1. Introduction

Organic solar cells (OSCs) have received considerable attention owing to their possibility of realizing low-cost, large-area, flexible devices [1, 2]. However, the highest power-conversion efficiency reported in literature is still below 10% [3], limiting its practical deployment. One of the important device parameters determining the power-conversion efficiency is the short-circuit current density (J_sc), which is the current density passing through the illuminated device when it is short-circuited. It can be expressed as

Absorption of a photon in an organic semiconductor creates an exciton, a bound electron-hole pair with a binding energy ranging from ∼ 0.1 eV to ∼ 1.0 eV [4, 5]. In OSCs, dissociation of this tightly bound exciton into an electron and a hole typically occurs at an interface between two organic semiconductors with an appropriate band offset, called a donor–acceptor (DA) interface. To achieve high η_int, most excitons generated in an active layer must diffuse to the DA interface, which means that the thickness of the active layer must be chosen to be smaller than ∼ L_d, where L_d is the exciton diffusion length in the active layer. Since L_d of organic semiconductors (∼ 10 nm [6–8]) is typically much less than the optical absorption length (= 1/α ∼ 100 nm, where α is the absorption coefficient), an active layer whose thickness is smaller than ∼ L_d is too thin to have high η_abs. In short, J_sc in OSCs is limited by a trade-off between η_int and η_abs [9].

One strategy to overcome this limitation is to increase the optical absorption in thin (∼ L_d) active layers by exploiting optical resonances. In planar microcavity devices, where the active layers are sandwiched between optically thick and semitransparent metal layers, by varying the device geometry, Fabry-Perot resonances are tuned to locate the maximum of the enhanced optical field intensity near the active layers [10–12]. Surface plasmon (SP) resonances associated with metallic periodic structures [13–17] or nanoparticles [18–21] have also been utilized to enhance the optical absorption in thin active layers. Although these demonstrations have shown improved device performance, in most cases exploiting SP resonances, a thorough analysis as to how the device geometry affects its performance has not been performed, and the trade-off between η_abs and η_int has not been fully examined in device optimizations.

Here, we systematically analyze a model device representative of SP-enhanced OSCs employing an optically thick metallic electrode and a two-dimensional (2D) metallic crossed grating electrode, examining both optical absorption and exciton diffusion. Based on electromagnetic and exciton-diffusion calculations using the Fourier modal and finite-element methods, respectively, we investigate how the variation in device geometry affects η_abs and η_int. The results of the investigation are then applied to a realistic device employing a copper phthalocyanine (CuPc)–fullerene (C₆₀) heterojunction (HJ), which demonstrates general guidelines for maximizing J_sc of the SP-enhanced OSCs. The optimized CuPc–C₆₀ device has J_sc that is 75 % larger than that of the optimized device with an ITO-based conventional structure.

This paper is organized as follows. In Sec. 2, we provide a brief analysis of short-circuit currents of planar HJ OSCs. Section 3 examines optical absorption and exciton diffusion in a model device representing SP-enhanced OSCs with a 2D metallic crossed grating electrode. In Sec. 4, we present the optimization of a SP-enhanced OSC with a CuPc–C₆₀ heterojunction, followed by conclusion in Sec. 6.

2. Analysis of short-circuit currents of planar heterojunction organic solar cells

One strategy to overcome the trade-off between η_abs and η_int is to properly tailor the optical property of the device so that optical resonance allows for high η_abs in an active layer with a thickness t ≤∼ L_d that guarantees high η_int. A layer in a solar cell is called an active layer in this paper, if photon absorption in that layer contributes to photocurrent. A solar cell can have multiple active layers for broad spectral sensitivity. For simplicity, we assume that there is only one active layer in devices discussed in Secs. 2 and 3. For a device with multiple active layers, η_abs and η_int are the summations of the contributions from each active layer. In a planar HJ (as opposed to bulk-HJ) OSCs, η_int(λ) under short-circuit condition can be determined by

Meanwhile, η_abs(λ) is given by

When t is sufficiently thin so that the variation in G_exc along the direction normal to the device surface can be ignored, and the characteristic dimension of the in-plane variation in G_exc is much smaller than t, the exciton diffusion can be considered a one-dimensional problem. Under this condition, the analytic solution of Eq. (3) can be used to approximate Eq. (2) as [6]:

Defining the solar-spectrum-weighted absorption efficiency [16] as

3. Electromagnetic and exciton-diffusion analyses of model devices

Figure 1 schematically shows a structure of a planar HJ OSC employing a 2D Ag grating electrode supporting SP resonances. The device consists of, from the bottom layer in Fig. 1, 100 nm Ag electrode / organic multilayer / 2D Ag grating electrode / glass. The 2D grating electrode has a square lattice symmetry with a period of Λ_G, and the linewidth and the thickness of the grating are 0.25Λ_G and 20 nm, respectively. The organic multilayer with total thickness t_org consists of lower transport layer (LTL) / active layer / upper transport layer (UTL), where the LTL and UTL are optically inactive and transport photo-generated holes and electrons, respectively, from the active layer to the respective electrode. The LTL and UTL thicknesses are t_l and t_u, respectively. For efficient collection of holes, square regions between the grating lines are filled with the same material chosen for the UTL. The active layer with thickness t_a is composed of an absorbing material with Re(ñ) = 1.75 and α = 1.5 × 10⁵ cm⁻¹ throughout the spectral region that we consider, 300 nm ≤ λ ≤ 800 nm. For the UTL and LTL, ñ = 1.75, and for glass, ñ = 1.5. For Ag, we use the values for ñ reported in literature [24]. The exciton diffusion length in the active layer is L_d, and the exciton dissociation velocities at the LTL– and UTL–active layer interfaces are infinite and zero, respectively. We also assume that the glass substrate occupies the infinite lower (z < 0) half-space, ignoring small reflection at the air-glass interface, which in practice is minimized by an anti-reflection coating. With these assumptions, the device shown in Fig. 1 serves as a model device, of which we perform electromagnetic and exciton-diffusion simulations to investigate how η_abs and η_int vary with the device geometry in the broad spectral region.

 

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 Λ_G, whose unit cell is drawn in red-dotted lines. The grating linewidth is 0.25Λ_G. 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.

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Figure 2(a) shows calculated η_abs, as a function of λ and Λ_G, of the 10-nm-thick active layer in the model device with t_u = 30 nm and t_l = 30 nm, when it is illuminated by a x-polarized (E || x̂) plane wave with wavelength λ and a wave vector normal to the device surface. The active layer thickness is chosen to be similar to L_d’s of organic semiconductors commonly employed in OSCs [6–8]. The calculation was performed using the Fourier modal method [25, 26]. We applied Li’s Fourier factorization rules [27] and the enhanced transmittance matrix method [28], and exploited the two-fold mirror-reflection symmetry [29] to obtain E(r, λ), from which η_abs was obtained from Eq. (5). The high-η_abs region including point marked ‘a’ is attributed to resonant excitation of a SP mode. The z-component of the electric field (E_z) spreads throughout the organic multilayer, with induced charges localized at the LTL–Ag interface and the top and bottom surfaces of the grating, as shown in Fig. 2(b). There exists another SP mode that can be resonantly excited, whose E_z profile corresponding to point marked ‘b’ in Fig. 2(a) is shown in Fig. 2(d). In this case, the field is more concentrated near the grating compared with the profile in Fig. 2(b), displaying the field profile characteristic of the localized dipolar SP resonance associated with a metallic nanoparticle. The profiles of the electric field intensity in the horizontal planes bisecting the active layer are shown in Figs. 2(c) and 2(e). The intensity profile for point ‘a’ is distributed throughout the active layer regions below the grating holes, with some degree of inter-hole coupling through the grating lines parallel to the x axis (Fig. 2(c)). In contrast, for the case of point ‘b’, the electric field intensity is localized along the regions below the edges of the grating lines parallel to the y axis, with negligible inter-hole coupling. Noting the contrasts in electric field intensity distribution in the active layer (Fig. 2(c) and 2(e)), as well as in E_z profile throughout the device (Fig. 2(b) and 2(d)), we refer to the mode corresponding to point ‘a’ (or ‘b’) as the distributed-SP (or localized-SP) mode. Although the intensity maximum in the active layer for the localized-SP (LSP) mode is higher that that for the distributed-SP (DSP) mode, the high-intensity region for the LSP mode is limited in its extent, resulting in lower η_abs compared with the DSP case.

 

Fig. 2 (a) Calculated absorption efficiency (η_abs) of the model device with t_org = 70 nm, t_u = 30 nm, t_a = 10 nm, and t_l = 30 nm, as a function of the grating period (Λ_G) and the wavelength (λ) of the incident light. The maximum of η_abs is 0.71. (b) The z-component of the electric field corresponding to point ‘a’ (λ = 680 nm, Λ_G = 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, Λ_G = 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.

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The field profile shown in Fig. 2(d) suggests that if t_org is decreased, the overlap between the high-intensity region of the LSP mode and the active layer may increase, allowing one to utilize both DSP and LSP modes for the absorption enhancement. Figure 3(a) shows η_abs(λ, Λ_G) of the active layer in a model device, where t_org is decreased from 70 nm to 50 nm by decreasing t_u from 30 nm to 10 nm. The other geometrical parameters and materials properties are not changed. The E_z and the intensity profiles of the DSP mode (point ‘a’ in Fig. 3(a)), shown in Figs. 3(b) and 3(c), respectively, resemble the corresponding profiles shown in Fig. 2, resulting in the enhancement in η_abs similar to that obtained in the model device with t_org = 70 nm. More notable is that another high-η_abs region, including point ‘b’, associated with the LSP modes is now clearly visible. As shown in Fig. 3(d), the decrease in t_org leads to stronger coupling between SPs localized in the grating region and at the LTL–Ag interface. As a result, compared with the previous case, the electric field intensity is more uniform along the z direction. This, along with the fact that the active layer is located closer to the grating–UTL interface, results in a much higher field intensity in the active layer (Fig. 3(e)), thereby leading to high η_abs. Consequently, unlike the previous case with t_org = 70 nm, both DSP and LSP modes contribute to the absorption enhancement, which is obtained over a broad spectral region.

 

Fig. 3 (a) Calculated absorption efficiency (η_abs) of the model device with t_org = 50 nm, t_u = 10 nm, t_a = 10 nm, and t_l = 30 nm, as a function of the grating period (Λ_G) and the wavelength (λ) of the incident light. The maximum of η_abs is 0.76. (b) The z-component of the electric field corresponding to point ‘a’ (λ = 660 nm, Λ_G = 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, Λ_G = 320 nm). (e) The electric field intensity corresponding to point ‘b’.

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The linewidth of the grating is another factor that affects η_abs. By calculating η_abs(λ, Λ_G) of the model device with t_org = 50 nm for different grating fill factors (F), defined as the ratio of the grating linewidth to Λ_G, we find the following. When ∼ 0.2 < F <∼ 0.3, the magnitudes and the extents of the high-η_abs regions in the (λ, Λ_G)-plane associated with the DSP and LSP modes remain similar to those in Fig. 3(a). Also, with increasing F (in ∼ 0.2 < F <∼ 0.3), (i) the absorption enhancement associated with the LSP modes occurs at longer wavelengths, since the width of the metallic “particles” increases, and (ii) the location of that associated with the DSP modes in the (λ, Λ_G)-plane remains relatively unchanged, since the distributed nature of the DSP modes makes them sensitive primarily to Λ_G. When F deviates farther from 0.25, η_abs decreases due to decreased resonance features (for small F) or increased reflection (for large F). In optimizing a practical SPP-enhanced OSC, the optimum F in ∼ 0.2 < F <∼ 0.3 is chosen considering the overlap between the absorption spectra of active materials used and the high-η_abs regions.

Next, we examine the dependence of η_int of the model device with (t_org, t_u, Λ_G) = (50 nm, 10 nm, 320 nm) on L_d, t_a, and λ, by solving Eq. (3) using the finite element method [30], where the exciton generation term, G_exc, is obtained by the electromagnetic simulations based on the Fourier modal method. For the illumination wavelengths, we choose λ = 400, 580, and 760 nm, corresponding to off-, DSP-, and LSP-resonance cases, respectively, for the model device with t_a = 10 nm. The results plotted versus γ ≡ t_a/L_d show that all data points closely follow those calculated using Eq. (6) (Fig. 4(a)). Since t_a is sufficiently small, G_exc does not vary significantly along the z-direction in a thin active layer. This means that the exciton diffusion in the z-direction is mostly driven by the boundary conditions at the LTL– and UTL–active layer interfaces. The exciton diffusion in the xy-directions, however, is driven by the horizontal variation in G_exc, whose characteristic dimension is much larger than t_a. Consequently, the exciton diffusion in the active layer is well described by the analytical solution of the one-dimensional case with constant G_exc [Eq. (3)], as Fig. 4(a) clearly shows. Deviation from the analytical solution increases with t_a, since the variation in G_exc along the z-direction can no longer be ignored as t_a increases. We note that the dependence of η_int on λ is very weak, and therefore Eq. (9) is valid. Figure 4(b) shows the steady-state exciton density profile in the active layer when t_a = 3.5 nm, L_d = 5 nm, and λ = 760 nm.

 

Fig. 4 (a) Internal quantum efficiency (η_int) of the model device with t_org = 50 nm, t_u = 10 nm, and Λ_G = 320 nm versus γ ≡ t_a/L_d, calculated for different values of L_d and λ. The black solid line shows η_int calculated using Eq. (6). (b) Steady-state exciton density profile (n_exc) in the active layer when t_a = 3.5 nm, L_d = 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).

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4. Optimization of SP-enhanced organic solar cells based on CuPc and C₆₀

Building upon the analyses in Sec. 3, we optimize small-molecule organic solar cells based CuPc–C₆₀ DA heterojunction. The device structure is, from the bottom layer in Fig. 5(b), Ag / 4, 7-diphenyl-1, 10-phenanthroline (BPhen) / C₆₀ / CuPc / poly(3, 4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS) / 2D Ag grating electrode / glass. In comparison to the structure of the model device discussed in Sec. 3, the bilayer of CuPc and C₆₀ is the active layer; the BPhen and the PEDOT:PSS are the LTL and the UTL, respectively, since they are optically inactive in the spectral region where CuPc and C₆₀ are sensitive, and possess good charge transport properties [6, 11, 31, 32]. Depending on its thickness, the BPhen layer may need to be doped with, for example, ytterbium, where the absorption coefficient of the doped film is almost identical to that of the pristine BPhen layer [32].

 

Fig. 5 (a) (Top) Absorption coefficient (α) of CuPc (red) and C₆₀ (blue). (Bottom) Absorption efficiency (η_abs), as a function of the grating period (Λ_G) and the wavelength (λ), of the active layer in the organic solar cell based on the CuPc and C₆₀ DA heterojunction. The maximum of η_abs is 0.74. (b) The z-component of the electric field corresponding to point ‘a’ (λ = 600 nm, Λ_G = 320 nm) in (a). (c) The z-component of the electric field corresponding to point ‘b’ (λ = 620 nm, Λ_G = 200 nm).

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Since when γ ≪ (or ≫)1.0, η_ext is limited by too small η_abs (or η_int), we first set γ = t_CuPc/L_CuPc = t_C60/L _C60 = 1.2, where t_CuPc (or t_C60) and LCuPc (or LC₆₀) are the thickness and the exciton diffusion length of the CuPc (or C₆₀) layer, respectively. Assuming that L_CuPc = 7.4 nm and L_C60 = 14.4 nm [33], the thicknesses of the CuPc and the C₆₀ are then determined as: t_CuPc = 8.9 nm, t_C60 = 17.3 nm (t_a = t_CuPc + t_C60 = 26.2 nm). Under this condition, η_int = 0.694 from Eq. (6). Figure 5(a) shows η_abs(λ, Λ_G) of the CuPc–C₆₀ active layer in the SP-enhanced solar cell, where t_u = 5 nm, t_a = 26.2 nm, t_l = 18.8 nm (t_org = 50 nm), and the grating geometry is the same as that in the model devices. As in the case of the model device in Fig. 3, the active layer is located close to the UTL–Ag grating interface to maximize its optical absorption. The values for ñ of all materials are measured using spectroscopic ellipsometry. The enhancement in η_abs is mainly attributed to the enhanced absorption in the CuPc layer, since the region in the λ–Λ_G plane where resonant excitation of the DSP or LSP mode occur overlaps mostly with the absorption spectrum of CuPc; the high-η_abs region in Fig. 5(a) approximately coincides with that in Fig. 3(a) overlapped with α(λ) of CuPc (the top portion of Fig. 5(a)). The electric field profiles for points ‘a’ and ‘b’, shown in Figs. 5(b) and 5(c), resembles those for the corresponding points in Fig. 3(a), confirming that the enhanced absorption is due to the LSP and DSP resonances.

The maximization of J_sc of the SP-enhanced device is performed as the following. From η_abs(λ, Λ_G) shown in Fig. 5(a), we first choose Λ_G that maximizes 〈η_abs〉: Λ_G = 250 nm, 〈η_abs〉 = 0.164, resulting in J_sc = 8.78 mA/cm². Recalling that this result is obtained for γ = 1.2 (t_CuPc = 8.9 nm and t_C60 = 17.3 nm), J_sc can be further increased, if an increase (or decrease) in the active layer thickness leads to a gain in 〈η_abs〉 (or η_int) that more than compensates a concomitant loss in η_int (or 〈η_abs〉). To investigate this possibility, we vary γ with the values of t_org and t_u fixed, and calculate the maximum value of 〈η_abs〉 at different γ. Since the maximum J_sc is expected to be obtained not too far away from γ = 1.2, we assume that η_abs(λ, Λ_G) does not change with γ, meaning that 〈η_abs〉 is still maximized at Λ_G = 250 nm. For more rigorous optimization, η_abs(λ, Λ_G) can be re-calculated to find Λ_G maximizing 〈η_abs〉 for each γ. Figure 6(a) shows, as functions of γ, the maximum 〈η_abs〉, η_int given by Eq. (6), and resulting J_sc obtained using Eq. (9), where the trade-off between η_int and η_abs is clearly seen. Furthermore, it shows that our initial guess of γ = 1.2 is not the optimum choice: by decreasing the thickness of the active layer, J_sc can be increased owing to the increase in η_int, until γ becomes 1.0, where J_sc is maximized at J_sc = 8.88 mA/cm².

 

Fig. 6 (a) Short-circuit current density (J_sc) (red), solar-spectrum-weighted absorption efficiency (〈η_abs〉) (blue), and internal quantum efficiency (η_int) (black) versus γ = t_CuPc/L_CuPc = t_C60/L_C60 of the surface plasmon (SP)-enhanced CuPc–C₆₀ solar cell with t_org = 50 nm, and t_u = 5 nm. (b) External quantum efficiency (η_ext) 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.

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Figure 6(b) shows the η_ext spectrum of the SP-enhanced CuPc–C₆₀ device with γ = 1.0, compared with that of the optimized ITO-based conventional device based on the same materials. The structure of the ITO-based device is glass / 150 nm ITO / 5 nm PEDOT:PSS / 13 nm CuPc / 21 nm C₆₀ / 29 nm BPhen / 100 nm Ag, where the thicknesses of the CuPc, C₆₀, and BPhen layers are chosen so as to maximize J_sc. Compared with the ITO-based device, the SP-enhanced device has greater η_ext in the entire spectral region shown in Fig. 6(b), with the enhancement in the CuPc-active region is more pronounced than that in the C₆₀-active region. As a result, the SPP-enhanced device has J_sc (= 8.88 mA/cm²) that is 75 % higher than that of the ITO-based device (J_sc = 5.07 mA/cm²).

5. Discussion

The type of OSCs that our analysis and optimization approach are directly applicable is multilayer planar HJ OSCs. In essence, what we have discussed in this paper is how to design a plasmonic structure shown in Fig. 1 so that an active layer whose thickness is much smaller than its optical absorption length can absorb most incident photons. In other words, to overcome the trade-off between η_int and η_abs, we have begun with a device configuration with high η_int, and increased η_abs by exploiting SP resonances. Organic solar cells based on a bulk-heterojunction (BHJ) [34, 35], which refers to an extended region of interpenetrating networks of donor and acceptor, can be viewed as an alternative approach to overcome the η_int–η_abs trade-off; owing to the interpenetrating networks, the active layer thickness of a BHJ device can be increased much beyond the exciton diffusion lengths of donor and acceptor materials to achieve high η_abs without sacrificing η_int. Therefore, the optimization methodology presented in this paper, as well as absorption enhancement by SP resonances in general, is less effective in enhancing J_sc of BHJ OSCs than in enhancing that of planar HJ OSCs with thin active layers. Nevertheless, various device structures with metallic grating electrodes have been proposed to enhance optical absorption in BHJ OSCs, since a decrease in the active layer thickness typically leads to the decreased recombination of photo-generated carriers and series resistance [15, 17, 36].

In contrast to SP-enhanced OSCs with one-dimensional metallic grating, where only p-polarized (electric field perpendicular to grating lines) illumination can excite SP resonances [13, 16, 37], the four-fold rotational symmetry of the 2D grating electrode in our device leads to polarization-insensitive absorption enhancement for normal-incidence illumination. For practical implementation, the variation of J_sc with respect to the incident angle of solar illumination is important. In Fig. 7, J_sc of the optimized SPP-enhanced device discussed in Sec. 4 is shown as a function of incident angle, and compared with that of the ITO-based device. The calculation was performed for different azimuthal (ϕ) and polar angles (θ), where θ refers to an angle between the wave vector k and the z-axis in air, and the reflection at the air-glass interface is ignored for both SPP-enhanced and ITO-based devices. We also examine the dependency of J_sc on polarizations. The s-polarized (or p-polarized) light refers to a plane wave whose electric (or magnetic) field is perpendicular to the plane of incidence drawn as green dotted lines in Fig. 7(a). For normal incidence (θ = 0), owing to the four-fold rotational symmetry of the grating electrode, the values of J_sc are identical for both polarizations at all ϕ. Although this no longer holds for off-normal cases, our calculation shows that the angle and polarization dependencies of J_sc are weak: data points in Fig. 7(c) closely follow the three black lines, which are J_sc(θ = 0°)cosθ with the cosine factor representing the decrease in the solar power flux as θ deviates from 0°.

 

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 (J_sc) 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, J_sc 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 $J_{\text{sc}}^{\text{max}}\text{cos}\theta$, where $J_{\text{sc}}^{\text{max}}$ is J_sc(θ = 0°) for each device.

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Also shown in Fig. 7 is the comparison of the absorption enhancement in the SPP-enhanced device with the so-called ergodic limit, which represents the maximum possible absorption enhancement that can be obtained in the geometrical optics regime [38]. For this comparison, we consider a device shown in Fig. 7(b) consisting of an active layer sandwiched between a perfect reflector and a Lambertian front surface with random texturing coated with an ideal anti-reflection coating. For simplicity, we assume that the active layer in this device is composed of an effective single material, whose thickness is t_a (= t_CuPc + t_C60) of the optimized SPP-enhanced device, with its real part of the refractive index (ñ_eff) and absorption coefficients (α_eff) given by, respectively,

Here, t_CuPc = 7.4 nm, t_C60 = 14.4 nm, and t_a = 21.8 nm, as in the optimized SPP-enhanced device. The absorption efficiency of this device is then obtained by the summation of a geometric series, with each term in the series is the light absorption in a single round-trip between the reflector and the front surface [39, 40]:

As an alternative method for absorption enhancement, a dielectric grating structure has also been applied to thin film solar cells [41]. Coherent light scattering by a dielectric grating can enhance the electric field intensity in the active layer, as in the plasmonic cases. Since optical loss by metal absorption can be avoided, this approach can be advantageous over the plasmonic approach in certain cases, especially when the absorption coefficient of the active layer is not very large. In the SPP-enhanced device based on the CuPc–C₆₀ active layer discussed in Sec. 4, optical loss due to absorption in the grating layer is quite limited: at λ = 580 nm, absorption in the grating and back metal electrodes, and reflection are 17.4 %, 5.3 %, and 5.8 %, respectively, and η_abs of the active layer is 0.702. Furthermore, in addition to creating surface plasmon resonances, the 2D metallic grating in our device functions as a transparent electrode by replacing a brittle and expensive ITO or Al-doped zinc oxide, being suitable for flexible solar cells.

6. Conclusion

We have performed a systematic analysis of a model device representative of SP-enhanced planar HJ OSCs where one electrode is optically thick and the other consists of 2D metallic grating, taking into account both optical absorption and exciton diffusion. Our analysis has provided the following guidelines by which J_sc of such SP-enhanced OSCs can be maximized: (i) to maximize optical absorption in a thin active layer, the device thickness needs to be decreased until the SPs associated with the grating electrode are coupled with those localized at the interface between the organic and thick metal layers, with the active layer located near the grating electrode; (ii) for high η_int (> 0.7), the thickness of the active layer should be smaller than ∼ L_d, in which case η_int is closely approximated by Eq. (6), independent of wavelengths where active materials are sensitive; (iii) device optimization is achieved by determining the grating period maximizing 〈η_abs〉, followed by fine-tuning the active layer thickness to fully maximize J_sc. As an example, we have optimized the performance of a small-molecule organic solar cell employing the CuPc–C₆₀ donor–acceptor pair, demonstrating that the optimized device has J_sc that is 75 % larger than that of the optimized device with an ITO-based conventional structure.

Successful realization of the SPP-enhanced OSCs depends critically on the capability to accurately create metallic nanostructures over large area at low cost. Metal patterning by imprint [42] or layer-transfer techniques [43], or methods using metal nanowires [44] may be utilized to achieve this goal.