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A photonic crystal design that significantly enhances the absorption of tandem thin-film solar cells composed by amorphous and microcrystalline silicon (i.e., a-Si:H/μc-Si:H tandem cell) is proposed. The top junction with a-Si:H is nanopatterned as a one-dimensional photonic crystal. Considering the photocurrent matching, we optimally design the junction thickness and the configuration of the nanopattern; moreover, both transverse electric and magnetic incidences with various illuminating angles are taken into account. Calculations by rigorous coupled-wave approach and finite-element method show that the nanophotonic crystal design can improve the absorption and output photocurrent by over 20%, which shows very low sensitivity to the incident polarization. Moreover, the proposed structure is able to sustain the performance for a very wide angle ranges from 0° to ~80°.
©2013 Optical Society of America
1. Introduction
The introduction of hydrogenated microcrystalline silicon (μc-Si:H) into hydrogenated amorphous silicon (a-Si:H) thin-film solar cells is an important advancement which greatly alleviates the Staebler-Wronski degradation due to the a-Si:H material and helps to improve the light-conversion efficiency of the cell by raising open-circuit voltage (Voc) benefiting from the tandem setup [1]. The a-Si:H/μc-Si:H tandem system was first proposed by IMT Neuchâtel in 1994 with an initial η = 9.1% [2] and then attracted a lot of attention in the next two decades. Compared to a-Si:H/a-Si:H systems, a-Si:H/μc-Si:H tandem cells realize a broader-band light harvesting with better operation stability. In improving the performance of a-Si:H/μc-Si:H tandem solar cells, optical means (especially light-trapping) plays an important role [3]. Asahi random textures are commercially used which contribute randomly-oriented light scattering and lead to broadband performance enhancement. IMT Neuchâtel proposed a better light-trapping by using top ZnO transparent conductive oxide (TCO) layer with controllable performance outperforms Asahi texture [4]. An intermediate TCO layer between the top and bottom junctions has also been proposed [5] with the consequence of an initial efficiency of 14.5% [6]. The optical mechanism is the intermediate layer can reflect the unabsorbed short-wavelength light back into the top cell without affecting the part for the bottom cell.
Besides the random texturing or even more complicated nanostructures, photonic crystal is another important optical option which improves the light-trapping performance of solar cells consisted of different material groups or with various structures. Bermel et al proposed a photonic crystal-based light-trapping approach for 2 μm crystalline silicon (c-Si) solar cells and obtained power generation enhancement over 25% [7]. Park et al used the similar scheme for improving the absorption of a-Si:H solar cells with thickness of only 100 nm; the absorption was observed to be increased by 35% over 300-750nm wavelength range [8]. For the similar 100nm-thick a-Si:H solar cells, Daif et al proposed to pattern the photoactive layer as a planar photonic crystal and found 50% increase of the absorption over 380-750nm [9]. Peters et al reported an electro-optical simulation of diffraction in c-Si solar cells and found that grating enhances the short-circuit current density (Jsc) by more than 1 mA/cm2 [10]. Patterning TCO layer to improve the light-trapping in 300nm-thick a-Si:H solar cells has showed that Jsc can be increased from 19.9 to 21.1 mA/cm2 [11]. Moreover, a detailed comparison on the performance of photonic light-trapping and Lambertian limits in thin film silicon solar cells has been presented recently, which affirms the potential of photonic crystal in enhancing the performance of solar cells [12].
The above photonic crystal ways are solely for single-junction solar cells with an obvious spectral band to be optimized. However, for tandem cells, situations become very different: 1) multiple junctions with specified spectral bands have to be considered; 2) the effects of photonic crystal on every junction has to be discussed; and 3) most importantly current matching is a critical criteria for this type of solar cell, which has to be examined carefully when trying to find optimal photonic crystal designs with maximized system performance.
In this paper, we concentrate on the application of photonic light trapping in a-Si:H/μc-Si:H tandem solar cells. Instead of patterning top TCO layer, we find that it is more efficient to structure a-Si:H layer as a grating (1D photonic crystal) in order to raise the absorptions of both junctions. Keeping the photocurrent matching condition in mind, we focus especially on the light-trapping properties, the absorption of the whole device and each junction, the parameter optimization of the nanopatterned layer, and the angular performance of the tandem system for transverse electric (TE) and transverse magnetic (TM) incidences under various incident angles using rigorous coupled-wave approach (RCWA) and finite-element method (FEM) [13]. The ultimate objective is to find a photonic crystal way to realize broadband and angle/polarization-insensitive absorption/photocurrent enhancement for a-Si:H/μc-Si:H tandem solar cells.
2. Device and method
The schematic of the a-Si:H/μc-Si:H tandem solar cell is shown in Fig. 1 under a superstrate configuration, which is composed (along the direction of light injection) by substrate, SnO2:F top TCO with thickness 80 nm, a-Si:H top junction, μc-Si:H bottom junction, ZnO:Al bottom TCO with thickness 80 nm, and back silver (Ag) reflector [1]. For a fair and meaningful evaluation of the systems under various configurations, we assume that the material consumption of a-Si:H layer is kept unchanged before and after being nanopatterned by inserting silicon dioxide (SiO2), i.e., ΛdaSi = bdg.
Fig. 1 a-Si:H/μc-Si:H tandem solar cells under superstrate configuration with nanopatterned a-Si:H layer. The equivalent a-Si:H layer thickness in planar is defined as daSi by assuming an identical a-Si:H volume after being nanopatterned, i.e., ΛdaSi = bdg. Λ = 500 nm is used throughout this paper.
The proposed structure can be modeled by using RCWA which is especially useful for modeling multi-layered planar structure containing grating (e.g., one of the authors has used this method to perform researches on plasmonics and diffraction in concentric-circular grating [14, 15]). With the consideration of sufficient high-order diffraction modes under solar incidence, the reflection (R) and transmission (T) for every wavelength can be calculated, enabling to obtain the device absorption (A = 1 ‒ R ‒ T which is simplified here as A = 1 ‒ R since T = 0 with the presence of Ag back reflector). RCWA is especially helpful in quickly finding the optimal design by sweeping the device parameters in very broad ranges. However, limitations also exist, e.g., 1) the calculated device absorption includes all layers instead of the key a-Si:H and μc-Si:H layers only; 2) the contributions from a-Si:H and μc-Si:H parts are difficult to be distinguished. These information is nevertheless crucial for the design of multi-junction solar cells connected in series since the device photocurrent has to take the lowest among those contributed from all junctions [16].
To compensate the limitation of RCWA, we also perform the electromagnetic calculation for the nanopatterned device by using finite-element method (FEM) [17]. The exact calculation of electric and magnetic field inside the device exports the detailed spatial information of field and power density, allowing to directly calculate absorption percentage in each layer. The FEM results can be used to improve the accuracy of RCWA through the following treatments. According to our calculation, we find that 1) the substrate shows almost no light absorption; 2) the absorption spectrum of top TCO (SnO2:F) is relatively stable with various nanopatterns; 3) bottom TCO only absorbs short-wavelength light, which has already been totally absorbed by top TCO and photoactive materials before reaching the layer; 4) the thick Ag layer on the rear is found also not to consume the solar energy noticeably. Therefore, by eliminating the top TCO absorption (calculated from FEM) from the total absorption (A calculated from RCWA), the new absorption (Pabs) is now contributed mainly from a-Si:H and μc-Si:H layers and hence well reflects the absorption characteristics of the designed tandem solar cells. Utilizing the photon flux spectrum from solar, the total photocurrent can be obtained under the assumption of a perfect internal quantum process [18, 19].
3. Results and discussions
To obtain the best performance through nanopatterning the a-Si:H layer, the grating parameters (dg, b and Λ) have to be optimized. Our calculations show that Λ = 500 nm is a promising choice, which leaves the a-Si:H width b in each period to be determined [dg = b/(ΛdaSi)]. The refractive indices of the materials used in this paper are from [1, 20].
The photocurrent converted from device absorption calculated by RCWA is actually a direct summation of photocurrent densities contributed by a-Si:H and μc-Si:H layers, i.e., Jtot = JaSi + JμcSi, which indeed shows interesting information on the electrical performance of the solar cells, but does not tell us how much current can be collected from the tandem device with junctions electrically connected in series. The realistic device output photocurrent should be min(JaSi, JμcSi). To fulfill this photocurrent matching condition, the thicknesses of a-Si:H and μc-Si:H have to be carefully chosen in advance. We find that daSi = 170 nm and dμcSi = 1700 nm give JaSi = 11.27 mA/cm2 and JμcSi = 11.17 mA/cm2, indicating output photocurrent density of 11.17 mA/cm2. These thickness choices are typical for the a-Si:H/μc-Si:H tandem cells reported in previous literatures [1].
With nanopatterning the a-Si:H layer, both JaSi and JμcSi will be modified. The most desirable situation is both of them can be improved equally under various advanced designs so that the device output can obtain the maximal enhancement. According to our RCWA calculation, the optimal b maximizing Jtot is around 390 nm. However, the proportions of JaSi and JμcSi in the total enhancement have to be clearly distinguished. To do so, we simulate the electromagnetic response of the tandem solar cells by FEM and calculate the photocurrent from each junction. Results are listed in Table 1 where JaSi and JμcSi for various situations have been listed with the inclusion of the average of TE and TM, i.e., (TE + TM)/2. It is found that the peak output photocurrent under TE (TM) is 13.00 (12.05) mA/cm2 at b = 360 (380) nm, while that for (TE + TM)/2 is 12.51 mA/cm2 (increased by 1.34 mA/cm2 from 11.17 mA/cm2 with an enhancement of ~12.0%) at b = 350 nm. Although the enhancement looks encouraging, space for further improvement is still possible. This is because, as shown in Table 1, JμcSi can be close to 15 mA/cm2 under TM, while the maximum of JaSi only slightly exceeds 12 mA/cm2. Due to such biased effects on the two junctions, the photocurrent mismatch can be high up to 2.7 mA/cm2, leaving a lot of energy collected by μc-Si:H layer unused. Therefore, breaking the limitation of a-Si:H part under TM injection is crucial for further improving the device performance.
Table 1. Photocurrent densities under various nanoparttern configurations for TE, TM, and (TE + TM)/2, where daSi = 170 nm and dμcSi = 1700 nm. JaSi and JμcSi are both in mA/cm2. Photocurrent densities with the highest device outputs are in bold.
Above distinct photocurrent mismatch can be greatly decreased after redesigning the device dimension. Since the light absorption in bottom photoactive layer is enhanced in a more dramatic way by nanopatterning the top junction, it is necessary to slightly increase the contribution from a-Si:H layer (according to our calculation, daSi = 190 nm with dμcSi = 1700 nm). By doing so, a photocurrent mismatch is deliberately introduced into the original planar system, i.e., JaSi = 11.70 mA/cm2 and JμcSi = 10.75 mA/cm2. This reveals an important point concerning designing multi-junction solar cells: increasing the thickness of one junction without well balancing the photocurrents from the rest junctions will counter-intuitively degrade the device performance. However, a properly designed photocurrent mismatch allows it to be better matched with the introduction of optimized nanopattern, thus a higher device output. This can be seen from Table 2, which is the recalculation of Table 1 by using the new daSi = 190 nm. It is obvious that the photocurrent for (TE + TM)/2 can be up to 12.94 mA/cm2, which shows an enhancement of 20.4% (increment of 2.19 mA/cm2) compared to the planar case with Jsc = 10.75 mA/cm2. Such an enhancement is even higher than that obtained in single-junction solar cells [10, 11]. This is promising since it is a common increase of all junctions in the tandem system; in other words, the increment of Jtot can be almost doubled.
Table 2. Photocurrent densities under various nanopattern configurations for TE, TM, and (TE + TM)/2, where daSi = 190 nm and dμcSi = 1700 nm to be used in the rest parts of this paper. JaSi and JμcSi are both in mA/cm2. Photocurrent densities with the highest device outputs are in bold.
We then concentrate on the detailed response of the tandem solar cells under various device configurations and solar incident conditions. Plotted in Figs. 2(a) and 2(b) are the images of optical absorption Pabs (a-Si:H + μc-Si:H) versus wavelength λ and grating parameter b for TE and TM incidences, respectively, calculated from RCWA. The modal dispersion of the nanopatterned multilayer solar device with respect to b is observed quite complicated due to the rich interactions among multilayer Fabry-Perot, grating diffraction, and other hybrid modes. However, the shift of resonant peaks with varying b can still be seen, and under some b values strong peaks can be generated in long wavelength range, in which μc-Si:H dominates the light absorption.
Fig. 2 Pabs versus b and λ for TE (a) and TM (b) incidences. Total photocurrent Jtot ( = JaSi + JμcSi) versus b under TE and TM incidences, where the average value for TE and TM, i.e., (TE + TM)/2, and unpatterned case (i.e., w/o) are shown for reference.
Based on the calculated Pabs and typical solar spectrum (AM 1.5 [21]), the photocurrent Jtot can be obtained through spectral integration. Calculation results for w/o, TE, TM, and (TE + TM)/2 are displayed in Fig. 2(c). It shows that, with the introduction of nanopattern, Jtot can be improved in most of the parameter range. Exceptions are b < 50 nm for TM, b ~100 nm for TE, and b < 10 nm for (TE + TM)/2. The peaked values for all cases can be achieved when b ~390 nm. Further increasing b, the grating effect is weakened rapidly, driving the system to go back to w/o case at b = Λ = 500 nm [see Fig. 2(c)]. This reveals that properly engineered photonic crystal can indeed lead to significant improvement on the performance of a-Si:H/μc-Si:H tandem solar cells; moreover, there is a wide parametrical range with good enough performance, showing a high fabrication tolerance.
To find more information on how the device, especially the two photoactive junctions, responds to the solar incidence under nanopattern design, it is necessary to focus on the absorption characteristics of each junction. FEM results are exhibited in Fig. 3 for w/o, TE, and TM cases, respectively. b configuration with the highest Jtot (@ b = 390 nm) is used for TE and TM. Moreover, the corresponding reflection spectra are plotted as well in Fig. 3(b). It is obvious that a number of strong Pabs peaks and R dips appear in the long-wavelength region dominated by the bottom junction absorption (μc-Si:H layer). For example, at λ = 992 nm, Pabs = 59.41% and R = 6.501% for TE (Pabs = 1.436% and R = 97.2% for w/o); at λ = 1002 nm, Pabs = 15.94% and R = 47.19% for TM (Pabs = 1.144% and R = 97.2% for w/o). The significantly improved optical performance in bottom junction is the joint effect of 1) the suppressed device surface reflection and 2) the enhanced light absorption. The broadband enhancement in the long-wavelength region contributes to the large increment in JμcSi as listed in Table 1 and 2. For the top junction (a-Si:H layer), JaSi is also improved; however, the dominant mechanism is solely the suppressed R as there are no obvious peaks in the Pabs spectrum. Due to the enhanced absorption in the top junction, the bottom junction absorbs less at the crossing spectral range [i.e., 500 nm < λ < 700 nm in Fig. 3(a)] as also noted in [6].
Fig. 3 Absorption spectra Pabs of a-Si:H and μc-Si:H layers (a) and reflection spectrum of the entire device (b) under optimal grating configurations, i.e., b = 390 nm for both TE and TM. Results for w/o case are also included in this figure.
The spatial profiles of the absorbed power density in the core photoactive layers are plotted in Fig. 4, where TE at peak wavelength λ = 992 nm (a), TM at peak wavelength λ = 1002 nm (b), and w/o at λ = 992 nm (c) are considered. It is observed from Fig. 4(c) that without nanopatterning a-Si:H layer (w/o), although with the presence of Fabry-Perot modes arising from the planar multilayered waveguides [6], the power absorbed successfully by the photoactive layers is extremely low compared to the nanopatterned case. With properly engineered nanopattern introduced into the system, 1) a number of diffraction modes with various propagation directions can be generated [15] and 2) the a-Si:H/μc-Si:H interface has a higher index contrast, strengthening the cavity resonant effect; therefore, strong hybrid modes composed by Fabry-Perot and grating diffraction modes are excited, which contribute to the dramatically enhanced light absorption in μc-Si:H layer, as shown in Fig. 4(a) and 4(b). There are a large number of this kind of hybrid resonant mode; therefore, a broadband enhancement with sharp peaks can be obtained.
Fig. 4 Absorbed power density distributions inside the two junctions (i.e., a-Si:H and μc-Si:H) for two optimal wavelengths with peaked Pabs, i.e., λ = 992 nm for TE (b) and λ = 1002 nm for TM (b). The pattern of w/o case at λ = 992 nm is also plotted as reference. The rest system parameters are same to those used in Fig. 3.
We now focus on the Pabs and R response related to the degraded photocurrent observed in Fig. 2(c). Results are shown in Fig. 5 for TE (a) and TM (b), respectively, with b taken from Fig. 2(c) (see caption of Fig. 5). Under TE incidence, no consistent suppression of R or enhancement of Pabs can be obtained. Especially, in most of the interested spectrum the device absorption is degraded with exception only for μc-Si:H layer at λ < 600 nm and several peaks at long-wavelength region. The enhanced μc-Si:H absorption is due to the incomplete absorption by a-Si:H layer according to our FEM simulation (not shown). Under TM incidence, R is close to zero when λ < 380 nm, leading to very high Pabs contributed by the top junction [Fig. 5(a)]. However, no obvious optimization on the reflection and absorption performance can be seen in the remaining band. In the intersecting spectral region of the two junction, the enhanced Pabs for μc-Si:H is accompanied by the lower value for a-Si:H, leading to a reduced overall photocurrent Jtot. Especially, significantly reduced JaSi will become a key factor limiting the device output photocurrent. But fortunately Fig. 2(b) tells us that the range for b which degrades the cell performance is extremely narrow.
Fig. 5 Absorption spectra Pabs of a-Si:H and μc-Si:H layers (a) and reflection spectrum of the entire device (b) under two configurations degrading the system performance, i.e., b = 100 nm for TE and b = 25 nm for TM. Results for w/o case are also included in this figure.
The angular performance of the nanopatterned tandem solar cells is now investigated in the end of this study. The insensitivity of solar cells against the change of incident angle (θ) is an important feature in order to sustain the system performance under varying operating situations. Figure 6 exhibits the images of Jtot (in mA/cm2) versus b and θ for TE, TM, and (TE + TM)/2. It is found that max(Jtot) = 26.47 mA/cm2 for TE @ b = 305 nm and θ = 4°; max(Jtot) = 27.55 mA/cm2 for TM @ b = 390 nm and θ = 2°; and max(Jtot) = 26.94 mA/cm2 for (TE + TM)/2 @ b = 375 nm and θ = 2°. Therefore, the best performance is to be obtained for the incidence close to the normal direction. Moreover, a high Jtot can be sustained for θ ranging from 0° to over 80° for most b options. This is the typical feature of wide-angle enhancement, which can be easily seen from Fig. 7 where the effects of θ on Jtot for w/o cases (TE and TM have to be considered separately under oblique incidences) and optimized nanopatterned device under TE, TM, and (TE + TM)/2 are illustrated. A photocurrent increment of 3 ~4 mA/cm2 can be always achieved under solar illumination with θ < 70°.
Fig. 6 Jtot versus b and incident angle θ for TE (a) and TM (b) cases with their averaged value (TE + TM)/2 shown in (c).
Fig. 7 Angular dependence of Jtot vs θ for TE, TM, and (TE + TM)/2 at the corresponding b values obtained from Fig. 6.
However, we are interested normally in whether the wide-angle enhancement can be obtained for each junction. In order to find an answer, FEM simulation is used for the systems under various oblique incidences. Table 3 listed the detailed values of JaSi and JμcSi, where two typical incident angles (θ = 16° and 62°) are considered. More device output photocurrents are also highlighted in bold. It is obvious that even with a very large θ, the photocurrent from each junction shows no apparent degradation and thus the device output photocurrent can sustain an increment over 2 mA/cm2, showing the capability of achieving a wide-angle performance enhancement.
Table 3. JaSi and JμcSi for w/o under TE or TM and grating under TE, TM, or (TE + TM)/2 for two incident angels (i.e., 18° and 62°). JaSi and JμcSi are both in mA/cm2. For gratings under various situations, optimal values for b maximizing Jtot will be calculated and used.
4. Conclusion
In summary, we demonstrated the broadband and polarization/angularly insensitive absorption enhancement in a-Si:H/μc-Si:H tandem solar cells by nanopatterning the top a-Si:H junction as one dimensional nanophotonic crystal. The device optimization is realized by using RCWA and the physical insights into the special absorption enhancement mechanisms are obtained from FEM calculation. Considering the photocurrent matching conditions for all junctions, the solar cell dimension and the introduced nanopattern are optimally designed. By deliberately introducing an initial slight photocurrent mismatch in the tandem cell, the nanophotonic crystal design is able to contribute a broadband absorption enhancement and an output photocurrent increase by over 2 mA/cm2, originated from suppressed surface reflection loss, internal Fabry-Perot oscillation, and most importantly the greatly enhanced diffraction modes. We have also examined the sensitivity of the device performance on incident polarization and angle. It shows that the system performance can be sustained for both TE and TM with the low angular sensitivity.
Finally, we would like to indicate that there is a slight performance overestimation due to the use of perfect internal quantum process. As indicated in our previous papers [22, 23], the detailed electrical characteristics needs an electromagnetic and carrier transport calculation, which enables to examine simultaneously the optical and electrical response accurately. For tandem solar cells, the carrier transport modeling is still challenging due to the difficulty of treating the tunneling effect in a precise way. The progress of such a simulation will be reported in our forthcoming publications.
Acknowledgments
This work is supported by National Natural Science Foundation of China (No. 91233119, No. 61204066), “1000 Young Experts Plan” of China, and Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.
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