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Morphology-dependent light trapping in thin-film organic solar cells

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Abstract

The active layer materials used in organic photovoltaic (OPV) cells often self-assemble into highly ordered morphologies, resulting in significant optical anisotropies. However, the impact of these anisotropies on light trapping in nanophotonic OPV architectures has not been considered. In this paper, we show that optical anisotropies in a canonical OPV material, P3HT, strongly affect absorption enhancements in ultra-thin textured OPV cells. In particular we show that plasmonic and gap-mode solar cell architectures redistribute electromagnetic energy into the out-of-plane field component, independent of the active layer orientation. Using analytical and numerical calculations, we demonstrate how the absorption in these solar cell designs can be significantly increased by reorienting polymer domains such that strongly absorbing axes align with the direction of maximum field enhancement.

© 2013 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1 (a) Surface plasmon (SP) and gap mode (GM) OPV architectures and |Ez|2 mode profiles, (b) molecular orientation of P3HT and a model material, zP3HT, which consists of P3HT molecules oriented such that the polymer chains are aligned out-of-plane, (c) anisotropic real and imaginary parts of the P3HT and zP3HT dielectric functions versus wavelength. The P3HT dielectric function is measured by spectroscopic ellipsometry, while zP3HT is modeled by switching the in-plane (||) and out-of-plane (⊥) optical coefficients of P3HT.
Fig. 2
Fig. 2 (a) Real part of the SP effective index for P3HT (black), zP3HT (red), and air (blue, dashed), and the real part of the out-of-plane top dielectric material index for P3HT (black) and zP3HT (red). (b) Imaginary part of the SP effective index and out-of-plane dielectric index for the same materials, showing that out-of-plane absorption is the dominant contributor to SP modal loss. The dashed line indicates λp, the wavelength at which the plasma resonance ε d , | | ε d , = ε m 2 occurs.
Fig. 3
Fig. 3 (a) Fraction of power absorbed in the polymer for an SP mode. The dashed line indicates λp. (b) Integrated absorption weighted by the AM1.5 solar spectrum [41] for increasing thickness, h, of the polymer thin film atop a Ag substrate (shown in inset). Single pass absorption through each material is plotted with dashed lines for comparison.
Fig. 4
Fig. 4 (a) Effective indices of a gap mode with P3HT and zP3HT in the gap as a function of gap height and wavelength, (b) integrated absorbance of the gap-mode structure for both P3HT (black) and zP3HT (red) as a function of gap height using the following methods: transfer matrix method (TMM, left panel, dashed-dotted lines), electrostatic limit (ES, left panel, solid lines), rigorous coupled wave analysis (RCWA, right panel, solid lines), and single pass absorption (right panel, dashed lines). (inset) Out-of-plane field profile at 550 nm in the active layer beneath the numerically optimized coupling grating from [7]. (c) Side view of the grating structure used for RCWA calculations and indices used for TMM calculations where the scattering layer has been replaced with an average index of ns = 1.87.
Fig. 5
Fig. 5 (a) Real part of the SP effective index for P3HT, zP3HT, P3HT(rotated, y-direction), and zP3HT(max). (b) Imaginary part of the SP effective index for the same set of materials showing the theoretical bounds of losses with reorientation.
Fig. 6
Fig. 6 Geometry and propagation vector definitions for anisotropic SP dispersion derivation.
Fig. 7
Fig. 7 (a),(c) RCWA calculated absorption versus wavelength and active layer thickness, (b),(d) field intensities and absorption density inside the active area at λ0 = 550 nm and h = 5 nm for P3HT and zP3HT, indicated by white circles in (a), (c).

Equations (42)

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D ( ω ) = ε 0 ε ( ω ) E ( ω ) = ε 0 [ ε ˜ | | ( ω ) 0 0 0 ε ˜ | | ( ω ) 0 0 0 ε ˜ ( ω ) ] E ( ω )
A ( ω ) = ω ε 0 2 V E Im { ε } E * d V = ω ε 0 2 V ε | | | E x | 2 + ε | | | E y | 2 + ε | E z | 2 d V
β ˜ SP = k 0 [ ε ˜ d , ε ˜ m ( ε ˜ d , | | ε ˜ m ) ε ˜ d , | | ε ˜ d , ε ˜ m 2 ] 1 2
A SP , total = 1 1 + [ 4 π n SP κ SP ] 1 .
A SP , polymer = ξ a A SP , total .
F ES = 4 n H n L ( 1 3 + 1 3 + n H 4 3 n L 4 ) .
A ES = α L , | | h α L , | | h + [ 4 n H n L , | | ( 2 3 + 1 3 ε L , ε L , | | n H 4 | n ˜ L , | 4 ) ] 1 .
ε P 3 HT = [ ε ˜ | | 0 0 0 ε ˜ | | 0 0 0 ε ˜ ] = [ ε ˜ SA 0 0 0 ε ˜ SA 0 0 0 ε ˜ WA ]
ε P 3 HT ( rotated ) = [ ε ˜ WA 0 0 0 ε ˜ SA 0 0 0 ε ˜ SA ] .
ε z P 3 HT = [ ε ˜ WA 0 0 0 ε ˜ WA 0 0 0 ε ˜ SA ] .
χ eff = χ 0 π cos ( θ ) cos ( θ ) d θ 0 π d θ = χ 2 .
ε ˜ SA = 1 + χ eff = 1 + χ 2 .
ε ˜ z P 3 HT ( max ) , = 1 + χ = 2 ε ˜ S A 1 .
ε z P 3 HT ( max ) = [ 1 0 0 0 1 0 0 0 2 ε ˜ SA 1 ] .
H y = H 0 { exp ( j β ˜ x + j k ˜ z I z ) Region I exp ( j β ˜ x j k ˜ z I z ) Region II .
ε d = ( ε ˜ d , | | 0 0 0 ε ˜ d , | | 0 0 0 ε ˜ d , ) ,
E x = { k ˜ z I ω ε 0 ε ˜ d , | | H y Region I k ˜ z II ω ε 0 ε ˜ m H y Region II
E z = { β ˜ ω ε 0 ε ˜ d , H y Region I β ˜ ω ε 0 ε ˜ m H y Region II .
ε d ( ω ) E ( ω ) = x ε ˜ d , | | E x + z ε ˜ d , E z I = 0 ,
E x = k ˜ z I ε ˜ d , β ˜ ε ˜ d , | | E z I = k ˜ z II β ˜ E z II
k ˜ z II = ε ˜ m ε ˜ d , | | k ˜ z I ,
k ˜ z I 2 ε ˜ d , | | + β ˜ 2 ε ˜ d , = k 0 2
ε m k ˜ z I 2 ε ˜ d , | | + β ˜ 2 ε ˜ m = k 0 2 .
A w g = α eff h α eff h + [ 4 ( ρ t o t ν g ρ 0 c ) ] 1 .
A w g = α eff h α eff h + [ n eff λ 0 h ] 1 = 1 1 + [ 4 π n eff κ eff ] 1 ,
F w g = 2 π γ eff α 0 h d ω M w g N ,
N = 2 π k 0 2 ( L 2 π ) 2 ,
m w g = π β w g 2 ( L 2 π ) 2 .
M w g = d m w g = 2 π β w g 2 ν g ( L 2 π ) 2 d ω
F w g = α eff n eff λ 0 α 0 h ,
A w g = α 0 h α 0 h + F w g 1 = α eff h α eff h + [ n eff λ 0 h ] 1 = 1 1 + [ 4 π n eff κ eff ] 1 .
A = ω ε 0 2 [ 0 ε d , | | | E x | 2 + ε d , | E z | 2 d z + ε m 0 | E x | 2 + | E z | 2 d z ] .
A I = 1 4 ω ε 0 [ ε d , | | | k ˜ z I | 2 | ε d , | | | 2 k ˜ z I + ε d , | β ˜ | 2 | ε d , | 2 k ˜ z I ] H 0 2 exp ( 2 β x ) ,
A II = 1 4 ω ε 0 [ ε m | k ˜ z II | 2 | ε m | 2 k ˜ z II + ε m | β ˜ | 2 | ε m | 2 k ˜ z II ] H 0 2 exp ( 2 β x ) .
ξ a = A I A I = A II = ε d , | | | k z I | 2 | ε ˜ d , | | | 2 k z I + ε d , | β ˜ | 2 | ε ˜ d , | 2 k z I ε d , | | | k z I | 2 | ε ˜ d , | | | 2 k z I + ε d , | β ˜ | 2 | ε ˜ d , | 2 k z I + ε m | k z II | 2 | ε ˜ m | 2 k z II + ε m | β ˜ | 2 | ε ˜ m | 2 k z II ,
γ m = A m W m = ω gap ε L , | | | E x , m | 2 + ε L , | | | E y , m | 2 + ε L , | E z , m | 2 d V n 2 ( r ) | E | 2 d V .
n 2 ( r ) | E | 2 d V n H 2 | E 0 | 2 L 2 D .
γ m = ω ( ε L , | | | E x , m 0 | 2 + ε L , | | | E y , m 0 | 2 + ε L , n H 4 | n ˜ L , | 4 | E z , m 0 | 2 ) L 2 h n H 2 | E 0 | 2 L 2 D
m | E x , m 0 | 2 = m | E y , m 0 | 2 = m | E z , m 0 | 2 = 1 3 M | E 0 | 2 ,
a ES = m 2 π γ m N d ω = 4 n H n L , | | ( 2 3 + 1 3 ε L , ε L , | | n H 4 | n ˜ L , | 4 ) α L , | | h .
F ES a ES α L , | | h = 4 n H n L , | | ( 2 3 + 1 3 ε L , ε L , | | n H 4 | n ˜ L , | 4 )
A E S = α L , | | h α L , | | h + F ES 1 = α L , | | h α L , | | h + [ 4 n H n L , | | ( 2 3 + 1 3 ε L , ε L , | | n H 4 | n ˜ L , | 4 ) ] 1 .
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