Light trapping by backside diffraction gratings in silicon solar cells ...

8 downloads 363 Views 2MB Size Report
Abstract: This numerical study investigates the influence of rectangular backside diffraction gratings on the efficiency of silicon solar cells. Backside gratings are ...
Light trapping by backside diffraction gratings in silicon solar cells revisited Markus Wellenzohn* and Rainer Hainberger AIT Austrian Institute of Technology GmbH, Health & Environment Department, Nano Systems, Vienna, Austria * [email protected]

Abstract: This numerical study investigates the influence of rectangular backside diffraction gratings on the efficiency of silicon solar cells. Backside gratings are used to diffract incident light to large propagation angles beyond the angle of total internal reflection, which can significantly increase the interaction length of long wavelength photons inside the silicon layer and thus enhance the efficiency. We investigate the influence of the silicon thickness on the optimum grating period and modulation depth by a simulation method which combines a 2D ray tracing algorithm with rigorous coupled wave analysis (RCWA) for calculating the grating diffraction efficiencies. The optimization was performed for gratings with period lengths ranging from 0.25 µm to 1.5 µm and modulation depths ranging from 25 nm to 400 nm under the assumption of normal light incidence. This study shows that the achievable efficiency improvement of silicon solar cells by means of backside diffraction gratings strongly depends on the proper choice of the grating parameters for a given silicon thickness. The relationship between the optimized grating parameters resulting in maximum photocurrent densities and the silicon thickness is determined. Moreover, the thicknesses of silicon solar cells with and without optimized backside diffraction gratings providing the same photocurrent densities are compared. ©2011 Optical Society of America OCIS codes: (350.6050) Solar energy; (050.1950) Diffraction gratings.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

A. Goetzberger, J. Knobloch, and B. Voss, Crystalline silicon solar cells (John Wiley & Sons, 1998). M. J. Kerr, A. Cuevas, and P. Campbell, “Limiting efficiency of crystalline silicon solar cells due to Coulombenhanced Auger recombination,” Prog. Photovolt. Res. Appl. 11(2), 97–104 (2003). K. Taretto and U. Rau, “Modeling extremely thin absorber solar cells for optimized design,” Prog. Photovolt. Res. Appl. 12(8), 573–591 (2004). P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983). C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). R. H. Morf, H. Kiess, and C. Heine, Diffractive optics for solar cells,“ in Diffractive Optics for Industrial and Commercial Applications edited by J. Turunen and F. Wyrowski, 361-389 (Akademie Verlag, 1997). R. H. Morf and J. Gobrecht, “Optimized diffractive structures for light trapping in thin silicon solar cells,” Proc. of the 10th Workshop on Quantum Solar Energy Conversion (1998). P. Voisin, M. Peters, H. Hauser, C. Helgert, E. B. Kley, T. Pertsch, B. Bläsi, M. Hermle, and S. W. Glunz, “Nanostructured back side silicon solar cells,” 24th European PV Solar Energy Conference and Exhibition, paper 2DV.1.4. (2009). M. Peters, M. Rüdiger, D. Pelzer, H. Hauser, M. Hermle, and B. Bläsi, “Electro-optical modelling of solar cells with photonic structures,” 25th European PV Solar Energy Conference and Exhibition, 87–91 (2010). J. Gjessing, E. S. Marstein, and A. Sudbø, “2D back-side diffraction grating for improved light trapping in thin silicon solar cells,” Opt. Express 18(6), 5481–5495 (2010). 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). J. G. Mutitu, S. Shi, A. Barnett, and D. W. Prather, “Light trapping enhancement in thin silicon solar cells using photonic crystals,” 35th IEEE Photovoltaic Spec. Conf. (IEEE,2010), pp. 2208–2212. M. Wellenzohn and R. Hainberger, “A 2D numerical study of the photo current density enhancement in silicon solar cells with optimized backside gratings,” 37th IEEE Photovoltaic Spec. Conf. (IEEE, 2011), paper 836.

#154175 - $15.00 USD (C) 2011 OSA

Received 6 Sep 2011; revised 2 Nov 2011; accepted 4 Nov 2011; published 15 Nov 2011 2 January 2012 / Vol. 20, No. S1 / OPTICS EXPRESS A20

14. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi angle investigation,” J. Appl. Phys. 83(6), 3323–3326 (1998). 15. K. Rajkanan, R. Singh, and J. Shewchun, “Absorption coefficient of silicon for solar cell calculations,” SolidState Electron. 22(9), 793–795 (1979). 16. M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995). 17. M. O. D. Diffract, www.rsoftdesign.com 18. S. H. Zaidi, J. M. Gee, and D. S. Ruby, Diffraction grating structures in solar cells,” in Conference Record of the Twenty-Eighth IEEE Photovoltaic Specialists Conference (IEEE, 2000), pp. 395–398. 19. D. Abou-Ras, T. Kirchartz, and U. Rau, Advanced Characterization Techniques for Thin Film Solar Cells (Wiley-VCH, 2011).

1. Introduction In order to maximize light absorption inside silicon solar cells, on the one hand, reflection losses at the front side have to be minimized and, on the other hand, the optical interaction length of photons, in particular in the wavelength region between 900 nm and 1140 nm, which contains 25% of the photons in the useable range of the solar spectrum between 300 nm and 1140 nm but is only weakly absorbed by silicon, has to be increased. The former can be accomplished by antireflection coatings and pyramid structures fabricated by anisotropic etching [1]. The latter can to some extent be achieved by pyramid structures. Increasing the silicon thickness is a further option, however, at the cost of higher material use and increased electrical losses [2,3]. Another approach are backside gratings that diffract the incident light to large propagation angles beyond the angle of total internal reflection and, thus, significantly increase the interaction length of long wavelength photons. This light trapping scheme was first studied by Sheng for thin film solar cells with amorphous [4] and later in more detail by Morf and Heine for crystalline silicon solar cells [5–7]. During the past years this concept has attracted the interest of several research groups, which investigated different grating geometries [8–10] as well photonic crystals at the backside of silicon solar cells [11,12]. However, in all these studies the thickness of the silicon solar cell was either kept constant or the influence of the silicon thickness on the optimum grating structure was neglected. Previously published preliminary results showed that the thickness of the solar cell has to be taken into account when optimizing the grating design [13]. In this paper, we perform an optimization of the grating geometry parameters for silicon thicknesses dSi ranging from 1 µm up to 200 µm, which provides deeper insight into the relationship of these parameters. Different to the majority of other studies, we extend our investigation to a wide range of grating periods Λ and modulation depths h. Moreover, we compare the silicon thicknesses of cells with and without optimized backside gratings having the same efficiencies. 2. Simulation model and method Figure 1 depicts the structures of the silicon solar cells without and with backside grating investigated in this study. The flat front surface is covered with a single layer antireflection (AR) coating made of 80 nm silicon nitride (SiNx), which minimizes the reflection losses at the solar cell front side. The rear side is covered with a 100-nm thick SiO2 layer, which increases the reflectance of the backside aluminum electrode. In order to accurately model the impact of a backside grating on the efficiency of a silicon solar cell, precise knowledge of the imaginary part, i.e., the extinction coefficient is indispensible. Various sources provide the wavelength dependent complex refractive index of silicon determined either by ellipsometry or intensity transmission measurements [14,15]. In this study, we use Green’s data [16]. For calculating the photocurrent density generated in the solar cell we combined a 2D ray tracing algorithm with rigorous coupled wave analysis (RCWA) for determining the diffraction efficiencies of the gratings [17]. First, a database containing the diffraction efficiencies of gratings with different period lengths and modulation depths depending on the angle of incidence, wavelength, polarization, and diffraction order m was prepared employing the RCWA method. In a second step, the transfer matrix method was

#154175 - $15.00 USD (C) 2011 OSA

Received 6 Sep 2011; revised 2 Nov 2011; accepted 4 Nov 2011; published 15 Nov 2011 2 January 2012 / Vol. 20, No. S1 / OPTICS EXPRESS A21

a)

Air

b)

Incident beam

SiNx

Air

dSiNx=80nm

Si

SiNx

m=1

dSiNx=80nm

m=2

Θ2Θ1 Θm

m>-2

m>2

dSi

h

dSiO2=100nm

SiO2

m=0 m=-1

m=-2

Si

dSi

Al

Incident beam

Al

Λ

dSiO2=100nm

SiO2

Fig. 1. Investigated silicon solar cells structures a) without and b) with backside grating.

used to calculate the reflection coefficient of the front surface antireflection coating as a function of angle of incidence, wavelength, and polarization resulting in a second database. Next, for each grating configuration the light absorbed inside the silicon was calculated by means of a ray tracing algorithm, which sums up the absorption experienced by the rays according to Beer Lambert’s law. For a given wavelength each ray was traced until its fractional intensity was smaller than a minimum limit or the number of reflections at the backside grating exceeded six. Diffraction at the backside grating was taken into account up to the fifth order (m=5) generating new rays with fractional intensities according to the corresponding diffraction efficiency values stored in the database. At the front side, the fractional intensity of each ray propagating inside the silicon was attenuated according to the reflection loss. This procedure was performed for 85 wavelengths in the range of 300 nm to 1140 nm in 10-nm steps for both polarizations. The photocurrent density was obtained by summing up the number of absorbed photons over the solar spectrum (AM 1.5) and averaging over both polarizations assuming that each absorbed photon generates an electron hole pair, i.e., electrical loss mechanisms are omitted. The photocurrent is defined by λ =1140 nm



J ph = e

A(λ ) S (λ )d λ ,

(1)

λ = 300 nm

where A(λ) is the photon absorption inside the silicon, S(λ) is the incident photon flux, and e is the elementary charge. The theoretical limit of the photocurrent density is reached in the case when all photons are absorbed in the silicon layer and generate an electron-hole pair, which corresponds to a photocurrent density of about −40 mA/cm2 omitting electrical losses. The correctness of our combined RCWA/ray tracing approach we verified by comparing the absorption spectra of 3-µm and 60-µm thick silicon solar cells with results of full RCWA simulations, which are much more computationally expensive. Figure 2 plots the results for a)

dSi=3 µm, Λ=700 nm, h=50 nm

b)

dSi=60 µm, Λ=925 nm, h=75 nm

80

0.8 80

absorption (%)

1.0 100

absorption (%)

100

60 40 20 0

600 600

800 800

wavelength (nm)

0.4 40 0.2 20

full RCWA 2D raytracing & RCWA 400 400

0.6 60

1000 1000

0.00

full RCWA 2D raytracing & RCWA 400 400

600 600

800 800

wavelength (nm)

1000 1000

Fig. 2. Absorption spectra calculated by the combined RCWA/ray tracing approach and by full RCWA simulations for 3-µm and 60-µm thick silicon solar cells with backside gratings. Results for TE and TM polarization are averaged. The dashed lines indicate results of the combined RCWA/ray tracing approach for structures without grating.

two structures with gratings indicating a good match between both methods. The oscillations in the full RCWA simulation results are due to interference effects not taken into account by

#154175 - $15.00 USD (C) 2011 OSA

Received 6 Sep 2011; revised 2 Nov 2011; accepted 4 Nov 2011; published 15 Nov 2011 2 January 2012 / Vol. 20, No. S1 / OPTICS EXPRESS A22

the ray tracing method. These oscillations are averaged out when calculating the photocurrent densities. The photocurrent densities derived from the results of the two methods differ by