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Fundamental limit of light trapping in grating structures

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We use a rigorous electromagnetic approach to analyze the fundamental limit of light-trapping enhancement in grating structures. This limit can exceed the bulk limit of 4n 2, but has significant angular dependency. We explicitly show that 2D gratings provide more enhancement than 1D gratings. We also show the effects of the grating profile’s symmetry on the absorption enhancement limit. Numerical simulations are applied to support the theory. Our findings provide general guidance for the design of grating structures for light-trapping solar cells.

©2010 Optical Society of America

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Figures (8)

Fig. 1
Fig. 1 a) Grating structure with periodicity L = 600nm. Brown ribbons are non-absorptive dielectric medium with index n2 = 12.5. The widths of three air slots are 4%, 12%, and 24% of the period respectively. The absorptive film (grey) is d = 3000nm thick. The whole structure is placed on a perfect mirror (yellow). b) and c) Absorption spectra obtained by numerical simulations for s (b) and p (c) polarized incident light. Light is incident from the normal direction. Red lines represent spectrally-averaged absorption in the presence of the grating and blue lines represent single-pass absorption in the absence of the grating.
Fig. 2
Fig. 2 a) Channels in 1D k-space. b) Resonances in a film with 1D grating. Dots represent resonances. c) Upper limit of absorption enhancement in 1D grating films without mirror symmetry.
Fig. 3
Fig. 3 a) 1D grating structure with mirror symmetry. Air slot width is 40% of the period. The film is the same as that in Fig. 1a. b) Limit of absorption enhancement in grating structures with mirror symmetry. c) and d) Absorption spectra obtained by numerical simulations for s and p polarization lights, respectively. Lights are incident from the normal direction.
Fig. 4
Fig. 4 Absorption spectra for off-normally incident light (averaged among s and p lights). Light incidence angle is 30° and incident plane is oriented at azimuthal angle 30°. a) for the asymmetrical structure in Fig. 1a. b) for the symmetrical structure in Fig. 3a.
Fig. 5
Fig. 5 a) Channels in 2D k-space. Blue and grey dots represent channels when the incident light comes in from normal and off-normal directions, respectively. The radius of the circle is k0 . b) Limit of absorption enhancement in 2D grating structures. c) Angular response of the average enhancement factor integrated over wavelength from 600nm to 1200nm. The periodicity of the grating is 600nm. d) the same as (c) except the periodicity is 3000nm.
Fig. 6
Fig. 6 a) The unit of cell of a 2D grating structure. Film thickness is the same as the structure in Fig. 1a. b) Absorption spectrum for normally incident light (averaged among two polarizations). c) Spectra of the running average enhancement factors. Blue: simulation result. Red: analytical theory. d. average enhancement factor for different incidence angles θ. The azimuthal angle is fixed at φ = 0 . Blue dots are simulation results and red is analytical theory.
Fig. 7
Fig. 7 a) Channels in 2D k-space for a grating with triangular lattice periodicity. The lattice constant is L. b) Upper limit of absorption enhancement for gratings with triangular lattice periodicity.
Fig. 8
Fig. 8 Absorption spectrum for structure shown in Fig. 6a. except that the film is replaced with crystalline silicon. Dashed line is single-pass absorption spectrum.

Equations (17)

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d d t a = ( j ω 0 N γ e + γ i 2 ) a + j γ e S
A ( ω ) = γ i γ e ( ω ω 0 ) 2 + ( γ i + N γ e ) 2 / 4
σ = A ( ω ) d ω
σ = 2 π γ i N + γ i / γ e
σ max = 2 π γ i N
A = σ max Δ ω = 2 π γ i Δ ω M N
F = A α d = 2 π γ i α d Δ ω M N
N = 2 k 0 2 π / L = 2 L λ
M = 2 n 2 π ω c 2 ( L 2 π ) ( d 2 π ) Δ ω
F = A d α = π n
N = 2 k 0 2 π / L + 1 = 2 L λ + 1
L > > λ / n d > > λ / n
M s y m = M / 2
S e v e n = 1 2 ( S k / / + S k / / ) S o d d = 1 2 ( S k / / S k / / )
M = 8 π n 3 ω 2 c 3 ( L 2 π ) 2 ( d 2 π ) Δ ω .
G m , n = m 2 π L x ^ + n 2 π L y ^ ,
k = k / / + G m , n   ,
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