Abstract

We theoretically investigate the light-trapping properties of one- and two-dimensional periodic patterns etched on the front surface of c-Si and a-Si thin film solar cells with a silver back reflector and an anti-reflection coating. For each active material and configuration, absorbance A and short-circuit current density Jsc are calculated by means of rigorous coupled wave analysis (RCWA), for different active materials thicknesses in the range of interest of thin film solar cells and in a wide range of geometrical parameters. The results are then compared with Lambertian limits to light-trapping for the case of zero absorption and for the general case of finite absorption in the active material. With a proper optimization, patterns can give substantial absorption enhancement, especially for 2D patterns and for thinner cells. The effects of the photonic patterns on light harvesting are investigated from the optical spectra of the optimized configurations. We focus on the main physical effects of patterning, namely a reduction of reflection losses (better impedance matching conditions), diffraction of light in air or inside the cell, and coupling of incident radiation into quasi-guided optical modes of the structure, which is characteristic of photonic light-trapping.

© 2011 OSA

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  33. S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express18, 4260–4274 (2010).
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    [CrossRef]
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    [CrossRef]
  42. A. Mellor, I. Tobs, A. Mart, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt: Res. Appl.19, 676–687 (2011).
    [CrossRef]
  43. N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films451–452, 397–401 (2004).
    [CrossRef]
  44. H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, “Silicon thin-film solar cells with rectangular-shaped grating couplers,” Prog. Photovolt: Res. Appl.14, 13–24 (2006).
    [CrossRef]
  45. L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett.89, 111111 (2006).
    [CrossRef]
  46. L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett.93, 221105 (2008).
    [CrossRef]
  47. I. Prieto, B. Galiana, P. A. Postigo, C. Algora, L. J. Martnez, and I. Rey-Stolle, “Enhanced quantum efficiency of Ge solar cells by a two-dimensional photonic crystal nanostructured surface,” Appl. Phys. Lett.94, 191102 (2009).
    [CrossRef]
  48. J. Zhu, Z. Yu, G. F. Burkhard, C. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9, 279–282 (2009).
    [CrossRef]
  49. O. El Daif, E. Drouard, G. Gomard, A. Kaminski, A. Fave, M. Lemiti, S. Ahn, S. Kim, P. Roca i Cabarrocas, H. Jeon, and C. Seassal, “Absorbing one-dimensional planar photonic crystal for amorphous silicon solar cell,” Opt. Express18, A293–A299 (2010).
    [CrossRef] [PubMed]
  50. M. Tsai, H. Han, Y. Tsai, P. Tseng, P. Yu, H. Kuo, C. Shen, J. Shieh, and S. Lin, “Embedded biomimetic nanostructures for enhanced optical absorption in thin-film solar cells,” Opt. Express19, A757–A762 (2011).
    [CrossRef] [PubMed]
  51. Q. Hu, J. Wang, Y. Zhao, and D. Li, “A light-trapping structure based on Bi2O3 nano-islands with highly crystallized sputtered silicon for thin-film solar cells,” Opt. Express19, A20–A27 (2011).
    [CrossRef] [PubMed]
  52. A. Naqavi, K. Söderström, F. J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express19, 128–140 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  54. D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B60, 2610–2618 (1999).
    [CrossRef]
  55. M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, “Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media,” Phys. Rev. B77, 035324 (2008).
    [CrossRef]
  56. M. Caglar, S. Ilican, Y. Caglar, and F. Yakuphanoglou, “The effect of Al doping on the optical constants of ZnO thin films prepared by spray pyrolysis method,” J. Mater. Sci: Mater. Electron.19, 704–708 (2008).
    [CrossRef]
  57. Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510, 95–101 (2006).
    [CrossRef]

2011

J.N. Munday and H.A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett.11, 2195–2201 (2011).
[CrossRef]

M. Agrawal and M. Frei, “Rigorous optical modeling and optimization of thin-film photovoltaic cells with textured transparent conductive oxides,” Prog. Photovolt: Res. Appl. DOI: (2011).
[CrossRef]

T. Lanz, B. Ruhstaller, C. Battaglia, and C. Ballif, “Extended light scattering model incorporating coherence for thin-film silicon solar cells,” J. Appl. Phys.110, 033111 (2011).
[CrossRef]

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys.110, 033104 (2011).
[CrossRef]

R. Dewan, I. Vasilev, V. Jovanov, and D. Knipp, “Optical enhancement and losses of pyramid textured thin-film silicon solar cells,” J. Appl. Phys110, 013101 (2011).
[CrossRef]

A. Mellor, I. Tobs, A. Mart, M. J. Mendes, and A. Luque, “Upper limits to absorption enhancement in thick solar cells using diffraction gratings,” Prog. Photovolt: Res. Appl.19, 676–687 (2011).
[CrossRef]

X. Meng, G. Gomard, O. E. Daif, E. Drouard, R. Orobtchouk, A. Kaminski, A. Fave, M. Lemiti, A. Abramov, P. Roca i Cabarrocas, and C. Seassal, “Absorbing photonic crystals for silicon thin-film solar cells: Design, fabrication and experimental investigation,” Solar Energy Mat. Solar Cells95, S32–S38 (2011).
[CrossRef]

Q. Hu, J. Wang, Y. Zhao, and D. Li, “A light-trapping structure based on Bi2O3 nano-islands with highly crystallized sputtered silicon for thin-film solar cells,” Opt. Express19, A20–A27 (2011).
[CrossRef] [PubMed]

A. Naqavi, K. Söderström, F. J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express19, 128–140 (2011).
[CrossRef] [PubMed]

M. Tsai, H. Han, Y. Tsai, P. Tseng, P. Yu, H. Kuo, C. Shen, J. Shieh, and S. Lin, “Embedded biomimetic nanostructures for enhanced optical absorption in thin-film solar cells,” Opt. Express19, A757–A762 (2011).
[CrossRef] [PubMed]

2010

S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express18, 4260–4274 (2010).
[CrossRef] [PubMed]

O. El Daif, E. Drouard, G. Gomard, A. Kaminski, A. Fave, M. Lemiti, S. Ahn, S. Kim, P. Roca i Cabarrocas, H. Jeon, and C. Seassal, “Absorbing one-dimensional planar photonic crystal for amorphous silicon solar cell,” Opt. Express18, A293–A299 (2010).
[CrossRef] [PubMed]

R. Esteban, M. Laroche, and J. J. Greffet, “Dielectric gratings for wide-angle, broadband absorption by thin film photovoltaic cells,” Appl. Phys. Lett.97, 221111 (2010).
[CrossRef]

C. Ulbrich, M. Peters, B. Bläsi, T. Kirchartz, A. Gerber, and U. Rau, “Enhanced light trapping in thin-film solar cells by a directionally selective filter,” Opt. Expr.18, A133–A138 (2010).
[CrossRef]

M. Peters, M. Rüdiger, B. Bläsi, and W. Platzer, “Electro optical simulation of diffraction in solar cells,” Opt. Expr.18, A584–A593 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18, A367–A380 (2010).
[CrossRef]

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

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

2009

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys.106, 074901 (2009).
[CrossRef]

I. Prieto, B. Galiana, P. A. Postigo, C. Algora, L. J. Martnez, and I. Rey-Stolle, “Enhanced quantum efficiency of Ge solar cells by a two-dimensional photonic crystal nanostructured surface,” Appl. Phys. Lett.94, 191102 (2009).
[CrossRef]

J. Zhu, Z. Yu, G. F. Burkhard, C. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9, 279–282 (2009).
[CrossRef]

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, A95–A107 (2009).
[CrossRef]

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, 14312–14321 (2009).
[CrossRef] [PubMed]

2008

Y. Lee, C. Huang, J. Chang, and M. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling-factor gratings,” Opt. Express16, 7969–7975 (2008).
[CrossRef] [PubMed]

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Opt. Express16, 15238–15248 (2008).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express16, 21793–21800 (2008).
[CrossRef] [PubMed]

M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, “Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media,” Phys. Rev. B77, 035324 (2008).
[CrossRef]

M. Caglar, S. Ilican, Y. Caglar, and F. Yakuphanoglou, “The effect of Al doping on the optical constants of ZnO thin films prepared by spray pyrolysis method,” J. Mater. Sci: Mater. Electron.19, 704–708 (2008).
[CrossRef]

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett.93, 221105 (2008).
[CrossRef]

M. Kroll, S. Fahr, C. Helgert, C. Rockstuhl, F. Lederer, and T. Pertsch, “Employing dielectric diffractive structures in solar cells a numerical study,” Phys. Stat. Sol. (a)205, 2777–2795 (2008).
[CrossRef]

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys.103, 093102 (2008).
[CrossRef]

2007

K. R. Catchpole, “A conceptual model of the diffuse transmittance of lamellar diffraction gratings on solar cells,” J. Appl. Phys.102, 013102 (2007).
[CrossRef]

K. R. Catchpole and M. A. Green, “A conceptual model of light coupling by pillar diffraction gratings,” J. Appl. Phys.101, 063105 (2007).
[CrossRef]

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, 16986–17000 (2007).
[CrossRef] [PubMed]

2006

Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films510, 95–101 (2006).
[CrossRef]

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, “Silicon thin-film solar cells with rectangular-shaped grating couplers,” Prog. Photovolt: Res. Appl.14, 13–24 (2006).
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett.89, 111111 (2006).
[CrossRef]

J. Krc̆, G. Cernivec, A. Campa, J. Malmström, M. Edoff, F. Smole, and M. Topic̆, “Optical and electrical modeling of Cu(In,Ga)Se2 solar cells,” Optical and Quantum Electronics38, 1115–1123 (2006).
[CrossRef]

2004

N. Senoussaoui, M. Krause, J. Müller, E. Bunte, T. Brammer, and H. Stiebig, “Thin-film solar cells with periodic grating coupler,” Thin Solid Films451–452, 397–401 (2004).
[CrossRef]

2003

J. Krc̆, M. Zeman, O. Kluth, F. Smole, and M. Topic̆, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films426, 296–304 (2003).
[CrossRef]

2002

M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Progr. Photovolt: Res. Appl.10, 235–241 (2002).
[CrossRef]

M. I. Alonso, M. Garriga, C. A. Durante Rincán, E. Hernández, and M. León, “Optical functions of chalcopyrite CuGaxIn1−xSe2 alloys,” Appl. Phys. A74, 659–664 (2002).
[CrossRef]

2000

S. Hava and M. Auslender, “Design and analysis of low-reflection grating microstructures for a solar energy absorber,” Solar Energy Mat. Solar Cells61, 143–151 (2000).
[CrossRef]

1999

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B60, 2610–2618 (1999).
[CrossRef]

1995

1982

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

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29, 300–305 (1982).
[CrossRef]

1972

D. T. Pierce and W. E Spicer, “Electronic structure of amorphous Si from photoemission and optical studies,” Phys. Rev. B5, 3017–3029 (1972).
[CrossRef]

1911

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93, 191113 (2008).

Aberle, A. G.

M. Peters, C. Battaglia, A. G. Aberle, B. Bläsi, J. Luther, and S. Glunz, “3D optical simulation of scattering in thin film silicon solar cells,” in Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition, (Hamburg, September 5–9, 2011) paper 3AV.3.4.

Abramov, A.

X. Meng, G. Gomard, O. E. Daif, E. Drouard, R. Orobtchouk, A. Kaminski, A. Fave, M. Lemiti, A. Abramov, P. Roca i Cabarrocas, and C. Seassal, “Absorbing photonic crystals for silicon thin-film solar cells: Design, fabrication and experimental investigation,” Solar Energy Mat. Solar Cells95, S32–S38 (2011).
[CrossRef]

Agrawal, M.

M. Agrawal and M. Frei, “Rigorous optical modeling and optimization of thin-film photovoltaic cells with textured transparent conductive oxides,” Prog. Photovolt: Res. Appl. DOI: (2011).
[CrossRef]

Ahn, S.

Alamariu, B. A.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett.93, 221105 (2008).
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett.89, 111111 (2006).
[CrossRef]

Algora, C.

I. Prieto, B. Galiana, P. A. Postigo, C. Algora, L. J. Martnez, and I. Rey-Stolle, “Enhanced quantum efficiency of Ge solar cells by a two-dimensional photonic crystal nanostructured surface,” Appl. Phys. Lett.94, 191102 (2009).
[CrossRef]

Alonso, M. I.

M. I. Alonso, M. Garriga, C. A. Durante Rincán, E. Hernández, and M. León, “Optical functions of chalcopyrite CuGaxIn1−xSe2 alloys,” Appl. Phys. A74, 659–664 (2002).
[CrossRef]

Andreani, L. C.

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Optical and Quantum Electronics

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Figures (11)

Fig. 1
Fig. 1

Short-circuit current density Jsc for c-Si (indirect band-gap), a-Si, CdTe and CuIn1−xGaxSe2 (CIGS, direct band-gap, taking x = 0.08) as a function of thickness, under AM1.5 solar spectrum [3]. Solid lines refer to the single pass case, while dashed lines refer to the Lambertian light-trapping limit denoted as LLα in this paper [9]. In both cases reflection losses are not considered.

Fig. 2
Fig. 2

Scheme of silicon PV cells patterned with a simple 1D photonic lattice (a) and with a square 2D lattice (b).

Fig. 3
Fig. 3

(a) Multilayer subdivision of PV cells along z (the unit cell volume used for A calculation is enclosed with dash line). (b) Convergence of the calculated absorbance (main panel) and Jsc (inset) as a function of the number NPW of plane waves involved in the calculation.

Fig. 4
Fig. 4

Contour plot of short-circuit current density Jsc as a function of etching depth h and ratios b/a and r/a (in %) for c-Si PV cells patterned with a simple 1D lattice (a) and square 2D lattice (b). For both patterns the thickness d=1μm and the optimal period a=600 nm.

Fig. 5
Fig. 5

Calculated optical spectra (for unpolarized light) for c-Si PV cells patterned with optimal 1D simple lattice (d=1 μm, a=600 nm, h=240 nm, b/a=0.3): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (a), absorbance A (b) and absorption enhancement F (c). Calculated optical spectra (for unpolarized light) for c-Si PV cells patterned with optimal 2D square lattice (d=1 μm, a=600 nm, h=190 nm, r/a=0.33): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (d), absorbance A (e) and absorption enhancement F (f). For absorbance the Lambertian limits LL0 and LLα are reported, together with single pass (SP) absorption with and without reflection losses. The thin grey lines refer to the calculated data, while the thick black lines are the corresponding smoothed quantities.

Fig. 6
Fig. 6

Spectral contributions dJsc/dE to short-circuit current density Jsc for c-Si PV cells patterned with optimized 1D and square 2D square lattices. Thickness d=1μm, optimal period a=600 nm.

Fig. 7
Fig. 7

(a) Calculated short-circuit current densities Jsc for c-Si PV cells patterned with optimized 1D and square 2D lattices varying the thickness d of the starting active material’s slab. (b) Jsc for optimal configurations as a function of period a and thickness d.

Fig. 8
Fig. 8

Contour plot of short-circuit current density Jsc as a function of etching depth h and ratios b/a and r/a (in %) for a-Si PV cells patterned with a simple 1D photonic lattice (a) and square 2D lattice (b). For both patterns the thickness d=300 nm and the optimal period a=300 nm.

Fig. 9
Fig. 9

Calculated optical spectra (for unpolarized light) for a-Si PV cells patterned with optimal 1D simple lattice (d=300 nm, a=300 nm, h=210 nm, b/a=0.55): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (a), absorbance A (b) and absorption enhancement with respect to single pass absorption without reflection losses, F (c). Calculated optical spectra (for unpolarized light) for a-Si PV cells patterned with optimal 2D square lattice (d=300 nm, a=300 nm, h=215 nm, b/a=0.4): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (d), absorbance A (e) and absorption enhancement with respect to single pass absorption without reflection losses, F (f). For absorption the Lambertian limits LL0 and LLα are reported, together with single-pass absorption with and without reflection losses.

Fig. 10
Fig. 10

Spectral contributions dJsc/dE to short-circuit current density Jsc for a-Si PV cells patterned with optimized 1D and square 2D lattices. The thickness d=300 nm, the optimal period a=300 nm.

Fig. 11
Fig. 11

(a) Calculated short-circuit current densities Jsc for a-Si PV cells patterned with optimized 1D and square 2D lattices varying the thickness d of the starting active material’s slab. (b) Jsc for optimal configurations as a function of period a and thickness d.

Equations (9)

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F F S i = 1 π r 2 a 2 F F A R C = π r 2 a 2 .
J ( V ) = J s c J 0 [ e e V K B T 1 ] ,
J s c = e E g A ( E ) d 𝒩 d E I Q E ( E ) d E e E g A ( E ) d 𝒩 d E d E E g d J s c ( E ) d E d E ,
E ( ρ , z ) = n = 0 N P W 1 E ˜ ( G n , z ) e i ( k / / + G n ) ρ ,
A + R + T + n 0 R n + n 0 T n = 1 ,
4 n 2 α d 1 ,
A s p ( E ) = 1 e α ( E ) d .
A L L 0 ( E ) = 1 e 4 n 2 α ( E ) d ,
F ( E ) = A ( E ) A s p ( E ) = A ( E ) 1 e α ( E ) d ,

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