Emerging low cost and large area periodic texturing methods promote the fabrication of complex absorber structures for thin film silicon solar cells. We present a comprehensive numerical analysis of a 2μm square periodic polycrystalline silicon absorber architecture designed in our laboratories. Simulations are performed on the basis of a precise finite element reconstruction of the experimentally realized silicon structure. In contrast to many other publications, superstrate light trapping effects are included in our model. Excellent agreement to measured absorptance spectra is obtained. For the inclusion of the absorber into a standard single junction cell layout, we show that light trapping close to the Yablonovitch limit can be realized, but is usually strongly damped by parasitic absorption.
© 2012 Optical Society of America
Random light trapping geometries still dominate current industrial thin film silicon solar cell production, relying on a small set of available surface textures which are usually determined by material growth or etching processes [1, 2]. Depending on the cell technology, the available textures with good optical properties may critically influence the electrical device properties and require careful processing . The creation of a geometrically tailored light trapping system, which provides both excellent light trapping and growth support for the solar cell stack is therefore highly desirable.
Periodic surface textures allow such an excellent light trapping at strongly controllable surface characteristics. By means of statistical coupled mode theory it was shown by Yu that periodic textures can, under certain circumstances, even provide light trapping beyond Yablonovitch’s geometrical limit for perfectly randomized light [4–6]. Periodic thin film absorber geometries with extreme light path enhancement at the geometrical limit  and beyond [4, 8] have already been realized in simulations. However, these geometries were not designed regarding fabrication constraints and electrical properties and are unlikely to be implemented in a solar cell. Furthermore, these textures working at the light trapping limits often lack optically important layers which are present in solar cell stack of current technology. However, a good light trapping by periodic geometries, which is comparable to current optimized rough surface technology, has also already been realized experimentally by several groups for amorphous [9, 10] and nanocrystalline absorbers .
To further promote the future development of thin film silicon photovoltaics, not only light trapping optimization of current technologies, but also advances in time and cost efficiency of the coating process as well as a shift towards the higher quality polycrystalline absorber material are required. A corresponding advance for the creation of several micrometer thick polycrystalline absorbers has been made through the combination of rapid amorphous silicon deposition by electron beam evaporation and subsequent annealing by SPC . The crystallization step, which is necessary to obtain a polycrystalline absorber, was shown to yield controllable results only on mildly textured random surfaces. The use of periodically textured deposition substrates, however, also allowed controllable coating of high aspect textures with promising absorption enhancement properties [13, 14].
In this contribution we study the light trapping provided by such an experimentally fabricated, high-aspect 3-dimensional polycrystalline absorber structure, implemented in a single junction device layout in the superstrate configuration. We perform all simulations using the same absorber model, as it is determined by growth conditions and structure optimizations thereon can usually not be transferred to the experiment. As contacting scheme to the cell, we employ the conventional contacting scheme of ZnO:Al front and ZnO:Al / silver back contacts. In contrast to many other contributions with simulations of cells in the superstrate configuration, we include an approximation of the superstrate light trapping in our computational model, to provide reliable predictions of the device absorptance. Our focus lies on the evaluation of the impact of superstrate light trapping, assessment of the optical quality of the experimentally provided absorber structure in the conventional design and possible improvements to this design. An analysis of losses allows us to make a more general remark on achievable light path enhancement factors in the standard thin film stack configuration.
2. Computational model
The 3-dimensional geometrical model of the absorber structure used for all simulations in this paper was constructed from experimental TEM and SEM data of silicon layers on a square periodically textured solgel surface, with an intermediate layer of 70 nm ZrO2. To create the experimental structure, amorphous silicon was deposited by e-beam evaporation on the textured substrate at an effective height of 2.4μm. Following deposition, the silicon layers were thermally annealed. Residual areas of amorphous silicon, known to form at steep flanks when using this fabrication procedure , were removed by selective etching. Further details on the fabrication process can be found in corresponding references [13, 14]. SEM images of the silicon layers prior and after the etching step are depicted in Fig. 1(a) and (b). The etching of amorphous silicon creates a groove bounded by two approximately conical surfaces that extends over the complete height of the absorber. These two surfaces have a similar opening angle of about θ ≈ 20°. Their horizontal distance is approximately d ≈ 0.34μm. The corresponding computational model of the silicon texture unit cell is shown in Fig. 1(c). In the center cross-sectional image, crystalline and etched amorphous silicon regions are marked with letters “c” and “a”, respectively.
Maxwell’s equations were solved on space discretized versions of the computational model, as depicted in the perspective view in Fig. 1(c), using the finite element package JCMsuite . Absorptance integrals and scattered intensity were computed from the obtained solution. Computational convergence was measured for these derived quantities and not directly for the electromagnetic field. The quality of all simulations was assured through a convergence analysis. Computational errors of all simulations should be smaller than 2% of the incident irradiance at wavelengths below 700 nm and smaller than 1% at higher wavelengths.
Our objective is to estimate the optical performance of solar cells in the superstrate configuration, i.e. cells which are illuminated through their deposition substrate, as depicted in Fig.1(e). In contrast to the solar cell absorber, which is on the order of a few microns thick, the superstrate thickness is usually a millimeter and more. As measurements normally integrate over wavelength intervals much larger than the free spectral range of the superstrate, we use an incoherent coupling of iterations between the finite element domain and a transfer matrix solver to approximate the light trapping contribution by multiple internal reflection inside the superstrate layer. No anti-reflective coating was applied in the simulations presented here. A conventional anti-reflection system consisting of flat layers would not interfere substantially with the computed superstrate light trapping, as the important angle for total internal reflection between superstrate and air remains unchanged.
All simulations presented here were performed using a refractive index of 1.52 for the glass superstrate as well as the solgel layer. Standard refractive index and extinction coefficient values were used for silver . For the optical properties of the silicon absorber volume the material parameters of crystalline silicon were used, as only polycrystalline silicon was assumed to remain in the etched silicon layer. The etching grooves in the absorber bulk were assumed to be filled with air, when present. Experimentally it may eventually be required to fill these grooves with organic material. The refractive index and absorption coefficient of the transparent conductive oxide (TCO) ZnO:Al, used as front and back layers to the silicon absorber, and ZrO2, used in the experimental comparison, are depicted in Fig. 1(d), together with the data of crystalline silicon. ZrO2 was assumed to be non-absorptive over the spectral range of interest.
The absorption coefficient of the ZnO:Al used here is higher than for the newest generation of high charge carrier mobility ZnO:Al . However, in the red part of the spectrum, i.e. at wavelengths greater than 900 nm where light trapping is most important, the absorption coefficient values of high mobility ZnO:Al are of the same order of magnitude as the data set used here. At wavelengths above 1000 nm, the absorption coefficient of crystalline silicon is up to several orders of magnitude lower. The cell results should thus not show a substantial difference with respect to optimized contact layers in that high wavelength range.
3. Analysis of experimental absorptance spectra
A comparison between simulated and measured absorptance of the etched silicon layers on solgel / ZrO2 substrates, as depicted in Fig. 1(a) and (b), allows to test the computational model and to discriminate defect and parasitic absorption from crystalline silicon absorption in the experimental case. The absorptance measurements were performed using an integrating sphere with a sample mount inside the sphere, inclined by 10° to the incident beam direction. Simulations of a corresponding cell model with a ZrO2 intermediate layer were performed for normally incident light. The experimental and computed results are compared in Fig. 2. Correspondence between simulated and measured curves is excellent for the wavelength range between 500 nm and 920 nm. For higher wavelengths the simulated absorptance rapidly converges to zero at the band edge of crystalline silicon. The measured absorptance, in contrast, levels off to about 20% at wavelengths above the silicon band edge, resulting in the region of high difference between model and measurement which is marked as a gray area in Fig. 2. We stress the importance of the good correspondence in the low wavelength region of crystalline silicon, which verifies the quality of our model. The substantial experimental absorptance in the sub bandgap wavelength region should not be present for a crystalline silicon absorber and may arise from absorption by defects in the non-optimized polycrystalline absorber material. As defect absorption is not included in our material model used for simulation, a defect free experimental absorber should show a similarly reduced high wavelength absorption as in the simulation.
From the results of this experimental comparison we also highlight the importance of taking the superstrate light trapping into account to be able to predict cell absorptance in the superstrate configuration. A natural definition for this contribution can be found in our incoherent coupling scheme by summing up the absorptance arising from light which passes the solar cell absorber more than once. The superstrate light trapping is important at wavelengths above 900 nm, where it makes up between 20% and 50% of the total silicon absorptance. This contribution does not change substantially between the different configurations of the cell layout with the 2μm periodic absorber, which are discussed below.
4. Anti-reflection properties of the front texture
Good anti-reflection properties of the front texture are required to allow light to be trapped inside the silicon absorber of a solar cell. We test the anti-reflection properties of our high-aspect solgel interface texture by measuring the transmittance into a silicon half space through the glass superstrate and an absorbing front TCO layer of 300 nm ZnO:Al. This study cannot be performed for the etched absorber model which is experimentally realized.
Transmittance results at different aspect ratios and for a complete unit cell scaling to smaller texture periods are summarized in Fig. 3. The original height to period aspect ratio of our 2μm periodic model is 0.87. The wavelength resolved transmittance into silicon for this geometry is depicted as an inset to the left subplot. A reduction of transmittance, which is partially due to the interference pattern of the 300 nm thick TCO layer, is visible at low and high wavelengths. For high wavelengths, the transmittance is further reduced by increased absorptance in the ZnO:Al layer. All other tested front side geometries are summarized in the form of box plots. In the right subplot of Fig. 3, a height scaling between the flat interface and the experimental solgel interface texture quantifies the anti-reflection effect of the texturing. With increasing aspect, the average transmittance into silicon gradually increases by 7% from the value of the flat interface. At the same time the spread of the distribution is reduced to about half of the value of the flat interface, which indicates less pronounced interference effects at higher texture aspect ratios.
In the complete scaling series summarized in the left subplot in Fig. 3, we observe a further decrease of the spread of the transmittance distribution and increase of the average transmittance, with respect to the 2μm periodic case. However, these effects can to a large part be attributed to reduced TCO absorption, as the intermediate TCO layer was scaled along with the interface texture. Generally, the anti-reflection properties of the texture are good throughout a wide range of texture periods. For very small surface corrugations, as in case of the simulated simulated 300 nm periodic texture, the good anti-reflection properties are not maintained any more.
5. Texture performance in the conventional single junction solar cell design
For solar cell simulation a simplified version of the standard single junction thin film silicon solar cell structure was chosen. The device structure is depicted in Fig. 4 (a) and a cross-sectional image through the cell as configuration “B” in Fig. 5(a). The highly doped thin silicon layers necessary for the electrical operation of the device were neglected for our optical simulations in the wavelength range λ > 600 nm. The modeled cells consist of a glass superstrate, a vertically extruded, 300 nm thick front TCO layer (ZnO:Al), the structured silicon absorber layer, a back TCO layer (ZnO:Al) of 85 nm thickness in the surface normal direction and the silver reflector. As absorber model, the 2μm periodic silicon absorber with 1.93μm effective silicon height was used, as in the experimental comparison above. The back TCO layer was created using a translation along the surface normal and not a vertical translation to avoid very thin layer thickness in high slope regions of the texture, which is known to reduce the reflector quality .
Detailed simulation results for the conformal reflector geometry are depicted in Fig. 4(b) and (c). Diagram (b) shows an area plot of the total device absorptance, separated into absorptance fractions of the different material regions. The superstrate light trapping contribution to silicon absorptance is included as a white line. To identify the absorptance change due to the conformal back reflector, a reflector-less reference simulation with the identical front TCO layer and an air half space instead of the back TCO and silver layers is further included in the form of broken red lines. Silicon absorptance differences between the two cases are shown in diagram (c). For our absorber geometry, the implementation of the conformal back reflector with lossy back ZnO:Al and silver layers does not result in an enhancement over the reflector-less case. It should be noted that this latter case already has good rear-reflection properties due to the many high-slope parts of the silicon structure and the large difference in refractive index between silicon and air. Interestingly, almost all of the light which is transmitted in absence of the back reflector gets attributed to parasitic absorptance in the reflector layers. The total parasitic absorptance rises to about 60% close to the band edge, of which the largest part is distributed among the two TCO layers. In the spectral range above 800 nm, the back TCO vs. front TCO layer absorptance ratio is about 0.58, which is not much higher than the two layers’ volume ratio of 0.53. Plasmonic absorption enhancement should therefore not play a major role for the back TCO layer in this configuration.
The cell model with a conformal reflector was also simulated for a textured homogeneous crystalline silicon absorber layer, i.e. without etching grooves, to assess the absorptance loss due to the etchings. A wavelength resolved plot of the absorptance differences between the two cases is depicted in diagram (c) of Fig. 4. The material loss due to the etching grooves, which is of about 19.5% of the unetched silicon volume, results in a silicon absorptance loss of about 5% of the integrated unetched silicon absorptance and extends, apart from a local interference effect at around 900 nm wavelength, over the whole wavelength range, with maximum losses between 800 nm and 950 nm. As the etching grooves in our absorber structure may always guide light to the reflector layers, the losses from back TCO and silver absorptance are also not expected to vanish completely for wavelengths in the high absorptance region of silicon, i.e. with λ ≲ 500 nm.
6. Loss analysis and possibilities for optimization
For further analysis, we include a flat back reflector layout besides the conformal back reflector layout. The flat layout, which is depicted as configuration “C” in Fig. 5(a), has been stated as advantageous for light trapping by Haase . This advantage may be case dependent as in recent experimental studies of detached reflector concepts by Moulin, no distinct difference was found between flat back reflectors and rough reflectors . We therefore choose an implementation close to the case Haase studied and fill the complete rear volume, up to the flat back reflector, with TCO material. If our absorbing ZnO:Al is used as back TCO, as for the results in in Fig. 5(b), the almost 8-fold increase of the back TCO volume in the flat reflector design does not damp silicon absorptance with respect to the conformal reflector and reflector-less layouts. This indicates an improvement of silicon light trapping for the flat back reflector layout. When computing the back vs. front TCO volume and absorptance ratios for this layout, we obtain 4.2 and 2.1, respectively, in average over wavelengths above 800 nm. In comparison to the numbers computed for the conformal layout in the previous section, we find that the volumic absorption of the back TCO is smaller in case of the flat reflector design. The fact that the TCO absorption does not scale with TCO volume suggests that these parasitic losses may be dominated by light trapped in modes inside the silicon absorber, which extend into the TCO volume.
To further quantify in how far the TCO parasitic absorption can be attributed to silicon absorptance, we individually set the absorption coefficient of the front and back TCO layers to zero. The results of this study are summarized in Fig. 5(c). Generally, silicon absorptance increases when setting one of the TCO domains non-absorptive, with a larger increase in the light trapping region at λ > 850 nm than in the lower wavelength interval. For both reflector designs the silicon absorptance increase varies between 35% and 50% of the parasitic absorptance decrease. Front and back TCO are not independent regarding their contribution to silicon absorptance when set non-absorptive: The sum of silicon absorptance increase for the two separately non-absorptive TCO regions is smaller than the increase with both regions set non-absorptive. In this latter case the flat back reflector layout provides the superior light trapping of all configurations, with an average absorptance increase greater than 10% of the incoming light between 600 nm and 1100 nm wavelength.
In addition to the depiction in diagram (c) in Fig. 5, we also compare the different cases of TCO absorption in terms of light path enhancement factors (LPEF), both to highlight the light trapping performance of our etched nanodome absorber design and to facilitate comparison to other publications. Average LPEF values are calculated from the Lambert-Beer law for the wavelength interval between 1000 nm and 1100 nm, according to21].
The computed band edge LPEF values are depicted in Fig. 6. Light path enhancement using the conformal reflector design “B” and absorptive TCO regions reaches values between 3 and 16, with a value greater than 13 at 2μm domain period. For periods above 1.4μm, the enhancement factor shows no strong dependence on the texture period any more. The light trapping at these larger texture periods is comparable to experimental results of nanocrystalline silicon solar cells with etched ZnO:Al substrates . For domain periods smaller than 1μm, enhancement factors are strongly dependent on the period. Local maxima are located at 500 nm and 900 nm domain period. The location of maxima in that range is consistent with the findings of other groups who performed light trapping optimization in periodic structures [7, 8, 11, 19, 23, 24]. The exact position of the optimum period, however, depends on the measured quantity and observed wavelength range. In our case, the optimum light trapping with an enhancement factor greater 16 is located at 900 nm texture period. We notice that the height and position of this local maximum are strongly influenced by the superstrate light trapping, which makes a major contribution to total light trapping at this domain period by total internal reflection of the first diffraction order. This kind of light trapping may be subject to a strong sensitivity regarding changes of the illumination angle from normal incidence [4, 5]. All computed LPEF values of the conformal back reflector layout with absorptive TCO seem rather low, when compared to theoretical estimates of light trapping limits for uniform layers and weak absorption. Yablonovitch’s statistical geometrical limit for light trapping is around 50 for the chosen integration interval . Light trapping in symmetric periodic textures, as simulated here, was estimated by Yu using statistical coupled mode theory . He predicts path enhancements of up to about 80 for structures with periods which are smaller than the the lowest wavelength of the desired light trapping region. As the texture period exceeds the highest wavelength in the desired interval Yu predicts a convergence of the path enhancement towards Yablonovitch’s limit.
Parasitic absorption was already identified above as a major loss factor for silicon absorptance in the standard single junction cell layout. In case of randomly etched ZnO:Al substrates, these losses were proposed by Berginski, who used an estimate model for computation, as the main reason for which light trapping at the Yablonovitch limit is not reached experimentally in solar cells . We quantify this impact by disabling either only back or back as well as front TCO absorption in our flat back reflector solar cells. The LPEF values then rise to over 20 and 40, respectively. Without any TCO absorption, a highest light path enhancement of 44 is found for the 2μm periodic layout. This value is not far from Yablonovitch’s limit. We thereby confirm that it is possible to reach light trapping close to the geometrical limit in a standard thin film solar cell stack, while parasitic absorption is a major reason for the small enhancement factors found in the experimental case.
7. Conclusion and outlook
We have shown that superstrate light trapping into account can make a substantial difference in optical modeling of superstrate thin film solar cells employing periodic light management textures. Due to its dependence on the texture period, the superstrate contribution cannot be savely neglected in predictive simulations and for texture optimization. Regarding the performance of our experimental absorber texture, we found that it does provide both, good anti-reflection and light trapping properties, when sandwiched between lossless TCO layers and employing a flat back reflector design. Light trapping not far from the geometrical limit was found for this configuration. However, when sandwiched between lossy TCO material, light path enhancement factors drop substantially, approximately to the level which is provided by high performance rough TCO substrates in nanocrystalline silicon thin film technology.
Polycrystalline cell concepts can still outperform their nanocrystalline counterparts in the classical solar cell stack configuration by providing high quality layers at thicknesses of 3μm and more. However, a general change of the contacting scheme, with less direct contact zones between the TCO and silicon, as for point contacts, seems desirable in view of our simulations. Additional light trapping may also be provided by the use of a white paint reflector, which could not be included in our model.
We thank Martin Hammerschmidt, Sven Burger, Lin Zschiedrich and Veit Preidel for many discussions and valuable suggestions. We further thank the company JCMwave for supplying their finite element solver, which we use for optical simulations. The open source software packages Python, Octave, Veusz and Mayavi were used for creating this work.
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