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Abstract
Evaporated charge extraction layers from organic molecular materials are vital in perovskite-based solar cells. For opto-electronic device optimization their complex refractive indices must be known for the visible and near infrared wavelength regime; however, accurate determination from thin organic films below 50 nm can be challenging. By combining spectrophotometry, variable angle spectroscopic ellipsometry, and X-ray reflectivity with an algorithm that simultaneously fits all available spectra, the complex refractive index of evaporated Spiro-TTB and C60 layers is determined with high accuracy. Based on that, an optical losses analysis for perovskite silicon solar cells shows that 15 nm of Spiro–TTB in the front of a n-i-p device reduces current by only 0.1 mA/cm2, compared to a substantial loss of 0.5 mA/cm2 due to 15 nm of C60 in a p-i-n device. Optical device simulation predicts high optical generation current densities of 19.7 and 20.1 mA/cm2 for the fully-textured, module-integrated p-i-n and n-i-p devices, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Organic molecular materials are widely used as functional layers in photovoltaic devices. Although they primarily serve as selective contacts for either hole or electron transport, their ability to passivate interfaces and suppress current-voltage hysteresis has also been reported, e.g for fullerenes [1–3]. Thermal evaporation can be applied to deposit compact thin films of such organic molecular materials allowing for automated, solvent- and residual-free, deposition on large area. Moreover, layers can be conformally deposited on rough or textured substrates. This makes organic molecular functional materials explicitly interesting for the emerging field of monolithic perovskite-silicon tandem solar cells [4–7] featuring µm-sized pyramidal texturing for effective light management and the highest energy yield potential [8].
The optical properties of thin films applied in multi-layered photovoltaic devices, such as tandem devices, have decisive influence on the generated current and performance. Reliable optical data of individual layers is needed for simulation of full devices allowing for detailed loss analysis and thickness optimization guidelines. Moreover, optical data should be freely accessible and shared in a comprehensive manner to serve the scientific community.
However, the determination of the complex refractive index of thin films consisting of organic molecules can often be challenging and requires careful characterization and evaluation. Furthermore, some optical data of state-of-the-art charge transport materials, such as 2,2′,7,7′-tetrakis-(N,N,-di-p-methylphenylamino)-9,9′-spirobifluorene (Spiro-TTB), have not yet been published. Spectral ellipsometry is a well-established technology to obtain optical constants of thin films [9]. Its main advantage is the simultaneous acquisition of amplitude and phase information allowing to determine two optical constants at once, e.g. the refractive and absorption index n and k. In many cases, the film thickness t can be additionally deducted via spectral curve fitting. With the optical thickness – i.e., the product n × t – as the governing parameter for the number and spectral positions of interference fringes, a simultaneous extraction of n, k, t from spectral ellipsometry may be still ambiguous due to parameter correlation. The introduction of variable angle spectral ellipsometry [10] creates additional information by variation of the effective optical path due to different angles of incidence. However, this method can be still inaccurate in case of very thin layers or if additional intrinsic layer properties such as porosity alter the effective optical constants [11]. Data extraction in such cases is more reliable if the film thickness and optical constants are obtained separately by complementary analysis methods.
As an example, it is possible to obtain the film thickness of very thin layers, e.g. with a thickness below 50 nm, with high accuracy from X-ray reflectivity (XRR) measurements. With this additional information the fitting procedure of the data from spectral photometry and ellipsometry can focus on optical constants and other intrinsic layer properties. This approach was used to separate opto-electronic properties of thin Ag layers from their physical thickness and surface roughness [12] and further applied for metal oxides such as indium tin oxide (ITO) [13].
The present work focuses on complex refractive indices of the hole transport material Spiro–TTB and the electron transport material C60, both deposited by thermal evaporation. These two-charge transport materials can be employed in n-i-p as well as p-i-n device architectures of perovskite solar cells and usually exhibit a thin layer thickness of 10 - 20 nm. As significant porosity or inclusion of voids could potential be present in evaporated films, the combined XRR/ spectral ellipsometry method is used to evaluate their optical constants independently from their physical film thickness. Undoped layers were prepared by thermal evaporation as applied in perovskite [14] and fully-textured perovskite-silicon tandem [4–7] and perovskite-perovskite-silicon triple-junction solar cells [15]. Both films are characterized by variable angle spectral ellipsometry, spectrophotometry and X-ray reflectivity. Based on these two examples of organic molecular functional layers, general guidelines for determination of complex refractive indices are presented. Finally, that data is used for optical simulation of all-textured monolithic perovskite-silicon tandem solar cells in order to conduct detailed optical loss analysis and determine optical optimization pathways. Our simulation study shows that the layer thickness of the C60 electron front contact has significant impact on parasitic absorption losses in the tandem module; switching the device polarity to n–i–p using Spiro–TTB as hole front contact turns out as a viable alternative resulting in more leeway in layer thickness and slightly increased tandem current.
2. Experimental and modelling methods
2.1 Thin film deposition
Individual layers of the hole transport material 2,2′,7,7′-tetra(N,N-di-tolyl)amino-9,9-spiro-bifluorene (Spiro-TTB, > 99%, Lumtec) and the electron transport material C60 (> 99.5%, Solenne) were deposited in a thermal evaporation system (Creaphys/ Leybold) using corundum crucibles, a base pressure of <5·10−6 mbar, and an evaporation rate of 0.3 Å/s. Crystalline silicon (polished) and optical glass (Corning EagleXG) were used as substrates. The SnOx capping layer was deposited by atomic layer deposition (Oxford Instruments FlexAL system) at 80 °C temperature using tetrakis(dimethylamino)tin (TDMASn) and H2O as precursors.
2.2 Characterization
Optical properties were determined using a PerkinElmer Lambda 950 spectrophotometer in the spectral range of 250 - 1200 nm and by variable angle spectroscopic ellipsometry (SENTECH-SE850) in the spectral range of 250 - 1200 nm with microspots (spot size 200 µm). XRR spectra were determined using an X-Ray diffractometer (Philips-Panalytical: X’Pert MRD Pro) with Cu Kα radiation.
2.3 Modelling of all spectra and procedure to obtain optimized model parameters
To obtain the refractive indices and thicknesses of the deposited thin films, all spectra from spectrophotometry (SP), variable angle spectral ellipsometry (VASE) and X-ray reflectivity (XRR) are modelled and simultaneously fitted against all measured curves as illustrated in Fig. 1. The algorithms for modelling the spectra of thin film interference stacks, X-ray reflectivity as well as the fitting algorithm are embedded as modules in a scripting language RIG-VM developed at Fraunhofer IST [16].
Fig. 1. Data extraction procedure by simultaneously fitting all spectra obtained from spectrophotometry, variable angle spectral ellipsometry, and X-ray reflectivity.
The approach is to minimize the weighted square sum χ2 of the deviations between all spectra and their modelled counterparts. For SP, VASE, and XRR spectra, separated weighting factors σSP, σVASE, and σXRR are used to account for different value scales used in the different measurement methods. The computation of spectra for reflection, transmission and ellipsometry as a function of the wavelength is based on a transfer matrix method for coherent and incoherent layers described by Harbecke [17]. While for reflection and transmission, the substrate is treated as incoherent layer, for ellipsometry it is assumed that the backside reflection is not detected and thus the substrate is treated as infinite half space. Instead of the primary ellipsometric parameters Ψ and Δ their Stokes parameters S1 and S2 are used,
which yields more continuous spectra than e.g. Δ(λ), where offsets of ±2π could occur at random wavelengths, which is difficult to handle for the fitting algorithm. The optical constants of the layer materials are represented by Lorentz oscillators which could have a Gaussian broadening parameter [18].The algorithm of the XRR spectra is based on the same interference principle; however, at the used Cu Kα wavelength of 0.154 Å, the scale of the surface roughness is larger than the wavelength. Therefore, surface scattering has to be considered with a height-height correlation function which could be simplified by a gaussian distribution [19].
In the fitting procedure, the parameters for optical constants are shared by models for reflection and transmission as well as ellipsometry. XRR spectra are taken at a much shorter and constant wavelength, where the complex refractive index is n = 1-δ+iβ with δ and β in the order of 10−6 - 10−7 [20] Click or tap here to enter text. Instead, parameters relevant for XRR are the mass density of the film and the surface roughness. The parameter which is shared by all models is the film thickness t.
In the implementation of the fitting routine in RIG-VM the minimization of χ2 can be either performed by the so-called Simplex method [21] or the Levenberg-Marquardt algorithm [22].
2.4 Device simulation
The optical simulation model was set up in the comprehensive tool of Sentaurus Device [23]. The model was experimentally validated in Messmer et al. [24] and was extended for module application in [25]. The optical device simulation parameters are listed in Table 1. The optical data for the perovskite absorber is taken from Werner et al. [26] as analyzed films were processed via a hybrid route, combining evaporation and wet-chemical processing, that allows for perovskite thin film formation on µm-sized pyramid silicon textures [4,27].
Table 1. Optical Device Simulation Parameters
3. Results
3.1 Complex refractive index of Spiro-TTB
The dielectric function of thermally evaporated, undoped Spiro-TTB is determined according to the procedure shown in section 2.3. Table 2. Fitting parameter for optical and XRR model of Spiro-TTB (Levenberg-Marquardt) shows the fitted parameter for the determination of the refractive index. With respect to the XRR parameters, it should be noted that the density of the Spiro-TTB film is very small. This is due to the fact that the density of the substrate dominates the critical angle of the total reflection. Thus, the density of the film has only an indirect impact onto the curve and cannot be accurately fitted. Table 2. Fitting parameter for optical and XRR model of Spiro-TTB (Levenberg-Marquardt) contain parameters for the dispersion of Spiro-TTB determined from the combined fit of optical and XRR data as shown in Fig. 2. The XRR beam covers the whole substrate area. The density of the substrate ρglass (2.38 g/cm3) was kept constant.
Table 2. Fitting parameter for optical and XRR model of Spiro-TTB (Levenberg-Marquardt)
Fig. 2. Measured and modeled transmittance, reflectance, ellipsometry as well as XRR-spectrum of Spiro-TTB on EagleXG glass and evaluated refractive and absorption index (n,k) of the material.
3.2 Complex refractive index of C60
For the determination of the dielectric function of C60, a glass substrate coated with a stack of C60 and SnOx as protective top layer was used. Undesired formation of C60 agglomerates was observed when thin films were exposed to ambient environment; thus, a SnOx layer was added to avoid any change of the C60 thin film in air to allow for proper optical characterization. As described before, ellipsometric measurements were recorded at three different angles of incidence (50°, 60°, 70°) as well as transmission and reflection in the wavelength range from 250–1200 nm (see Fig. 3). Additionally, as before, XRR measurements were recorded to determine the exact thickness values of the two different materials.
Fig. 3. Measured and modeled transmittance, reflectance, ellipsometry as well as XRR-spectrum of C60/SnOx on EagleXG glass and evaluated refractive and absorption index (n,k) of the material.
For a two-layer model, an overall fit of optical spectra and XRR data will all fitting parameters released leads to ambiguous results. Therefore, this coating stack is evaluated in a stepwise approach: Prior to these measurements, the dispersion of a single SnOx layer was obtained from a glass/ SnOx sample [23] with a Gaussian broadened Lorentz oscillator [18] as optical model. Fitting parameters can be found in Table 3
Afterwards only the XRR data of the combined glass/C60/SnOx sample were fitted (see Table 4). In this case the divergence of the beam δ (0.009 °) and the density of the substrate ρglass (2.38 g/cm3) were kept constant.
Table 3. Fitting parameter for optical model of glass/ SnOx (Levenberg-Marquardt)
Table 4. Fitting parameter for XRR model of glass/C60/SnOx (Simplex)
Table 5. Fitting parameter for optical model of C60 using a glass/C60/SnOx stack (Levenberg Marquardt)
Finally, for determination of the optical constants of the C60 layer, the ellipsometric, transmission and reflection data, and the XRR data were simultaneously fitted, but only the two film thicknesses and the parameters for the dielectric function of C60 could be varied. For the C60 three Lorentz oscillators (according Ren et al. [35]) were used for the optical model with fitting parameter shown in Table 5.
The complex refractive indices data of Spiro-TTB and C60 presented in this paper are available in [36].
3.3 Impact of Spiro-TTB and C60 on optical performance of fully textured perovskite silicon tandem solar cells in module stacks
The impact of the parasitic absorption of the Spiro-TTB and C60 layer was investigated by means of a TCAD simulation using Sentaurus Device [23]. The optical model was experimentally validated in Messmer et al. [24] based on a monolithic p-i-n perovskite top cell and a silicon heterojunction (SHJ) bottom cell with textured rear as published by Schulze et al. [37], which features a similar layer stack investigated in this publication. The complex refractive indices for Spiro–TTB and C60 are according to the data of this publication. Further details on the optical simulation model are stated in Table 1.
Figure 4 shows the complete layer stack of the fully-textured perovskite-silicon tandem solar cell within a module for a p-i-n and n-i-p configuration of the perovskite top cell, respectively. For the p-i-n configuration the front extraction layer collects electrons by means of a SnOx/C60 stack, whereas for the n-i-p configuration Spiro-TTB is used as a hole extraction layer at the front side of the top cell.
Fig. 4. Sketch of a fully-textured perovskite silicon tandem solar cell stack in a module configuration: (left) p-i-n configuration with C60 as front transport layer (right) n-i-p configuration with Spiro-TTB as front transport layer
The results of the optical simulation are shown in Fig. 5. Figure 5(a) shows the results for the p-i-n configuration featuring C60 at the front side. The blue and red lines show the absorption of the perovskite and silicon absorber, respectively. The sum of the two absorption curves is shown by the gray dotted line. Moreover, one can see the reflection (or more precisely 1-R) in green. The remaining white area is the sum of all parasitic absorption within the whole device. It includes the front encapsulation (glass and EVA encapsulation), all thin layers at the front and rear, as well as metallization. Details and parasitic absorption current of all-important layers are listed in the tables of the legend in Fig. 5(a) and (b), respectively. The generated photo current of the two absorbers was (photo-)current-matched by thickness adaption of the perovskite absorber (dPero = 610 nm, band gap EG = 1.665 eV) and is Jgen = 19.7 mA/cm2 for both perovskite and silicon (as it was done in [38]). Especially, one can see the parasitic absorption curve of the front ITO, SnOx and C60 as purple, light green and brown dotted lines, respectively, whereby the ITO layer thickness and transparency was chosen according to the optimization in Messmer et al.[25] and the other layer thicknesses are in accordance with state-of-the-art experimental tandem devices. The parasitic current due to the 15 nm of C60 is about 1.2 mA/cm2, and the SnOx layer adds another 0.1 mA/cm2 on top. We compare this result to the simulation of the n-i-p configuration (see Fig. 5(b)), where we can see that 15 nm of Spiro-TTB at the front side only lead to 0.3 mA/cm2 parasitic current loss. One can also see that the reflection stays similarly high as for the p-i-n configuration (3.2 mA/cm2). The absorption curve of the perovskite absorber (shown in blue) between 300 - 550 nm is significantly improved. In order to (photo-)current-match the two absorbers, the perovskite thickness (with same EG = 1.665 eV) can be reduced from 610 - 530 nm, resulting in a photogenerated current of 20.1 mA/cm2 in both silicon and perovskite absorber, which is about 0.4 mA/cm2 higher than for the p-i-n configuration in a module stack.
Fig. 5. (a) Wavelength-dependent absorption for the p-i-n and (b) the n-i-p configuration. The reflectance is shown in green (1-R), perovskite and silicon generation in blue and red, respectively. The parasitic absorptance within the C60 and Spiro-TTB layer is shown in brown and green (dotted lines), respectively. The parasitic absorptance in the most important other layers is shown according to the legend.
Finally, our simulation model allows us to quantify the parasitic absorption losses of C60 and Spiro-TTB in dependence of the layer thicknesses, as shown in Fig. 6. One can see an almost linear increase in parasitic absorption with the respective front layer thickness of C60 and Spiro-TTB. For C60, each 5 nm lead to about 0.40 mA/cm2 parasitic absorption loss (shown in solid brown, right axis), whereas for Spiro-TTB, each 5 nm lead to only about 0.09 mA/cm2 (shown in solid green, right axis). For the summed generated current within the perovskite and silicon absorber, this leads to a reduction of 0.35 mA/cm2 in generation current per 5 nm C60 in a p-i-n configuration (see dashed brown curve), whereas the reduction in generation current is only about 0.08 mA/cm2 per 5 nm Spiro-TTB in an n-i-p configuration (see dashed green curve. Therefore, our simulation model predicts that an n-i-p configuration featuring the Spiro-TTB as characterized in this publication, could be more beneficial than the p-i-n configuration using the SnOx/C60 layer stack at the front side in terms of highest achievable currents The authors encourage to validate this simulation finding by experimental test structures. However, please note that this is a purely optical simulation study which does not consider the electrical requirements of the HTL and ETL. From an electrical point of view, in order to yield efficient charge carrier extraction, a minimum thickness of the ETL and HTL layer is required, respectively, which is not considered here. Furthermore, the optical generation rate at the front TL is much higher than at the top cell’s rear contact, which may also impact the electrical characteristics of p-i-n vs. n-i-p devices based on differences in the electron and hole mobilities [39]. Here, studies on the electrical properties of these devices are needed.
Fig. 6. The summed generation current of perovskite and silicon absorber for the p-i-n and n-i-p configuration, in brown and green, respectively, in dependence of the thickness of the front transport layer (C60 for p-i-n, Spiro-TTB for n-i-p). Right axis shows the parasitic absorption for the respective front transport layer (C60 for p-i-n, Spiro-TTB for n-i-p).
4. Conclusion
This paper elaborates the determination of complex refractive indices of organic molecular thin films applied in perovskite-based tandem solar cells. We present an approach combining spectrophotometry, variable angle spectroscopic ellipsometry, and X-ray reflectivity with an algorithm that simultaneously fits all available spectra. This approach is used to determine the complex refractive indices of evaporated Spiro-TTB and C60 thin films, two well established charge transport material in perovskite and perovskite-silicon tandem solar cells. Such a combined approach allows for the determination of reliable optical data of thin films well below 50 nm thickness.
Applying the n and k data in an optical simulation model for perovskite-silicon tandem solar cell modules, we find that C60 as electron front contact in the common p-i-n device architecture has significant impact on parasitic absorption loss, increasing almost linearly with the respective layer thickness of about 0.40 mA/cm2 per 5 nm. Instead, switching the device polarity to n-i-p using Spiro-TTB as hole front contact results in reduced parasitic absorption of 0.09 mA/cm2 per 5 nm. At current-matching condition, an overall tandem current of 20.1 mA/cm2 is reached for the n-i-p module compared to 19.7 mA/cm2 for the p-i-n module.
Based on our work, we conclude that the less common n-i-p tandem device structure is promising and could potentially increase the maximum achievable current in textured perovskite silicon tandem modules. For p-i-n tandem devices, research needs to focus on a more transparent electron contact material to replace C60. Furthermore, we encourage the community to share reliable material data for generating meaningful recommendations from simulation.
Funding
Deutsche Bundesstiftung Umwelt (PhD scholarship); Fraunhofer-Gesellschaft (FEMOVATION Program and Fraunhofer LIGHTHOUSE PROJECT MaNiTU).
Acknowledgments
This work was supported from the Fraunhofer LIGHTHOUSE PROJECT (MaNiTU). Furthermore, Patricia S. C. Schulze was supported by the project SUMMIT in the course of the internal funding program FEMOVATION. Christoph Messmer would like to thank the “Deutsche Bundesstiftung Umwelt (DBU)” for funding his dissertation project.
Disclosures
The authors declare no conflicts of interest.
Data availability
Complex refractive indices data underlying the results presented in this paper are available in Ref. [36]. Further Data can be requested from the authors.
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