Enhanced light trapping in thin-film solar cells by a directionally selective filter

doi:10.1364/OE.18.00A133

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Enhanced light trapping in thin-film solar cells by a directionally selective filter

Carolin Ulbrich, Marius Peters, Benedikt Bläsi, Thomas Kirchartz, Andreas Gerber, and Uwe Rau »View Author Affiliations

Optics Express, Vol. 18, Issue S2, pp. A133-A138 (2010)
http://dx.doi.org/10.1364/OE.18.00A133

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– Abstract
1. Introduction
2. Experiment
3. Results
4. Conclusions
– References and links

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Abstract

A directionally selective multilayer filter is applied to a hydrogenated amorphous silicon solar cell to improve the light trapping. The filter prevents non-absorbed long-wavelength photons from leaving the cell under oblique angles leading to an enhancement of the total optical path length for weakly absorbed light within the device by a factor of κ_r = 3.5. Parasitic absorption in the contact layers limits the effective path length improvement for the photovoltaic quantum efficiency to a factor of κ_EQE = 1.5. The total short-circuit current density increases by ΔJ_sc = 0.2 mAcm⁻² due to the directional selectivity of the Bragg-like filter.

1. Introduction

The enhancement of the optical path length w _opt of the incoming solar light within the photovoltaic absorber material of solar cells is a key issue for improving the performance of these devices and at the same time reducing material consumption [1

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983). [CrossRef]

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

]. The span of photon energies relevant for light trapping in solar cells is limited to a range more or less close to the band gap energy of the absorber material, where its absorption coefficient is relatively low such that this light cannot be absorbed within a single or double path through the absorber. To improve the absorptance and, in consequence, the quantum efficiency of the solar cell scattering at textured surfaces is routinely used in both thin-film and crystalline silicon solar cell technologies. The theoretical maximum path length of weakly absorbed light was calculated by Yablonovitch [3

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]

] to be

w_{opt} = k w = 4 n^{2} w,

(1)

where w is the absorber thickness, n the refractive index of the material, and k denotes the path length enhancement factor. This limit assumes that the solar cell absorbs radiation from the entire half-space above the solar cell. Consequently, restricting the angle of acceptance and by virtue of the reversibility of the light path also the angle of (re-)emittance, enhances the maximum optical path length for perpendicularly incident radiation. For instance, a restriction of the angle of acceptance θ to values below a threshold value θ_th leads to [4

J. C. Miñano, “Optical confinement in photovoltaics,“ in Physical Limitations to the Photovoltaic Solar Energy Conversion, A. Luque and G. L. Araújo, eds. (Hilger, Bristol, UK,1990), p. 55.

M. A. Green, “High efficiency solar cells,” (Trans Tech Publications, Switzerland, 1987), p. 80.

]

w_{opt} = k w = 4 n^{2} w / \sin^{2} (θ_{th}) .

(2)

Directional selectivity might be an inherent property of a specific light trapping scheme [5

M. A. Green, “High efficiency solar cells,” (Trans Tech Publications, Switzerland, 1987), p. 80.

R. Brendel, “Thin-film crystalline silicon solar cells,” (Wiley-VCH, Weinh., Germany, 2003), pp. 193–199.

] but may also result from combining statistical, directionally insensitive light trapping with an angular selective filter [7

V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005). [CrossRef]

–9

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008). [CrossRef]

]. Such directionally selective configurations also result in an enhancement of the theoretical Shockley Queisser limit [10

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961). [CrossRef]

] of the solar cell efficiency via the reduction of radiative losses in analogy to the efficiency enhancement obtained by concentration of the incident light [11

G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994). [CrossRef]

As shown previously [8

C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008). [CrossRef]

], directionally selective filters combined with a Lambertian scatterer may significantly enhance the light trapping of crystalline silicon solar cells. Due to the restricted acceptance angle these gains are only realized if the solar cells are tracked to the incident angle of the sunlight. First experimental studies [12

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009). [CrossRef]

] already demonstrated that a Bragg filter attached to an amorphous Si solar cell improves the external quantum efficiency within a certain spectral range. However, an increase of the integral short-circuit current density was not observed until now.

The present paper reports the experimental realization of a directionally selective filter consisting of a multilayer stack deposited onto the glass superstrate of a hydrogenated amorphous Si (a-Si:H) solar cell. We compare the reflection and the external quantum efficiency before and after filter deposition to quantify the improvement of light trapping. We demonstrate that the optical path length within the device is enhanced by up to a factor of κ_r = 3.5 where a factor of κ_EQE = 1.5 contributes to the improvement of the short-circuit current density of the solar cell by up to ΔJ _sc = 0.2 mAcm⁻².

2. Experiment

Figure 1 depicts a schematic cross section of the experimental a-Si:H solar cell. A Bragg-like filter consisting of 73 alternating layers of SiO₂ and Ta₂O₅ with a total thickness of 5.5 µm was deposited by a plasma ion assisted deposition process by mso Jena Mikroschichtoptik GmbH. Due to the Bragg-effect the transmission and reflection of the filter are spectrally and directionally selective. The design of the filter allows perpendicularly incident radiation with wavelengths λ smaller then the threshold wavelength λ_th to traverse the filter with almost no absorption loss. Radiation that passed the filter and the glass superstrate is scattered by the etched front transparent conductive oxide layer (TCO) into the photovoltaic absorber material. The absorber consists of a p-type (p), an intrinsic (i), and an n-type (n) layer. A second TCO layer and silver (Ag) act as reflector and electrical back contact. Traversing the different layers of the solar cell, the radiation is partly absorbed. The non-absorbed fraction of the light reflected at the rear side impinges onto the filter`s rear side under angles varying -in most cases- from the perpendicular incident angle. According to the Bragg characteristic, the filter is transparent for perpendicularly incident and opaque for obliquely incident angles. Thus, most non-absorbed photons are reflected back into the solar cell. The light paths for photons of high wavelengths therefore increase. The threshold wavelength λ_th of a Bragg filter shifts to lower wavelengths with increasing incidence angle θ according to [13

J. Turunen, and F. Wyrowski, Diffractive Optics for industrial and commercial applications (Akademie Verlag, Berlin, Germany, 1997), Chap. 12.4.

]

Fig. 1 The investigated solar cells consist of a glass superstrate, a transparent conductive oxide (TCO) layer, a pin-absorber of hydrogenated amorphous silicon (a-Si:H), and a back contact of TCO and silver (Ag). The Bragg filter is applied on top of the front glass after a first characterization of the cell without filter. The filter reflects light with incidence angles θ > θ_th in the respective wavelength range. (Thicknesses are not to scale.)

λ_{th} (θ) = 2 d \sqrt{n^{2} - \sin^{2} (θ)} = \sqrt{λ_{0}^{2} - (λ_{0}^{2} - λ_{1}^{2}) \sin^{2} θ} .

(3)

Here, d is the thickness of one layer of the filter and n the refractive index of its material. The quantities λ₀ and λ₁ denote the threshold wavelengths at sin θ = 0 and sin θ = 1, respectively. Though not representing the full physics of our non-periodic multilayer Bragg-like stack, Eq. (3) is sufficiently accurate to explain our experimental results as will be shown below.

The external quantum efficiency is used to quantify the light trapping effect. In order to have a good comparison we measured the external quantum efficiency of each investigated solar cell before and after depositing the filter. We tested the filter on two different superstrates for the a-Si:H solar cells (textured SnO₂:F on AsahiU glass and etched [14

A. Löffl, S. Wieder, B. Rech, O. Kluth, C. Beneking, and H. Wagner, “Al-doped ZnO films for thin-film solar cells with very low sheet resistance and controlled texture,” Proc. 14th Europ. PV Sol. En. Conf., Barcelona, 1997, p. 2089.

] ZnO:Al on Corning glass). The absorber layer thickness was varied between approx. 175 nm and 410 nm.

3. Results

Figure 2 (a) shows the total reflectance of an a-Si:H solar cell measured for perpendicularly incident light using an integrating sphere. The thickness of the absorber layer is 322 nm, the superstrate used here is Corning glass with etched ZnO:Al [14

]. The reflectance of the solar cell without filter (black line, reflectance r ₀(λ)) rises for higher wavelengths where the light path becomes smaller than the absorption length of photons in the solar cell material. After the deposition of the filter the reflectance r _fi(λ) is substantially decreased in the wavelength range 650 nm < λ < 770 nm due to the directional selectivity of the filter suppressing re-emission of non-absorbed light. For λ ≥ λ₀ = 767 nm, the reflectance r _fi steeply rises to unity when the Bragg condition [Eq. (3)] is met for normal incidence. In the wavelength range 350 nm < λ < 650 nm, we observe a slight reduction of reflectance due to the antireflective properties of the filter. The filter induces a high reflectance for λ < 350 nm, i.e. in a spectral range that is not important for a-Si:H solar cells. Figure 2(b) shows the difference Δr(λ) = r _fi(λ)-r ₀(λ) highlighting a reduction of the reflectance by 40% at λ = 764 nm.

Fig. 2 (a) The total reflectance (r ₀/r _fi, without/with filter, black/orange line) of a 322 nm thick a-Si:H solar cell prepared on ZnO:Al on Corning glass increases for wavelengths λ > 600 nm because non-absorbed light is re-emitted from the cell. The filter increases the reflectance at wavelengths λ < 350 nm and λ > 770 nm but suppresses the re-emission of photons for 650 nm < λ < 770 nm. (b) The difference Δr = r _fi-r ₀ is reduced due to enhanced light trapping to a minimum of −40% at λ < 764 nm. (c) The external quantum efficiency EQE of the same solar cell measured with and without filter and (d) the difference ΔEQE=EQE _fi-EQE ₀ show that the filter acts as antireflective coating for 350 nm < λ < 600 nm and increases the light trapping for 650 nm < λ < 770 nm.

The external quantum efficiency (EQE) of a solar cell is defined as the number of elementary charges measured at the contacts divided by the number of photons impinging on the device. Figure 2(c) depicts the external quantum efficiency EQE of the same sample. The difference ΔEQE(λ) = EQE _fi(λ)-EQE ₀(λ) between the external quantum efficiency EQE _fi(λ) with filter and EQE ₀(λ) without filter is shown in Fig. 2(d). The difference ΔEQE(λ) essentially reflects the features already observed in Fig. 2(b). The wavelength interval where the quantum efficiency decreased significantly corresponds to the range where the filter is opaque, i.e. λ < 350 nm. The antireflective effect of the filter results in an increase of EQE _fi with respect to EQE ₀ in the wavelength range 420 nm < λ < 550 nm. An enhancement of EQE _fi is also observed in the range 650 nm < λ < 770 nm due to the directional selectivity of the filter. Integrating the standardized AM1.5g solar spectrum [15

R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985). [CrossRef]

] over the EQE without and with filter, yields short-circuit current densities J _SC of 13.40 and 13.66 mAcm⁻², respectively. Thus, we detect a total gain of 0.26 mAcm⁻². Thereof 0.20 mAcm⁻² are due to the improvement in the wavelength range 650 nm – 770 nm resulting from the directional selectivity of the filter.

In order to find a measure to quantify the improvement of light trapping, we compare the measured reflectance r(λ) to the prediction of Lambert-Beer’s law

r (λ) = e^{- α (λ) w_{opt} (λ)} .

(4)

Under the assumption of negligible reflectance at the front surface, Eq. (4) defines the effective (or equivalent) optical path length w _opt(λ) (regardless whether or not the actual reflectance is physically described by Lambert-Beer.) The path length enhancement factor k _0/fi(λ) for the solar cell without/with filter is defined by the relation w _opt(λ) = k _0/fi(λ)w between the optical path length w _opt and the geometrical thickness w. From Eq. (4) we obtain

k_{0/fi} (λ) = - \ln (r_{0/fi} (λ)) / (w α (λ)) .

(5)

Since our experiment compares the reflectance of the same device with and without filter the absorption α as well as geometrical thickness w remain unchanged. Thus, the ratio

κ_{r} (λ) : = \frac{k_{fi} (λ)}{k_{0} (λ)} = \ln (r_{fi} (λ)) / \ln (r_{0} (λ))

(6)

can be determined directly from the reflectance data. With similar arguments we define

κ_{EQE} (λ) : = \frac{\ln [1 - E Q E_{fi} (λ)]}{\ln [1 - E Q E_{0} (λ)]} .

(7)

The quantities κ_r and κ_EQE can be considered as improvement factors for the additional light trapping provided by the filter. Figure 3(a) depicts these factors obtained with the help of Eqs. (6) and (7) from the reflectance and EQE data in Fig. 2. For 350 nm < λ < 650 nm, κ_r is above unity due to the reduction of direct reflection by the filter. According to the relatively small increase in the EQE seen in Fig. 2(d), the quantity κ_EQE is only slightly larger than unity in this spectral range. In contrast for λ > 650 nm both quantities, κ_r as well as κ_EQE, increase significantly above unity because of the additional light trapping due to the directional selectivity of the filter. In this range, κ_r represents a factor quantifying the additional light path prolongation in the device. The peak value κ_r,max ≈3.5 seen in Fig. 3(a) implies that close to the threshold wavelength λ₀ = 767 nm the light path in the device is enhanced by a factor of 3.5 due to the filter. The factor κ_EQE obtained from the EQE is again below κ_r and peaks at a maximum value of κ_EQE,max ≈1.5. The quantity κ_EQE represents that portion of the light path prolongation that is useful for generating additional short-circuit current density. The large difference between the improvement factor κ_EQE and κ_r is due to parasitic absorption in the TCO and at the back contact. Such losses impose limitations on any effort to maximize light trapping in solar cells [16

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983). [CrossRef]

]. At the peak values the light path in the device is prolonged by κ_r,max-1 ≈250%. However, the useful enhancement is only κ_EQE,max-1 ≈50%, i.e. only 20% of the additional light confinement is used for generating additional short-circuit current density and 80% is parasitically absorbed.

Fig. 3 (a) The optical path length improvement κ_r calculated from the data in Fig. 2(a) demonstrates the enhanced light trapping in the device for wavelengths 650 nm < λ < 770 nm. In the range 350 nm < λ < 650 nm the improvement is not due to the spectral selectivity, but rather to the anti reflective properties of the filter. The effective path length improvement κ_EQE shows the same wavelength dependence but a weaker increase than κ_r. (b) The maximum values of the improvement factors

\bar{κ}

_r and

\bar{κ}

_EQE depend on absorber layer thickness and the used superstrate (dots: AsahiU, squares: Corning glass). The error bars represent the standard deviation of the 5-12 investigated samples for each data point.

Figure 3(b) demonstrates that the maximum values for the improvement factors

\bar{κ}

_r and

\bar{κ}

_EQE depend on the absorber thicknesses and especially on the superstrates (textured SnO2:F on AsahiU glass and etched ZnO:Al on Corning glass). For all thicknesses and superstrates we have achieved a substantial reduction of the re-emission leading to

\bar{κ}

_r,max > 2 in all cases. The plotted error bars represent the standard deviation obtained from the number of investigated cells (5-12 cells per data point). The significantly enhanced parasitic absorption of AsahiU glass, however, impedes an improvement of the EQE leading to

\bar{κ}

_EQE,max < 1 except for the 420 nm cells. The fact that the values of

\bar{κ}

_EQE,max increase for thicker cells on Asahi-U may be due to a better ratio between effective and parasitic absorption.

Figure 4(a) shows the external quantum efficiency EQE _fi(θ) measured under various angles of incidence θ. A steeper decrease with increasing θ is observed in the active wavelength range of the filter 650 nm < λ < 770 nm. An additional decrease in EQE _fi(θ) at λ ~390 nm occurs due to destructive interference in the multilayer filter. Figure 4(b) shows the quotient EQE _fi(θ)/EQE ₀(θ) obtained from a cell with filter and a cell from the same preparation run without filter. The ratio EQE _fi/EQE ₀ drops sharply if θ exceeds the wavelength dependent threshold value. Losses are marked in black. The beneficial effect of the filter is represented by the white area where EQE _fi(θ) > EQE ₀(θ). The grey area around λ = 650 nm with 1.0 < EQE _fi/EQE ₀ < 0.9 most probably results from the fact that two different samples are used to generate the plot. The dashed line in Fig. 4(b) is calculated from Eq. (3) with λ₀ = 767 nm and λ₁ = 600 nm and demonstrates that the directional selectivity of the filter is well described by the simple Bragg characteristic. The spectral range of the improvement corresponds to the upper and lower threshold wavelengths λ₀ and λ₁ in Eq. (3). The restriction of the directional selectivity of the filter to the relatively small spectral range between λ₀ and λ₁ as well as the small selectivity close to λ₁ explain the relatively small increase in the short-circuit current density. A use of a higher dielectric contrast as provided by the present combination of Ta₂O₅/SiO₂ possibly could provide a larger spectral width for the directional selectivity.

Fig. 4 (a) The dependence of the external quantum efficiency EQE _fi of a 414 nm thick a-Si:H solar cell (prepared on Corning glass) on the angle of incidence θ is used to characterize the Bragg filter. (b) The effect of the filter is visualized by dividing EQE _fi by EQE ₀ obtained from a sample without filter prepared in the same run. The dashed line is calculated from Eq. (3) using λ₀ = 767 nm and λ₁ = 600 nm.

4. Conclusions

This paper has demonstrated that the use of a directional selective filter can improve light trapping in solar cells and enhance the overall short-circuit current density. For a-Si:H thin-film solar cells the improvement depends on the texture of the front TCO and the thickness of the active absorber layer. A maximum improvement of ΔJ _sc = 0.26 mAcm⁻² is found when using textured ZnO and an absorber thickness of 322 nm. Here 0.06 mAcm⁻² are due to the antireflective effect of the filter and 0.20 mAcm⁻² due to its directional selectivity. The demonstrated enhancement of the optical path length up to a factor of κ_r = 3.5 emphasizes the potential of directional selectivity for improving the light trapping. The full use of this potential is limited by parasitic absorption in the contact layers of the present devices.

Acknowledgements

Partial funding of this project by the German Federal Ministry of Education and Research (Nanovolt, 03SF0322H) and the German Research Foundation (Nanosun, RA 473/6-1) is acknowledged. We are grateful for valuable discussions with all our project partners and colleagues. Special thank to Andreas Lambertz for providing the samples and to Christoph Zahren, Dirk Erdweg, Wilfried Reetz and Muhammad Tayyib for experimental support.

References

1.	T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983). [CrossRef]
2.	H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]
3.	E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]
4.	J. C. Miñano, “Optical confinement in photovoltaics,“ in Physical Limitations to the Photovoltaic Solar Energy Conversion, A. Luque and G. L. Araújo, eds. (Hilger, Bristol, UK,1990), p. 55.
5.	M. A. Green, “High efficiency solar cells,” (Trans Tech Publications, Switzerland, 1987), p. 80.
6.	R. Brendel, “Thin-film crystalline silicon solar cells,” (Wiley-VCH, Weinh., Germany, 2003), pp. 193–199.
7.	V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005). [CrossRef]
8.	C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008). [CrossRef]
9.	C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008). [CrossRef]
10.	W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961). [CrossRef]
11.	G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994). [CrossRef]
12.	M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009). [CrossRef]
13.	J. Turunen, and F. Wyrowski, Diffractive Optics for industrial and commercial applications (Akademie Verlag, Berlin, Germany, 1997), Chap. 12.4.
14.	A. Löffl, S. Wieder, B. Rech, O. Kluth, C. Beneking, and H. Wagner, “Al-doped ZnO films for thin-film solar cells with very low sheet resistance and controlled texture,” Proc. 14th Europ. PV Sol. En. Conf., Barcelona, 1997, p. 2089.
15.	R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985). [CrossRef]
16.	H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983). [CrossRef]

OCIS Codes
(220.1770) Optical design and fabrication : Concentrators
(230.1480) Optical devices : Bragg reflectors
(310.1620) Thin films : Interference coatings
(350.6050) Other areas of optics : Solar energy
(310.6188) Thin films : Spectral properties

ToC Category:
Thin Films

History
Original Manuscript: April 9, 2010
Revised Manuscript: May 12, 2010
Manuscript Accepted: May 12, 2010
Published: May 19, 2010

Citation
Carolin Ulbrich, Marius Peters, Benedikt Bläsi, Thomas Kirchartz, Andreas Gerber, and Uwe Rau, "Enhanced light trapping in thin-film solar cells by a directionally selective filter," Opt. Express 18, A133-A138 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S2-A133

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References

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983). [CrossRef]
H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]
E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]
J. C. Miñano, “Optical confinement in photovoltaics,“ in Physical Limitations to the Photovoltaic Solar Energy Conversion, A. Luque and G. L. Araújo, eds. (Hilger, Bristol, UK,1990), p. 55.
M. A. Green, “High efficiency solar cells,” (Trans Tech Publications, Switzerland, 1987), p. 80.
R. Brendel, “Thin-film crystalline silicon solar cells,” (Wiley-VCH, Weinh., Germany, 2003), pp. 193–199.
V. Badescu, “Spectrally and angularly selective photothermal and photovoltaic converters under one-sun illumination,” J. Phys. D Appl. Phys. 38(13), 2166–2172 (2005). [CrossRef]
C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and light trapping in solar cells,” Photonics for Solar Energy Systems II,” Proc. SPIE 7002, 70020A (2008). [CrossRef]
C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light trapping in solar cells,” Phys. Status Solidi., A Appl. Mater. Sci. 205(12), 2831–2843 (2008). [CrossRef]
W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961). [CrossRef]
G. Araújo and A. Martí, “Absolute limiting efficiencies for photovoltaic energy conversion,” Sol. Energy Mater. Sol. Cells 33(2), 213–240 (1994). [CrossRef]
M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap – improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009). [CrossRef]
J. Turunen, and F. Wyrowski, Diffractive Optics for industrial and commercial applications (Akademie Verlag, Berlin, Germany, 1997), Chap. 12.4.
A. Löffl, S. Wieder, B. Rech, O. Kluth, C. Beneking, and H. Wagner, “Al-doped ZnO films for thin-film solar cells with very low sheet resistance and controlled texture,” Proc. 14th Europ. PV Sol. En. Conf., Barcelona, 1997, p. 2089.
R. Hulstrom, R. Bird, and C. Riordan, “Spectral solar irradiance data sets for selected terrestrial conditions,” Solar Cells 15(4), 365–391 (1985). [CrossRef]
H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous silicon solar cells,” Appl. Phys. Lett. 42(11), 968–970 (1983). [CrossRef]

Abeles, B.
Araújo, G.
Atwater, H. A.
Badescu, V.
Bird, R.
Bläsi, B.
Cebulka, J. M.
Deckman, H. W.
Fahr, S.
Goldschmidt, J. C.
Gombert, A.
Hulstrom, R.
Kirchartz, T.
Lederer, F.
Löper, P.
Martí, A.
Pelz, J.
Peters, M.
Polman, A.
Queisser, H. J.
Rau, U.
Riordan, C.
Rockstuhl, C.
Shockley, W.
Tiedje, T.
Ulbrich, C.
Üpping, J.
Wehrspohn, R.
Witzke, H.
Wronski, C. R.
Yablonovitch, E.

Appl. Phys. Lett.

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