation mapping of silver grains. The average grain size calculated is 239nm, and the twin grain size is determined to be 114nm.

Figure 2: Difference in quality factors for the three sets of published silver optical constants from Palik, J&C and N&S for localized surface plasmons. Furthermore, Dionne and co-workers conducted a numerical analysis on surface plasmon properties using both J&C and Palik’ data [18]. Notably, the discrepancy observed for the propagation distance in their calculation

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XRD is another method for grain size calculation. It shows the diffraction pattern of each orientation. The grain size can be calculated by Scherrer equation τ = Kλ / bcosθ. Here τ is the grain size; K is a dimensionless shape factor, with a value about 0.9; λ is the X-ray wavelength; β is the line broadening at half the maximum intensity (FWHM), in radians; θ is the Bragg angle. The grain size calculated by this method (strongest peak) is 120nm after subtracting the instrumental line broadening, which is similar with the twin grain size by EBSD scanning.

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very likely due to the inaccuracy from the tarnished silver layer.

Results and Analysis

A preliminary set of optical constants from the evaporated silver film on the 75nm thick silicon nitride membrane is extracted. As a way of ascertaining the accuracy of our values, we decomposed the free electron contribution from the bound electron contribution. Electron behaviour has been comprehensively analysed by Drude [21]. Drude applied the electromagnetic theory to the optical constants by treating metals as a gas of free electrons. [22]. The dielectric constants described by Drude free-electron theory for real part and imaginary part are εr = 1 - ( ωp2 τD 2 ) / (1 + ω2 τD 2 ) and εi = ( ωp2 τD 2 ) / ω (1 + ω2 τD 2 ) , respectively. Here τ is the relaxation time and ωp is the plasma frequency. It is well known that the Drude model is used to describe the behaviours of metals in free electron region valid for low photon energies. The theory has been confirmed by comparing with experimental work [23]. Ehrenreich and Phillipp presented an expression to separate the free electron ε(f) and bound electron δε(b) contribution of the complex dielectric constants ε = ε(f) + δε(b) [24]. Free electron contribution ε(f)can be derived from random phase approximation (RPA) ε(f) = 1 - ωp2 / ω (ω + i /τD), where τD is the relaxation time and ωp is the plasma frequency. τD and ωp values are derived from the experimental values. The decomposition of free electron and bound electron contribution applies for the real part and imaginary part as well εr = εr(f) + δεr(b), εi = εi(f) + δεi(b). We are more interested in the real part of dielectric constants εr(f) and δεr(b). Bound electron contribution δεr(b) can be calculated by Kramers-Kroing relations in free electron region, and then we can obtain the free electron effects by εr(f)calculated = εrexperimental - δε(b)calculated to compare with εr(f)RPA derived from RPA. We applied this method to Palik, J&C and our data to check whether the calculated free electron behaviours εr(f)calculated match with the values εr(f)RPA , as shown in Fig.4. Moreover, the free electron should follow Drude model. It is obvious that Palik’s work do not follow the Drude model in the free electron region, that results from the inconsistency of the original optical data set. An obvious Drude trend can be seen in J&C’s and our data. However, around 4% mismatch can be seen in the zoomed Fig.4 (c) for J&C’s data, while our data show good agreement between the calculated free electron behaviours εr(f)calculated and the values εr(f)RPA (Fig.4 (e)). Our data shows very good agreement compared with the others as expected. The deviation seen in J&C data is

Figure 4: Decomposition of the experimental values of εr for Ag into free and bound contributions εr(f)calculated and δε(b)calculated , respectively for (a) Palik’s values, (b) Johnson and Christy’s values, and (d) our values. (c) (e) are the corresponding zoomed insets of (b) and (d).

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[16] Green, M.A. and S. Pillai, Harnessing plasmonics for solar cells. Nature Photonics, 2012. 6(3): p. 130-132. [17] West, P.R., et al., Searching for better plasmonic materials. Laser & Photonics Reviews, 2010. 4(6): p. 795-808. [18] Dionne, J., et al., Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model. Physical Review B, 2005. 72(7). [19] Maier, S.A., et al., Observation of coupled plasmonpolariton modes of plasmon waveguides for electromagnetic energy transport below the diffraction limit. Materials and Devices for Optoelectronics and Microphotonics, 2002. 722: p. 431-436. [20]Quinten, M., Optical constants of gold and silver clusters in the spectral range between 1.5 eV and 4.5 eV. Zeitschrift Fur Physik B-Condensed Matter, 1996. 101(2): p. 211-217. [21] Drude, P., On the electron theory of metals. Annalen Der Physik, 1900. 1(3): p. 566-613. [22] Dynamics at Solid State Surfaces and Interfaces: Volume 2: Fundamentals, H.P. Uwe Bovensiepen, and Martin Wolf, Editor 2012: Wiley-VCH Verlag GmbH & Co. KGaA. p. 181-236. [23] Schulz, L.G., An Experimental Confirmation of the Drude Free Electron Theory of the Optical Properties of Metals for Silver, Gold, and Copper in the near Infrared. Journal of the Optical Society of America, 1954. 44(7): p. 540-545. [24] Ehrenreich, H. and H. Philipp, Optical Properties of Ag and Cu. Physical Review, 1962. 128(4): p. 1622-1629.

Conclusions

Extracting the most accurate set of data for silver will prove quite important since circa 80% of the literature in plasmonic research cite questionable data. A preliminary set of optical constants from a silver film (evaporation rate 20Å/s) evaporated on a 75nm thick silicon nitride membrane is extracted. This value is derived from the WVASE software based on ellipsometry and optical reflection data. Accurate and reliable data will help optimize plasmonic light trapping in solar cells and assist calculations for other applications as well. Optical constants can depend on grain structures. We anticipate to come up with a relation between optical constants and different grain sizes. References [1] Palik, E.D., Handbook of Optical Constants of Solids, 1985, Academic Press: Orlamdo. [2] Johnson, P.B. and R.W. Christy, Optical Constants of the Noble Metals. Physical Review B, 1972. 6(12): p. 4370-4379. [3] Dionne, J., et al., Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization. Physical Review B, 2006. 73(3). [4] Beck, F.J., S. Mokkapati, and K.R. Catchpole, Plasmonic light-trapping for Si solar cells using selfassembled, Ag nanoparticles. Progress in Photovoltaics, 2010. 18(7): p. 500-504. [5] Dunbar, R.B., T. Pfadler, and L. Schmidt-Mende, Highly absorbing solar cells-a survey of plasmonic nanostructures. Optics Express, 2012. 20(6): p. A177-A189. [6] Ferry, V.E., et al., Plasmonic Nanostructure Design for Efficient Light Coupling into Solar Cells. Nano Letters, 2008. 8(12): p. 4391-4397. [7] Ferry, V.E., J.N. Munday, and H.A. Atwater, Design considerations for plasmonic photovoltaics. Advanced Materials, 2010. 22(43): p. 4794-808. [8] Rakic, A.D., et al., Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied Optics, 1998. 37(22): p. 5271-5283. [9] Bennett, H.E., et al., Formation and Growth of Tarnish on Evaporated Silver Films. Journal of Applied Physics, 1969. 40(8): p. 3351-&. [10] Burge, D.K., et al., Growth of Surface Films on Silver. Surface Science, 1969. 16: p. 303-&. [11] Bennett, H.E., et al., Validity of Ellipsometry for Determining Average Thickness of Thin Discontinuous Absorbing Films. Journal of the Optical Society of America, 1969. 59(6): p. 675-&. [12] Bennett, J.M., J.L. Stanford, and E.J. Ashley, Optical Constants of Silver Sulfide. Journal of the Optical Society of America, 1969. 59(4): p. 499-&. [13] Kovacs, G.J., Sulfide Formation on Evaporated Ag Films. Surface Science, 1978. 78(1): p. L245-L249. [14] Nash, D.J. and J.R. Sambles, Surface plasmonpolariton study of the optical dielectric function of silver. Journal of Modern Optics, 1996. 43(1): p. 81-91. [15] Rasigni, G. and P. Rouard, On Variation with Wavelength of Optical Constants of Thin Metallic Films. Journal of the Optical Society of America, 1963. 53(5): p. 604-&.

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