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Analysis and optimization of surface plasmon-enhanced organic solar cells with a metallic crossed grating electrode

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Abstract

We perform a systematic analysis of enhanced short-circuit current density (Jsc) in organic solar cells (OSCs) where one metallic electrode is optically thick and the other consists of a two-dimensional metallic crossed grating. By examining a model device representative of such surface plasmon (SP)-enhanced OSCs by the Fourier modal and finite-element methods for electromagnetic and exciton diffusion calculations, respectively, we provide general guidelines to maximize Jsc of the SP-enhanced OSCs. Based on this study, we optimize the performance of a small-molecule OSC employing a copper phthalocyanine–fullerene donor–acceptor pair, demonstrating that the optimized SP-enhanced device has Jsc that is 75 % larger than that of the optimized device with an ITO-based conventional structure.

© 2012 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1 Schematic of a model device representative of a surface plasmon-enhanced OSC. The two-dimensional Ag grating electrode has a square lattice with a period of ΛG, whose unit cell is drawn in red-dotted lines. The grating linewidth is 0.25ΛG. The orientation of the Cartesian coordinates is shown, with O on the grating surface denoting the origin. Also shown are the directions of the wave vector (k) and electric field (E) of an incident plane wave.
Fig. 2
Fig. 2 (a) Calculated absorption efficiency (ηabs) of the model device with torg = 70 nm, tu = 30 nm, ta = 10 nm, and tl = 30 nm, as a function of the grating period (ΛG) and the wavelength (λ) of the incident light. The maximum of ηabs is 0.71. (b) The z-component of the electric field corresponding to point ‘a’ (λ = 680 nm, ΛG = 380 nm) in (a). (c) The electric field intensity (|E|2 = E · E*) corresponding to point ‘a’. (d) The z-component of the electric field corresponding to point ‘b’ (λ = 760 nm, ΛG = 320 nm). (e) The electric field intensity corresponding to point ‘b’. E0 denotes the amplitude of the incident electric field. In (b) to (e), solid lines represent materials boundaries, and grating boundaries that do not lie on the planes shown are drawn as dotted lines.
Fig. 3
Fig. 3 (a) Calculated absorption efficiency (ηabs) of the model device with torg = 50 nm, tu = 10 nm, ta = 10 nm, and tl = 30 nm, as a function of the grating period (ΛG) and the wavelength (λ) of the incident light. The maximum of ηabs is 0.76. (b) The z-component of the electric field corresponding to point ‘a’ (λ = 660 nm, ΛG = 380 nm) in (a). (c) The electric field intensity (|E|2 = E · E*) corresponding to point ‘a’. (d) The z-component of the electric field corresponding to point ‘b’ (λ = 760 nm, ΛG = 320 nm). (e) The electric field intensity corresponding to point ‘b’.
Fig. 4
Fig. 4 (a) Internal quantum efficiency (ηint) of the model device with torg = 50 nm, tu = 10 nm, and ΛG = 320 nm versus γta/Ld, calculated for different values of Ld and λ. The black solid line shows ηint calculated using Eq. (6). (b) Steady-state exciton density profile (nexc) in the active layer when ta = 3.5 nm, Ld = 5 nm, and λ = 760 nm. The top (z = 30 nm) and bottom (z = 33.5 nm) faces correspond to the UTL– and LTL–active layer interfaces, respectively, where at the former (or latter) interface the exciton dissociation velocity is zero (or infinite).
Fig. 5
Fig. 5 (a) (Top) Absorption coefficient (α) of CuPc (red) and C60 (blue). (Bottom) Absorption efficiency (ηabs), as a function of the grating period (ΛG) and the wavelength (λ), of the active layer in the organic solar cell based on the CuPc and C60 DA heterojunction. The maximum of ηabs is 0.74. (b) The z-component of the electric field corresponding to point ‘a’ (λ = 600 nm, ΛG = 320 nm) in (a). (c) The z-component of the electric field corresponding to point ‘b’ (λ = 620 nm, ΛG = 200 nm).
Fig. 6
Fig. 6 (a) Short-circuit current density (Jsc) (red), solar-spectrum-weighted absorption efficiency (〈ηabs〉) (blue), and internal quantum efficiency (ηint) (black) versus γ = tCuPc/LCuPc = tC60/LC60 of the surface plasmon (SP)-enhanced CuPc–C60 solar cell with torg = 50 nm, and tu = 5 nm. (b) External quantum efficiency (ηext) of the optimized SP-enhanced device (red, γ = 1.0), compared with that of the optimized ITO-based device (black) consisting of: glass / 150 nm ITO / 5 nm PEDOT:PSS / 13 nm CuPc / 21 nm C60 / 29 nm BPhen / 100 nm Ag.
Fig. 7
Fig. 7 (a) Schematic diagram showing the orientation and polarization of an incident plane wave. An s-polarized (or p-polarized) plane wave whose electric field is drawn as a red (or blue) arrow has the electric (or magnetic) field vector perpendicular to the plane of incidence drawn as green dotted lines. (b) Schematic of a device considered to calculate the ergodic limit shown in (c), where an active layer is sandwiched between a perfect back reflector and an ideal front Lambertian surface with an ideal anti-reflection coating. (c) Short-circuit current density (Jsc) of the optimized SP-enhanced device in Sec. 4 versus incident polar angle (θ) for three azimuthal angles, ϕ = 0° (red), 22.5° (blue), and 45° (green). For comparison, Jsc of the optimized ITO-based device in Sec. 4 (brown) and the device shown in (b) (Ergodic limit, black open squares) are also shown. ‘+’ and ‘×’ symbols refer to s- and p-polarizations, respectively. The three black lines are J sc max cos θ, where J sc max is Jsc(θ = 0°) for each device.

Equations (12)

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J sc = q η ext ( λ ) S ( λ ) d λ ,
η int = 𝒜 J sc ( r , λ ) / q d 2 r 𝒱 G exc ( r , λ ) d 3 r ,
L d 2 τ 2 n exc n exc τ + G exc = 0 ,
J sc = q L d 2 τ | e n n exc ( r , λ ) | ,
η abs = 𝒱 G exc ( r , λ ) d 3 r 𝒜 I 0 ( r , λ ) d 2 r = 𝒱 Re { n ˜ ( λ ) } α ( λ ) E ( r , λ ) E * ( r , λ ) d 3 r n 0 | E 0 | 2 𝒜 ,
η int L d t tanh t L d ,
J sc q η int η abs ( λ ) S ( λ ) d λ .
η abs = η abs ( λ ) S ( λ ) d λ S ( λ ) d λ ,
J sc q η int η abs S ( λ ) d λ ,
Re ( n ˜ eff ) = Re ( n ˜ CuPc ) t CuPc + Re ( n ˜ C 60 ) t C 60 t a and
α eff = α CuPc t CuPc + α C 60 t C 60 t a .
η abs = 1 e 4 α eff t a 1 e 4 α eff t a + e 4 α eff t a ( Re ( n ˜ eff ) ) 2 .
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