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  • Editor: Christian Seassal
  • Vol. 21, Iss. S4 — Jul. 1, 2013
  • pp: A607–A615
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Surface-concentrated light and efficient carrier collection in microhole-patterned Si solar cells

Joondong Kim, Eunsongyi Lee, Minkyu Ju, Hyunyub Kim, Junsin Yi, Sang-Jin Moon, Moon Seop Hyun, and Dong-Wook Kim  »View Author Affiliations


Optics Express, Vol. 21, Issue S4, pp. A607-A615 (2013)
http://dx.doi.org/10.1364/OE.21.00A607


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Abstract

We investigate photovoltaic characteristics of crystalline Si solar cells with microhole-patterned surface. We compare patterned samples with different hole-widths and periods with a planar counterpart. From the finite-difference time-domain simulation, the patterned and planar samples are expected to have similar short circuit current density, Jsc (difference: 1.2%). In contrast, the difference in the measured Jsc is as large as 12.6%. The simulated optical field patterns reveal that the sample with more significantly concentrated light near the surface has higher quantum efficiency due to more efficient carrier collection. We report the highest efficiency of 15.6% among the hole-patterned solar cells.

© 2013 OSA

1. Introduction

Si photovoltaics currently dominate the industry; however, the cost burden of Si wafers accounts for 40% of the module cost, and this has retarded the mass deployment of Si photovoltaics [1

1. J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

,2

2. T. Saga, “Advances in crystalline silicon solar cell technology for industrial mass production,” NPG Asia Mater. 2(3), 96–102 (2010). [CrossRef]

]. Obviously use of a thin light-absorber can relieve the cost burden, and hence minimization of ‘optical loss’, i.e., reflection and transmission, is required to raise the energy conversion efficiency of the thin-absorber solar cell [1

1. J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

]. Conventional approach to improve the light absorption is to use antireflection coating layer and surface texturing [3

3. J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar-cells,” IEEE Trans. Electron. Dev. 38(8), 1925–1934 (1991). [CrossRef]

,4

4. J. Ko, D. Gong, K. Pillai, K.-S. Lee, M. Ju, P. Choi, K.-R. Kim, J. Yi, and B. Choi, “Double layer SiNx:H films for passivation and anti-reflection coating of c-Si solar cells,” Thin Solid Films 519(20), 6887–6891 (2011). [CrossRef]

]. Recently front-surface patterning (one-dimensional, two-dimensional, regular, and random shapes) has been suggested as a new light trapping strategy [5

5. S. J. Jang, Y. M. Song, C. I. Yeo, C. Y. Park, J. S. Yu, and Y. T. Lee, “Antireflective property of thin film a-Si solar cell structures with graded refractive index structure,” Opt. Express 19(S2Suppl 2), A108–A117 (2011). [CrossRef] [PubMed]

17

17. A. Abass, K. Q. Le, A. Alù, M. Burgelman, and B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012). [CrossRef]

]. Wire or hole arrays, as whole absorbers or front patterns, have been intensively investigated, and they exhibit omni-directional and enhanced optical absorption, compared with the planar counterparts [18

18. N. Huang, C. Lin, and M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012). [CrossRef]

31

31. C. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. 112(11), 113107 (2012). [CrossRef]

]. Recent studies suggest that an efficient design may reduce the thickness of a Si wafer from the conventional 100-300 µm to less than 3 µm [9

9. K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012). [CrossRef] [PubMed]

,12

12. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]

,28

28. A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

30

30. L. Li, K.-Q. Peng, B. Hu, X. Wang, Y. Hu, X.-L. Wu, and S.-T. Lee, “Broadband optical absorption enhancement in silicon nanofunnel arrays for photovoltaic applications,” Appl. Phys. Lett. 100(22), 223902 (2012). [CrossRef]

]. Such significant reduction of the absorber materials is a very promising way to realize high efficiency and low-cost Si solar cells. In spite of such expectations, the promise has not been much fulfilled and the efficiencies of the patterned Si solar cells still have not surpassed those of the conventional cells [19

19. E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, “Nanowire solar cells,” Annu. Rev. Mater. Res. 41(1), 269–295 (2011). [CrossRef]

26

26. K.-T. Park, Z. Guo, H.-D. Um, J.-Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J.-H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express 19(101), A41–A50 (2011). [CrossRef] [PubMed]

]. In most calculations, only optical absorption is considered, but carrier transport and recombination are excluded. Thus, the calculated photocurrent is just a theoretical limit, less than the measured values in the real devices undergoing ‘electrical loss’. In real patterned structures, however, it is a formidable task to suppress surface and interface recombination [20

20. M. D. Kelzenberg, D. B. Turner-Evans, M. C. Putnam, S. W. Boettcher, R. M. Briggs, J. Y. Baek, N. S. Lewis, and H. A. Atwater, “High-performance Si microwire photovoltaics,” Energy Environ. Sci. 4(3), 866–871 (2011). [CrossRef]

24

24. H. P. Yoon, Y. A. Yuwen, C. E. Kendrick, G. D. Barber, N. J. Podraza, J. M. Redwing, T. E. Mallouk, C. R. Wronski, and T. S. Mayer, “Enhanced conversion efficiencies for pillar array solar cells fabricated from crystalline silicon with short minority carrier diffusion lengths,” Appl. Phys. Lett. 96(21), 213503 (2010). [CrossRef]

,28

28. A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

,29

29. T.-G. Chen, P. Yu, S.-W. Chen, F.-Y. Chang, B.-Y. Huang, Y.-C. Cheng, J.-C. Hsiao, C.-K. Li, and Y.-R. Wu, “Characteristics of large-scale nanohole arrays for thin-silicon photovoltaics ,” Prog. Photovolt: Res. Appl. (on-line published, DOI: ). [CrossRef]

]. Optimal devices definitely require a way to minimize both ‘optical’ and ‘electrical’ losses.

We present here investigation of 6 inch-sized crystalline Si (c-Si) solar cells, which have microhole-patterns on the surface. The depth of the hole patterns are only 2 μm, and hence the diode characteristics are almost the same of those for the planar samples without any signature of serious deterioration. The microhole-patterns improve optical absorption and calculated photocurrent increase is up to 1.2%. In contrast, the measured photocurrent increase is as large as 12.6%. Optical simulation shows that the microhole-patterns concentrate incoming solar radiation near the Si surface, enabling very efficient carrier collection. The measured quantum efficiency well supports the calculation results.

2. Microhole-patterned Si fabrication

Four different periodic microhole-patterns were simultaneously fabricated on a 6 inch c-Si wafer (Si technology Co.) with thickness of 675 µm and resistivity of 3-25 Ωcm [Fig. 1(a)
Fig. 1 (a) A photograph image of a hole-array-patterned 6 inch Si wafer. (b) A schematic illustration of the device structure. Each device was fabricated at an identical size (3 × 3 cm2). Scanning electron microscopy (SEM) images of (c) first quadrant, (d) second quadrant, (e) third quadrant, and (f) fourth quadrant, referred to as Area 1, Area 2, Area 3, and Area 4, respectively.
]. Designated photoresist (PR)-masks were shaped on four quadrants of the Si wafer by conventional photolithography processes. Subsequently, reactive ion etching was performed with an initial flow of C4F8 gas forming a polymer coating layer. SF6-plasma was used to etch the residual polymer layer and the exposed Si substrate. After the PR mask patterns were removed, periodic holes-array-patterns were achieved on four quadrants while holding a uniform depth (D) of about 2 µm.

These four patterns bear peculiar features in periods (P) and hole widths (W), which are factors to control the spectral photoresponse of Si absorbers [6

6. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). [CrossRef] [PubMed]

12

12. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]

]. The first and second quadrants have identical hole features but different periods, similar to the third and fourth quadrants (Hereafter referred to as Area 1, Area 2, Area 3, and Area 4). The geometric information is given in Table 1

Table 1. Geometric information and solar cell performances

table-icon
View This Table
.

The p-n junction was achieved by n-type doping on a p-type Si wafer. The hole-array-patterned 6 inch p-type Si wafer was n-doped in a diffusion furnace. Phosphorous oxychloride (POCl3) as an n-type doping source was drove-in a furnace for 40 min at 800 °C. A buffered hydrofluoric acid (5% HF) solution was used to remove phosphosilicate glass (PSG). A 70 nm thick-SiNx:H film, as an antireflection coating and passivation layer, was deposited by plasma-enhanced chemical vapor deposition (PECVD). For metal contacts, a conventional screen method was used to print Al paste and Ag paste for back and front metal contacts, respectively. After this, a co-firing step was performed in a furnace. The microhole-patterned device is schematically presented in Fig. 1(b). For comparison, planar and hole-patterned regions of 3 × 3 cm2 were simultaneously formed on each cell.

3. Device performance

All devices show quality p-n junction formation with good ideality factors, 1.69-1.84 [Fig. 2(a)
Fig. 2 Performance of microhole-patterned and the planar solar cells. Current-voltage characteristics (a) in the dark and (b) under one sun illumination. (c) EQE and (d) IQE profiles.
]. Only 2 μm-deep patterns do not significantly deteriorate the diode performance [28

28. A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

30

30. L. Li, K.-Q. Peng, B. Hu, X. Wang, Y. Hu, X.-L. Wu, and S.-T. Lee, “Broadband optical absorption enhancement in silicon nanofunnel arrays for photovoltaic applications,” Appl. Phys. Lett. 100(22), 223902 (2012). [CrossRef]

]. For the solar cell performance, it is crucial to form a quality junction to directly take advantage of the optical enhancement of the patterned absorbers; otherwise, the photovoltaic effect will fade away by recombination before harvesting photogenerated-carriers [20

20. M. D. Kelzenberg, D. B. Turner-Evans, M. C. Putnam, S. W. Boettcher, R. M. Briggs, J. Y. Baek, N. S. Lewis, and H. A. Atwater, “High-performance Si microwire photovoltaics,” Energy Environ. Sci. 4(3), 866–871 (2011). [CrossRef]

24

24. H. P. Yoon, Y. A. Yuwen, C. E. Kendrick, G. D. Barber, N. J. Podraza, J. M. Redwing, T. E. Mallouk, C. R. Wronski, and T. S. Mayer, “Enhanced conversion efficiencies for pillar array solar cells fabricated from crystalline silicon with short minority carrier diffusion lengths,” Appl. Phys. Lett. 96(21), 213503 (2010). [CrossRef]

]. The light current-voltage (I-V) characteristics were obtained under one sun illumination (100 mW/cm2) using a cell tester (McSicence, K3000). Under one sun illumination, the planar device exhibits an open circuit voltage (Voc) of 559 mV and a short circuit current density (Jsc) of 29.4 mA/cm2 with a fill factor (FF) of 66%, for an energy conversion efficiency (η) of 10.8%. A substantial improvement was obtained in Area 2 for η = 12.7% accompanied with improved FF (68.4%) and Jsc (33.1 mA/cm2). It should be noted that Area 2 provides the highest Jsc.

Considering the similar shunt resistance (Rsh) values (50.4-56.0 Ω/□), the series resistance (Rs) dominates the photovoltaic behavior by controlling the current flow and the contact resistance [1

1. J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

]. Considering the simultaneous fabrication processes, the contact resistance should be similar for all the devices. Thus, the current flow is a determining factor of Rs and Area 2 has the lowest value of 264 mΩ. All microhole-patterned devices were investigated for quantum efficiencies (QE) (Figs. 2(c) and 2(d)). The external QE (EQE) of all the microhole-array patterns is much improved over broad wavelengths compared to that of the planar device. The internal QE (IQE) determines the collection probability of photogenerated electron-hole pairs. All the hole-patterns exhibit strongly improved IQE values, indicating the enhanced carrier collection.

4. Simulation and measurement

4.1. Optical simulation method

To describe real-space optical electric field distributions in the Si absorbers, the Maxwell’s equations were numerically solved by the finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions). A broad-band pulse (wavelength 400-1100 nm) was used to simulate a plane wave incident from the top; the polarization and propagation directions of this wave were parallel to the x-axis and the z-axis, respectively, as shown in Fig. 3(a)
Fig. 3 (a) Schematic illustration of the hole-patterned sample used for the FDTD modeling. (b) Planar Si absorber shows an exponential decay of electric field at the top surface. (c) SEM images and electric field distribution for Area 1-Area 4 at λ = 660 nm.
. The hole-array pattern has a periodic structure, and hence the electric field distribution in a unit cell can be simulated by using the periodic boundary conditions. Perfectly matched layer boundary conditions, which completely absorb incident radiation, were used at the top and bottom faces of the unit cell in order to avoid non-meaningful reflection from the simulation boundaries. Monitors, located at the surface above the hole-patterns, were used to measure the power of the incident and reflected waves, in order to estimate reflectance.

4.2. Comparison of simulations and measurements

For short wavelengths (λ) below 400 nm, the incident light decays out within a shallow surface region due to the high absorption coefficient of Si, resulting in little difference in the optical field distribution regardless of the microhole designs [28

28. A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

,29

29. T.-G. Chen, P. Yu, S.-W. Chen, F.-Y. Chang, B.-Y. Huang, Y.-C. Cheng, J.-C. Hsiao, C.-K. Li, and Y.-R. Wu, “Characteristics of large-scale nanohole arrays for thin-silicon photovoltaics ,” Prog. Photovolt: Res. Appl. (on-line published, DOI: ). [CrossRef]

]. Meanwhile, a noticeable difference has been observed for longer wavelengths. As shown in Fig. 3(c), the electric field intensity in the near surface region of the hole-patterned Si wafers is much larger than that of the planar counterpart, which can be attributed to the geometric antireflection effect due to their low optical density and guided-mode-excitation [11

11. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun 3(692), 692 (2012). [CrossRef] [PubMed]

19

19. E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, “Nanowire solar cells,” Annu. Rev. Mater. Res. 41(1), 269–295 (2011). [CrossRef]

,26

26. K.-T. Park, Z. Guo, H.-D. Um, J.-Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J.-H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express 19(101), A41–A50 (2011). [CrossRef] [PubMed]

31

31. C. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. 112(11), 113107 (2012). [CrossRef]

]. All the patterned structures show a significantly enhanced electric field in both the hole-connect region (A-A’) and the interconnect region (B-B’). In contrast, the field intensity of planar Si decays exponentially as a function of distance from the surface [Fig. 3(b)]. This indicates that the microhole-patterns concentrate incoming light near the surface. Thus, more photogenerated carriers are created close to a space charge region with a higher collection probability than those in the neutral bulk region, leading to the enhanced QE performance.

Absorption enhancement (AE), defined as the absorption ratio of the hole-pattern to the planar reference, clearly shows that the microhole-patterned samples have higher optical absorption than that of the reference over broad wavelengths [Fig. 4(a)
Fig. 4 (a) Light absorption enhancement spectra of microhole-patterned and planar Si wafers with infinite optical thickness. (b) Comparison results of calculated and measured photocurrent.
]. The less AE of hole-patterns is observed around 600 nm, where the planar reference shows higher absorption due to the SiNx layer-induced complete destructive interference. The filling ratio (FR), defined as (1 − fW2/P2), should be considered for AE effects (f = 1 for square-shaped holes in Area 3 and 4: f = π/4 for circular holes in Area 1 and 2). The overall AE could be reduced by increasing the FR because a hole-array with a larger FR behaves more like planar Si [12

12. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]

,18

18. N. Huang, C. Lin, and M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012). [CrossRef]

,29

29. T.-G. Chen, P. Yu, S.-W. Chen, F.-Y. Chang, B.-Y. Huang, Y.-C. Cheng, J.-C. Hsiao, C.-K. Li, and Y.-R. Wu, “Characteristics of large-scale nanohole arrays for thin-silicon photovoltaics ,” Prog. Photovolt: Res. Appl. (on-line published, DOI: ). [CrossRef]

31

31. C. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. 112(11), 113107 (2012). [CrossRef]

]. As the FR becomes smaller, the antireflection effect becomes more significant by lowering the optical density. The smaller FR, however, also decreases the volume of the absorber in the surface region, where significant optical field concentration appears. Figure 4(b) shows calculated Jsc obtained from the following equation,
Jsc,calculated=400nmλgI(λ)A(λ)eλhcdλ
(1)
where I(λ) is the air mass (AM) 1.5 solar spectral irradiance, A(λ) is the Si absorption, and λg is the wavelength corresponding to the bandgap of Si (1100 nm) [32

32. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

]. The calculated Jsc values for the samples are very similar: the difference between the largest one (35.1 mA/cm2 for Area 2) and the smallest one (34.6 mA/cm2 for the planar reference) is only 1.2%. Figure 4(a) shows that the largest AE is less than 10% and the AE peak wavelength is far from that of the maximum solar spectral irradiation intensity (500 nm). This well explains the reason why the calculated Jsc values of all the samples are more or less similar [Fig. 4(b)]. In contrast, the measured Jsc values show noticeable difference: the difference between the largest one (33.1 mA/cm2 for Area 2) and the smallest one (29.4 mA/cm2 for the planar reference) is as large as 12.6%. It should be noted that Area 2 has the least discrepancy in the calculated and the measured photocurrent. The discrepancy between the measured and calculated photocurrent can be caused by any disorder in the fabricated patterns [6

6. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). [CrossRef] [PubMed]

]. In such a case, the measured photocurrent for the pattern with dense array of small holes, i.e., Area 2 in this study, would show significant reduction compared with the calculated photocurrent. However, the experimental data show opposite tendency. Thus, the imperfection in the patterned structures may not be the primary reason to explain the discrepancy shown in Fig. 4(b).

It would be also interesting to compare two groups with identical hole size: one group of Area 1 and Area 2 (small hole) and the other of Area 3 and Area 4 (large hole). For each group, the hole-pattern with larger sidewall surface area (i.e., smaller FR) would undergo more serious surface recombination and exhibit lower photocurrent. The experimental data, however, show opposite tendency. The calculation of Jsc was performed by assuming perfect carrier collection, as like others’ calculation studies [9

9. K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012). [CrossRef] [PubMed]

,12

12. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]

15

15. R. Biswas and C. Xu, “Nano-crystalline silicon solar cell architecture with absorption at the classical 4n2 limit,” Opt. Express 19(S4Suppl 4), A664–A672 (2011). [CrossRef] [PubMed]

,28

28. A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

,32

32. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

]. Therefore, the comparison of the calculation and the experiments in Fig. 4(b) suggests that Area 2 (the planar reference) should have the largest (smallest) carrier collection efficiency in spite of the larger surface area.

4.3. Junction formation in a Si absorber

We have performed the low-voltage SEM (LVSEM) analysis to investigate the junction formation in the Si absorber. Figures 5(a)
Fig. 5 (a) A LVSEM image of a patterned Si absorber coated with a 70 nm SiNx film. A n-type emitter layer (thickness: 270 nm) was formed adjacent to a p-type Si base. (b) A schematic diagram of the cross-sectional view of the surface region.
and 5(b) show an LVSEM image and a schematic diagram of the cross-sectional view of the solar cell, respectively. Considering the doping concentrations of the heavily doped n-emitter (1018 cm−3) and the moderately doped p-base (1016 cm−3), the depletion region is primarily formed in the p-base region with a 320 nm thickness.

The photocurrent is determined by the collection probability of photogenerated carriers as well as the absorption of the incident light in the absorber. For the depletion region where a strong electric field exists, the probability of carrier collection is close to unity due to the efficient separation of electron-hole pairs. The FDTD simulation showed formation of the strongest optical field intensity near the top surface of the microhole-patterned wafers [Fig. 3(c)]. In particular, the overall optical field intensity near the surface is the largest in Area 2 among all the four microhole-patterned samples. Thus, the experimental Jsc value of Area 2 is close to the calculated value (i.e., a theoretical limit).

4.4. Micron-thick microhole-patterned Si solar cell

We have performed calculations for a 3-μm-thick Si absorber with an Al back contact. Thin Si has weak absorption at long wavelengths and thus requires a back reflector for utilizing the transmitted light. Notable AE can be achieved in microhole-patterned structures with a thin absorber [Fig. 6(a)
Fig. 6 (a) Light absorption enhancement spectra for a 3 μm-thick Si absorber with a thin 100 nm-Al back contact. Area 2 shows notable enhancement at long wavelengths. (b) Calculated Jsc values and volume ratio of Si according to the hole-patterned structures.
]. For Area 2, the AE is increased by 250% from that of a planar Si slab at a wavelength of 1100 nm. Its Jsc (25.2 mA/cm2) is larger than that of a planar Si reference with the identical thickness, even though only about 70% of Si is used compared with the planar sample [Fig. 6(b)]. These calculation results clearly reveal that the microhole-patterned absorbers have enhanced optical absorption near the surface region with high carrier collection probability, allowing higher energy conversion efficiency. This suggests that the spatial distribution of the high optical field intensity as well as the amount of the total optical absorption should be carefully considered to raise the solar cell efficiency.

Moreover, it should be noted that the estimated Jsc of our 3-μm-thick microhole-patterned Si solar cell is comparable to the calculated result of patterned c-Si solar cells with optimized square two-dimensional lattices in Bozzola et al.’s recent report [12

12. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]

]. It has been reported that the choice of antireflection coating layer and thickness should be varied depending on the hole-pattern geometry [3

3. J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar-cells,” IEEE Trans. Electron. Dev. 38(8), 1925–1934 (1991). [CrossRef]

]. In addition, optimal design of the etch depth and the antireflection coating layer thickness depends on the thickness of the Si absorber [32

32. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

,33

33. L. Zeng, P. Bermel, Y. Yi, N.-N. Feng, B. A. Alamariu, C.-Y. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Optimized textured photonic crystal backside reflector for Si thin film solar cells,” Proc. MRS 974E, CC02–CC06 (2007).

]. Thus, optimization of the geometric patterns, based on all these considerations, will raise the efficiency of the hole-patterned c-Si solar cells. In order to achieve the ultimate efficiency, sophisticated design of electrodes can be adopted and will allow us to take advantage of plasmonic enhancement [7

7. S. Y. Chou and W. Ding, “Ultrathin, high-efficiency, broad-band, omni-acceptance, organic solar cells enhanced by plasmonic cavity with subwavelength hole array,” Opt. Express 21(S1Suppl 1), A60–A76 (2013). [CrossRef] [PubMed]

]. Through all these efforts, patterned c-Si solar cells can provide an extension of the optical thickness by efficient light trapping in the long wavelengths.

4.5. Improved electrical designs

As shown in Table 1, the microhole-patterned samples exhibit distinct characteristics in not only the optical absorption spectra but also the photovoltaic device parameters, including FF and parasitic resistance. Such electrical factors can significantly affect the energy conversion efficiency [1

1. J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

]. Considering the electrical loss, Area 3 is the worst sample. The efficiency of Area 3 is 10.8%, smaller than the value of 12.0% for Area 4, although Jsc of Area 3 is higher than that of Area 4 [Fig. 4(b)]. A clue can be found from the highest series resistance (Rs) of Area 3, since Area 3 has too low FR. Hole-patterns optically generate more photo-carriers, as discussed above. From the electrical aspect, electrons should pass through the patterned front surface region of the absorber to be collected by the top metal electrode. If FR is too small, then a current crowding effect occurs resulting in increase of Rs [34

34. K. Kotsovos and K. Misiakos, “Three-dimensional simulation of carrier transport effects in the base of rear point contact silicon solar cells,” J. Appl. Phys. 89(4), 2491–2496 (2001). [CrossRef]

]. This eventually lowers the overall efficiency despite the enhanced photocurrent.

As a remark, we have investigated the optimal grid design for Area 2 and have recently improved the efficiency up to 15.6%. The former design of Area 2 (η = 12.7%) had 36 fingers (Grid 1). Each finger width was 30 μm to give a total shading ratio (SR) of 4.30%. The hole-arrayed Si absorbers produce a high current density over the design range resulting in current crowding. The improved grid pattern (Grid 2) has 23 fingers with a widened width of 45 μm. Although, this design has a larger SR of 5.31%, which induces a higher optical loss, there are electrical benefits for decreasing Rs (199 mΩ) and increasing Rsh (292.1 Ω/□) from 264 mΩ and 50.4 Ω/□, respectively. As a result, Grid 2 provides superior improvements, yielding for Jsc of 34.45 mA/cm2 and FF of 72.9%. This clearly demonstrates that a further investigation is highly required in terms of electrical design, and thus to fully exploit the optical advantage of the microhole-patterned wafers.

5. Conclusion

In conclusion, we have investigated photovoltaic characteristics of a microhole-patterned crystalline Si solar cell. The microhole-patterns effectively enhance the electric field intensity near the surface, where the depletion region can effectively separates the photo-generated electron-hole pairs, yielding 18% enhanced efficiency compared to that of a planar Si wafer. In patterned absorber, the electric field distribution is determined by various optical phenomena, including scattering, interference, and resonant mode excitation. In addition, such patterned structures should affect electrical parameters of the device, including parasitic resistance and fill factor. Therefore simultaneous consideration of both optical and electrical aspects is crucial to improve the energy conversion efficiency of the solar cell. Among the microhole-patterned solar cells, we have achieved the highest efficiency of 15.6%. Moreover, our patterned structures can provide a viable approach to realizing cost-effective micron-thick Si solar cells due to their efficient light trapping for long wavelengths. We anticipate that a further investigation would accomplish the theoretical expectation for large scale solar cell applications.

Acknowledgments

The authors acknowledge the financial support of the Korea Institute of Energy Technology Evaluation and Planning grant funded by the Ministry of Knowledge and Economy (KETEP-20113030010110) and the Converging Research Center Program through the Ministry of Education, Science and Technology (MEST, 2012K001278). E.L. and D.-W.K were also supported by the Pioneer Research Center Program (2010-0002231) funded by MEST.

References and links

1.

J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

2.

T. Saga, “Advances in crystalline silicon solar cell technology for industrial mass production,” NPG Asia Mater. 2(3), 96–102 (2010). [CrossRef]

3.

J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar-cells,” IEEE Trans. Electron. Dev. 38(8), 1925–1934 (1991). [CrossRef]

4.

J. Ko, D. Gong, K. Pillai, K.-S. Lee, M. Ju, P. Choi, K.-R. Kim, J. Yi, and B. Choi, “Double layer SiNx:H films for passivation and anti-reflection coating of c-Si solar cells,” Thin Solid Films 519(20), 6887–6891 (2011). [CrossRef]

5.

S. J. Jang, Y. M. Song, C. I. Yeo, C. Y. Park, J. S. Yu, and Y. T. Lee, “Antireflective property of thin film a-Si solar cell structures with graded refractive index structure,” Opt. Express 19(S2Suppl 2), A108–A117 (2011). [CrossRef] [PubMed]

6.

C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). [CrossRef] [PubMed]

7.

S. Y. Chou and W. Ding, “Ultrathin, high-efficiency, broad-band, omni-acceptance, organic solar cells enhanced by plasmonic cavity with subwavelength hole array,” Opt. Express 21(S1Suppl 1), A60–A76 (2013). [CrossRef] [PubMed]

8.

J. S. Li, H. Y. Yu, Y. L. Li, F. Wang, M. F. Yang, and S. M. Wong, “Low aspect-ratio hemispherical nanopit surface texturing for enhancing light absorption in crystalline Si thin film-based solar cells,” Appl. Phys. Lett. 98(2), 021905 (2011). [CrossRef]

9.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012). [CrossRef] [PubMed]

10.

M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett. 12(6), 2894–2900 (2012). [CrossRef] [PubMed]

11.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun 3(692), 692 (2012). [CrossRef] [PubMed]

12.

A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]

13.

X. Meng, V. Depauw, G. Gomard, O. El Daif, C. Trompoukis, E. Drouard, C. Jamois, A. Fave, F. Dross, I. Gordon, and C. Seassal, “Design, fabrication and optical characterization of photonic crystal assisted thin film monocrystalline-silicon solar cells,” Opt. Express 20(S4Suppl 4), A465–A475 (2012). [CrossRef] [PubMed]

14.

S.-K. Kim, K.-D. Song, and H.-G. Park, “Design of input couplers for efficient silicon thin film solar absorbers,” Opt. Express 20(S6), A997–A1004 (2012). [CrossRef]

15.

R. Biswas and C. Xu, “Nano-crystalline silicon solar cell architecture with absorption at the classical 4n2 limit,” Opt. Express 19(S4Suppl 4), A664–A672 (2011). [CrossRef] [PubMed]

16.

J. Kim, M. Kim, H. Kim, K. Song, E. Lee, D.-W. Kim, J.-H. Yun, S. Lee, C. Jeong, and J. Yi, “Effective light management of three-dimensionally patterned transparent conductive oxide layers,” Appl. Phys. Lett. 101(14), 143904 (2012). [CrossRef]

17.

A. Abass, K. Q. Le, A. Alù, M. Burgelman, and B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B 85(11), 115449 (2012). [CrossRef]

18.

N. Huang, C. Lin, and M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012). [CrossRef]

19.

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, “Nanowire solar cells,” Annu. Rev. Mater. Res. 41(1), 269–295 (2011). [CrossRef]

20.

M. D. Kelzenberg, D. B. Turner-Evans, M. C. Putnam, S. W. Boettcher, R. M. Briggs, J. Y. Baek, N. S. Lewis, and H. A. Atwater, “High-performance Si microwire photovoltaics,” Energy Environ. Sci. 4(3), 866–871 (2011). [CrossRef]

21.

M. Gharghi, E. Fathi, B. Kante, S. Sivoththaman, and X. Zhang, “Heterojunction silicon microwire solar cells,” Nano Lett. 12(12), 6278–6282 (2012). [CrossRef] [PubMed]

22.

E. Lee, Y. Kim, M. Gwon, D.-W. Kim, S.-H. Baek, and J. H. Kim, “Comparative experimental and simulative investigations of radial p-n junction Si microwire array solar cells,” Sol. Energy Mater. Sol. Cells 103, 93–97 (2012). [CrossRef]

23.

D. R. Kim, C. H. Lee, P. M. Rao, I. S. Cho, and X. Zheng, “Hybrid Si microwire and planar solar cells: passivation and characterization,” Nano Lett. 11(7), 2704–2708 (2011). [CrossRef] [PubMed]

24.

H. P. Yoon, Y. A. Yuwen, C. E. Kendrick, G. D. Barber, N. J. Podraza, J. M. Redwing, T. E. Mallouk, C. R. Wronski, and T. S. Mayer, “Enhanced conversion efficiencies for pillar array solar cells fabricated from crystalline silicon with short minority carrier diffusion lengths,” Appl. Phys. Lett. 96(21), 213503 (2010). [CrossRef]

25.

J. Kim, J.-H. Yun, C.-S. Han, Y. J. Cho, J. Park, and Y. C. Park, “Multiple silicon nanowires-embedded Schottky solar cell,” Appl. Phys. Lett. 95(14), 143112 (2009). [CrossRef]

26.

K.-T. Park, Z. Guo, H.-D. Um, J.-Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J.-H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express 19(101), A41–A50 (2011). [CrossRef] [PubMed]

27.

J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, M. S. Hyun, J. M. Yang, and J.-H. Lee, “A waferscale Si wire solar cell using radial and bulk p-n junctions,” Nanotechnology 21(44), 445303 (2010). [CrossRef] [PubMed]

28.

A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

29.

T.-G. Chen, P. Yu, S.-W. Chen, F.-Y. Chang, B.-Y. Huang, Y.-C. Cheng, J.-C. Hsiao, C.-K. Li, and Y.-R. Wu, “Characteristics of large-scale nanohole arrays for thin-silicon photovoltaics ,” Prog. Photovolt: Res. Appl. (on-line published, DOI: ). [CrossRef]

30.

L. Li, K.-Q. Peng, B. Hu, X. Wang, Y. Hu, X.-L. Wu, and S.-T. Lee, “Broadband optical absorption enhancement in silicon nanofunnel arrays for photovoltaic applications,” Appl. Phys. Lett. 100(22), 223902 (2012). [CrossRef]

31.

C. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. 112(11), 113107 (2012). [CrossRef]

32.

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

33.

L. Zeng, P. Bermel, Y. Yi, N.-N. Feng, B. A. Alamariu, C.-Y. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Optimized textured photonic crystal backside reflector for Si thin film solar cells,” Proc. MRS 974E, CC02–CC06 (2007).

34.

K. Kotsovos and K. Misiakos, “Three-dimensional simulation of carrier transport effects in the base of rear point contact silicon solar cells,” J. Appl. Phys. 89(4), 2491–2496 (2001). [CrossRef]

OCIS Codes
(040.5350) Detectors : Photovoltaic
(040.6040) Detectors : Silicon
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.6875) Diffraction and gratings : Three-dimensional fabrication
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Photovoltaics

History
Original Manuscript: April 16, 2013
Revised Manuscript: May 12, 2013
Manuscript Accepted: May 13, 2013
Published: May 22, 2013

Citation
Joondong Kim, Eunsongyi Lee, Minkyu Ju, Hyunyub Kim, Junsin Yi, Sang-Jin Moon, Moon Seop Hyun, and Dong-Wook Kim, "Surface-concentrated light and efficient carrier collection in microhole-patterned Si solar cells," Opt. Express 21, A607-A615 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S4-A607


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References

  1. J. Nelson, The Physics of Solar Cells (Imperial College, 2003).
  2. T. Saga, “Advances in crystalline silicon solar cell technology for industrial mass production,” NPG Asia Mater.2(3), 96–102 (2010). [CrossRef]
  3. J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar-cells,” IEEE Trans. Electron. Dev.38(8), 1925–1934 (1991). [CrossRef]
  4. J. Ko, D. Gong, K. Pillai, K.-S. Lee, M. Ju, P. Choi, K.-R. Kim, J. Yi, and B. Choi, “Double layer SiNx:H films for passivation and anti-reflection coating of c-Si solar cells,” Thin Solid Films519(20), 6887–6891 (2011). [CrossRef]
  5. S. J. Jang, Y. M. Song, C. I. Yeo, C. Y. Park, J. S. Yu, and Y. T. Lee, “Antireflective property of thin film a-Si solar cell structures with graded refractive index structure,” Opt. Express19(S2Suppl 2), A108–A117 (2011). [CrossRef] [PubMed]
  6. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt.34(14), 2476–2482 (1995). [CrossRef] [PubMed]
  7. S. Y. Chou and W. Ding, “Ultrathin, high-efficiency, broad-band, omni-acceptance, organic solar cells enhanced by plasmonic cavity with subwavelength hole array,” Opt. Express21(S1Suppl 1), A60–A76 (2013). [CrossRef] [PubMed]
  8. J. S. Li, H. Y. Yu, Y. L. Li, F. Wang, M. F. Yang, and S. M. Wong, “Low aspect-ratio hemispherical nanopit surface texturing for enhancing light absorption in crystalline Si thin film-based solar cells,” Appl. Phys. Lett.98(2), 021905 (2011). [CrossRef]
  9. K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett.12(3), 1616–1619 (2012). [CrossRef] [PubMed]
  10. M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett.12(6), 2894–2900 (2012). [CrossRef] [PubMed]
  11. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3(692), 692 (2012). [CrossRef] [PubMed]
  12. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]
  13. X. Meng, V. Depauw, G. Gomard, O. El Daif, C. Trompoukis, E. Drouard, C. Jamois, A. Fave, F. Dross, I. Gordon, and C. Seassal, “Design, fabrication and optical characterization of photonic crystal assisted thin film monocrystalline-silicon solar cells,” Opt. Express20(S4Suppl 4), A465–A475 (2012). [CrossRef] [PubMed]
  14. S.-K. Kim, K.-D. Song, and H.-G. Park, “Design of input couplers for efficient silicon thin film solar absorbers,” Opt. Express20(S6), A997–A1004 (2012). [CrossRef]
  15. R. Biswas and C. Xu, “Nano-crystalline silicon solar cell architecture with absorption at the classical 4n2 limit,” Opt. Express19(S4Suppl 4), A664–A672 (2011). [CrossRef] [PubMed]
  16. J. Kim, M. Kim, H. Kim, K. Song, E. Lee, D.-W. Kim, J.-H. Yun, S. Lee, C. Jeong, and J. Yi, “Effective light management of three-dimensionally patterned transparent conductive oxide layers,” Appl. Phys. Lett.101(14), 143904 (2012). [CrossRef]
  17. A. Abass, K. Q. Le, A. Alù, M. Burgelman, and B. Maes, “Dual-interface gratings for broadband absorption enhancement in thin-film solar cells,” Phys. Rev. B85(11), 115449 (2012). [CrossRef]
  18. N. Huang, C. Lin, and M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt.14(2), 024004 (2012). [CrossRef]
  19. E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, “Nanowire solar cells,” Annu. Rev. Mater. Res.41(1), 269–295 (2011). [CrossRef]
  20. M. D. Kelzenberg, D. B. Turner-Evans, M. C. Putnam, S. W. Boettcher, R. M. Briggs, J. Y. Baek, N. S. Lewis, and H. A. Atwater, “High-performance Si microwire photovoltaics,” Energy Environ. Sci.4(3), 866–871 (2011). [CrossRef]
  21. M. Gharghi, E. Fathi, B. Kante, S. Sivoththaman, and X. Zhang, “Heterojunction silicon microwire solar cells,” Nano Lett.12(12), 6278–6282 (2012). [CrossRef] [PubMed]
  22. E. Lee, Y. Kim, M. Gwon, D.-W. Kim, S.-H. Baek, and J. H. Kim, “Comparative experimental and simulative investigations of radial p-n junction Si microwire array solar cells,” Sol. Energy Mater. Sol. Cells103, 93–97 (2012). [CrossRef]
  23. D. R. Kim, C. H. Lee, P. M. Rao, I. S. Cho, and X. Zheng, “Hybrid Si microwire and planar solar cells: passivation and characterization,” Nano Lett.11(7), 2704–2708 (2011). [CrossRef] [PubMed]
  24. H. P. Yoon, Y. A. Yuwen, C. E. Kendrick, G. D. Barber, N. J. Podraza, J. M. Redwing, T. E. Mallouk, C. R. Wronski, and T. S. Mayer, “Enhanced conversion efficiencies for pillar array solar cells fabricated from crystalline silicon with short minority carrier diffusion lengths,” Appl. Phys. Lett.96(21), 213503 (2010). [CrossRef]
  25. J. Kim, J.-H. Yun, C.-S. Han, Y. J. Cho, J. Park, and Y. C. Park, “Multiple silicon nanowires-embedded Schottky solar cell,” Appl. Phys. Lett.95(14), 143112 (2009). [CrossRef]
  26. K.-T. Park, Z. Guo, H.-D. Um, J.-Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J.-H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express19(101), A41–A50 (2011). [CrossRef] [PubMed]
  27. J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, M. S. Hyun, J. M. Yang, and J.-H. Lee, “A waferscale Si wire solar cell using radial and bulk p-n junctions,” Nanotechnology21(44), 445303 (2010). [CrossRef] [PubMed]
  28. A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012). [CrossRef] [PubMed]
  29. T.-G. Chen, P. Yu, S.-W. Chen, F.-Y. Chang, B.-Y. Huang, Y.-C. Cheng, J.-C. Hsiao, C.-K. Li, and Y.-R. Wu, “Characteristics of large-scale nanohole arrays for thin-silicon photovoltaics,” Prog. Photovolt: Res. Appl. (on-line published, DOI: ). [CrossRef]
  30. L. Li, K.-Q. Peng, B. Hu, X. Wang, Y. Hu, X.-L. Wu, and S.-T. Lee, “Broadband optical absorption enhancement in silicon nanofunnel arrays for photovoltaic applications,” Appl. Phys. Lett.100(22), 223902 (2012). [CrossRef]
  31. C. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys.112(11), 113107 (2012). [CrossRef]
  32. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express15(25), 16986–17000 (2007). [CrossRef] [PubMed]
  33. L. Zeng, P. Bermel, Y. Yi, N.-N. Feng, B. A. Alamariu, C.-Y. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Optimized textured photonic crystal backside reflector for Si thin film solar cells,” Proc. MRS974E, CC02–CC06 (2007).
  34. K. Kotsovos and K. Misiakos, “Three-dimensional simulation of carrier transport effects in the base of rear point contact silicon solar cells,” J. Appl. Phys.89(4), 2491–2496 (2001). [CrossRef]

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