1. Introduction

Multi-colored solar cells, solar cells with controlled, tunable spectral reflection and absorption profiles, are of significant interest due to their potential to be coated on exterior surfaces of urban infrastructures, such as building facades, rooftops and automotive skins, to serve both aesthetic and functional purposes [1,2]. In tandem cell applications, there is also a need to systematically control absorption and, in turn, achieve the required current-matching in cells that possess different spectral absorption profiles. Additionally, semitransparent solar cells are attractive for integration into portable electronics [3] and for window coatings to help with building and vehicular heat management [4,5]. Solar cells based on solution-processed materials are especially promising for these large-area applications because of their thin-film and lightweight nature, ease and flexibility of fabrication, associated low costs, and high efficiency potential.

Past examples of colored solution-processed solar cell technologies include using combinations of dyes [6], photonic filters [7], physically- or chemically-modified absorbing/transport layers [8–15], integrated liquid/photonic crystals [16,17], embedded optical microcavities and dielectric mirrors [10,18,19], and modified top/bottom electrodes [20–23] in dye-sensitized, organic, and perovskite solar cells. Although multi-colored and semitransparent solar cells based on perovskites and organic materials have been demonstrated, their narrow spectral absorbing ranges, which lie mainly within the visible portion of the spectrum, represent a significant drawback for achieving high photocurrents. As a result, light management strategies to produce cell colors or achieve transparency come with an unavoidable loss of device efficiency.

Colloidal quantum dots (CQDs), semiconducting nanocrystals stabilized in solution, are a promising candidate material for achieving multicolored and semitransparent solar cells [24,25] due to their band gap tunability, which is enabled by the quantum size effect [26]. Specifically, lead sulfide and lead selenide (PbS, bulk band gap energy of 0.41 eV [27], and PbSe, bulk band gap energy of 0.27 eV [28]) CQDs have band gaps that can be tuned from the near-infrared to the visible portion of the spectrum. As a result, visible absorption losses induced by the design of multicolored or semitransparent cells can potentially be compensated for by enhanced absorption in the infrared region.

Standard CQD film-based devices [24,25,29] (Fig. 1) employ different electronic layers that have thicknesses on the order of the optical wavelengths of interest. The layer thicknesses and design are typically optimized for their electrical properties, but optical thin-film interference plays a large role in these devices as well, as demonstrated by efforts to utilize interference effects to achieve semitransparency and absorption enhancement via electrode modification [30,31] and microcavity structuring [32,33]. Traditionally, transparency in CQD-based devices is induced by employing thin absorbing layers [34,35]. In this study, we design, optimize and fabricate multicolored and transparent CQD solar cells based on thin-film interference engineering concepts to customize both optical and electrical device properties [36]. Using physical and mathematical modeling techniques, including Transfer Matrix Method (TMM) calculations [37] and multiobjective optimization algorithms [38,39], we have developed an optimization method for the custom-design of multicolored and transparent CQD solar cells that could be generalized to other materials systems. The optimization sequence is depicted in Fig. 1(c). The method maximizes reflection and transmission at specific wavelengths, creating a desired cell color, while simultaneously requiring high photocarrier generation rates in a solar cell device.

 

Fig. 1 (a) Schematic of a CQD-based solar cell illustrating the spectrally-dependent optical interference patterns that can result from tuning the thicknesses of the different cell layers. As incident broadband sunlight passes through the device, constructive or destructive interference occurs at certain wavelengths, resulting in wavelength-dependent reflectivity and transmission, giving the cell its apparent color or semitransparency. (b) Cross-sectional scanning electron microscope (SEM) image of the structure shown in (a) with the layers labeled. (c) Graphic representation of the optimization technique to produce cells with defined color characteristics. Space set of thickness combinations is (i) initialized and each combination is transformed to (ii) a reflection spectrum via TMM. These spectra in combination with incident (iii) AM1.5G and color matching functions are translated to rgb colors on (iv) chromaticity plots where the distance to the intended color is (v) minimized. This optimization cycle repeats until a global minimum is realized.

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Our multi-layer thin film calculations were based on a depleted heterojunction architecture [40] design for CQD photovoltaics, but could be generalized to include any optoelectronic layer structure. Figure 1 shows an example of this architecture, which consists of an optically thick glass substrate, followed by indium tin oxide (ITO, the bottom contact), TiO₂ (the n-type layer), PbS CQD film (the p-type layer), MoO₃ (buffer layer), and Ag (the top electrode).

2. Optimization of the photocurrent-color tradeoff

Our device model makes the following initial assumptions: (1) layers included in the multi-layer device are considered homogeneous and isotropic; (2) interfaces are parallel and optically flat; (3) light is incident normal to the device and can be modeled as a plane wave; (4) all photogenerated charge carriers contribute to photocurrent in the device (100% internal quantum efficiency). All of these assumptions can be removed as-needed by modifying the materials models and incorporating experimental data into the calculations.

We use the TMM, which takes the thicknesses and complex refractive indices of all layers as inputs, and calculates normalized electrical field profiles within the multi-layer structure. In our simulations, the materials models are composed of complex refractive index data from the literature and experimental ellipsometry measurements, and we consider a broadband illumination source with a wavelength range of 300–1800 nm. In the case of opaque reflective colored solar cells, Ag is used as the back contact, and ITO is used as the back contact for the semitransparent solar cells. We calculate the reflection spectrum of the device, and predict the expected “color” by combining this spectrum with an appropriate set of color matching functions (1931 CIE [41]) and an illuminating spectrum (AM1.5G). The predicted color can be represented on a 2-dimensional chromaticity plot, as shown in Fig. 3(a) Cell “transparency” is calculated by averaging transmittance data over the visible wavelength range (420 nm – 680 nm) output by the TMM calculations.

In order to optimize the color response of our cells, we use particle swarm optimization (PSO), a population-based algorithm [38], tailored for our specific application, as illustrated in Fig. 1(c). A “swarm size” of solution thickness sets is initialized and fed into the TMM to generate associated reflection spectra, which are then transformed to apparent color. These [rgb] co-ordinates are then optimized for a specific reflected color/wavelength response by minimizing the distance between the target point and solution point on the chromaticity plot, yielding a global solution via multiple iterations. The presence of two different populations (pbest and pcurrent) and particle movements in PSO allows for both greater degrees of exploration and faster convergence when compared to other optimization methods, such as genetic algorithms. Due to the multilayer architecture of our device and highly multidimenstional search space involved, a semi-periodic reflectivity landscape with multiple local minima emerges. Therefore, employing a PSO with a relatively large “swarm size” provides an efficient route to identifying the global minimum for our highly multidimensional optimization problem.

Despite the infrared responsivity of the PbS CQDs, there still exists a trade-off between the available photocurrent and visible transparency in device designs. This trade-off can be partially mitigated by taking the advantage of multi-layer interference effects to reduce visible field overlap with the CQD layer while maintaining absorption in the infrared. In order to achieve high photocurrent with minimum loss of visible transparency, we used PSO to perform single-objective optimizations on the layer thicknesses, keeping the PbS layer thickness constant. The three optimization targets chosen to explore the entire parameter space involved with the trade-off were high transparency, high photocurrent, and low transparency. The available photocurrent and average transparency of each solution to the three optimization problems are shown in Fig. 2.

 

Fig. 2 (a) Calculated average transparency (%) and corresponding available photocurrent density (mA/cm², color bar) versus PbS CQD film thickness (nm). Top curve: optimized for maximum average visible transparency. Middle curve: optimized for maximum available photocurrent density. Bottom curve: calculated for minimum average transparency. Calculated electric field intensity as a function of wavelength and position in the transparent device structure (ITO back contact) with a PbS CQD layer thickness of 200 nm for: (b) transparency-optimized case; (c) photocurrent-optimized case.

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In Fig. 2(a), the average transparency is plotted as a function of CQD layer thickness, and the available photocurrent is represented by the color. The top curve is the set of solutions at each given PbS CQD film thickness optimized for the highest transparency. The middle curve is optimized for the highest photocurrent at each film thickness. Higher photocurrent comes with the expected trade-off of lower transparency. The bottom curve is calculated for the lowest transparency, and it has the lowest available photocurrent of the three sets of solutions. The difference between the bottom curve and the middle curve represents both the photocurrent and degree of transparency that can be gained for a given active layer thickness by doing a rational layer thickness optimization via our method.

The high photocurrent for the middle curve is achieved by maximizing the electric field intensity within the absorbing layer. The high transparency of the top curve is achieved by employing multi-layer interference to minimize the electric field intensity at visible wavelengths within the absorbing layer. The difference between these two cases is visualized in Figs. 2(b) and 2(c). In the optimized photocurrent case (Fig. 2(c)), there is an intensity peak at a wavelength near 700 nm within the CQD film, allowing more longer wavelength light to be absorbed within this layer. In the optimized transparency case (Fig. 2(b)), there is no electric field intensity peak at the edge of the visible spectral range; instead, there is a peak closer to 800 nm at the NIR edge, allowing visible light to be transmitted and maintaining a relatively high photocurrent through NIR photon absorption.

The tradeoffs between attainable color or transparency and minimum device photocurrent are illustrated in Fig. 3(a). From this plot, it is apparent that photocurrent requirements more strongly affect “redder” colors, whereas the range of “bluer” colors that can be achieved shows little correlation with achievable photocurrent. Figure 3(b) shows transmittance plots for devices optimized for their transparency based on photocurrent restrictions. As expected, lower required device photocurrents result in higher potential visual transparency levels. Figure 3(c) shows the dependence of the photocurrent/transparency tradeoff on the CQD excitonic peak wavelength.

 

Fig. 3 (a) Chromaticity plot showing achievable colors given minimum photocurrent requirements (J > 10 mA/cm², J > 15 mA/cm², and J > 20 mA/cm²). Calculated Transmittance plots showing: (b) trade-off between transparency and photocurrent (for CQDs with 950 nm exciton peak wavelength), and (c) achievable transparency given minimum photocurrent requirements for different CQD excitonic peak wavelengths.

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3. Effects of non-ideal layers on color saturation

In evaluating the prospects for real devices, it is important to take into account non-ideal effects, such as interface roughness, non-uniformity of the layer physical properties, and the presence of scattering centers formed by impurities and contaminants. We can incorporate these effects into our model by using another parameter, the effective “optical roughness” of each layer. We create a sufficiently large number of samples with random thicknesses by adding the standard deviation of a Gaussian distribution based on the measured or assumed roughness to the mean thickness for each layer. We then calculate the reflectance curve of each sample in the distribution and statistically average the reflectance from all samples to derive the effective reflectance curves.

Due to the nanostructured nature of the material itself as well as the deposition technique, the CQD layer typically has a geometrical roughness of 3-10 nm [42]. The geometrical roughness of the underlying electrodes and oxide layers deposited by evaporation, which can be determined from surface profilometry, is usually smaller than that of the CQD films. However, the effective optical roughness can be significantly greater than the geometrical roughness. One possible origin of optical inhomogeneity in the ITO and TiO₂ layers is the compositional and structural non-uniformity introduced during the deposition and processing steps, which can be seen as a spatial variation in the refractive index profile of the electrode films.

Figure 4 shows the effects of non-ideal interference on the reflectance curves as well as the effective colors of the devices. As can be seen in Fig. 4(a), the reflectance from devices with rough CQD layers is smoothed in the red spectral region, while the shorter-wavelength region is mostly unaffected by the roughness. For rough TiO₂ and ITO layers, the deviations from the ideal case are greater in the blue region. The changes in the reflectance curves reduce the wavelength selectivity, and make the apparent color less saturated. The chromaticity plot in Fig. 4(b) demonstrates this effect for a device that is designed to be blue in color. As the effective optical roughness of the ITO/TiO₂ layer increases, the chromaticity point moves towards the white point, decreasing the saturation, and shifting the color towards brown-grey. In Fig. 4(c), after accounting for the optical roughness, all 3 points corresponding to the maximum achievable saturation of red, blue and green, are closer to the white point. This approach to considering the effects of non-ideal interference is particularly useful for understanding color in real devices.

 

Fig. 4 (a) Simulated reflectance curves for a specific color objective with and without an effective optical roughness of 10% for the ITO/TiO₂ layers and 10% for the CQD layer. (b) Effects of different levels of roughness on the chromaticity of a “blue” device. Percentages refer to the ratio of the standard deviation to the ideal thickness of the ITO/TiO₂ layer. The white point of the standard illuminant is also plotted as a reference point. (c) Roughness (10%) has the effect of moving the vertices on the largest achievable triangle of color profiles closer to the white point.

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4. Application in tandem structures

Our proposed method for color-tuning CQD solar cells is of particular interest for applications in all-CQD and hybrid tandem photovoltaics, where current-matching is critical to series-connected device performance. CQDs are particularly suited to tandem applications because of their band gap tunability, infrared responsivity, and compatibility with a variety of materials systems afforded by their solution-processing. This flexibility effectively eliminates the difficulty of finding a materials combination possessing both appropriate band gaps and suitable lattice matching for optimized multijunction cells [43]. Proof-of-principle studies have demonstrated tandem structures utilizing all-CQD materials systems [44–46] and CQDs in conjunction with polymer materials [47,48].

In these series-connected CQD tandem structures, current matching is essential to obtain high efficiency devices. Generally, this is achieved by empirically adjusting the layer thicknesses until approximately equal photon absorption occurs in the two active layers. Here, we use our optimization algorithm to take into account the effects of interference in a multilayered stack to design optimum absorbing layer thicknesses.

For our optimization simulation, we employed a PbS CQD system comprised of 1.55 eV and 0.95 eV dots which are both within 5% of the optimum band gaps for the maximum efficiency in a two-junction tandem structure [49]. In addition, our simulated tandem structure integrated a graded recombination layer as demonstrated in a previous study [44]. Calculating absorption using only the Beer-Lambert law [50] in the active layers, not taking into account reflection, gave optimum thicknesses of 350 nm and 247 nm for the front and back cells, respectively, predicting a maximum photocurrent of 18.1 mA/cm². Using our optimization process, we obtained optimum thicknesses of 350 nm and 196 nm for the front and back cells, respectively, achieving an output-matched photocurrent of 18.6 mA/cm². We achieved a ~3% increase in expected photocurrent using our optimized approach, even though it takes into account reflection and the detrimental parasitic absorptions in the electrodes and the other non-active layers in the 9 layer tandem stack, whereas the control case does not. Our optimization method, accounting for both interference and reflection, provides an efficient route for tandem layer designs in both CQD and hybrid systems.

5. Experimental results and discussion

We fabricated several proof-of-principle CQD solar cell devices based on our optimization method designs for different colors using PbS CQDs with exciton peak wavelengths near 950 nm. To minimize the fabrication uncertainty in the layer thicknesses, we used commercial ITO-coated glass substrates with ITO thicknesses of 28 nm for our “red” and “green” cell designs. For the “blue” cell, we deposited ITO on a glass substrate via e-beam evaporation, followed by an annealing process, to obtain our target optical thickness. The TiO₂ layer was also deposited using e-beam evaporation for precise thickness control, and a TiCl₄ solution treatment was applied afterwards [51]. The PbS CQD layer was built up using a layer-by-layer solid state ligand exchange process [51]. Two or three drops of oleic acid capped PbS CQD solution at a concentration of 50 mg/mL per layer were deposited through a 0.22 μm pore filter and spin-cast on the substrate. 0.5% mercaptopropionic acid (MPA) in methanol was used to soak the film for 3 seconds to replace the oleic acid, then the film was spin-cast dry. Lastly, the films were washed with methanol twice to remove the unbound ligands, completing the deposition of one CQD film layer. The total CQD film thickness was controlled through the acceleration, spin speed, spin time and number of layers and verified using profilometry measurements. We were able to control the thickness of the CQD layers to within +/− 15 nm. The top contact was composed of a thin MoO₃ buffer layer and Ag, which were both deposited via e-beam evaporation.

Photographs of the colored and transparent cells are shown in Fig. 5(a). We measured the reflectance of each solar cell using an Agilent Cary 5000 UV-Vis-NIR spectrophotometer with an integrating sphere insert, calculated the corresponding xyz color values by integrating over the AM1.5G spectrum, and plotted them in a chromaticity diagram. The reflectance spectra are plotted in Fig. 5(b), and the calculated color of the fabricated devices is shown in Fig. 5(d).

 

Fig. 5 (a) Experimental reflectance and transmittance spectra for colored and semi-transparent solar cells, respectively. (b) Chromaticity plot showing the calculated coordinates for different colored devices. Crosses indicate design points while corresponding colored shapes indicate experimental points. (c) J-V characteristics taken under simulated solar illumination for colored and semi-transparent devices. (d) Photographs of blue (upper left), green (lower left), red (center), yellow (upper right), and semi-transparent (lower right) CQD solar cells.

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We also fabricated semi-transparent devices based on our optimization method. The top contact of these devices was a composite electrode consisting of spin-coated Ag nanowires and ITO nanoparticles. Our test devices had measured visible transparencies ranging from 27.3% to 32.2%. The measured transmittance spectrum of the highest efficiency device is plotted in Fig. 5(c).

All current density-voltage measurements were carried out in a nitrogen-purged environment. Current density−voltage curves were measured using a Keithley 2400 source meter with illumination provided by a Sciencetech solar simulator with an irradiance of 1000 W/m². The active area of the solar cell was illuminated through a circular aperture with an area of 0.044 cm² ± 0.003 cm². The power through the aperture, measured using a Thorlabs broadband power meter, was used to calibrate the power density. The measured short circuit current (J_SC), open circuit voltage (V_OC), fill factor (FF), and power conversion efficiency (PCE) for the different cells are summarized in Table 1.

Table 1. Average performance characteristics of colored and transparent solar cell devices showing open-circuit voltage (V_OC), short-circuit current (J_SC), fill factor (FF) and power conversion efficiency (PCE). All measurements are for at least 6 devices.

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The differences in performance between the devices are related to their different design parameters, which are determined by the need to optimize reflection and transmission over specific wavelength ranges. Blue is a relatively difficult color to produce using this method, since the reflections are minimized due to the strong absorption of the CQD film in the blue region of the spectrum. The optimal design included a very thick CQD film layer. The lower FF of the semi-transparent device is related to the difficulty in making a strongly conducting top transparent contact without heat-processing due to the presence of the temperature-sensitive underlying CQD film.

Generally, the experimental photocurrents were smaller than those predicted by the simulations by approximately 50-60%, due to experimental deviations from the model assumptions. The simulations make the assumption of perfect carrier collection (IQE = 100%), whereas CQD solar cell IQE is typically on the order of 50-90% above the band gap [51,52]. Additionally, experimental variations in the device layer thicknesses can contribute to lower average photocurrents. On average, the ITO, TiO₂, and PbS CQD layer thicknesses in our devices were within 15 nm, 10 nm, and 15 nm, respectively, of the design thicknesses.

6. Conclusion and outlook

We developed a method for producing arbitrary spectral profiles in layered solar cell structures using thin film interference modeling techniques combined with optimization algorithms. At selected wavelengths, our model maximizes reflection and/or transmission to create a target color and transparency level while simultaneously maximizing photocarrier generation rates. Our study revealed that designs with minimum transparency do not necessarily correspond to the highest attainable device photocurrent, providing a pathway for high efficiency colored devices. Although effective optical roughness in the films decreases the color saturation, CQD solar cell devices with well-defined color profiles can still be produced. Our optimization method produced layer designs for tandem solar cell applications, with increases in expected photocurrent over conventional designs despite taking into account optical losses. Experimentally, we fabricated proof-of-principle blue, green, yellow, red and semi-transparent devices. The measured reflectance and transmittance spectra agreed well with the perceived color and transparency levels.

Future work will focus on broadening the application of our model to hybrid materials systems (single junction and tandem design structures based on non-CQD-based films) and explicitly including additional loss mechanisms. The device layer structure used in this study includes a wide band gap n-type TiO₂ layer, an absorbing p-type CQD thin film, and a MoO₃ buffer layer. The overall device performance could be improved by employing the current best-performing CQD device architecture strategies which inlcude graded doped CQD layers formed using solution-based halide passivation treatments [53,54]. This architecture strategy substitutes the TiO₂ layer for a ZnO thin film with higher electron mobility, eliminates the buffer layer, and incorporates a graded doped CQD layer for higher charge extraction efficiency. Finally, this work, coupled with the development of more efficient room-temperature-processed transparent electrode materials, should extend the range of functionalities of flexible optoelectronic devices.