1. Introduction

Periodically structured materials can interact with light in unusual ways that can serve as a new platform for enhancing many optoelectronic devices. We describe polymer microlens array structures that can enhance perovskite solar cell photocurrents and light emission from organic light emitting diodes (OLEDs).

In the area of solar cells, methyl ammonium lead iodide (MAPbI₃) type perovskite solar cells (PSCs) have attracted enormous interest from the photovoltaic community due to their rapidly increasing efficiency from ~12% in 2013 to > 22% in 2016 [1]. Although the perovskite material has very high absorption coefficient and solar cells made of thin layers of ~300-400 nm thickness absorb light very effectively, there is still considerable loss in light absorption at ~440-480 nm, ~550-650 nm, and near the band edge ~700-800 nm [2–5]. Most PSC research has focused on improving the efficiency by modifying the materials and/or their underlying properties, the processing techniques, and different transport layers.

Very recently, few light management schemes to enhance the performance of PSCs have emerged. Incorporation of periodic inverted cones in the perovskite layer simulated 6% absorption enhancement (25.1 mA/cm²) compared to the Lambertian limit (23.7 mA/cm²) [6]. Inverted pyramid cones with Bragg-stack reflectors have also been proposed to theoretically enhance the performance of perovskite/c-Si tandem solar cells in recent reports [7,8]. In another study, texturing the front surfaces and back reflector showed that the maximum photocurrent enhancement is found for 97 nm thick absorber layers [9], thinner than in the common PSCs. Incorporating nano-dendrites in the TiO₂ electron transport layer experimentally showed 22% and 25% enhancements in the average photocurrent and power conversion efficiency (PCE) respectively compared to the TiO₂ nanorods due to enhanced light trapping [3]. The localized plasmon resonances of metallic nanoparticles have been utilized extensively to enhance the performance of PSCs [4,5,10,11]. For instance, the addition of Au-Ag alloy popcorn-shaped nanoparticles increased the PCE from 8.9% to 10.3% [5], whereas the core-shell Ag/TiO₂ nanoparticles increased the PCE from 14.5% to 16.3%, due to plasmonic effects [10]. However, Snaith et al. reported increase in PCE from 10.7% to 11.4% by incorporating core-shell gold nanoparticles due to the lowering of the exciton dissociation energy from ~100 meV to ~35 meV, rather than enhanced light absorption [12].

In this paper, we implement an experimentally realizable microlens-based light trapping scheme for a PSC where a microlens array (μLA) can be attached to the glass side of the solar cell without affecting the internal absorbing layers. We use rigorous scattering matrix simulations to optimize the solar cell architecture. The μLA-based light trapping is easier to implement due to the ease of fabrication over large-areas (>1 inch²) using the roll-to-roll nanoimprint lithography approach. It does not involve disturbing the internal layers which might affect the change transport and synthesis procedures adversely. In our previous work, the P3HT- and PTB7-based organic solar cells with μLAs have been successful in yielding enhancement of ~12% in photocurrent [13]. In a recent report, quasi-periodic microstructured hole transport layer with conformal Au cathode showed enhanced light harvesting in thin 240 nm PSCs with PCE of 17.7% [2]. Although internal texturing of the absorber layer shows greater promise for enhancement, the deposition on corrugated substrates is very challenging.

2. Simulation methodology

We use the rigorous scattering matrix (SM) method [14,15] where Maxwell’s equations are solved in Fourier space, in a basis of plane waves for both polarizations, to obtain the total reflectance R (including diffracted beams) and transmission T (which is 0) at each incident wavelength. The absorption at each wavelength is then A = 1 −R – T as described previously [16]. We characterize solar architectures by their broad-band absorption <A_w>, weighted by the AM1.5 solar intensity dI/dλ, and the idealized short circuit current J_sc, where

3. Results and discussion

We simulate a standard n-i-p device architecture with layers stacked as glass/FTO/TiO₂/ perovskite/Spiro-OMeTAD/Au shown in Fig. 1(a). The thickness of glass, FTO, TiO₂, Spiro, and Au are fixed at 700 μm, 300 nm, 40 nm, 250 nm and 100 nm, respectively, similar to typical experimental values. The measured complex refractive index (n₁ + in₂) values for FTO, TiO₂, Spiro [17] and perovskite [18] are taken from the literature. The wavelength-dependent photon decay length (ζ) for perovskite calculated using ζ(λ) = l/4πn₂(λ) is plotted in Fig. 1(b), where n₂ is the imaginary part of the measured perovskite complex refractive index.

 

Fig. 1 (a) Schematic of PSC architecture without μLA. (b) Photon decay length of perovskite.

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We first show the variation in J_SC with the perovskite layer thickness in Fig. 2(a), where Jsc increases until perovskite layer thickness reaches ~400 nm and nearly saturates for thicknesses exceeding 400 nm. The J_SC variation with thickness is in agreement with results previously reported in the literature [17]. Consequently, we employ the perovskite layer thickness of ~400 nm in the rest of our simulations, consistent with the experiments reported in the literature for efficient charge collection in PSCs. The variation of J_SC with absorber layer thickness can be fitted well using the function:

 

Fig. 2 (a) Variation of photocurrent (J_SC) as a function of perovskite layer thickness. (b) ln (1-J_SC/J_{SC, max}) as a function of perovskite layer thickness. (c) Simulated absorption as a function of wavelength for 400 nm thick perovskite absorber layer.

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Figure 2(c) shows that the absorption spectra for 400nm thick perovskite layer has >90% absorption at all wavelengths except for λ ~450-550nm and 600-700nm where it falls to ~80%, and can be improved by incorporating a microlens.

The μLA can easily be fabricated on an ITO/FTO-coated glass substrate using nanoimprint lithography as described in our previous publication [19]. A typical polymer (e.g. polystyrene, polyurethane) index-matched to glass is spin-coated on a thick glass substrate. The polymer is then stamped using a PDMS mold replicated from a flexible master pattern under the effect of temperature and pressure. The PDMS mold is then released to reveal the inverse of the PDMS pattern on the polymer surface.

Figure 3(a) shows the atomic force microscopy (AFM) image of a representative μLA fabricated in polystyrene using the nanoimprinting process. As shown in Fig. 3(a), the AFM image illustrates the well-defined microlens array arranged in triangular lattice with the period ~750 nm. The AFM line scan confirms the height of microlens to be ~120 nm. The μLA period and height can be conveniently changed by starting with a master pattern having different geometrical parameters (e.g. periodicity, height, depth). Figure 3(b) illustrates the diffraction pattern generated due to the μLA when it is normally illuminated with the white light source from the glass side. The diffraction pattern is collected on a sheet of paper normal to the glass surface, and is imaged using a digital camera.We now couple the μLA on the air-glass side of the PSC, as schematically shown in Fig. 4(a). We optimize the period (a) and height (h) of the μLA for the solar cell architecture, through simulation. For each period the optimal lens height is determined and we plot the enhancement as a function of μLA period in Fig. 4(b). The photocurrent enhancement is highest (~6.3%) for μLA period a~700 nm with height h~800 nm for a/h ratio ≈1. Shallower heights (~500nm) decrease the enhancement by ~1%. The optimal period is in the range of band-edge wavelengths where light trapping is needed [20]. The optimal period of ~700 nm agrees well with our previous calculations for thin silicon [21] and organic solar cells [16]. There is a second maximum of μLA pitch ~1300 nm exhibiting ~5% enhancement, as shown in Fig. 4(b). Figure 4(c) shows absorption for the solar cell without μLA and with μLA of optimal period ~700 nm and height ~800 nm, showing absorption enhancement for the μLA-based device at all wavelengths, with high enhancements at 440-480 nm, 550-650 nm, and beyond ~780 nm, relative to without the μLA. The enhancement is due to light focusing by the μLA. Narrow waveguiding modes are evident above 800 nm. Fig. 4(d) illustrates the electric field intensity distribution at λ = 550 nm inside the PSC with the top μLA with high intensity enhancement by a factor >2.5 inside the absorber layer, resulting in enhanced absorption and photocurrent in solar cell. Regions of maximum field intensity occur directly above the μLA and are separated in x-direction by the μLA period ~700 nm. The positions of field maxima with enhancement ~3.5 (red regions) residing mostly in FTO region, are separated by ~100 nm in z-direction indicating the formation of standing waves, where maxima are separated by λ/2n_FTO (~140 nm). Similar standing-waves were observed in our previous results on organic [16] and silicon [15,22] solar cells. Most of the enhanced field intensity does not lie deep inside the perovskite absorber layer but stays near the perovskite-TiO₂ interface. This is due to the high index of the perovskite layer and most of the electric field intensity absorbed near the FTO-perovskite interface, especially at shorter λ.

 

Fig. 3 (a) AFM image of the μLA. The inset illustrates AFM line scan showing the height of the microlens ~120 nm. The right panel shows three-dimensional view of the μLA. (b) The diffraction pattern from the μLA when illuminated with white light.

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Fig. 4 (a) Schematic of PSC architecture showing stacking of different layers with μLA on air-glass side. (b) 2D plot showing optimal microlens height as a function of period. (c) Absorption as a function of wavelength for solar cell with μLA of a ~700nm and h ~800nm. The absorption of flat solar cell without μLA is overlaid for comparison. (d) Electric field intensity plot for the PSC with μLA a ~800nm and h = 700nm at λ = 550 nm.

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μLAs have also been greatly beneficial in enhancing OLEDs. In OLEDs the fraction of the outcoupled light is only ~17-20% in the absence of extraction measures. This is due to several loss paths within the device, such as photons trapped in the substrate due to total internal reflection (TIR) at the glass (n ~1.5)/air interface, photons waveguided in the high index organic (n ~1.7-1.8) + anode (often ITO, n ~1.8-2.1) layers, and photons dissipated at the organic/metal cathode by surface plasmon excitation. While recapturing all photons for useful emission remains a challenge, the use of a microlens array provides a solution for mitigating the loss due to TIR at the substrate/air interface.

Figure 5(a) shows the effect of attaching a uniform 2 μm-period, 1.6 μm diameter, and 1.2 μm height polyurethane microsphere μLA to the opposite (blank) side of a 1.1 mm thick glass substrate on which the OLED pixels were fabricated. The μLA was fabricated using soft lithography whose advantages include ease of fabrication of large area designs with very ordered and uniform patterns. To achieve the observed maximal (~100%) enhancement in the forward electroluminescence, the array size (15x15 mm²) was ~25 fold that of the pixel (3x3 mm²). This approach avoids confining the microlens to an area directly under the pixel, which typically results in a lower enhancement, measured in green and blue OLEDs based on Al (Alq3) and DPVBi, respectively [23].

 

Fig. 5 (a) Light emission from green and blue OLEDs, using a μLA on the air-glass side. The pixel on the right is devoid of such an array and its emission is ~2 fold lower in comparison to the other. (b) Spectral emission of the green OLED without and with μLA collected with different integrating sphere opening diameter d = 10, 25 mm. (c) Power efficiency and luminous efficiency of green OLED without and with μLA. (d) Simulated enhancement factor as a function of lens height for smaller and larger size source as compared to 1μm-period μLA.

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The square-shaped, sharp pixel shown in Fig. 5(a) is devoid of the microlens array. The defocused green and blue images are of pixels in which the light scatters through the μLA. That spreading light demonstrates that the μLA actually extracts light from the glass substrate, outside the pixel area. Figure 5(b) shows measured intensity increases with the size of the collection region surrounding the pixel, with an enhancement of ~50% for a 10 mm opening diameter of an integrating sphere and >100% for a 25 mm opening diameter. Figure 5(c) shows that the power efficiency and luminous efficiency (L) are enhanced by ~100% with the μLA over the shown range of voltages, with peak efficiencies near 6V. We observed additionally that pixels adjacent to those with a μLA also contribute to the enhanced light extraction. A similar enhancement in light extraction was obtained in simulations as shown in Fig. 5(d), showing higher enhancement (>100%) for a microlens considerably larger than the small source. We also obtained an enhancement of ~60% in the OLEDs’ electroluminescence by easily forming thin microporous films on the blank side of the glass substrate [24]. Micropores that scatter light are formed from phase separation of the blends’ constituents during film drying process.

4. Conclusion

We show that μLA-based light management scheme for PSCs and OLEDs can enhance their performance significantly. This scheme is particularly useful since large-area scalable manufacturing of μLA is possible and the lens array can be placed external to the actual device without disturbing the internal active layers which can adversely affect the electronic properties. External μLAs can enhance absorption and photocurrent in perovskite solar cells by >6%, through light focusing within the active layer. In OLEDs external μLAs larger than the pixel size show measured light extraction enhancement >100% by reducing waveguided modes in the substrate and collecting light outside the pixel area.