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  • Editor: Christian Seassal
  • Vol. 21, Iss. S3 — May. 6, 2013
  • pp: A515–A527
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Photonic crystals and optical mode engineering for thin film photovoltaics

Guillaume Gomard, Romain Peretti, Emmanuel Drouard, Xianqin Meng, and Christian Seassal  »View Author Affiliations


Optics Express, Vol. 21, Issue S3, pp. A515-A527 (2013)
http://dx.doi.org/10.1364/OE.21.00A515


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Abstract

In this paper, we present the design, analysis, and experimental results on the integration of 2D photonic crystals in thin film photovoltaic solar cells based on hydrogenated amorphous silicon. We introduce an analytical approach based on time domain coupled mode theory to investigate the impact of the photon lifetime and anisotropy of the optical resonances on the absorption efficiency. Specific design rules are derived from this analysis. We also show that, due to the specific properties of the photonic crystal resonances, the angular acceptance of such solar cells is particularly high. Rigorous Coupled Wave Analysis simulations show that the absorption in the a-Si:H active layers, integrated from 300 to 750nm, is only decreased from 65.7% to 60% while the incidence angle is increased from 0 to 55°. Experimental results confirm the stability of the incident light absorption in the patterned stack, for angles of incidence up to 50°.

© 2013 OSA

1. Introduction

The recent development of nanophotonics has triggered the emergence of novel concepts for light management in photovoltaic solar cells. This includes incident light trapping and strategies to control light absorption in thin film solar cells. The interest of the whole range of accessible nanophotonic structures has been considered by an increasing number of research groups during the past years (see e.g [1

1. A. Naqavi, F.-J. Haug, C. Battaglia, H. P. Herzig, and C. Ballif, “Light trapping in solar cells at the extreme coupling limit,” J. Opt. Soc. Am. B 30(1), 13–20 (2013). [CrossRef]

,2

2. Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109(17), 173901 (2012). [CrossRef] [PubMed]

].).

Periodic dielectric structures like diffraction gratings positioned at the back of solar cells appear promising to increase the photon path length, especially for high wavelengths, i.e. when the absorption of the active material is low [3

3. 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]

]. On the top of the devices, novel anti-reflecting structures have been proposed, based on the integration of sub-wavelength structures with a large range of shapes [4

4. R. Bouffaron, L. Escoubas, J. J. Simon, P. Torchio, F. Flory, G. Berginc, and P. Masclet, “Enhanced antireflecting properties of micro-structured top-flat pyramids,” Opt. Express 16(23), 19304–19309 (2008). [CrossRef] [PubMed]

,5

5. Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small 6(9), 984–987 (2010). [CrossRef] [PubMed]

], up to complex multi-scale biomimetic structures. On the other hand the use of plasmonic resonances to control light capture and absorption by scattering or near field enhancement has been proposed by many groups (see e.g [6

6. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

].). In particular, various ways to implement such light trapping strategies on solar cells based on hydrogenated amorphous silicon (a-Si:H), have been introduced during the past years. Most approaches rely on the deposition of more or less conformal layers onto a patterned substrate [7

7. M. Despeisse, C. Battaglia, M. Boccard, G. Bugnon, M. Charrière, P. Cuony, S. Hänni, L. Löfgren, F. Meillaud, G. Parascandolo, T. Söderström, and C. Ballif, “Optimization of thin film silicon solar cells on highly textured substrates,” Phys. Status Solidi A 208(8), 1863–1868 (2011). [CrossRef]

9

9. 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]

]. Using an efficient light trapping strategy on such a-Si:H-based devices appears particularly relevant since it could lead to a high absorption level, while reducing the active layer thickness, and therefore the impact of bulk carrier recombination.

Although all these approaches are promising and could end up in a real increase of the conversion efficiency, sometimes larger than the one calculated considering the lambertian limit, a more in-depth modification of the optical properties of the absorber is needed if one wishes to drastically reduce the thickness of the solar cell, and therefore its cost, or to significantly increase its efficiency. To reach this goal, photonic crystals (PhC) may offer their wide variety of optical modes, including slow light or Fano-like resonances, while they do not suffer from the parasitic absorption of metallic nanostructures. In 2008, a novel approach was proposed to reach an in-depth modification of the optical density of state, thanks to the use of slow light Bloch modes standing over the light line of PhC. This is achieved by patterning the absorbing layer itself as a planar 1D or 2D PhC [10

10. C. Seassal, Y. Park, A. Fave, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” Proc. SPIE 7002, 700207, 700207-8 (2008). [CrossRef]

13

13. S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express 18(5), 4260–4274 (2010). [CrossRef] [PubMed]

]. If all kinds of absorbing materials could be patterned as such structures, it appears more beneficial in the case of inorganic solar cells, where the refractive indices of the active materials are much higher than in the organic case. Indeed, it has been shown both theoretically and experimentally that incident light absorption in a 100nm thick layer of a-Si:H can be increased by a factor of 2 by the sole impact of the patterning, and in a wavelength range expanding from 300 to 750nm [14

14. G. Gomard, X. Meng, E. Drouard, K. E. Hajjam, E. Gerelli, R. Peretti, A. Fave, R. Orobtchouk, M. Lemiti, and C. Seassal, “Light harvesting by planar photonic crystals in solar cells: the case of amorphous silicon,” J. Opt. 14(2), 024011 (2012). [CrossRef]

]. Moreover, the characteristics of these devices rely on the properties of the multiple Bloch modes of the PhC, which exhibits relatively flat dispersion bands. This is expected to provide a good stability of the device characteristics with regards to the angle of incidence of the sunlight.

In former papers, we have introduced the design of such PhC assisted a-Si:H solar cells [15

15. G. Gomard, E. Drouard, X. Letartre, X. Meng, A. Kaminski, A. Fave, M. Lemiti, E. Garcia-Caurel, and C. Seassal, “Two-dimensional photonic crystal for absorption enhancement in hydrogenated amorphous silicon thin film solar cells,” J. Appl. Phys. 108(12), 123102 (2010). [CrossRef]

]. Using Rigorous Coupled Wave Analysis (RCWA), and scanning the main topographical parameters, it is possible to optimize the design of such devices, enabling to increase the integrated absorption in a-Si:H by 27%. Such PhC can be patterned into the active layers of the solar cells, using laser interference lithography and reactive ion etching.

However, while the basic properties of the surface addressable slow light modes are well known, the best way to control them to tailor the absorption over a wide wavelength range is still to be investigated. Indeed, more advanced designs could enable to reach a much higher increase in absorption, and therefore, a substantial increase in terms of conversion efficiency. Moreover, the impact of the unique properties of such Bloch modes on the angular acceptance of PhC solar cells still requires a specific theoretical and experimental investigation.

2. Design and basic properties of a-Si:H based photonic crystal assisted solar cells

The targeted devices are based on a thin film solar cell stack, comprising from the back to the front, a silver (Ag) layer deposited on a glass substrate, a transparent and conductive oxide (TCO) layer made of zinc oxide (ZnO), a p-i-n a-Si:H junction, and another TCO layer formed by the deposition of indium tin oxide (ITO), corresponding to the top electrode. The ZnO layer, with a thickness of 100nm, is expected to act as a barrier against the diffusion of Ag in a-Si:H; it may also play a role in maximizing sunlight absorption. The total thickness of the p-i-n junction is 100nm, which is lower than the diffusion length of the minority carriers in a-Si:H. It is chosen in such a way that the bulk recombination of photocarriers in the active layer is minimized. It also reduces the amount of active material used in the device, compared to more standard designs of a-Si:H based solar cells. The top TCO layer thickness of 50nm is chosen in order to limit the absorption in this material. In the approach proposed, the top layers (ITO and a-Si:H) are fully patterned as a PhC. More precisely, it consists in a 2D square lattice of circular holes, as schematized in Fig. 1(a)
Fig. 1 Schematic view of the 2D PhC assisted a-Si:H solar cells (a), simulated absorption spectra in the active layer for the patterned and for the reference solar cell stacks, both illuminated at normal incidence (b).
.

Optimizing the lattice parameter, L, and the holes diameter, D, of the PhC leads to an integrated absorption of 82% in the whole stack, between 300 and 720nm. This value, which is limited to 65.7% if only the useful part of the absorption, namely the one in a-Si:H is considered, is reached for L = 380nm, and D = 237.5nm. Figure 1(b) displays the corresponding absorption spectra for the 2D PhC patterned solar cell and a reference constituted of the same but unpatterned stack, including layers with the same thicknesses. It should be highlighted that this does not correspond to the final optimum for two main reasons. First, only a square lattice of air holes has been considered and second, L and D are the sole parameters which have been varied in a range limited by fabrication constraints, L was tuned in the 200-800nm range, while D was varied in order to explore the full range of surfacic air filling fraction from 0 to 1. Still, at this stage, it should be mentioned that this corresponds to a substantial increase with regards to the unpatterned structure, where the absorption in a-Si:H is only of 51.7%. Moreover, the integrated absorption achieved for a PhC solar cell is quite stable with regards to technological uncertainties, since it is only reduced by 1% when L or D are tuned by 5% from the above-mentioned parameters.

3. Light trapping and absorption in thin film semiconductor solar cell: a physical insight

The first step consists in describing, in a low-absorbing spectral region, the optical properties of a PhC membrane, which is supposed to support a single mode without any assumption on its symmetry properties. This can be achieved thanks to the TDCMT using the same methodology and terminology as in [20

20. R. Peretti, G. Gomard, C. Seassal, X. Letartre, and E. Drouard, “Modal approach for tailoring the absorption in a photonic crystal membrane,” J. Appl. Phys. 111(12), 123114 (2012). [CrossRef]

], which gives the differential Eq. (1) describing the evolution of the field amplitude in a mode in the time domain:
dadt=(jω01τ01τe)a+κ1S+1.
(1)
where a is the amplitude of the field in the mode, ω0 is the resonant frequency of the mode, τe is the decay time of losses due to external coupling (in s), τ0 is the decay time of losses due to absorption, and S+1 is the field amplitude of the incident light. This differential equation has to be coupled with the equations that apply to the coupling with the reflected and transmitted light:
S1=ejβdκ2aS2=ejβd(S+1κ1a).
(2)
where S-1 is the field amplitude of the reflected light, S-2 is the field amplitude of the transmitted light, κ1 is the coupling coefficient associated with the incident light and κ2 is the coupling coefficient associated with the transmitted light. This is represented in Fig. 2(a)
Fig. 2 TDCMT parameters used to describe the optical properties of the photonic membrane (a) and schematic view of the photonic crystal (b).
, together with a schematic view of the photonic membrane (Fig. 2(b)).

ς=τe2τe1.
(4)

The parameter ζ can be infinite, as encountered in many devices involving a back reflector, but can also be adjusted within a sole absorbing layer by introducing a specific nano-patterning, for instance a double-layer 2D PhC [22

22. S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010). [CrossRef] [PubMed]

] or by using patterns with non vertical sidewalls, e.g. like holes with radii changing along the membrane thickness [23

23. 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]

].

Using the harmonic steady-state hypothesis, one can solve Eq. (1) for any frequency (ω) detuned from the mode resonant frequency (ω0) by ω-ω0 = δω:
a(ω)=κ1S+1jδω1τ01τe.
(5)
Starting from the above equations and introducing the expression of the field amplitude in the mode and of ζ, the reflection (r) and transmission (t) coefficients in field, can be expressed as follows:
S1S+1=r=ejβdej(θ1θ2)τe2(ζ+2+1ζ)1jδω1τ01τeS2S+1=t=ejβd(1+21τe(1+1ζ)1(jδω1τ01τe)).
(6)
From Eq. (6), it is then possible to get the reflection (R) and transmission (T) coefficients in energy, as well as the resulting absorption (A = 1-R-T) as in (7);

R=rr*=4ς(1+1ς)2[(τeτ0+1)2+τe2δω2]T=tt*=4(1+1ς)1(1+1ς)(τeτ0+1)(τeτ0+1)2+τe2δω2+1A=1RT=4[((τeτ0+1)2+τe2δω2)(1+1ς)τ0τe]1.
(7)

In the remainder of the paper, these expressions will be used in order to assess the influence of the τe/τ0 ratio and of ζ on the width and on the highest achievable value of the absorption peak corresponding to the mode considered, and finally to determine the coupling conditions which maximize the integrated absorption of this isolated mode.

It can be first inferred from Eq. (7) that the expressions of R, (T-1) and A correspond to Lorentzian functions with a full width at half maximum (FWHM, denoted Γ) defined as:

Γ=2(τeτ0+1)τe.
(8)

To illustrate Eq. (8), the FWHM was calculated for different τe/τ0 ratios.

The results, gathered in Fig. 3
Fig. 3 FWHM (in τe units) of the R, T or A peaks as a function of τe/τ0.
, indicate that the FWHM increases together with the absorption losses, that is when τ0 decreases. Conversely, the value of Γ is constant when the absorption losses are small compared to the external ones. As shown in [20

20. R. Peretti, G. Gomard, C. Seassal, X. Letartre, and E. Drouard, “Modal approach for tailoring the absorption in a photonic crystal membrane,” J. Appl. Phys. 111(12), 123114 (2012). [CrossRef]

], this can be expressed in terms of quality factors:
1Qtot(κ)=γ×kabsorptionlosses+1Qeesternallosses.
(9)
k being the extinction coefficient of the material considered proportional to τ0−1, γ a coupling coefficient and Qe = ω0τe. It can be noticed that due to the symmetry of Eq. (8) with respect to the parameters τ0 and τe, the same curve as in Fig. 3 would be obtained by expressing the FWHM in τ0 units.

In addition to the FWHM, another characteristic of the absorption peak impacting its integral is the maximum absorption value which can be attained. This occurs when the frequency is set to the one of the resonance of the mode, namely when δω = 0. After modifying Eq. (7) accordingly, one can compute Rδω = 0, Tδω = 0 and Aδω = 0 as a function of τ0/τe for different ζ values (see Fig. 4(a)
Fig. 4 Reflection, transmission and absorption of a single mode membrane, calculated as a function of τ0/τe for different coupling anisotropy values (ξ) (a) and as a function of ξ for different τe/τ0 ratios (b). Values are plotted at the resonant frequency.
) or the other way around, i.e. as a function of ζ for different τe/τ0 ratios (see Fig. 4(b)).

Firstly, Fig. 4(a) underlines the superposition of the reflection curves for ζ and 1/ζ. This results from the destructive interferences occurring between the transmitted and the reemitted waves since the mode is supposed to be at its resonance. For the symmetric membrane (ζ = 1), it can be observed that a total reflection is obtained when the absorption losses are negligible. The value of the reflection is progressively decreasing when the coupling anisotropy increases.

Besides, small values of ζ (such as 10−2) are associated with a high transmission (Tδω = 0 close to the unity whatever the τe/τ0 ratio, see for instance Fig. 4(b)), since the front side coupling of the mode is weak and almost no energy can be injected in it, leading to both a low absorption and a low reflection. When the τ0/τe ratio matches exactly the critical coupling conditions (τ0/τe = 1), the transmission equals 25% for the symmetric membrane (same value as the one of the reflection) but tends to zero if ζ>10, which means that back side coupling can be neglected and that the absorption is then completely determined by the Rδω = 0 value.

Finally, this enables to understand the evolution of the absorption as a function of ζ and of the τ0e ratio. It should be first emphasized that a maximum absorption is obtained when the intrinsic losses counterbalance the external ones, in other words, when the critical coupling conditions are fulfilled [14

14. G. Gomard, X. Meng, E. Drouard, K. E. Hajjam, E. Gerelli, R. Peretti, A. Fave, R. Orobtchouk, M. Lemiti, and C. Seassal, “Light harvesting by planar photonic crystals in solar cells: the case of amorphous silicon,” J. Opt. 14(2), 024011 (2012). [CrossRef]

]. Under this condition (τ0e = 1), the maximal absorption of the symmetric membrane is 50%. This value can be exceeded by increasing ζ. Indeed, after introducing a strong coupling anisotropy (for instance ζ = 102), a quasi-total absorption is achieved. Thus, it can be concluded that at the resonant frequency of the mode, a total absorption of the incoming light is possible provided that the best conditions on the coupling anisotropy (ζ close to 102) and on the τ0e ratio (τ0e = 1) are both achieved.

To go further, it should be precised that for most applications including photovoltaic devices or sensors, an optimization of the integrated absorption of the peak is required rather than just a maximization of Aδω = 0 for a targeted and single wavelength. Once again, it is possible to compute this integrated absorption (Aint) by considering the general expression of the integral of Lorentzian functions. Aint is then defined by Aδω = 0 and Γ, which depend directly on the coupling parameters ζ and τ0/τe as seen previously.

Aint=Aδω=0πΓ2=4π(τe+τ0)(1+1ζ).
(10)

As an illustration of Eq. (10), Aint was calculated and plotted in Fig. 5
Fig. 5 Integrated absorption (in τ0−1 units) calculated for different coupling parameters.
as a function of τ0/τe, for different values of ζ. It can be noticed that increasing ξ from 10−2 to 102 enables to significantly increase the integrated absorption, regardless of the coupling regime considered. Moreover, for a given value of ζ, two distinct domains can be defined as regards the τe/τ0 ratio, with a transition occurring around the critical coupling conditions. More precisely, Aint rises as τe/τ0 decreases and eventually converges towards an optimal value when the external losses are dominating. As it was highlighted in [19

19. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). [CrossRef] [PubMed]

], the spectral cross-section of a single resonance is maximized in this over-coupling regime. Furthermore, one can observe in Fig. 5 that a −3dB cutoff takes place precisely at critical coupling. This means that increasing the external losses so that they can equal the intrinsic ones is a must, and strengthening them to overcome the absorption losses is a plus.

So as to achieve a broadband absorption enhancement, the goal is not only to select a mode operating in the over-coupling regime, but also to fill properly the targeted spectral range with a collection of such modes. A generalization of Eq. (10) to a set of N non-overlapping modes enables to calculate the total integrated absorption Aint,tot:

Aint,tot=4πi=1i=N1(τe,i+τ0,i)(1+1ξi).
(11)

In summary, we have analyzed the coupling properties of resonant modes, and we have presented their potential to optimize their peak and integrated absorption in a low-absorbing spectral region. In this context, it was first concluded that the coupling anisotropy of the system should be maximized as much as possible. A second requirement was to bring the external losses at least at the critical coupling conditions. The goal is then to broaden the modes so as to reach the over-coupling regime, and to fill properly the spectral region with a collection of modes, in order to optimize the resulting absorption enhancement. A general objective of the design is then to generate additional optical resonances which are strongly coupled to the radiative continuum. This can be achieved simply by changing the main parameters of the PhC, or, more efficiently, by including a multiple periodicity, or even a controlled degree of disorder, in a simply periodic pattern. Example of such structures can be found in the recent literature [25

25. A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012). [CrossRef]

27

27. K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012). [PubMed]

]. In this section, the results were illustrated in the case of a simple 1D PhC made of a-Si:H. However, they are also valid in the case of a full solar cell stack patterned as a 2D PhC or more complex structures. In particular, the computed spectrum displayed in Fig. 1(b), in the case of the optimized 2D PhC solar cell, illustrate the positive impact of multiple damped optical resonances.

In the case of crystalline silicon (c-Si) thin film solar cells, like those discussed in [28

28. 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]

30

30. C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012). [CrossRef]

], one can draw similar conclusions. However, as the resonances are then very densely packed, Eq. (7) cannot be applied in a straightforward way: the interplay between the optical modes is hardly taken into account by this simple analytical model. It remains that in this practical case, as the thickness of the c-Si layer is necessarily much higher than in the a-Si:H case, since the absorption coefficient is lower. Then, the PhC membrane may support a much higher spectral density of optical resonances, with increased quality (Q) factors. The optimization process then tends to select such densely packed modes, close to the critical coupling conditions; this leads to a higher integrated absorption.

4. Angular acceptance of a-Si:H based photonic crystal assisted solar cells

Additionally to the necessary optimization of the absorption efficiency, any photonic engineering strategy for photovoltaics should be compatible with a reasonable angular acceptance. Although relying on optical resonances, absorbing PhC structures bring a key intrinsic advantage: these modes correspond to relatively flat dispersion curves. Such optical resonances are then expected to exhibit relatively stable properties with regards to the angle of incidence. Additionally, as it has been highlighted in the last section, the behavior of a single PhC layer relies on several optical modes; even if their behavior is modified with the incidence angle, it may be expected that the impact of these modifications could be globally compensated when integrated over a broad spectrum. Lastly, in the case of PhC structures, the coupling of light at normal incidence is prohibited for specific symmetries of modes [31

31. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001), vol. 80.

]. As a result, the integrated absorption may be increased while the incidence angle is tilted with regards to normal incidence. In order to assess the positive impact of these specific properties of PhC Bloch mode resonances, the integrated absorption has been calculated by Rigorous Coupled Wave Analysis (RCWA), for two different structures, between 300 and 720nm, considering the AM1.5G solar irradiance.

Figure 7(a)
Fig. 7 Simulated integrated absorption for an a-Si:H unpatterned and 2D PhC patterned layer (a) and for the unpatterned and 2D PhC patterned solar stack (b). The solar cell stack corresponds to the structure schematized in Fig. 1(a). In both cases, the absorption is integrated from 300 to 720nm, considering an AM1.5G solar distribution.
displays the integrated absorption evolution in the case of an optimized absorbing 2D PhC constituted of a 100nm a-Si:H layer, with a lattice parameter L = 300nm, and holes diameter of 240nm [15

15. G. Gomard, E. Drouard, X. Letartre, X. Meng, A. Kaminski, A. Fave, M. Lemiti, E. Garcia-Caurel, and C. Seassal, “Two-dimensional photonic crystal for absorption enhancement in hydrogenated amorphous silicon thin film solar cells,” J. Appl. Phys. 108(12), 123102 (2010). [CrossRef]

]. It clearly appears that the integrated absorption is much higher in the case of the PhC, for all incidence angles up to 80°. While the integrated absorption is increased by a factor of 2 at normal incidence, this factor is in excess of 3 at 80°. Moreover, the integrated absorption increase is clearly visible in the PhC case, when the incidence angle is increased from 0 to 10°. All these remarks illustrate the properties and confirm the tendencies discussed in the beginning of this section.

The computed data displayed in Fig. 7(b) corresponds to the structure schematized in Fig. 1(a): an a-Si:H solar cell stack patterned as a 2D PhC, with optimized integrated absorption (L = 380nm, and D = 237.5nm). In this second situation, similar results are obtained: a slight absorption increase from 0 to 10° for the patterned stack and a higher absorption at every angle in the case of the PhC, compared to the unpatterned reference. However, it turns out that the absorption increase is lower in this stack, compared to the sole patterned a-Si:H layer. The reason is that the presence of the back electrode and of the top ITO layer lead to a substantial absorption increase of the unpatterned stack. Still, the integrated absorption in a-Si:H is only decreased from 65.7% to 60%, while the angle of incidence is increased up to 55°.

Finally, Fig. 8(a)
Fig. 8 Absorption spectra measured for an a-Si:H based solar cell stack, patterned as a 2D PhC (with L = 600nm and D = 350nm). Measurements are performed in an integrating sphere, with angles of incidence from 10 to 50° (a scanning electron micrograph of the patterned solar cell stack is shown in the inset (a). The overall integrated absorptions calculated from those spectra are also reported (b).
exhibits measured absorption spectra obtained with an integrating sphere. In this case, a solar cell stack was deposited, and 2D PhC structures were patterned using laser interference lithography and reactive ion etching. Details of the processes can be found in [14

14. G. Gomard, X. Meng, E. Drouard, K. E. Hajjam, E. Gerelli, R. Peretti, A. Fave, R. Orobtchouk, M. Lemiti, and C. Seassal, “Light harvesting by planar photonic crystals in solar cells: the case of amorphous silicon,” J. Opt. 14(2), 024011 (2012). [CrossRef]

]. The PhC geometrical parameters were relatively far from the optimal situation, since L = 600nm, and D = 350nm. The spectra measured at angles of incidence α between 10 and 50° exhibit a relatively stable behavior. Indeed, there is no global decrease of the overall integrated absorption as underlined in Fig. 8(b). More precisely, it clearly appears that the wavelength of the resonant modes is tuned for increasing angles, and that there is a compensation phenomenon between the peaks which appear or disappear with a changing angle of incidence.

5. Conclusion

Patterning a silicon-based thin film solar cell as a 2D PhC enables a substantial increase of the absorption efficiency. In the case of a device including a 100nm thick a-Si:H p-i-n junction, and all the necessary layers to collect the electrical carriers, the relative increase is up 27%. This is achieved by a simple patterning of the stack as a square lattice of air holes. To further increase this absorption efficiency, it is necessary to refine the design of the photonic structure and to perform optical mode engineering. To reach this goal, we have introduced a method based on a TDCMT analysis. Using this method, it is possible to evaluate, and maximize the absorption around a given wavelength, which can be useful for indoor photovoltaics, or down-conversion structures for third generation solar cells. It is also possible to optimize the integrated absorption in a given wavelength range, increasing the spectral density of optical modes, and generating optical resonances operating in the over-coupling regime. Such resonances can be generated by a careful choice of the PhC structure parameters, or, more efficiently, by using a more complex unit cell, partially etched photonic structures or patterns with a controlled disorder. In the case of an absorbing layer with a thickness in the micrometer range, the spectral density of optical modes can be further increased, with the possibility to use resonances closer to the critical coupling conditions, with lower optical losses.

Another key characteristic of PhC resonances is that they enable a particularly high angular acceptance. Using RCWA simulations, we have shown that the integrated absorption in the a-Si:H active layer of a patterned solar cell stack is only decreased from 65.7% to 60%, while the incidence angle is increased from 0 to 55°. This excellent stability has been confirmed by optical measurements, for angles of incidence up to 50°.

Acknowledgments

This work was supported by Orange Labs Networks contract 0050012310-A09221. Ounsi El Daïf, from IMEC, is acknowledged for performing the angular acceptance measurements. Pere Roca i Cabarrocas, from LPICM, is acknowledged for the deposition of the solar cell stack used in section 4, and for fruitful discussions.

References and links

1.

A. Naqavi, F.-J. Haug, C. Battaglia, H. P. Herzig, and C. Ballif, “Light trapping in solar cells at the extreme coupling limit,” J. Opt. Soc. Am. B 30(1), 13–20 (2013). [CrossRef]

2.

Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109(17), 173901 (2012). [CrossRef] [PubMed]

3.

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]

4.

R. Bouffaron, L. Escoubas, J. J. Simon, P. Torchio, F. Flory, G. Berginc, and P. Masclet, “Enhanced antireflecting properties of micro-structured top-flat pyramids,” Opt. Express 16(23), 19304–19309 (2008). [CrossRef] [PubMed]

5.

Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small 6(9), 984–987 (2010). [CrossRef] [PubMed]

6.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

7.

M. Despeisse, C. Battaglia, M. Boccard, G. Bugnon, M. Charrière, P. Cuony, S. Hänni, L. Löfgren, F. Meillaud, G. Parascandolo, T. Söderström, and C. Ballif, “Optimization of thin film silicon solar cells on highly textured substrates,” Phys. Status Solidi A 208(8), 1863–1868 (2011). [CrossRef]

8.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6(3), 2790–2797 (2012). [CrossRef] [PubMed]

9.

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]

10.

C. Seassal, Y. Park, A. Fave, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” Proc. SPIE 7002, 700207, 700207-8 (2008). [CrossRef]

11.

D. Duché, L. Escoubas, J.-J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92(19), 193310 (2008). [CrossRef]

12.

Y. Park, E. Drouard, O. El Daif, X. Letartre, P. Viktorovitch, A. Fave, A. Kaminski, M. Lemiti, and C. Seassal, “Absorption enhancement using photonic crystals for silicon thin film solar cells,” Opt. Express 17(16), 14312–14321 (2009). [CrossRef] [PubMed]

13.

S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express 18(5), 4260–4274 (2010). [CrossRef] [PubMed]

14.

G. Gomard, X. Meng, E. Drouard, K. E. Hajjam, E. Gerelli, R. Peretti, A. Fave, R. Orobtchouk, M. Lemiti, and C. Seassal, “Light harvesting by planar photonic crystals in solar cells: the case of amorphous silicon,” J. Opt. 14(2), 024011 (2012). [CrossRef]

15.

G. Gomard, E. Drouard, X. Letartre, X. Meng, A. Kaminski, A. Fave, M. Lemiti, E. Garcia-Caurel, and C. Seassal, “Two-dimensional photonic crystal for absorption enhancement in hydrogenated amorphous silicon thin film solar cells,” J. Appl. Phys. 108(12), 123102 (2010). [CrossRef]

16.

H. A. Haus, Waves and Fields in Optoelectronics (Englewood Cliffs, 1984).

17.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]

18.

Z. Yu, A. Raman, and S. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process. 105(2), 329–339 (2011). [CrossRef]

19.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). [CrossRef] [PubMed]

20.

R. Peretti, G. Gomard, C. Seassal, X. Letartre, and E. Drouard, “Modal approach for tailoring the absorption in a photonic crystal membrane,” J. Appl. Phys. 111(12), 123114 (2012). [CrossRef]

21.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999). [CrossRef]

22.

S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010). [CrossRef] [PubMed]

23.

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]

24.

V. Mandelshtam, “Fdm: the filter diagonalization method for data processing in nmr experiments,” Prog. Nucl. Magn. Reson 38(2Spec.), 159–196 (2001). [CrossRef]

25.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012). [CrossRef]

26.

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B 86(4), 041404 (2012). [CrossRef]

27.

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012). [PubMed]

28.

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]

29.

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]

30.

C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012). [CrossRef]

31.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001), vol. 80.

OCIS Codes
(040.5350) Detectors : Photovoltaic
(350.6050) Other areas of optics : Solar energy
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Light Trapping in Solar Cells

History
Original Manuscript: February 4, 2013
Revised Manuscript: March 17, 2013
Manuscript Accepted: March 18, 2013
Published: April 22, 2013

Virtual Issues
Renewable Energy and the Environment (2013) Optics Express

Citation
Guillaume Gomard, Romain Peretti, Emmanuel Drouard, Xianqin Meng, and Christian Seassal, "Photonic crystals and optical mode engineering for thin film photovoltaics," Opt. Express 21, A515-A527 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S3-A515


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References

  1. A. Naqavi, F.-J. Haug, C. Battaglia, H. P. Herzig, and C. Ballif, “Light trapping in solar cells at the extreme coupling limit,” J. Opt. Soc. Am. B30(1), 13–20 (2013). [CrossRef]
  2. Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett.109(17), 173901 (2012). [CrossRef] [PubMed]
  3. 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]
  4. R. Bouffaron, L. Escoubas, J. J. Simon, P. Torchio, F. Flory, G. Berginc, and P. Masclet, “Enhanced antireflecting properties of micro-structured top-flat pyramids,” Opt. Express16(23), 19304–19309 (2008). [CrossRef] [PubMed]
  5. Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small6(9), 984–987 (2010). [CrossRef] [PubMed]
  6. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010). [CrossRef] [PubMed]
  7. M. Despeisse, C. Battaglia, M. Boccard, G. Bugnon, M. Charrière, P. Cuony, S. Hänni, L. Löfgren, F. Meillaud, G. Parascandolo, T. Söderström, and C. Ballif, “Optimization of thin film silicon solar cells on highly textured substrates,” Phys. Status Solidi A208(8), 1863–1868 (2011). [CrossRef]
  8. C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano6(3), 2790–2797 (2012). [CrossRef] [PubMed]
  9. 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]
  10. C. Seassal, Y. Park, A. Fave, E. Drouard, E. Fourmond, A. Kaminski, M. Lemiti, X. Letartre, and P. Viktorovitch, “Photonic crystal assisted ultra-thin silicon photovoltaic solar cell,” Proc. SPIE7002, 700207, 700207-8 (2008). [CrossRef]
  11. D. Duché, L. Escoubas, J.-J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett.92(19), 193310 (2008). [CrossRef]
  12. Y. Park, E. Drouard, O. El Daif, X. Letartre, P. Viktorovitch, A. Fave, A. Kaminski, M. Lemiti, and C. Seassal, “Absorption enhancement using photonic crystals for silicon thin film solar cells,” Opt. Express17(16), 14312–14321 (2009). [CrossRef] [PubMed]
  13. S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express18(5), 4260–4274 (2010). [CrossRef] [PubMed]
  14. G. Gomard, X. Meng, E. Drouard, K. E. Hajjam, E. Gerelli, R. Peretti, A. Fave, R. Orobtchouk, M. Lemiti, and C. Seassal, “Light harvesting by planar photonic crystals in solar cells: the case of amorphous silicon,” J. Opt.14(2), 024011 (2012). [CrossRef]
  15. G. Gomard, E. Drouard, X. Letartre, X. Meng, A. Kaminski, A. Fave, M. Lemiti, E. Garcia-Caurel, and C. Seassal, “Two-dimensional photonic crystal for absorption enhancement in hydrogenated amorphous silicon thin film solar cells,” J. Appl. Phys.108(12), 123102 (2010). [CrossRef]
  16. H. A. Haus, Waves and Fields in Optoelectronics (Englewood Cliffs, 1984).
  17. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]
  18. Z. Yu, A. Raman, and S. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process.105(2), 329–339 (2011). [CrossRef]
  19. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107(41), 17491–17496 (2010). [CrossRef] [PubMed]
  20. R. Peretti, G. Gomard, C. Seassal, X. Letartre, and E. Drouard, “Modal approach for tailoring the absorption in a photonic crystal membrane,” J. Appl. Phys.111(12), 123114 (2012). [CrossRef]
  21. C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron.35(9), 1322–1331 (1999). [CrossRef]
  22. S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express18(6), 5691–5706 (2010). [CrossRef] [PubMed]
  23. 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]
  24. V. Mandelshtam, “Fdm: the filter diagonalization method for data processing in nmr experiments,” Prog. Nucl. Magn. Reson38(2Spec.), 159–196 (2001). [CrossRef]
  25. A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett.100(18), 181110 (2012). [CrossRef]
  26. E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B86(4), 041404 (2012). [CrossRef]
  27. K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater.11(12), 1017–1022 (2012). [PubMed]
  28. 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]
  29. 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]
  30. C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett.101(10), 103901 (2012). [CrossRef]
  31. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001), vol. 80.

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