- Email: [email protected]
Design of ultrathin metal-based transparent electrodes including the impact of interface roughness
Materials and Design 104 (2016) 37–42
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Design of ultrathin metal-based transparent electrodes including the impact of interface roughness M. Bauch ⁎, T. Dimopoulos AIT-Austrian Institute of Technology, Energy Department, Photovoltaic Systems, Giefinggasse 2, 1210 Vienna, Austria
a r t i c l e
i n f o
Article history: Received 10 February 2016 Received in revised form 22 April 2016 Accepted 27 April 2016 Available online 28 April 2016 Keywords: Transparent electrodes Transparent conductive oxides Sputtering Ultra-thin metals Solar cells Optoelectronic devices
a b s t r a c t In this paper, an efficient model for the precise design and prediction of the optical properties of transparent electrodes that are composed of ultrathin metals embedded in dielectric layers, is introduced. Specifically, the investigated electrode employs an ultrathin Au layer on a TiOx-coated glass substrate and covered with Al-doped ZnO (AZO), deposited by sputtering. This structure was simulated with a transfer matrix algorithm and was optically characterized by measurements of direct and diffuse transmittance, as well as specular reflectance. The comparison of simulated and experimental spectra reveals significant differences, which is due to the increased absorption in the ultrathin metal. To achieve a more precise prediction of the optical properties, the roughness of the interfaces was included in the simulation through an effective medium approximation. The improved simulation model requires only one fitting parameter and was applied to optimize the electrode's performance through the variation of the dielectric layers' thickness. In agreement with the simulations, the deposited TiOx/Au/AZO electrodes showed a maximum transmittance of 0.88 at 550 nm (including the substrate) and average transmittance in the visible wavelength range of N 0.80, combined with a sheet resistance of 14 Ω/square. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Transparent electrodes (TEs) are key components of modern optoelectronic devices, optical coatings and photovoltaic cells [1]. Transparent conductive oxides (TCOs) are the most widely employed TEs, with prominent materials being the tin-doped indium oxide (ITO), aluminium-doped zinc oxide (AZO) and fluorine-doped tin oxide (FTO). ITO has been for long the material of choice for most applications, since it offers the best combination of transparency (80–90%) and resistivity (typically 1 × 10−4 Ω cm) [2], with the main disadvantage being its high cost due to the scarcity of indium. With the target to boost the performance/cost figure of TEs, current research embraces materials like carbon nanotubes, graphene, conductive polymer films, metal nanowires and meshes, as well as ultra-thin metals, the properties of which are summarized in recent reviews [3,4,5]. TEs should also be compatible with the challenging requirements of modern, highthroughput processing and device design. For example, device fabrication on flexible substrates by roll-to-roll processing demands lowtemperature deposition and stability to mechanical stress. The latter is not the case for standard TCOs, which are brittle and barely flexible, compromising their implementation in flexible optoelectronic devices and solar cells. Combinations of ultra-thin metals (Ag, Au, Cu, Al or Ni) and dielectric layers with high refractive index emerge as a very promising type ⁎ Corresponding author. E-mail address: [email protected] (M. Bauch).
http://dx.doi.org/10.1016/j.matdes.2016.04.082 0264-1275/© 2016 Elsevier Ltd. All rights reserved.
of TEs [5], offering exceptional features, such as: widely adjustable optical and electrical properties through film thickness and material variations, ambient- temperature deposition, better mechanical stability than TCOs on flexible substrates due to the metal ductility [5], low roughness (an advantage for devices with ultra-thin functional layers such as organic LEDs) [6], as well as high-temperature stability [7]. The sheet resistance of these components is mainly determined by the metal layer thickness, which needs to remain below 10–12 nm in order to avoid significant losses in transparency. The optical properties, on the other hand, are more prone to modifications of the multilayer architecture, having to do with the choice of the materials and of the layer thicknesses. Ideally, the optical properties of the TE (e.g. transmittance) should be optimized to meet specific device requirements (e.g. adjusted to the spectral response of a solar cell absorber). For the optimization process, a reliable simulation method is needed that precisely reproduces the experimental spectra and therefore gives the possibility to design improved components. The existing literature mainly reports symmetric TCO/metal/TCO structures [8], i.e. the metal is embedded between layers of the same TCO material. Furthermore, the comparison between simulation and experiment is limited to direct transmittance, not considering reflectance and scattering effects [9]. In this work, an improved transfer matrix simulation method is introduced that takes into account the roughness of the dielectric/metal interfaces through an effective medium approximation (EMA), allowing the precise prediction of the experimental transmittance and reflectance spectra. For our investigation, a model structure of Glass/TiOx/ Au/AZO is used. It is demonstrated that the improved simulation
38
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
algorithm allows designing and optimizing the multilayer structure in order to maximize the optical transmittance and the TE figure of merit in the desired wavelength window.
sheet resistance of the films was measured with a 4-point, in-line probe technique. 3. Results and discussion
2. Experimental 2.1. Thin film deposition The thin films were deposited by DC magnetron sputtering (Leybold Univex 450C) on clean soda-lime glass substrates (Menzel Gläser). TiOx was deposited in Ar/O2 (80/20 composition) atmosphere from a Ti target, at 120 W sputter power and 0.1 Pa gas pressure, yielding a sputter rate of 0.017 nm/s. Au was deposited in Ar atmosphere at a sputter power of 20 W and Ar-pressure of 0.2 Pa, resulting in a sputter rate of 0.44 nm/s. Al-doped ZnO (AZO) was sputtered from a ZnO target with 2 wt.% Al2O3, at 120 W and Ar pressure of 0.1 Pa, which yielded a sputter rate of 0.66 nm/s. The Ti and AZO targets had a diameter of 10.16 cm, while the diameter of the Au target was 7.62 cm. The target-tosubstrate distance was 10 cm and the sputter targets and substrates were water-cooled at 25 °C during the deposition process. The base pressure of the sputter system was 7 × 10−6–1.2 × 10−5 Pa. The layer thicknesses were determined by step-height analysis using a profilometer (KLA-Tencor—Alpha-Step IQ). In the following, the thickness of a specific layer is denoted with a subscript. For example, Au9 stands for Au layer of 9 nm thickness. 2.2. Characterization The samples were optically characterized using a Bruker Vertex 70 Fourier transform infrared spectrometer (FTIR), additionally equipped with a visible light source. Direct transmittance was measured for normal incident light and referenced to the sample holder without sample (air). Reflection was measured with the A513QA accessory of the spectrometer, at 13 deg angle of incidence and un-polarized light. The measured signal was referenced to a calibrated mirror (aluminium, coated with dielectric) in the range from 330 nm to 550 nm and to a thick, 150 nm Au-coated substrate, in the range from 550 nm to 1000 nm. Total transmittance (direct plus diffuse transmittance) was measured with a teflon (PTFE) integration sphere accessory for the Vertex 70. A GaP and a Si detector were used to record spectra in the range of 330–550 nm and 550–1000 nm, respectively. All optical measurements were performed with the light beam entering from the glass substrate (see Fig. 1(a)). The characterization of the surface morphology was done by atomic force microscopy (AFM) (Molecular Imaging, PicoPlus) in tapping mode and scanning electron microscopy (SEM) (Zeiss, SUPRA 40) with 5 kV acceleration voltage and in-lens detector. The
The investigated layer structure is a glass substrate, coated with a TiOx layer with thickness dTiOx, followed by an ultrathin Au layer with thickness dAu and an AZO top layer with thickness dAZO. The structure design is sketched in Fig. 1(a). dAu is fixed throughout this work to 9 nm. For the simulation of the direct transmittance at normal incidence and the specular reflectance of the samples at incident angle = 13 deg, a transfer matrix method (TMM) algorithm was implemented [10,11]. The TMM accounts for coherent layers (up to hundreds of nanometers thickness), while the glass substrate was treated incoherently and was implemented in the simulation by the following equations for a nonabsorbing substrate [12]: T TM ðαÞT 0 ðαÞ TðαÞ ¼ 1−R TM ðαÞR0 ðαÞ T 2 ðαÞR
ðαÞ
TM 0 RðαÞ ¼ R0 ðαÞ þ 1−R : TM ðαÞR0 ðαÞ
T( ) and R( ) are the transmittance and the reflectance of the complete structure including the glass substrate. TTM and RTM are the TMM-calculated transmittance and reflectance of the thin films and T0 and R0 the values of the transmittance and reflectance at the air/glass interface, which can be easily calculated by the Fresnel equations for a certain angle . The real and imaginary part of the refractive index (n and k, respectively) of Au and AZO were taken from the literature [13,6]. The optical constants of TiOx were extracted from the measured transmittance and reflectance spectra, through the implementation of a transfer matrix algorithm [14,15]. The experimental and simulated transmittance and reflectance of the TiOx film, as well as the extracted refractive index are shown in Fig. 1(b). The layer thicknesses dTiOx and dAZO of the dielectric layers were varied in the TMM simulation. Maximum transmittance at 550 nm was obtained for dTiOx = 36 nm and dAZO = 63 nm. These thicknesses were then used for the electrode fabrication. A structure without the AZO top layer was also fabricated, in order to gain deeper insight into the system's properties. The experimental transmittance and reflectance spectra and the associated TMM simulations are shown in Fig. 2(a) for Glass/TiOx36/Au9 and (b) Glass/TiOx36/Au9/AZO63. The maximum experimental transmittance of Glass/TiOx36/Au9 is Tmax = 0.726, while the minimum reflectance is Rmin = 0.134. By adding the additional AZO top layer the maximum transmittance is increased to Tmax = 0.862. The measured reflectance minimum at λ = 500 nm is as low as Rmin = 0.04, which is approximately the reflectance value of a single glass/air interface. Therefore, the layer design allows suppressing the reflection from the ultrathin Au layer almost completely. It can be seen that the simulation
Fig. 1. (a) Sketch of the transparent electrode with flat interfaces. (b) Experimental (solid line) and simulated (points) transmittance and reflectance measurements of a single TiOx layer with dTiOx = 36 nm, together with the extracted refractive index (green solid line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
39
Fig. 2. Experimental (solid line) and simulated (points) reflectance and transmittance of (a) Glass/TiOx36/Au9 and (b) Glass/TiOx36/Au9/AZO63. The inset shows the comparison between experimental direct (solid line) and total transmittance (triangles).
and experiment are in good agreement below λ b 500 nm, while for λ N 500 nm the transmittance and reflectance for Glass/TiOx36/Au9 and the transmittance of Glass/TiOx36/Au9/AZO63 are overestimated in the simulations. In the latter case the difference is up to 9% (absolute) in the considered range. For simulation-based optimization of the particular type of transparent electrodes, it is important to be able to predict the experimental transmittance and reflectance precisely. If one neglects scattering effects, the absorption, A, can be written as the difference between the specular reflectance, R and the direct transmittance, T, i.e. A = 1 – R − T. Since the simulation overestimates T and R, the simulated absorption is smaller than in the experiment. As the dielectric layers TiOx and AZO are almost lossless, the absorption has to take place in the ultrathin Au film. In the following, the phenomena giving rise to the observed difference between the simulated and experimental spectra will be investigated. Let us note that significant roughness, with rather large correlation length with respect to the light wavelength, causes light scattering and therefore reduces the direct transmitted light intensity [16]. To rule out this mechanism as the origin for the difference between simulation and experiment, the total transmittance (direct plus diffuse) was measured using an integration sphere. The direct and total transmittance is compared for a nominally identical sample as the one in
Fig. 2(b). The two curves practically coincide (inset of Fig. 2(b)) and therefore it is concluded that no diffuse transmittance is present. As a consequence, the difference between simulation and experiment must be solely due to increased absorption. A possible reason for the increased absorption is the presence of metal clusters that could form during the Au deposition and give rise to the excitation of localized surface plasmons [17]. To exclude this hypothesis and confirm that the Au film is continuous, SEM images of the Glass/TiOx36 and Glass/TiOx36/Au9 surfaces on the same sample were obtained (Fig. 3(a)). The different contrast obtained clearly shows that the Au film is continuous and therefore no excitation of localized surface plasmons is expected. The morphology of the fabricated films was characterized by AFM, as seen in the images of Figs. 3(b) and 3(c). The phase image (not shown) confirmed the continuity of the film. The layers have a subwavelength-size granular structure with root mean square roughness (RMS) values of σTiOx = 0.75 nm for Glass/TiOx36 and σAu = 0.95 nm for Glass/TiOx36/Au9, which are comparable to recently published roughness values for this type of transparent electrodes [18,19, 20]. The sputter parameters, namely the gas pressure and the sputter power, have been chosen to achieve films with a minimal roughness. In general, the roughness decreased with decreasing gas pressure and increasing sputter power. For example, by decreasing the Ar/O2
Fig. 3. (a) SEM image of Glass/TiOx36/Au9. Image was taken at a scratch where the TiOx (darker part) is only partly covered with Au. AFM images of (b) Glass/TiOx36 and (c) Glass/TiOx36/ Au9.
40
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
pressure from 0.5 Pa to 0.1 Pa, while keeping the sputter power at 120 W, the RMS roughness of the TiOx film decreased from 1.56 nm to 0.75 nm. The TMM simulations, in the so-far introduced form, only consider flat interfaces. An efficient way to include roughness with small correlation length and height (much smaller than the wavelength) in the TMM simulations, is by the use of an effective medium approximation. EMA describes the properties of a complex (composite) material, based on the properties and the relative fractions of its individual components, since a precise calculation at the micro-scale would be laborious [21]. Indeed, the effective medium approximation is a widely used method to analyze rough surfaces of metals and dielectrics in ellipsometry [22, 23,24,25,26]. It has been shown recently that, for a single ultrathin Au layer on a substrate, the transmittance can be accurately predicted when one takes into account the roughness within the effective medium theory [27]. According to this approach, the roughness of the interfaces is included in the TMM as an additional layer with an effective thickness, deff, and with an effective refractive index, neff , between the adjacent layers (see Fig. 4(a)). Effective medium theories can be applied when the feature sizes of the roughness (especially the correlation length) are much smaller than the wavelength of the incident light. The effective refractive index neff ¼ neff þ ikeff in the Bruggeman effective medium approximation of a layer is given by [23,28]:
neff ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω2 þ 8n22 −Ω 2
Ω ¼ ð1− f Þ n22 −2n21 þ f n21 −2n22 with n1, n2 being the complex refractive indices of the adjacent materials and f the volume fraction [16] (packing density factor) of material 1 with n1. The volume fraction f was determined from AFM height profiles, z(x), using the equation: f ¼
M
∑ j¼1 ðzðx j Þ−z min Þ∙Δx M∙ðz max −z min Þ∙Δx ,
where zmax and zmin are
the maximum and minimum height, respectively and j runs through the discrete lateral measurement points with distance Δx. M is the total number of measurement points. The thus extracted value is f ≈ 0.5. The volume fraction will be fixed throughout this work to f = 0.5 and will not be used as a fitting parameter, as recommended by several authors [23,27,22]. This value corresponds to equal volumes (symmetric height distribution) of the two materials n1 and n2 in the effective layer [23]. The sign before the square root in the equation of neff is chosen so that to assure that the resulting real refractive index, neff and the extinction coefficient, keff, are both positive. In Fig. 4(b) the imaginary part of the effective dielectric function εeff ¼ ε0 eff þ iε00 eff is shown,
which is related to the complex refractive index through the relation: pffiffiffiffiffiffiffi neff ¼ εeff . The imaginary part of the dielectric function is of special interest as it is proportional to the absorption, A, in the effective medium, given by A ∝ε ´´eff ∙ |E|2, with |E|2 the electric field intensity. The data for bulk Au from Johnson and Christy (Fig. 4(b)) show a clear increase of ε ´´eff below λ b 500 nm due to interband transitions [29], while for λ N 500 nm the losses are significantly lower. The calculated effective refractive index of the Au/dielectric interface shows the opposite behavior, i.e. reduced losses for wavelength λ b 500 nm and significantly increased losses for wavelength λ N 500 nm. The losses for the interface with the high refractive index material TiOx are the highest. The thickness of the effective layer deff,1 at the TiOx/Au interface is estimated by deff,1 = γ · σTiOx. Similarly, the thickness of the effective layer at the Au/AZO or Au/Air interface is deff,2 = γ · σAu. The surface roughness, σ, is expressed as the RMS roughness of the respective interface. The effective thickness is related to the roughness via the parameter γ, which is chosen to be the same for both effective medium layers. This is justified by the similar morphology of both interfaces, as seen in the AFM images. Therefore, γ is the only free parameter in the effective medium approximation. In the model, only the roughness between the TiOx/Au interface and the Au/Air, respectively Au/AZO, interface is considered, since purely dielectric interfaces (such as Glass/TiOx or AZO/Air) with small roughness values have only a negligible influence on the optical properties. The parameter γ was varied in the range from 0 to 4 to achieve best agreement between experiment and simulation. To do so, the difference between the simulated and the measured reflectance and transmittance spectra in the 400–800 nm window was calculated for the Glass/TiOx36/Au9 and Glass/TiOx36/Au9/AZO63 samples. The minimum difference was obtained for γ = 2, which further means that the thickness of the effective layer is equivalent to twice the RMS roughness value and contains therefore roughly 95% of the peak-to-peak topography variation. Due to the introduction of effective layers with a certain thickness and the volume fraction of f = 0.5, the initially assumed (deposited) thicknesses of the layers, used as input for the TMM simulation, need to be reduced as follows: dTiOx; mod ¼ dTiOx −deff ;1 =2 dAu; mod ¼ dAu −deff ;1 =2−deff ;2 =2 dAZO; mod ¼ dAZO −deff ;2 =2 The simulation results, including the effect of the interfacial layers aforementioned, are shown in Fig. 5. It can be seen that for Glass/ TiOx36/Au9 in Fig. 5 (a) the simulation allows to match the reflectance spectra precisely, while the simulated transmittance is slightly underestimated. The simulation and experiment agree significantly
Fig. 4. (a) Sketch of the structure including roughness of the interfaces. (b) Imaginary part of dielectric function ε´´eff derived for several interface combinations by EMA with f = 0.5.
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
41
Fig. 5. Experimental (solid line) and simulated (points) reflectance and transmittance of (a) Glass/TiOx36/Au9 and (b) Glass/TiOx36/Au9/AZO63. The simulation accounts for surface roughness by using EMA layers above and below the Au.
better than in the case without EMA. For the Glass/TiOx36/Au9/AZO63 sample a good agreement between EMA simulation and experiment was achieved, as well. Most interestingly, for the simulation of the transmittance and reflectance of both samples only a single value of the parameter γ = 2 was used, which demonstrates the physical validity of the model. The established EMA model was now applied to find the optimum performance in terms of maximum transmittance at λ = 550 nm (Tmax,550) and in the visible wavelength range from 400 nm to 700 nm (Tmax,400 – 700), by varying the thicknesses of the dielectric layers. The results of these simulations are shown in Fig. 6. Highest Tmax,550 is obtained for dTiOx = 41 nm and dAZO = 66 nm and highest Tmax,400 – 700 for dTiOx = 34 nm and dAZO =5 8 nm. As suggested from the simulations, samples have been prepared with nominally identical thickness values. Their measured transmittance spectra are shown, together with the EMA simulations, in Fig. 7. Again, there is very good agreement between simulations and experiment. For the simulations the parameter γ = 2 was used, as determined before. The figure of merit (FoM) for transparent electrodes ϕ is given as: ϕ = T10/RS [30] with T the transmittance at a certain wavelength and RS the sheet resistance. The measured sheet resistance is 14 Ω/ square. The maximum experimental transmittance value at λ =
550 nm is Tmax,550 = 0.878 which results in a FoM of ϕ550 =19.4×10−3Ω−1, while the maximum average transmittance in the visible wavelength range is .Tmax,400 – 700 = 0.805 and consequently a FoM of ϕ400−700 =8.2×10−3Ω−1 is obtained. The achieved transmittance of Tmax,550 = 0.878 is significantly higher than the values reported in literature for structures of TiOx/Au/TiOx or AZO/Au/AZO with a similar Au thickness, for which a maximum transmittance of 0.80 was achieved [31,32,9]. The improvement can be assigned to the careful design of the layer thicknesses and the low roughness of the TiOx layer. Compared to our previous work on AZO/Au/AZO a 3-fold increase of the FoM has been achieved [31]. Further, the FoM is comparable to the more frequently used Ag-based transparent electrodes with similar metal thickness [33,34]. Let us note that the FoM depends crucially on the absolute value of the transmittance and consequently on the reference used for the transmittance spectrum. The FoM value achieved by referencing to the glass substrate yields significantly higher FoM values than referencing to air (as it is done in this work). 4. Conclusion A new model for the precise simulation of the optical properties of transparent electrodes composed of dielectrics and ultra-thin metal
Fig. 6. Simulated transmittance (including EMA) for different thicknesses of dAZO and dTiOx for (a) λ = 550 nm and (b) wavelength range from λ = 400 nm to 700 nm. The black cross indicates the position of the respective maximum value.
42
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
Fig. 7. Experimental (solid lines) and simulated (points) transmittance for samples with maximum transmittance Tmax at 550 nm and maximum averaged transmittance from 400 nm–700 nm.
layers was presented. Samples were prepared by magnetron sputtering and were extensively optically characterized by direct transmittance, specular reflectance and total transmittance measurements. Simulations based on transfer matrix methods and assuming flat interfaces resulted in significant deviation from experiments, due to increased absorption in the ultrathin metal film. This discrepancy was eliminated by introducing the roughness of the interfaces by combining the transfer matrix method with an effective medium approximation. The model requires only one parameter and allows for accurate prediction of transmittance and reflectance spectra. The developed model was employed to predict optimum thickness parameters of the dielectric layers to achieve a maximum transmittance in the visible wavelength range for a TiOx/Au/AZO multilayer. The experimental results were in full accordance with the simulations. Acknowledgements The financial support from the Austrian “Klima- & Energiefonds” through the project “Flex!PV.at” (Project No. 838621) is acknowledged. References [1] Organic Photovoltaics: Materials, Device Physics, and Manufacturing Technologies, Wiley-VCH, Weinheim, 2008. [2] H. Liu, V. Avrutin, N. Izyumskaya, ü. Özgür, H. Morkoç, Transparent conducting oxides for electrode applications in light emitting and absorbing devices, Superlattice. Microst. 48 (5) (Nov. 2010) 458–484. [3] D.S. Hecht, L. Hu, G. Irvin, Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures, Adv. Mater. 23 (13) (Apr. 2011) 1482–1513. [4] K. Ellmer, Past achievements and future challenges in the development of optically transparent electrodes, Nat. Photonics 6 (12) (Nov. 2012) 809–817. [5] C. Guillén, J. Herrero, TCO/metal/TCO structures for energy and flexible electronics, Thin Solid Films 520 (1) (Oct. 2011) 1–17. [6] T. Dimopoulos, G.Z. Radnoczi, B. Pécz, H. Brückl, Characterization of ZnO:Al/Au/ZnO: Al trilayers for high performance transparent conducting electrodes, Thin Solid Films 519 (4) (Dec. 2010) 1470–1474. [7] T. Dimopoulos, G.Z. Radnoczi, Z.E. Horváth, H. Brückl, Increased thermal stability of Al-doped ZnO-based transparent conducting electrodes employing ultra-thin Au and Cu layers, Thin Solid Films 520 (16) (Jun. 2012) 5222–5226.
[8] M. Girtan, Comparison of ITO/metal/ITO and ZnO/metal/ZnO characteristics as transparent electrodes for third generation solar cells, Sol. Energy Mater. Sol. Cells 100 (May 2012) 153–161. [9] Z. Zhao, A.E. Khorasani, N.D. Theodore, A. Dhar, T.L. Alford, Prediction of transmittance spectra for transparent composite electrodes with ultra-thin metal layers, J. Appl. Phys. 118 (20) (Nov. 2015). [10] E. Centurioni, Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers, Appl. Opt. 44 (35) (Dec. 2005) 7532–7539. [11] L. Pettersson, L. Roman, O. Inganas, Modeling photocurrent action spectra of photovoltaic devices based on organic thin films, J. Appl. Phys. 86 (1) (Jul. 1999) 487–496. [12] M.M.A.-G. Jafar, Comprehensive formulations for the total normal-incidence optical reflectance and transmittance of thin films laid on thick substrates, European International Journal of Science and Technology Vol. 2 No. 5 (Jun. 2013) 214–274. [13] P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6 (12) (Dec. 1972) 4370–4379. [14] A. Djurisic, T. Fritz, K. Leo, Determination of optical constants of thin absorbing films from normal incidence reflectance and transmittance measurements, Opt. Commun. 166 (1–6) (Aug. 1999) 35–42. [15] D. Tsu, Obtaining optical constants of thin GexSbyTez films from measurements of reflection and transmission, J. Vac. Sci. Technol. Vac. Surf. FILMS 17 (4, 2) (Aug. 1999) 1854–1860. [16] D.E. Aspnes, J.B. Theeten, F. Hottier, Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry, Phys. Rev. B 20 (8) (Oct. 1979) 3292–3302. [17] O. Kedem, A.B. Tesler, A. Vaskevich, I. Rubinstein, Sensitivity and optimization of localized surface Plasmon resonance transducers, ACS Nano 5 (2) (Feb. 2011) 748–760. [18] C. Zhang, D. Zhao, D. Gu, H. Kim, T. Ling, Y.-K.R. Wu, L.J. Guo, An ultrathin, smooth, and low-loss Al-doped Ag film and its application as a transparent electrode in organic photovoltaics, Adv. Mater. 26 (32) (Aug. 2014) 5696+. [19] H.-J. Lee, J.-W. Kang, S.-H. Hong, S.-H. Song, S.-J. Park, MgxZn1-xO/Ag/MgxZn1-xO multilayers as high-performance transparent conductive electrodes, ACS Appl. Mater. Interfaces 8 (3) (Jan. 2016) 1565–1570. [20] J.H. Kim, Y.-J. Moon, S.-K. Kim, Y.-Z. Yoo, T.-Y. Seong, Al-doped ZnO/Ag/Al-doped ZnO multilayer films with a high figure of merit, Ceram. Int. 41 (10, B) (Dec. 2015) 14805–14810. [21] M. Wang, N. Pan, Predictions of effective physical properties of complex multiphase materials, Mater. Sci. Eng. R. Rep. 63 (1) (Dec. 2008) 1–30. [22] S. Gupta, B. Weiner, G. Morell, Spectroscopic ellipsometry studies of nanocrystalline carbon thin films deposited by HFCVD, Diam. Relat. Mater. 10 (11) (Nov. 2001) 1968–1972. [23] D. Franta, I. Ohlidal, Comparison of effective medium approximation and RayleighRice theory concerning ellipsometric characterization of rough surfaces, Opt. Commun. 248 (4–6) (Apr. 2005) 459–467. [24] T. Muneshwar, K. Cadien, Probing initial-stages of ALD growth with dynamic in situ spectroscopic ellipsometry, Appl. Surf. Sci. 328 (Feb. 2015) 344–348. [25] D. Schmidt, M. Schubert, Anisotropic Bruggeman effective medium approaches for slanted columnar thin films, J. Appl. Phys. 114 (8) (Aug. 2013). [26] J. Trollmann, A. Pucci, Infrared dielectric function of gold films in relation to their morphology, J. Phys. Chem. C 118 (27) (Jul. 2014) 15011–15018. [27] A. Kossoy, V. Merk, D. Simakov, K. Leosson, S. Kena-Cohen, S.A. Maier, Optical and structural properties of ultra-thin gold films, Adv. Opt. Mater. 3 (1) (Jan. 2015) 71–77. [28] D. Zhang, E. Cherkaev, M.P. Lamoureux, Stieltjes representation of the 3D Bruggeman effective medium and Pade approximation, Appl. Math. Comput. 217 (17) (May 2011) 7092–7107. [29] P.G. Etchegoin, E.C. Le Ru, M. Meyer, An analytic model for the optical properties of gold, J. Chem. Phys. 125 (16) (Oct. 2006). [30] G. Haacke, New figure of merit for transparent conductors, J. Appl. Phys. 47 (9) (1976) 4086–4089. [31] T. Dimopoulos, M. Bauch, R.A. Wibowo, N. Bansal, R. Hamid, M. Auer, M. Jaeger, E.J.W. List-Kratochvil, Properties of transparent and conductive Al:ZnO/Au/Al:ZnO multilayers on flexible PET substrates, Mater. Sci. Eng. B-Adv. Funct. SOLID-STATE Mater. 200 (Oct. 2015) 84–92. [32] P.C. Lansaker, J. Backholm, G.A. Niklasson, C.G. Granqvist, TiO2/Au/TiO2 multilayer thin films: Novel metal-based transparent conductors for electrochromic devices, THIN SOLID FILMS 518 (4, SI) (Dec. 2009) 1225–1229. [33] I. Crupi, S. Boscarino, V. Strano, S. Mirabella, F. Simone, A. Terrasi, Optimization of ZnO:Al/Ag/ZnO:Al structures for ultra-thin high-performance transparent conductive electrodes, Thin Solid Films 520 (13) (Apr. 2012) 4432–4435. [34] J.-A. Jeong, H.-K. Kim, Low resistance and highly transparent ITO-Ag-ITO multilayer electrode using surface plasmon resonance of Ag layer for bulk-heterojunction organic solar cells, Sol. Energy Mater. Sol. Cells 93 (10) (Oct. 2009) 1801–1809.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Design of ultrathin metal-based transparent electrodes including the impact of interface roughness M. Bauch ⁎, T. Dimopoulos AIT-Austrian Institute of Technology, Energy Department, Photovoltaic Systems, Giefinggasse 2, 1210 Vienna, Austria
a r t i c l e
i n f o
Article history: Received 10 February 2016 Received in revised form 22 April 2016 Accepted 27 April 2016 Available online 28 April 2016 Keywords: Transparent electrodes Transparent conductive oxides Sputtering Ultra-thin metals Solar cells Optoelectronic devices
a b s t r a c t In this paper, an efficient model for the precise design and prediction of the optical properties of transparent electrodes that are composed of ultrathin metals embedded in dielectric layers, is introduced. Specifically, the investigated electrode employs an ultrathin Au layer on a TiOx-coated glass substrate and covered with Al-doped ZnO (AZO), deposited by sputtering. This structure was simulated with a transfer matrix algorithm and was optically characterized by measurements of direct and diffuse transmittance, as well as specular reflectance. The comparison of simulated and experimental spectra reveals significant differences, which is due to the increased absorption in the ultrathin metal. To achieve a more precise prediction of the optical properties, the roughness of the interfaces was included in the simulation through an effective medium approximation. The improved simulation model requires only one fitting parameter and was applied to optimize the electrode's performance through the variation of the dielectric layers' thickness. In agreement with the simulations, the deposited TiOx/Au/AZO electrodes showed a maximum transmittance of 0.88 at 550 nm (including the substrate) and average transmittance in the visible wavelength range of N 0.80, combined with a sheet resistance of 14 Ω/square. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Transparent electrodes (TEs) are key components of modern optoelectronic devices, optical coatings and photovoltaic cells [1]. Transparent conductive oxides (TCOs) are the most widely employed TEs, with prominent materials being the tin-doped indium oxide (ITO), aluminium-doped zinc oxide (AZO) and fluorine-doped tin oxide (FTO). ITO has been for long the material of choice for most applications, since it offers the best combination of transparency (80–90%) and resistivity (typically 1 × 10−4 Ω cm) [2], with the main disadvantage being its high cost due to the scarcity of indium. With the target to boost the performance/cost figure of TEs, current research embraces materials like carbon nanotubes, graphene, conductive polymer films, metal nanowires and meshes, as well as ultra-thin metals, the properties of which are summarized in recent reviews [3,4,5]. TEs should also be compatible with the challenging requirements of modern, highthroughput processing and device design. For example, device fabrication on flexible substrates by roll-to-roll processing demands lowtemperature deposition and stability to mechanical stress. The latter is not the case for standard TCOs, which are brittle and barely flexible, compromising their implementation in flexible optoelectronic devices and solar cells. Combinations of ultra-thin metals (Ag, Au, Cu, Al or Ni) and dielectric layers with high refractive index emerge as a very promising type ⁎ Corresponding author. E-mail address: [email protected] (M. Bauch).
http://dx.doi.org/10.1016/j.matdes.2016.04.082 0264-1275/© 2016 Elsevier Ltd. All rights reserved.
of TEs [5], offering exceptional features, such as: widely adjustable optical and electrical properties through film thickness and material variations, ambient- temperature deposition, better mechanical stability than TCOs on flexible substrates due to the metal ductility [5], low roughness (an advantage for devices with ultra-thin functional layers such as organic LEDs) [6], as well as high-temperature stability [7]. The sheet resistance of these components is mainly determined by the metal layer thickness, which needs to remain below 10–12 nm in order to avoid significant losses in transparency. The optical properties, on the other hand, are more prone to modifications of the multilayer architecture, having to do with the choice of the materials and of the layer thicknesses. Ideally, the optical properties of the TE (e.g. transmittance) should be optimized to meet specific device requirements (e.g. adjusted to the spectral response of a solar cell absorber). For the optimization process, a reliable simulation method is needed that precisely reproduces the experimental spectra and therefore gives the possibility to design improved components. The existing literature mainly reports symmetric TCO/metal/TCO structures [8], i.e. the metal is embedded between layers of the same TCO material. Furthermore, the comparison between simulation and experiment is limited to direct transmittance, not considering reflectance and scattering effects [9]. In this work, an improved transfer matrix simulation method is introduced that takes into account the roughness of the dielectric/metal interfaces through an effective medium approximation (EMA), allowing the precise prediction of the experimental transmittance and reflectance spectra. For our investigation, a model structure of Glass/TiOx/ Au/AZO is used. It is demonstrated that the improved simulation
38
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
algorithm allows designing and optimizing the multilayer structure in order to maximize the optical transmittance and the TE figure of merit in the desired wavelength window.
sheet resistance of the films was measured with a 4-point, in-line probe technique. 3. Results and discussion
2. Experimental 2.1. Thin film deposition The thin films were deposited by DC magnetron sputtering (Leybold Univex 450C) on clean soda-lime glass substrates (Menzel Gläser). TiOx was deposited in Ar/O2 (80/20 composition) atmosphere from a Ti target, at 120 W sputter power and 0.1 Pa gas pressure, yielding a sputter rate of 0.017 nm/s. Au was deposited in Ar atmosphere at a sputter power of 20 W and Ar-pressure of 0.2 Pa, resulting in a sputter rate of 0.44 nm/s. Al-doped ZnO (AZO) was sputtered from a ZnO target with 2 wt.% Al2O3, at 120 W and Ar pressure of 0.1 Pa, which yielded a sputter rate of 0.66 nm/s. The Ti and AZO targets had a diameter of 10.16 cm, while the diameter of the Au target was 7.62 cm. The target-tosubstrate distance was 10 cm and the sputter targets and substrates were water-cooled at 25 °C during the deposition process. The base pressure of the sputter system was 7 × 10−6–1.2 × 10−5 Pa. The layer thicknesses were determined by step-height analysis using a profilometer (KLA-Tencor—Alpha-Step IQ). In the following, the thickness of a specific layer is denoted with a subscript. For example, Au9 stands for Au layer of 9 nm thickness. 2.2. Characterization The samples were optically characterized using a Bruker Vertex 70 Fourier transform infrared spectrometer (FTIR), additionally equipped with a visible light source. Direct transmittance was measured for normal incident light and referenced to the sample holder without sample (air). Reflection was measured with the A513QA accessory of the spectrometer, at 13 deg angle of incidence and un-polarized light. The measured signal was referenced to a calibrated mirror (aluminium, coated with dielectric) in the range from 330 nm to 550 nm and to a thick, 150 nm Au-coated substrate, in the range from 550 nm to 1000 nm. Total transmittance (direct plus diffuse transmittance) was measured with a teflon (PTFE) integration sphere accessory for the Vertex 70. A GaP and a Si detector were used to record spectra in the range of 330–550 nm and 550–1000 nm, respectively. All optical measurements were performed with the light beam entering from the glass substrate (see Fig. 1(a)). The characterization of the surface morphology was done by atomic force microscopy (AFM) (Molecular Imaging, PicoPlus) in tapping mode and scanning electron microscopy (SEM) (Zeiss, SUPRA 40) with 5 kV acceleration voltage and in-lens detector. The
The investigated layer structure is a glass substrate, coated with a TiOx layer with thickness dTiOx, followed by an ultrathin Au layer with thickness dAu and an AZO top layer with thickness dAZO. The structure design is sketched in Fig. 1(a). dAu is fixed throughout this work to 9 nm. For the simulation of the direct transmittance at normal incidence and the specular reflectance of the samples at incident angle = 13 deg, a transfer matrix method (TMM) algorithm was implemented [10,11]. The TMM accounts for coherent layers (up to hundreds of nanometers thickness), while the glass substrate was treated incoherently and was implemented in the simulation by the following equations for a nonabsorbing substrate [12]: T TM ðαÞT 0 ðαÞ TðαÞ ¼ 1−R TM ðαÞR0 ðαÞ T 2 ðαÞR
ðαÞ
TM 0 RðαÞ ¼ R0 ðαÞ þ 1−R : TM ðαÞR0 ðαÞ
T( ) and R( ) are the transmittance and the reflectance of the complete structure including the glass substrate. TTM and RTM are the TMM-calculated transmittance and reflectance of the thin films and T0 and R0 the values of the transmittance and reflectance at the air/glass interface, which can be easily calculated by the Fresnel equations for a certain angle . The real and imaginary part of the refractive index (n and k, respectively) of Au and AZO were taken from the literature [13,6]. The optical constants of TiOx were extracted from the measured transmittance and reflectance spectra, through the implementation of a transfer matrix algorithm [14,15]. The experimental and simulated transmittance and reflectance of the TiOx film, as well as the extracted refractive index are shown in Fig. 1(b). The layer thicknesses dTiOx and dAZO of the dielectric layers were varied in the TMM simulation. Maximum transmittance at 550 nm was obtained for dTiOx = 36 nm and dAZO = 63 nm. These thicknesses were then used for the electrode fabrication. A structure without the AZO top layer was also fabricated, in order to gain deeper insight into the system's properties. The experimental transmittance and reflectance spectra and the associated TMM simulations are shown in Fig. 2(a) for Glass/TiOx36/Au9 and (b) Glass/TiOx36/Au9/AZO63. The maximum experimental transmittance of Glass/TiOx36/Au9 is Tmax = 0.726, while the minimum reflectance is Rmin = 0.134. By adding the additional AZO top layer the maximum transmittance is increased to Tmax = 0.862. The measured reflectance minimum at λ = 500 nm is as low as Rmin = 0.04, which is approximately the reflectance value of a single glass/air interface. Therefore, the layer design allows suppressing the reflection from the ultrathin Au layer almost completely. It can be seen that the simulation
Fig. 1. (a) Sketch of the transparent electrode with flat interfaces. (b) Experimental (solid line) and simulated (points) transmittance and reflectance measurements of a single TiOx layer with dTiOx = 36 nm, together with the extracted refractive index (green solid line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
39
Fig. 2. Experimental (solid line) and simulated (points) reflectance and transmittance of (a) Glass/TiOx36/Au9 and (b) Glass/TiOx36/Au9/AZO63. The inset shows the comparison between experimental direct (solid line) and total transmittance (triangles).
and experiment are in good agreement below λ b 500 nm, while for λ N 500 nm the transmittance and reflectance for Glass/TiOx36/Au9 and the transmittance of Glass/TiOx36/Au9/AZO63 are overestimated in the simulations. In the latter case the difference is up to 9% (absolute) in the considered range. For simulation-based optimization of the particular type of transparent electrodes, it is important to be able to predict the experimental transmittance and reflectance precisely. If one neglects scattering effects, the absorption, A, can be written as the difference between the specular reflectance, R and the direct transmittance, T, i.e. A = 1 – R − T. Since the simulation overestimates T and R, the simulated absorption is smaller than in the experiment. As the dielectric layers TiOx and AZO are almost lossless, the absorption has to take place in the ultrathin Au film. In the following, the phenomena giving rise to the observed difference between the simulated and experimental spectra will be investigated. Let us note that significant roughness, with rather large correlation length with respect to the light wavelength, causes light scattering and therefore reduces the direct transmitted light intensity [16]. To rule out this mechanism as the origin for the difference between simulation and experiment, the total transmittance (direct plus diffuse) was measured using an integration sphere. The direct and total transmittance is compared for a nominally identical sample as the one in
Fig. 2(b). The two curves practically coincide (inset of Fig. 2(b)) and therefore it is concluded that no diffuse transmittance is present. As a consequence, the difference between simulation and experiment must be solely due to increased absorption. A possible reason for the increased absorption is the presence of metal clusters that could form during the Au deposition and give rise to the excitation of localized surface plasmons [17]. To exclude this hypothesis and confirm that the Au film is continuous, SEM images of the Glass/TiOx36 and Glass/TiOx36/Au9 surfaces on the same sample were obtained (Fig. 3(a)). The different contrast obtained clearly shows that the Au film is continuous and therefore no excitation of localized surface plasmons is expected. The morphology of the fabricated films was characterized by AFM, as seen in the images of Figs. 3(b) and 3(c). The phase image (not shown) confirmed the continuity of the film. The layers have a subwavelength-size granular structure with root mean square roughness (RMS) values of σTiOx = 0.75 nm for Glass/TiOx36 and σAu = 0.95 nm for Glass/TiOx36/Au9, which are comparable to recently published roughness values for this type of transparent electrodes [18,19, 20]. The sputter parameters, namely the gas pressure and the sputter power, have been chosen to achieve films with a minimal roughness. In general, the roughness decreased with decreasing gas pressure and increasing sputter power. For example, by decreasing the Ar/O2
Fig. 3. (a) SEM image of Glass/TiOx36/Au9. Image was taken at a scratch where the TiOx (darker part) is only partly covered with Au. AFM images of (b) Glass/TiOx36 and (c) Glass/TiOx36/ Au9.
40
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
pressure from 0.5 Pa to 0.1 Pa, while keeping the sputter power at 120 W, the RMS roughness of the TiOx film decreased from 1.56 nm to 0.75 nm. The TMM simulations, in the so-far introduced form, only consider flat interfaces. An efficient way to include roughness with small correlation length and height (much smaller than the wavelength) in the TMM simulations, is by the use of an effective medium approximation. EMA describes the properties of a complex (composite) material, based on the properties and the relative fractions of its individual components, since a precise calculation at the micro-scale would be laborious [21]. Indeed, the effective medium approximation is a widely used method to analyze rough surfaces of metals and dielectrics in ellipsometry [22, 23,24,25,26]. It has been shown recently that, for a single ultrathin Au layer on a substrate, the transmittance can be accurately predicted when one takes into account the roughness within the effective medium theory [27]. According to this approach, the roughness of the interfaces is included in the TMM as an additional layer with an effective thickness, deff, and with an effective refractive index, neff , between the adjacent layers (see Fig. 4(a)). Effective medium theories can be applied when the feature sizes of the roughness (especially the correlation length) are much smaller than the wavelength of the incident light. The effective refractive index neff ¼ neff þ ikeff in the Bruggeman effective medium approximation of a layer is given by [23,28]:
neff ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω2 þ 8n22 −Ω 2
Ω ¼ ð1− f Þ n22 −2n21 þ f n21 −2n22 with n1, n2 being the complex refractive indices of the adjacent materials and f the volume fraction [16] (packing density factor) of material 1 with n1. The volume fraction f was determined from AFM height profiles, z(x), using the equation: f ¼
M
∑ j¼1 ðzðx j Þ−z min Þ∙Δx M∙ðz max −z min Þ∙Δx ,
where zmax and zmin are
the maximum and minimum height, respectively and j runs through the discrete lateral measurement points with distance Δx. M is the total number of measurement points. The thus extracted value is f ≈ 0.5. The volume fraction will be fixed throughout this work to f = 0.5 and will not be used as a fitting parameter, as recommended by several authors [23,27,22]. This value corresponds to equal volumes (symmetric height distribution) of the two materials n1 and n2 in the effective layer [23]. The sign before the square root in the equation of neff is chosen so that to assure that the resulting real refractive index, neff and the extinction coefficient, keff, are both positive. In Fig. 4(b) the imaginary part of the effective dielectric function εeff ¼ ε0 eff þ iε00 eff is shown,
which is related to the complex refractive index through the relation: pffiffiffiffiffiffiffi neff ¼ εeff . The imaginary part of the dielectric function is of special interest as it is proportional to the absorption, A, in the effective medium, given by A ∝ε ´´eff ∙ |E|2, with |E|2 the electric field intensity. The data for bulk Au from Johnson and Christy (Fig. 4(b)) show a clear increase of ε ´´eff below λ b 500 nm due to interband transitions [29], while for λ N 500 nm the losses are significantly lower. The calculated effective refractive index of the Au/dielectric interface shows the opposite behavior, i.e. reduced losses for wavelength λ b 500 nm and significantly increased losses for wavelength λ N 500 nm. The losses for the interface with the high refractive index material TiOx are the highest. The thickness of the effective layer deff,1 at the TiOx/Au interface is estimated by deff,1 = γ · σTiOx. Similarly, the thickness of the effective layer at the Au/AZO or Au/Air interface is deff,2 = γ · σAu. The surface roughness, σ, is expressed as the RMS roughness of the respective interface. The effective thickness is related to the roughness via the parameter γ, which is chosen to be the same for both effective medium layers. This is justified by the similar morphology of both interfaces, as seen in the AFM images. Therefore, γ is the only free parameter in the effective medium approximation. In the model, only the roughness between the TiOx/Au interface and the Au/Air, respectively Au/AZO, interface is considered, since purely dielectric interfaces (such as Glass/TiOx or AZO/Air) with small roughness values have only a negligible influence on the optical properties. The parameter γ was varied in the range from 0 to 4 to achieve best agreement between experiment and simulation. To do so, the difference between the simulated and the measured reflectance and transmittance spectra in the 400–800 nm window was calculated for the Glass/TiOx36/Au9 and Glass/TiOx36/Au9/AZO63 samples. The minimum difference was obtained for γ = 2, which further means that the thickness of the effective layer is equivalent to twice the RMS roughness value and contains therefore roughly 95% of the peak-to-peak topography variation. Due to the introduction of effective layers with a certain thickness and the volume fraction of f = 0.5, the initially assumed (deposited) thicknesses of the layers, used as input for the TMM simulation, need to be reduced as follows: dTiOx; mod ¼ dTiOx −deff ;1 =2 dAu; mod ¼ dAu −deff ;1 =2−deff ;2 =2 dAZO; mod ¼ dAZO −deff ;2 =2 The simulation results, including the effect of the interfacial layers aforementioned, are shown in Fig. 5. It can be seen that for Glass/ TiOx36/Au9 in Fig. 5 (a) the simulation allows to match the reflectance spectra precisely, while the simulated transmittance is slightly underestimated. The simulation and experiment agree significantly
Fig. 4. (a) Sketch of the structure including roughness of the interfaces. (b) Imaginary part of dielectric function ε´´eff derived for several interface combinations by EMA with f = 0.5.
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
41
Fig. 5. Experimental (solid line) and simulated (points) reflectance and transmittance of (a) Glass/TiOx36/Au9 and (b) Glass/TiOx36/Au9/AZO63. The simulation accounts for surface roughness by using EMA layers above and below the Au.
better than in the case without EMA. For the Glass/TiOx36/Au9/AZO63 sample a good agreement between EMA simulation and experiment was achieved, as well. Most interestingly, for the simulation of the transmittance and reflectance of both samples only a single value of the parameter γ = 2 was used, which demonstrates the physical validity of the model. The established EMA model was now applied to find the optimum performance in terms of maximum transmittance at λ = 550 nm (Tmax,550) and in the visible wavelength range from 400 nm to 700 nm (Tmax,400 – 700), by varying the thicknesses of the dielectric layers. The results of these simulations are shown in Fig. 6. Highest Tmax,550 is obtained for dTiOx = 41 nm and dAZO = 66 nm and highest Tmax,400 – 700 for dTiOx = 34 nm and dAZO =5 8 nm. As suggested from the simulations, samples have been prepared with nominally identical thickness values. Their measured transmittance spectra are shown, together with the EMA simulations, in Fig. 7. Again, there is very good agreement between simulations and experiment. For the simulations the parameter γ = 2 was used, as determined before. The figure of merit (FoM) for transparent electrodes ϕ is given as: ϕ = T10/RS [30] with T the transmittance at a certain wavelength and RS the sheet resistance. The measured sheet resistance is 14 Ω/ square. The maximum experimental transmittance value at λ =
550 nm is Tmax,550 = 0.878 which results in a FoM of ϕ550 =19.4×10−3Ω−1, while the maximum average transmittance in the visible wavelength range is .Tmax,400 – 700 = 0.805 and consequently a FoM of ϕ400−700 =8.2×10−3Ω−1 is obtained. The achieved transmittance of Tmax,550 = 0.878 is significantly higher than the values reported in literature for structures of TiOx/Au/TiOx or AZO/Au/AZO with a similar Au thickness, for which a maximum transmittance of 0.80 was achieved [31,32,9]. The improvement can be assigned to the careful design of the layer thicknesses and the low roughness of the TiOx layer. Compared to our previous work on AZO/Au/AZO a 3-fold increase of the FoM has been achieved [31]. Further, the FoM is comparable to the more frequently used Ag-based transparent electrodes with similar metal thickness [33,34]. Let us note that the FoM depends crucially on the absolute value of the transmittance and consequently on the reference used for the transmittance spectrum. The FoM value achieved by referencing to the glass substrate yields significantly higher FoM values than referencing to air (as it is done in this work). 4. Conclusion A new model for the precise simulation of the optical properties of transparent electrodes composed of dielectrics and ultra-thin metal
Fig. 6. Simulated transmittance (including EMA) for different thicknesses of dAZO and dTiOx for (a) λ = 550 nm and (b) wavelength range from λ = 400 nm to 700 nm. The black cross indicates the position of the respective maximum value.
42
M. Bauch, T. Dimopoulos / Materials and Design 104 (2016) 37–42
Fig. 7. Experimental (solid lines) and simulated (points) transmittance for samples with maximum transmittance Tmax at 550 nm and maximum averaged transmittance from 400 nm–700 nm.
layers was presented. Samples were prepared by magnetron sputtering and were extensively optically characterized by direct transmittance, specular reflectance and total transmittance measurements. Simulations based on transfer matrix methods and assuming flat interfaces resulted in significant deviation from experiments, due to increased absorption in the ultrathin metal film. This discrepancy was eliminated by introducing the roughness of the interfaces by combining the transfer matrix method with an effective medium approximation. The model requires only one parameter and allows for accurate prediction of transmittance and reflectance spectra. The developed model was employed to predict optimum thickness parameters of the dielectric layers to achieve a maximum transmittance in the visible wavelength range for a TiOx/Au/AZO multilayer. The experimental results were in full accordance with the simulations. Acknowledgements The financial support from the Austrian “Klima- & Energiefonds” through the project “Flex!PV.at” (Project No. 838621) is acknowledged. References [1] Organic Photovoltaics: Materials, Device Physics, and Manufacturing Technologies, Wiley-VCH, Weinheim, 2008. [2] H. Liu, V. Avrutin, N. Izyumskaya, ü. Özgür, H. Morkoç, Transparent conducting oxides for electrode applications in light emitting and absorbing devices, Superlattice. Microst. 48 (5) (Nov. 2010) 458–484. [3] D.S. Hecht, L. Hu, G. Irvin, Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures, Adv. Mater. 23 (13) (Apr. 2011) 1482–1513. [4] K. Ellmer, Past achievements and future challenges in the development of optically transparent electrodes, Nat. Photonics 6 (12) (Nov. 2012) 809–817. [5] C. Guillén, J. Herrero, TCO/metal/TCO structures for energy and flexible electronics, Thin Solid Films 520 (1) (Oct. 2011) 1–17. [6] T. Dimopoulos, G.Z. Radnoczi, B. Pécz, H. Brückl, Characterization of ZnO:Al/Au/ZnO: Al trilayers for high performance transparent conducting electrodes, Thin Solid Films 519 (4) (Dec. 2010) 1470–1474. [7] T. Dimopoulos, G.Z. Radnoczi, Z.E. Horváth, H. Brückl, Increased thermal stability of Al-doped ZnO-based transparent conducting electrodes employing ultra-thin Au and Cu layers, Thin Solid Films 520 (16) (Jun. 2012) 5222–5226.
[8] M. Girtan, Comparison of ITO/metal/ITO and ZnO/metal/ZnO characteristics as transparent electrodes for third generation solar cells, Sol. Energy Mater. Sol. Cells 100 (May 2012) 153–161. [9] Z. Zhao, A.E. Khorasani, N.D. Theodore, A. Dhar, T.L. Alford, Prediction of transmittance spectra for transparent composite electrodes with ultra-thin metal layers, J. Appl. Phys. 118 (20) (Nov. 2015). [10] E. Centurioni, Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers, Appl. Opt. 44 (35) (Dec. 2005) 7532–7539. [11] L. Pettersson, L. Roman, O. Inganas, Modeling photocurrent action spectra of photovoltaic devices based on organic thin films, J. Appl. Phys. 86 (1) (Jul. 1999) 487–496. [12] M.M.A.-G. Jafar, Comprehensive formulations for the total normal-incidence optical reflectance and transmittance of thin films laid on thick substrates, European International Journal of Science and Technology Vol. 2 No. 5 (Jun. 2013) 214–274. [13] P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6 (12) (Dec. 1972) 4370–4379. [14] A. Djurisic, T. Fritz, K. Leo, Determination of optical constants of thin absorbing films from normal incidence reflectance and transmittance measurements, Opt. Commun. 166 (1–6) (Aug. 1999) 35–42. [15] D. Tsu, Obtaining optical constants of thin GexSbyTez films from measurements of reflection and transmission, J. Vac. Sci. Technol. Vac. Surf. FILMS 17 (4, 2) (Aug. 1999) 1854–1860. [16] D.E. Aspnes, J.B. Theeten, F. Hottier, Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry, Phys. Rev. B 20 (8) (Oct. 1979) 3292–3302. [17] O. Kedem, A.B. Tesler, A. Vaskevich, I. Rubinstein, Sensitivity and optimization of localized surface Plasmon resonance transducers, ACS Nano 5 (2) (Feb. 2011) 748–760. [18] C. Zhang, D. Zhao, D. Gu, H. Kim, T. Ling, Y.-K.R. Wu, L.J. Guo, An ultrathin, smooth, and low-loss Al-doped Ag film and its application as a transparent electrode in organic photovoltaics, Adv. Mater. 26 (32) (Aug. 2014) 5696+. [19] H.-J. Lee, J.-W. Kang, S.-H. Hong, S.-H. Song, S.-J. Park, MgxZn1-xO/Ag/MgxZn1-xO multilayers as high-performance transparent conductive electrodes, ACS Appl. Mater. Interfaces 8 (3) (Jan. 2016) 1565–1570. [20] J.H. Kim, Y.-J. Moon, S.-K. Kim, Y.-Z. Yoo, T.-Y. Seong, Al-doped ZnO/Ag/Al-doped ZnO multilayer films with a high figure of merit, Ceram. Int. 41 (10, B) (Dec. 2015) 14805–14810. [21] M. Wang, N. Pan, Predictions of effective physical properties of complex multiphase materials, Mater. Sci. Eng. R. Rep. 63 (1) (Dec. 2008) 1–30. [22] S. Gupta, B. Weiner, G. Morell, Spectroscopic ellipsometry studies of nanocrystalline carbon thin films deposited by HFCVD, Diam. Relat. Mater. 10 (11) (Nov. 2001) 1968–1972. [23] D. Franta, I. Ohlidal, Comparison of effective medium approximation and RayleighRice theory concerning ellipsometric characterization of rough surfaces, Opt. Commun. 248 (4–6) (Apr. 2005) 459–467. [24] T. Muneshwar, K. Cadien, Probing initial-stages of ALD growth with dynamic in situ spectroscopic ellipsometry, Appl. Surf. Sci. 328 (Feb. 2015) 344–348. [25] D. Schmidt, M. Schubert, Anisotropic Bruggeman effective medium approaches for slanted columnar thin films, J. Appl. Phys. 114 (8) (Aug. 2013). [26] J. Trollmann, A. Pucci, Infrared dielectric function of gold films in relation to their morphology, J. Phys. Chem. C 118 (27) (Jul. 2014) 15011–15018. [27] A. Kossoy, V. Merk, D. Simakov, K. Leosson, S. Kena-Cohen, S.A. Maier, Optical and structural properties of ultra-thin gold films, Adv. Opt. Mater. 3 (1) (Jan. 2015) 71–77. [28] D. Zhang, E. Cherkaev, M.P. Lamoureux, Stieltjes representation of the 3D Bruggeman effective medium and Pade approximation, Appl. Math. Comput. 217 (17) (May 2011) 7092–7107. [29] P.G. Etchegoin, E.C. Le Ru, M. Meyer, An analytic model for the optical properties of gold, J. Chem. Phys. 125 (16) (Oct. 2006). [30] G. Haacke, New figure of merit for transparent conductors, J. Appl. Phys. 47 (9) (1976) 4086–4089. [31] T. Dimopoulos, M. Bauch, R.A. Wibowo, N. Bansal, R. Hamid, M. Auer, M. Jaeger, E.J.W. List-Kratochvil, Properties of transparent and conductive Al:ZnO/Au/Al:ZnO multilayers on flexible PET substrates, Mater. Sci. Eng. B-Adv. Funct. SOLID-STATE Mater. 200 (Oct. 2015) 84–92. [32] P.C. Lansaker, J. Backholm, G.A. Niklasson, C.G. Granqvist, TiO2/Au/TiO2 multilayer thin films: Novel metal-based transparent conductors for electrochromic devices, THIN SOLID FILMS 518 (4, SI) (Dec. 2009) 1225–1229. [33] I. Crupi, S. Boscarino, V. Strano, S. Mirabella, F. Simone, A. Terrasi, Optimization of ZnO:Al/Ag/ZnO:Al structures for ultra-thin high-performance transparent conductive electrodes, Thin Solid Films 520 (13) (Apr. 2012) 4432–4435. [34] J.-A. Jeong, H.-K. Kim, Low resistance and highly transparent ITO-Ag-ITO multilayer electrode using surface plasmon resonance of Ag layer for bulk-heterojunction organic solar cells, Sol. Energy Mater. Sol. Cells 93 (10) (Oct. 2009) 1801–1809.