Bridging the Gap between Solar Cells and Batteries: Optical Design of Bifunctional Solar Batteries Based on 2D Carbon Nitrides

While solar cell technology is booming, intermittent availability of sunlight motivates new vistas for multifunctional devices capable of energy capture and storage on the same material, i.e., direct or two‐electrode bifunctional solar batteries. Herein, simulations and experiments are utilized to take a closer look at efficiency limitations and design considerations, and guidelines are proposed to operate a solar battery comprised of the 2D carbon nitride potassium poly(heptazine imide), K‐PHI, as a bifunctional solar battery photoanode in conjunction with the separator poly(N‐vinylcarbazole) and cathode poly(3,4‐ethylenedioxythiophene):polystyrene sulfonate. An optical design of this device is developed by proposing light absorption in a charge collection layer within the photoanode and calculating photocharging current and charging time as figures of merit. The much larger efficiency of operation via rear illumination for K‐PHI layer thicknesses >200 nm is highlighted and enhancement strategies without modifying the photoactive layer are proposed. Finally, adapted Ragone plots are introduced and it is shown how the solar batteries are capable of improving energy and charge output solely via illumination (for the design under 1 sun, the energy and charge output increase by 60% and 63%, respectively) without modifying the device.


Introduction
New devices to harvest energy from renewable sources such as abundant sunlight and store this energy are essential to transition our energy infrastructure into a sustainable and economically viable future. Solar cells present an easy way to extract electric storage at the same time. [8] An internal hole transfer cascade shuttles the hole to the cathode, enabling photocharging solely via illumination, without external wiring and under open circuit conditions. This is enabled by the fully earth-abundant 2D carbon nitride potassium poly(heptazine imide), K-PHI, [8,9] as the active material. Its versatile toolkit of optoelectronic and optoionic properties, [10] including a visible light bandgap of ≈2.7 eV (459 nm), enables a bifunctionality of light absorption and charge storage at the same time, leading to applications in (dark) photocatalysis, [11] photomemristive sensing, [12] as well as light driven micromachines. [13] To transform this solar battery concept into a working device, it is essential to develop a better understanding of its architectural design, i.e., which materials to choose, which geometric properties are suitable (e.g., layer thickness) and how the materials interact with each other (e.g., parasitic light absorption, interfacial charge separation and storage). Simulations as presented herein give pathfinding vistas to extract such parameters.
On a general note, while the emerging field of photoactive batteries possesses huge potential in theory, there are still key challenges to overcome, such as loss channels from photogenerated charge carriers, a precise understanding of the photocharging process, and design principles both regarding materials choice as well as device setup. [3c] More importantly, the nature of these devices presents the conceptual problem of active layer thickness (termed in this work "active layer thickness dilemma"), which on the one hand should be maximized to achieve a reasonable capacity (i.e., battery part), but on the other hand thick active layers suffer from worse photocharging kinetics as charge trans-port and parasitic light absorption become limiting (i.e., solar cell part). Solar cells based on bulk heterojunctions experience operational losses in efficiency (governing photocurrent, photopotential, fill factor, as well as power and energy output) due to the Shockley-Queisser limit, defects in layers, junction resistances, as well as limits in conductivity, the latter reducing charge diffusion distances in the active layer and with it, increasing recombination losses. [1,3c,14] In addition, a Lambert-Beer like decay of light intensity when penetrating the active layer causes uneven illumination. All these effects worsen solar cell performance with thicker active layers, which underlines the conceptual challenge solar batteries are facing, and further accentuates the need for simulations of how to design and operate such a device.
Herein, we present numerical optical simulations as well as electrochemical experiments for a solar battery based on K-PHI and an internal hole transfer cascade (Figure 1a) to understand the active layer thickness dilemma, derive design principles and propose approaches to work around this conceptional difficulty. We first develop an optical model, which introduces the idea of optimizing light absorption not within the entire active layer but rather in parts where the internal quantum efficiency (IQE) is highest and which we henceforth term collection layer. Subsequently, we utilize thickness and illumination modes as variables to tune photocurrent output and charging time as a proposed figure of merit. We then adapt the Ragone plot for solar batteries, which is commonly employed to compare energy storage devices, [15] and propose strategies toward addressing the abovementioned bottlenecks in the field of solar batteries.

Results and Discussion
The generic design of the integrated solid-state solar battery was recently realized by us and is depicted in Figure 1a. [16] In its simplest form, the device comprises three distinct layers. [3a,8] I) The electron storing and light absorbing anode, which we denote as electron storage material (ESM) layer (Figure 1a, yellow) and which is formed by the carbon nitride K-PHI. II) The hole transport layer (HTM; Figure 1a, green) is situated between anode and cathode. Its main task is to prevent a short circuit by acting as a rectifying separator between anode and cathode. Photogenerated holes are transported via a hole transfer cascade toward the cathode, which works in only one direction and herewith effectively prevents a self-discharge of the device. Its valence band edge should be located between the valence band (VB) of ESM and cathode, and the conduction band edge should be energetically higher than the conduction band (CB) of the ESM. Here, we utilize poly(N-vinylcarbazole) (PVK), an HTM which is widely employed for optoelectronic devices. [17] It has a suitable VB location of −5.5 eV, which allows a theoretical hole injection from the K-PHI VB (at −5.9 eV). [18] The materials' bandgap of 3.5 eV prevents electron injection from K-PHI (CB of PVK at −2.4 eV; CB of K-PHI at −3.1 eV) and ensures optical transparency at wavelengths where we expect absorption of K-PHI (<450 nm; see Tauc plots in Figure S1.1, Supporting Information). III) The hole storage cathode, which we term hole storage material (HSM) layer (Figure 1a, blue). We chose the conductive polymer poly (3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS) due to its organic and environmentally friendly nature, its well-known pseudocapacitive charge storage properties and no significant light absorption < 450 nm (see Figure S1.1, Supporting Information). [19] We give more details on the device and its experimental realization in our recent proof-of-concept report. [16] For the sake of simplicity and to focus our discussion of the device on the optical boundary conditions, we approximate the thickness capacity dependence of the charge storage layers as linear ( Figure 1b) and utilize respective capacity values of 6.3 mAh g −1 (see Section S4, Supporting Information, for details) for K-PHI and 51.3 mAh g −1 [20] for PEDOT:PSS.

Optical Design
With knowledge of the materials' properties, we can design an optical model for the device. While we obtain refractive index values for the substrate comprising of glass coated with the transparent substrate indium tin oxide (ITO), PVK, and PEDOT:PSS from literature (see Figure S1.2, Supporting Information), [21] we have extracted the refractive index of K-PHI via ellipsometry from a pellet pressed from K-PHI powder (see Section S1.2, Supporting Information, for details). Next, we have to define the thickness of the individual layers. The thickness of the K-PHI layer defines the main independent variable of device composition and major tuning route that we investigate in this work, vide infra. The thickness of PEDOT:PSS is governed by matching its charge storage capacity with that of K-PHI (see Figure 1b): d PEDOT:PSS [nm] = d K-PHI [nm] × 0.238). We fix the PVK thickness to a common value of 10 nm to provide optimum hole transfer properties. [22] ITO as well as glass thickness is dictated by commercial availability (Ossila Ltd.; 100 nm ITO and 1 mm soda lime glass).
With an exemplary layer thickness of d KPHI = 500 nm and corresponding d PEDOT:PSS = 119 nm, we can now calculate the spatial distribution of the normalized electric field intensity (abbreviated henceforth with E n ) ( Figure 1c) to evaluate how light travels through the device (see Section S2, Supporting Information, for details of calculations). Illumination occurs with wavelengths between 300 and 800 nm and with a spectral distribution and photon flux according to AM1.5 global. We propose two operation modes: illumination from the front (i.e., the active layer K-PHI is illuminated first) or the rear. When looking at illumination from the front (Figure 1c) left), the light intensity entering K-PHI (at a depth of 100 nm) is governed by absorption of the soda lime glass (compare E n at a depth of 0 nm) and ITO. The former produces significant absorption at < 320 nm and the latter shows no significant absorption across the analyzed wavelength range. When entering the K-PHI layer, the expected significant absorption occurs < 450 nm (see Figure S1.1, Supporting Information), reducing E n close to 0 within a depth of 50 to 100 nm. This underlines the strong light absorption ability of K-PHI. Illumination from the rear (Figure 1c, right) shows no significant absorption of both PEDOT:PSS and PVK in the chosen layer thicknesses (at a depth of 851 to 600 nm) and an absorption behavior of K-PHI analogous to front illumination. The rationale behind choosing the two illumination directions becomes evident: K-PHI shows significant light absorption only within the first 50-100 nm and this area can be situated either at the ITO and ESM or HTM and ESM junction with illumination from the front or rear, respectively.
To underline the magnitude of absorptance within the device, we show consecutive light absorptance of the individual layers in Figure 1d) for both illumination directions and two different thicknesses (d KPHI = 500 and 2000 nm; d PEDOT:PSS = 119 and 476 nm, respectively), calculated via numerical simulations (see Section S2, Supporting Information). As expected, K-PHI absorbs nearly all photons (>0.80) at < 450 nm independent of layer thickness, and at larger wavelengths thicker layers cause more absorption. When illuminating from the front, light absorption is larger in K-PHI and smaller in PEDOT:PSS, vice versa. Note that absorption of ITO, PEDOT:PSS, and PVK is miniscule in the wavelength region of 300-450 nm, underlining why from an optical perspective they are suitable candidates as substrate, HSM, and HTM, respectively. The nearly same absorptance profile of K-PHI under front-side and rear-side illumination further underlines this. With these observations, we set the stage to investigate the solar battery active layer thickness relationship in light of solar cells and batteries.

The Device Thickness Paradigm
As mentioned above, modifying active layer morphology in bulk heterojunction organic solar cells (OSCs) devices is a key tuning parameter. [14a,23] A first approach would thus suggest to increase light absorption via layer thickness. Utilizing the computed electric field intensity ( Figure 1c) calculated via numerical simulations, we can extract the spatially resolved absorptance in a solar battery device with a K-PHI thickness of d K-PHI = 500 nm, shown in Figure 2a). The majority of light absorption occurs in the part of the active layer where light enters first. Note that the amount The collection layer, where light absorption has the highest probability to lead to charging (IQE ≈ 100%), is marked with the red area. c) The internal photocurrent that a solar battery with different K-PHI active layer thicknesses provides under 1 sun illumination, depending on whether the device is illuminated from the front (blue) or the rear (orange). The latter leads to a much larger internal photocurrent for thicker devices. Internal photocurrents for different illumination intensities are given in Table S6.3 of the Supporting Information. d) The time required to charge the entire solar battery via illumination for different K-PHI active layer thicknesses, depending on whether the device is illuminated from the front (blue) or the rear (orange). The ratio between charging times from rear and front configurations (rear:front) is shown in the inset. While for thinner K-PHI layer devices the illumination direction matters less, for thicker devices only rear illumination makes sense. e) Influence of collection layer thickness on the charging time ratio between illumination from the rear and front (compare to inset in (d)), calculated for devices with four K-PHI active layer thicknesses (100 (blue), 500 (orange), 2000 (green), and 3000 nm (red)). Simulation steps of all results shown in this figure are summarized in Table S6.1 of the Supporting Information.
of absorption in the active layer is independent of illumination direction (front or rear), since the other layers show miniscule absorptance, as mentioned above.
Typically, solar cell charge generation is regulated by space charge limited photocurrent (SCLC) and will be discussed in the context of solar batteries in the following. [23,24] Note that while it is not entirely clear how well this model applies to K-PHI since many material properties are unknown or difficult to access, [11b] we assume a behavior similar to SCLC. In an OSC comprised of a thin active layer, electron and hole depletion zones develop at the respective cathode and anode, producing band bending and assisting to extract the charge carriers. [24] The electric field between cathode and anode is assumed to be sufficiently strong to extract all photogenerated carriers in the bulk of K-PHI. However, for thick active layers (as utilized for the solar battery herein) the electric field intensity shrinks, reducing the charge collection efficiency in the bulk. [24] Second, the ability to accumulate charges in the active layer, which is essential for solar batteries, increases the amount of electrons within the layer as a consequence of photocharging and the low electronic conductivity of K-PHI [10a] in parts of the active layer, spatially close to the collection layer. Both effects could produce an additional electron-accumulationinduced or mobility-induced space charge region, further reducing charge collection efficiency in the bulk. [24,25] Since we operate in a bilayer structure (planar heterojunction) and not a bulk het-erojunction, exciton and/or charge separation most likely only occurs at the junctions within the space charge region. Note that albeit bulk heterojunctions were designed for certain solar battery geometries, [7b] they are impractical for the geometry discussed here since the very thick active layers inhibit light absorption in the bulk anyways. All these effects lead us to conclude that when charging the solar battery via illumination, electron and hole collection occurs predominantly at the interfacial depletion region of the junction K-PHI/PVK. The K-PHI/ITO junction is not significant when charging the solar battery with illumination, since photogenerated charge carriers are transferred to the cathode internally via the HTM and thus, the device operates under open circuit-like conditions, i.e., no significant electron or hole extraction occurs via the substrate. Note that this effect should be independent of illumination direction (front or rear; comparable to inverse or regular solar cell architectures) and explain our rationale behind defining a collection layer where light absorption leads to photocharging. Thus, we define an area in the active layer next to the junction with the HTM, where light absorption produces such an internal photocurrent with a very high collection efficiency, i.e., the local IQE of K-PHI is assumed to be 100% (see red area in Figure 2b) and term it collection layer. In the remaining part of the active layer (which is the majority of K-PHI: for a 500 nm device: 92%), the IQE is assumed to be 0%. Note that the assumption for a very small collection layer with very high IQE and bulk with IQE of 0% is not uncommon for thick active layer [24] and low carrier mobility semiconductor OSCs. [26] As an approximation for further calculations, we have elaborated a rectangular collection layer function (step function), as proposed for the absorption edge by the Shockley-Queisser model, [1] with a width of 10 nm (we further discuss our rationale behind the rectangular shape in Section S3, Supporting Information). It is essential to maximize light absorption not in the entire active layer, but rather within the collection layer of the photoabsorber material.
We show the absorptance profile of two solar batteries with thicknesses of d K-PHI = 100 and 500 nm and d PEDOT:PSS = 23.8 and 119 nm in Figure 2b). Major absorption occurs only in K-PHI and shows an initial Lambert-Beer like decay when entering the active layer. Due to parasitic absorption of PVK and PEDOT:PSS, when illuminating from the front the initial absorption in K-PHI is slightly higher as compared to rear illumination. However, it becomes evident that illumination from the rear produces much more absorption in the collection layer (red area in Figure 2b). The device with the thinner active layers shows an increase in absorptance in the collection layer in conflict with the Lambert-Beer decay when illuminating from the front, indicating photonic resonance effects as a result of the active layer thickness being in the range of the incident light. [27] Note that we cannot utilize this effect, since thin layers do not yield a reasonable electric capacity.
To evaluate photo-electrochemical properties of the solar battery, we calculate the theoretically achievable internal photocurrent as a function of the active layer thickness (Figure 2c) using here A K-PHI is the absorptance profile of K-PHI, x is the collection layer thickness, ϕ is the incident photon flux according to AM1.5G, IQE is the step-function of the collection layer (100% inside the collection layer, 0% outside), and q e is the elementary charge. When illuminating from the front, the simulated device shows an initial internal photocurrent of 0.384 mA cm −2 at an active layer thickness of 50 nm, which quickly decays (half of its initial value at a thickness of 350 nm) and reaches merely 0.0589 mA cm −2 at 3 μm. Conversely, internal photocurrent generated via rear illumination remains far more constant with thickness, with 0.391 mA cm −2 at 50 nm and 0.369 mA cm −2 at 3 μm, underlining the significant advantage of the rear illumination mode for devices with thicker layers. Note that the calculated internal photocurrent has to be understood as a maximum possible internal photocurrent if nonidealities are absent, such as significant scattering of the film surface, conductivity limitations, exciton or charge recombination in the collection layer, or limited donor oxidation efficiency. To evaluate the dependence of both solar cell and battery performance metrics on thickness, we propose charging time t ch as a figure of merit, i.e., the time that is required to charge the solar battery solely via illumination to its calculated capacity for a given thickness. Shorter charging times are more desirable for a given layer thickness, since the internal photocurrent is more effective in charging the battery. We can calculate the charging time with where C K-PHI is the capacity (charges per mass) of the solar battery. Note that the decay of internal photocurrent with charging state, which we discuss in Section 2.3, is not taken into account here, i.e., we assume a constant initial internal photocurrent throughout the entire charging process. Scaling of charging time with thickness for both front and rear illumination is shown in Figure 2d. As expected, thicker layers require a longer charging time. Furthermore, rear illumination produces a far less significant increase of charging time compared to front illumination (at a thickness of 3 μm corresponding to a capacity of 13.3 mC cm -2 , illumination requires 0.60 min from the rear and 12.7 min from the front). Thus, a larger internal photocurrent leads to shorter charging times and at the same time, thicker layers with a larger capacity require a longer charging time. This becomes more evident when looking at the ratio between charging times from the rear and the front (inset in Figure 2d) At a thickness of 312 nm, front illumination is only half as efficient as rear illumination. It is also worth looking at the impact of the collection layer thickness on charging time, since it allows us to extrapolate our results to materials with different optoelectronic properties influencing the shape of this layer, as well as to evaluate the accuracy of our estimate of the collection layer thickness of 10 nm.
In Figure 2e, we show the calculated ratio between charging times from the rear and front for solar batteries with four different active layer thicknesses (100, 500, 2000, 3000 nm). In all cases, the ratio stays approximately constant for collection layer thicknesses < 10 nm and subsequently increases. With thinner active layers, the ratio becomes larger independent of the collection layer thickness, suggesting a more efficient operation via front illumination. We explain this increase in the ratio with a decreasing impact of "parasitic" absorption from parts of K-PHI outside of the collection layer, which only contribute to electron storage of charges generated within the collection layer. This part of the active layer becomes thinner with decreasing layer thickness, thus reducing the negative impact on the front illumination mode (see also decay in absorptance shown in Figure 2b). Note though that apart from when nearly the entire active layer is the collection layer, the ratio never rises above 1, which emphasizes the better operation via rear illumination for essentially all layer thicknesses. Front illumination is only advantageous when active layer absorptance outside of the collection layer is not significant, since parasitic light absorption from HTM and HSM then start to play a more dominant role. For 500 nm, the ratio increase above 1 is insignificant (1.05, when the entire active layer is the collection layer), which in turn underlines the insignificant absorption of PEDOT:PSS and PVK, in line with our discussion of absorption of the independent layers above.
To conclude, irrespective of illumination direction, changing the active layer thickness does not provide an effective pathway to enhance absorption in the collection layer due to its adverse impact on battery capacity. For instance, decreasing the active layer thickness to improve front illumination would also decrease the capacity of the device. This motivates us to propose alternative means of enhancing light absorption in the collection layer, which we disclose in Figure 3. A rough surface produces more scattering, which in return causes a longer effective pathway of photons through the collection layer, when scattered at a significant angle (Figure 3a). Note that in any case the film deposition of K-PHI produces films with significant surface roughness and scattering. [8,12] This optimization strategy is very facile and straightforward, however comes at the expense of increasing light absorption along the entire spectrum, which will conversely affect transparency of the device-potentially problematic for applications where transparency is key (e.g., solar batteries prepared on windows). Alternatively, a more controlled periodic surface structuring (e.g., via lithography techniques) could produce a grating in which diffraction orders maximize light absorption in the collection layer (Figure 3b), an approach that is already employed for photovoltaic devices. [28] This design follows a wavelength selective enhancement approach, at the price of a more complex preparation routine. Selective enhancement implies that by controlling the diffraction order via the type of diffraction grating, scattering increases only at selective wavelengths at energies larger than the bandgap. [28,29] Transparency is thus not negatively affected. In addition, no additional particles are required for these approaches, hence not reducing the amount of active material. Controlled diffraction can also be generated using dielectric nanoparticles (e.g., SiO 2 nanoparticles) deposited in-between K-PHI and HTM (Figure 3c). While generating controlled diffraction, the nanoparticles also produce dielectric inclusions which increase the electric field intensity due to photonic resonance effects, an approach which was recently postulated to increase efficiency in perovskite solar cells. [30] This effect produces a broader increase in absorption edge, making it very versatile for different active materials. Last, we also propose the inclusion of metal nanoparticles, capable of producing localized surface plasmon resonance effects which can maximize local electric field intensity and as a consequence increase absorption (Figure 3d). [31] This effect produces a very sharp absorption onset, which in comparison to the previously mentioned enhancement strategies might produce the most significant absorption improvement. Furthermore, the metal nanoparticle fabrication routine is very much optimized in respect to morphology. [32] In fact, Au and Ag plasmonic nanoparticles have already been employed for example to enhance the efficiency of carbon nitride based photocatalysts. [33]

Efficiency Limitations beyond Optical Engineering
Thus far, we have discussed the nature of the solar battery from a purely optical perspective in regard to absorption. We acknowledge that energy losses in real world solar cells depend on more, namely, resistive losses at junctions, electronic and ionic conductivity reducing charge transport in the active layer (particularly for very thick active layers) and recombination losses (radiative and/or nonradiative)-all of which govern the overall cell efficiency. [1,14] Likewise, battery efficiency is significantly governed by the electric potential gradient and electronic/ionic conductivity of electrodes and electrolyte, limiting its energy and power density. [34] Similarly, solar batteries possess further effects limiting their photocharging efficiency, also commonly referred to as solar-to-output efficiency [3c] or photoconversion efficiency, [7b] and defined as the ratio between electric discharging energy and incident light energy ( c = E output /E light ). We study in Section S5 of the Supporting Information two potential efficiency loss channels, which are unique to integrated solar batteries that rely on a bifunctionality of the active material. With more charges present on the material, the internal photocurrent charging the device actually decreases, which is expected since electron-hole pair recombination increases as more electrons are stored on the material. [35] This effect of decreasing internal photocurrent can probably be reduced when a more efficient sacrificial electron donor (SED) is used. We show in a photoelectrochemical experiment in Section S5.1 of the Supporting Information (we charge a K-PHI film with 1 sun illumination and perform hole extraction via an SED), that when K-PHI is 50% charged, 26% and 3% of the initial internal photocurrent remains when using the more and less efficient SED 4-methylbenzyl alcohol (4-MBA) and methanol (MeOH), respectively. The internal photocurrent charging the device thus is a function of the accumulated charge. It can be expressed as follows We discuss implementation of this equation into simulating the charging state of the solar battery in Section S5.1 of the Supporting Information and utilize it to calculate performance parameters in Section 2.4. . Energy gains are most significant for small discharging currents, since with longer illumination times, the photogenerated charge increases (bottom left and bottom right). b,c) Modified Ragone plot, which shows the solar battery performance when discharged with distinct currents (5.01, 50.1, 100, 501 A kg −1 ) in the dark (black dots; see Section S4, Supporting Information, for experimental details). The area above the black line shows the potential improvement via illumination during electric discharge. The generated photocharging current assists charge (re)generation and thereby increases the apparent extracted charge (i.e., capacity) and energy density. We show scaling with photocharging current in (b) and extracted charge from both electric and light charging in (c). Ragone plot energy conversion and storage device data. Adapted with permission. [15] Copyright 2018, American Chemical Society. Scaling of area with mass was normalized with a form factor of fofa = 1 × 10 −4 g cm −2 (see Section S6.2, Supporting Information). Simulation steps to obtain results shown in this figure are summarized in Table S6.1 of the Supporting Information.
Second, many charge storage materials show (photo)electrochromic behavior upon charging, which has stimulated the development of manifold devices such as dimmable windows of filters. [36] Moreover, both K-PHI and PEDOT:PSS employed herein are prone to color changes when charging (see Section S5.2, Supporting Information). It is important to evaluate such effects when choosing materials, since in the worst-case transmission through an HSM or HTM decreases when charging the device, leading to a smaller internal photocurrent. In case of K-PHI and PEDOT:PSS, however, upon charging the transmission at wavelengths < 450 nm is not affected for K-PHI and increases for PEDOT:PSS, underlining their good match for a solar battery device. In perspective, color/transmission changes accompanying charging/discharging of the device could even be used as a visual read-out for the charging state of such devices.

Evaluating Performance of Solar Batteries via Ragone Plots
We conclude our study by comparing the solar battery performance (gains) to other energy storage devices. A common way of comparing the performance of energy storage systems are Ragone plots, in which power output is plotted against energy output for different discharging currents. [15,37] Capacitors are typically located at low energy and high power outputs, batteries at high energy and low power outputs. Ideally, a device shows both high energy and high power. To understand how solar batteries fit into the Ragone plot, we first must understand how photocharging affects the plot. Based on the model we introduced above, we calculate iterative discharging of a solar battery device with properties as follows: d K-PHI = 500 nm, d PEDOT:PSS = 119 nm, mass = 100 μg, illumination area = 1 cm 2 . We give a thorough discussion of the calculations in Section S6 of the Supporting Infor-mation, performance data normalization in Section S6.2 of the Supporting Information, and assumptions as well as further conditions in Section S6.3 of the Supporting Information. In brief, we calculate the initial internal photocurrent according to Equation (1), the change with charging state according to experimental approximation of the decay of internal photocurrent of K-PHI upon charging (Section 2.3), and the photocharging efficiency using a constant solar-to-output efficiency of c = 0.1%-an average value for reported solar batteries. [3c] We denote the resulting current as "photocharging current". This current is the current which actually charges the device, i.e., theoretically the difference between discharging currents in the dark and under illumination. Note that with the charging state dependent internal photocurrent, the charging time shown in Figure 2d gets longer, as shown in Figure S6.2a of the Supporting Information. Front or rear illumination is affected similarly and the ration between front and rear charging times remains similar ( Figure S6.2b, Supporting Information).
In Figure 4a we show how energy increases due to photocharging during the discharging process as a function of electric discharging current. The area relates to energy gains via photocharging during battery operation (charging and discharging), which are larger with smaller electric discharging currents, causing a longer duration of the discharging process and thus longer illumination. Photocharging conditions govern the magnitude of energy gain. Larger illumination intensities cause a more significant photocharging current, which in return produces a larger energy gain (compare Figure 4a top left and top right). This effect is more pronounced at smaller electric discharging currents, which drop to the size of the photocharging current (see Equation (S6-3), Supporting Information). Note that for illuminations >1.3 sun, the photocharging current becomes larger than the electric discharging current, causing the energy gain to rise into infinity since discharging is never complete. This demonstrates the unique potential of solar batteries with this design in terms of capacity gain over conventional batteries. In fact, small currents and large illumination intensities cause a significant increase in discharge duration (Figure 4a bottom left) and a much larger extracted capacity (Figure 4a bottom right). As photocharging current depends on light absorption in the collection layer and not on active layer thickness, we refrain from normalizing (Figure 4a) against mass as commonly done for Ragone plots and instead normalize against the device's geometric area.
To combine both discharge performance of the solar battery in the dark and the enhancement via illumination during discharge, we measure the electric dark energy and power performance of a "separated" solar battery utilizing a K-PHI film and a PEDOT:PSS film in analogous film thicknesses and use them as an input for subsequent simulations on illumination performance gains (see Section S4, Supporting Information, for details). Briefly, the sample was charged as well as discharged at four different rates (5.01, 50.1, 100, 501 A kg −1 ) in the dark. Results are shown via the black dots and line (fit) in Figure 4b,c with 5.01 A kg −1 giving the largest energy and smallest power, etc. The areas above the black line represents the area of theoretical enhancement via illumination, increasing energy output of the device as expected. Energy output can be calculated with where E dark gives the energy density of electric discharge in the dark, V p is the photopotential, I avg,normP describes the decay of photocharging current with charging state according to Equation (S5-7) of the Supporting Information, ch(t) gives the charging state according to Equation (S5-4) of the Supporting Information, I pc is the initial photocharging current when fully discharged, t d gives the discharge time in the dark, and fofa is the form factor, which relates photocharging current scaling with area to mass of the battery. Power output remains approximately constant since it is governed by the electric discharging current, albeit the photovoltage decays slightly over the duration of the discharge (see Figure S4.1, Supporting Information). The energy enhancement gets more significant for smaller discharging currents (as discussed in Figure 4a)

Conclusion
In conclusion, utilizing optic simulations as well as (photo)electrochemical experiments we provide a more holistic view on performance of the novel class of integrated solar battery devices, which employ the active material K-PHI as a model system which is bifunctional in terms of light absorption and charge storage. We first suggest a model based on solar cell designs, in which light absorption with an IQE of 100% only occurs in a collection layer with a width of 10 nm at the junction between K-PHI and PVK HTM. By calculating the absorptance within the solar battery comprising different K-PHI active layer thicknesses and the corresponding PEDOT:PSS HSM layer thicknesses, we can extract certain design specifications and performances (as summarized in Table S6.1, Supporting Information). I) Thinner active layers lead to larger photocharging currents (better solar cell functionality), albeit with the payoff of a smaller electric capacity (worse battery functionality). This issue has been pinpointed as a key conceptual challenge of solar batteries.
[3c] II) Illumination through the rear of the device is superior irrespective of active layer thickness, assuming that the collection layer is thinner than the active layer. This mode helps to minimize the impact of active layer thickness on photocharging current, i.e., a pathway to improve apparent capacity (battery functionality) without limiting the photocharging current significantly (solar cell functionality), if HTM and HSM materials with no relevant absorption are used. III) We propose different qualitative approaches to increase absorption within the collection layer beyond tuning active layer thickness: via scattering of a rough surface which is a common strategy to improve light absorption for solar cells. [38] We further propose enhancement strategies incorporating a grating, which causes higher diffraction orders, dielectric nanoparticles supporting both diffraction as well as scattering, and plasmonic nanoparticles maximizing electric field intensity in their close vicinity. IV) We look at solar battery specific efficiency limitations beyond solar cells and batteries. The internal photocharging current is decreasing with increasing charging state, i.e., the more the battery is charged, the smaller the photocharging current becomes. V) Electrochromic effects upon charging are important to consider, but their influence on the K-PHI/PEDOT:PSS is negligible since they do not decrease transmission of blue light to the collection layer of K-PHI. We believe that these observations as well as proposed design pathways will prove to be valuable to understand the behavior of this novel class of devices and optimize their efficiency. To visualize the potential of solar batteries, we adapt Ragone plots to show not only a line corresponding to the power and energy density for different discharging currents, but also an area proportional to a potential enhancement via photocharging current generated under illumination. We show how energy output increases most significantly for small electric discharging currents which are in the range of the photocharging current generated via illumination. This leads us to conclude that only minor light intensity increases can lead to major performance boosts. Implementation of a low-intensity solar concentrator could yield a significant increase in energy efficiency. [39] While the solar battery based on a bifunctional photoanode and a hole transfer cascade via an HTM possesses the ability to be operated as a solar cell and facilitates simultaneous light charging and electric discharging, design and operation considerations as well as performance metrics presented herein are transferable to other solar battery concepts, such as photocapacitors or solar redox flow batteriesboth with bifunctional electrodes (photoanode or photocathode) or with separated light absorption and charge storage material heterojunctions.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.