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Broadband absorption and efficiency enhancement of an ultra-thin silicon solar cell with a plasmonic fractal

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Abstract

We report in this work that quantum efficiency can be significantly enhanced in an ultra-thin silicon solar cell coated by a fractal-like pattern of silver nano cuboids. When sunlight shines this solar cell, multiple antireflection bands are achieved mainly due to the self-similarity in the fractal-like structure. Actually, several kinds of optical modes exist in the structure. One is cavity modes, which come from Fabry-Perot resonances at the longitudinal and transverse cavities, respectively; the other is surface plasmon (SP) modes, which propagate along the silicon-silver interface. Due to the fact that several feature sizes distribute in a fractal-like structure, both low-index and high-index SP modes are simultaneously excited. As a whole effect, broadband absorption is achieved in this solar cell. Further by considering the ideal process that the lifetime of carriers is infinite and the recombination loss is ignored, we demonstrate that external quantum efficiency of the solar cell under this ideal condition is significantly enhanced. This theoretical finding contributes to high-performance plasmonic solar cells and can be applied to designing miniaturized compact photovoltaic devices.

©2013 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1 The schematic ultra-thin silicon solar cell with a plasmonic fractal, which consists of a silver (Ag) fractal-like pattern (thickness d1) coated on the top, a crystalline silicon (c-Si) absorb layer (thickness d2) in the middle and a silver (Ag) back reflector (thickness d3) on the bottom. The inset on top left is the front view of the pattern.
Fig. 2
Fig. 2 (a)-(c) Calculated reflectance spectra of three silicon solar cells with base-periodicity patterns: (a) P1 = 100nm, and W1 = 25nm; (b) P2 = 200nm, and W2 = 100nm; (c) P3 = 400nm, and W3 = 200nm, respectively. The insets show the related schematic patterns. (d)-(f) Dispersion maps of these three silicon solar cells, k// is the in-plane wave vector, and kg = 2π / P3 for normalization. Black dotted lines are the light cone lines. Color bar shows the calculated reflection intensity. In all three solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively.
Fig. 3
Fig. 3 Electric field distributions of three ultra-thin silicon solar cells with base-periodicity patterns. The cross sections are at the center of the silver nano cuboids (x-z plane, y = 0nm). C M is the longitudinal cavity mode in the left column, C M is the transverse cavity mode in the middle column, and SP is the surface plasmon mode in the right column, respectively. (a) For period P1 = 100nm, C M (1) and C M (1) are excited at λ = 430nm, 780nm. (b) For period P2 = 200nm, C M (2) , C M (2) and SP(2)(1,0) are excited at λ = 430nm, 754nm and 890nm. (c) For period P3 = 400nm, C M (3) , C M (3) , C M (3') , SP(3)(2,0), SP(3′)(5,0) are excited at λ = 430nm, 820nm, 875nm, 914nm, and 670nm, respectively.
Fig. 4
Fig. 4 Calculated absorbance spectra of the solar cells (i.e., the absorbance of 50nm thick Si film) and the absorbance spectra of Ag nano cuboids in the structures with different base-periodicity patterns, respectively. (a) and (d) P1 = 100nm and W1 = 25nm; (b) and (e) P2 = 200nm and W2 = 100nm; (c) and (f) P3 = 400nm and W3 = 200nm. In all three solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively. Besides, black-dotted and brown-dotted lines in Fig. 4(a) illustrate the absorbance spectra of ref-1 (free-standing 50nm-thick Si film) and ref-2 (50nm-thick Si film with a 250nm-thick Ag back reflector), and both of these references are without any plasmonic structures on the top.
Fig. 5
Fig. 5 (a) The schematic silicon solar cell with a plasmonic fractal, which contains 3 length-scales. (b) Dispersion map of this silicon solar cell with the fractal. k// is the in-plane wave vector, and kg = 2π / P3 for normalization. Black dotted lines are the light cone lines. Color bar shows the calculated reflection intensity. (c) Calculated reflectance spectrum of this silicon solar cell with the fractal. (d) Calculated absorbance spectrum of a silicon solar cell with this fractal (red line). Green, blue and orange lines are the absorbance spectra of silicon solar cells with base-periodicity patterns in Figs. 4(a)-4(c). In these solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively. (e) Calculated reflectance spectrum of this silicon solar cell with the fractal and a 100nm-thick SiO2 antireflection coating (ARC). (f) Calculated absorbance spectrum of this silicon solar cell with the fractal and a 100nm-thick SiO2 antireflection coating (ARC) (violet line).
Fig. 6
Fig. 6 Calculated quantum efficiencies of the 50nm-thick silicon solar cells: i) ref-1 (free-standing 50nm-thick Si film) and ref-2 (50nm-thick Si film with a 250nm-thick Ag back reflector). Both of these references are without any plasmonic structures on the top. ii) Three silicon solar cells with base-periodicity patterns (P1 = 100nm, P2 = 200nm, P3 = 400nm), and iii) the silicon solar cell with a plasmonic fractal and the one with a plasmonic fractal plus a dielectric ARC, respectively. The QEs are 3.16%, 6.55%, 7.46%, 8.05%, 9.27%, 12.05% and 14.22% respectively. In five plasmonic solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(bottom Ag) = 250nm, respectively. The dielectric ARC is a 100nm-thick SiO2 film, which deposits on Si film with the plasmonic fractal inside.
Fig. 7
Fig. 7 Calculated quantum efficiency of the silicon solar cells with plasmonic fractals for different base-units and duty ratios. The unit size (P) of fractals is defined as P = 4P1 = 2P2 = P3 and the duty ratio (f) of silver in the fractal patterns is defined as f = 2W1/P1 = W2/P2 = W3/P3. The period is varied from 400nm to 1000nm for every 100nm and duty ratio is varied from 0.3 to 0.7 for every 0.1. In all these solar cells, the thicknesses of the layers are d1(Ag) = 20nm, d2(Si) = 50nm, and d3(back Ag) = 250nm, respectively.

Equations (4)

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k SP = k 0 ε d ε m ε d + ε m ,
λ min = P i 2 + j 2 ε d ε m ε d + ε m .
A(λ)=ωIm(ε) | E | 2 dV,
QE= λ 1 λ 2 λ c A(λ)× I AM1.5G (λ) dλ λ 1 λ 2 λ c I AM1.5G (λ) dλ ,
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