Indoor photovoltaics (IPVs) based on the organic and organic–inorganic halide perovskite semiconductors are attracting attention due to their easy fabrication, good mechanical flexibility, and great application potential to power the Internet of Things (IoTs)^[1–3]. Different from the one-sun illumination (air mass 1.5G, 100mW/cm2), whose spectrum covers 250 to 2500 nm, the spectrum of the indoor light source is mainly in the visible region of 400–760 nm. The detailed balance between the light harvest and thermalization loss in the cells under indoor illumination for a semiconductor with a specific bandgap (Eg) is different from the case under one-sun illumination. The power conversion efficiencies (PCEs) of 20%–30% for organic IPVs^[1,4–10] and 30%–40% for perovskite IPVs^[3,11–13] have been reported. These are much higher than those PCE values of cells under one-sun illumination: the PCE record is over 19% for organic PVs^[14–17] and over 25% for perovskite PVs^[18] under one-sun illumination.

The Shockley–Queisser (SQ) efficiency limit^[19,20] of single-junction solar cells under one-sun illumination has now become widely acknowledged and is an important fundamental theory of PV research. For IPVs, similar calculations on the efficiency limit of IPVs have been performed based on the detailed balance method developed by Shockley–Queisser (SQ). The calculated efficiency limit of the IPVs is 50%–60% at the Eg of 1.8–1.9 eV^[21–23]. The limit values slightly change according to different spectra of indoor light. The literature reports that the highest efficiencies of indoor organic PVs and perovskite PVs are 33% (concentrating indoor light to 20,000 lux)^[6] and 36.36% (under indoor light of 1000 lux, measured at the Chinese National Photovoltaic Industry Measurement and Testing Center)^[11], respectively. These values are still far behind the calculated values. However, understanding the realistic losses of the efficiency and comparing this with the calculated theoretical limit of IPVs has not been discussed.

In this work, we analyze the realistic losses of the efficiency of indoor organic and perovskite PVs, comparing these realistic efficiency losses to the theoretical limit. The calculated theoretical efficiency limit was obtained based on assuming 100% photovoltaic external quantum efficiency (EQEPV) when E≥Eg, there was no nonradiative recombination, and there were no resistance losses. In reality, the maximum EQEPV at different wavelengths reported from the literature is 0.80–0.90^{[5,6,11,13,24–28]} (mainly due to optical losses). The portion of radiative recombination [typically by measuring the electroluminescent quantum efficiency (EQEEL)] in realistic devices is only 10−5−10−2^{[7–9,11,28]}, which causes the open-circuit voltage loss (ΔVloss) of 0.12–0.3 V. In addition, the fill factor (FF) is sensitive to shunt resistance (Rsh) while being less sensitive to series resistance (Rs). Thus, these realistic losses in the EQEPV, the EQEEL, and the Rsh cause the large efficiency gap between the realistic values and the theoretical limit. Accordingly, strategies to further increase the efficiency of IPVs include enhancing the EQEPV, suppressing the nonradiative combination to increase the EQEEL, and increasing the Rsh.

The methods for the calculation are included in Supplementary Material 1. The MATLAB codes are provided in Supplementary Material 2. Figures 1(a)–1(d) show the maximum PCE, FF, open-circuit voltage (VOC), and short-circuit current density (JSC) at different Eg ranging from 1.2 to 2.5 eV. Four different indoor light sources are included, i.e., two different incident light spectra, whose color temperatures are 2700 K and 4651 K, respectively, and two different light intensities (500 and 1000 lux). Figure 1(f) shows the indoor light spectra from the light-emitting diodes (LEDs). The light intensity of the 2700 K, 1000 lux LED is 310.102µW/cm2, while the light intensity of the 4651 K, 1000 lux LED is 299.193µW/cm2. As shown in Fig. 1(a) and Table 1, the PCE limit is 55.33% (under 1000 lux) and 54.54% (under 500 lux) under 2700 K light when the Eg is 1.771 eV. Under 4651 K indoor illumination, the PCE limit is 53.93% (under 1000 lux) and 53.20% (under 500 lux) when the Eg is 1.85 eV. The maximum FF and VOC curves at different Eg are almost identical under four different light sources [Figs. 1(b) and 1(c)]. The maximum FF and VOC monotonically increase as the Eg increases. Figure 1(d) shows the maximum JSC of the devices at different Eg. JSC under 1000 lux illumination is twice as high as that under 500 lux illumination. Under 1000 lux, the maximum JSC of the devices is about 150µA/cm2 for 2700 K light and 133µA/cm2 for 4651 K. Since the 1000 lux and 2700 K illumination is the commonly used indoor illumination for research^[9,29–31], we hereafter use this light source for the analysis of the realistic losses. At the Eg of 1.77 eV, the cells under 2700 K and 1000 lux can ideally have an efficiency limit of 55.33%, with an FF of 0.907, a VOC of 1.356 V, and a JSC of 139.53µA/cm2 (Table 1).

The above efficiency limit of IPVs was calculated on the basis of the following assumptions. (1) All photons with energy higher than or equal to the Eg of the semiconductor are fully absorbed, and photons with energy lower than the Eg are not absorbed. The EQEPV is a step function. The EQEPV is 1 at E≥Eg, and 0 at E<Eg. (2) Each photon absorbed produces only one electron-hole pair. (3) There is no nonradiative recombination but only radiative recombination in the devices. (4) The device emits the spectrum as a blackbody at room temperature (300 K).

The theoretical PCE limit of IPVs is 55.33% under 2700 K, 1000 lux illumination, while the realistic PCE of perovskite and organic IPVs are far lower. Understanding these realistic losses is important for further enhancing the efficiency of IPVs. The PCE is determined by the product of the JSC, the VOC, and the FF. Each of the three parameters will cause losses of the PCE.

For the loss of JSC, in the calculation, it is assumed that the EQEPV is 100% in the spectral region with E≥Eg. In reality, not all photons with energy exceeding Eg can be fully absorbed and converted into free charge carriers. The EQEPV of the device is not constant at 100%. The light reflection, the transmittance of transparent electrode, and the charge carrier recombination are the origin losses of EQEPV and JSC. Figure 2(a) shows the EQEPV of two high-efficiency perovskite^[12] and organic^[28] IPVs reported in the literature. The perovskite photovoltaics can deliver high EQEPV of about 90% and be quite constant in the indoor spectral region^{[11,24,26,27]}. The organic IPVs can deliver EQEPV in the range of 80%–90% but is not constant due to their small film thickness^[5,6,28]. That suggests that the practical JSC generally causes 10%–15% loss compared with the theoretical JSC. Figure 2(b) shows that limit of the JSC at different Eg when EQEPV is 0.7, 0.8, 0.9, and 1.0 under the 2700 K, 1000 lux illumination. Under such illumination, the maximum JSC is 149.3, 134.4, 119.5, and 104.5µA/cm2 for the EQEPV of 1.0, 0.9, 0.8, and 0.7 at the Eg of 1.2 eV, respectively. To achieve high PCE of the IPVs, it is important to further enhance the EQE_PV to a high value approaching 1 in the entire indoor spectral region.

For the loss of VOC, the open-circuit voltage loss (ΔVloss) mainly includes two parts of radiative and nonradiative recombination, as shown in Eq. (1), ΔVloss=Ege−VOC=ΔVrad+ΔVnon-rad,(1)where ΔVrad and ΔVnon-rad represent the loss caused by radiative recombination and nonradiative recombination, respectively. ΔVrad is associated with the temperature of the devices and Eg of semiconductors. Every photovoltaic device working under temperatures higher than 0 K will emit and cause the voltage loss. The ΔVrad is calculated with Eq. (2)^[32,33], which is correlated with the JSC and the J0rad [Fig. 1(e)], ΔVrad=Ege−nkTeln(JSCJ0rad+1),(2)where e represents the elementary charge; n is the ideality factor of the p-n junction, and its value is 1 here; k is the Boltzmann constant; T is the absolute temperature; and J0rad represents the reverse saturation current density caused by radiative recombination. Under indoor illumination, the ΔVrad is the difference between the Eg and the VOC when the EQEEL=1 and the EQEPV=1, included in Fig. 3, which is the larger, in the range of 0.4–0.5 V. It is higher than the ΔVrad under one-sun illumination (typically 0.2–0.3 V^[3]). That is because the JSC of the cells under indoor illumination is 2–3 orders of magnitude lower than that under one-sun illumination. Figure S1 (Supplementary Material 1) shows that the higher temperature of the cells would result in the stronger radiation of the blackbody and a higher ΔVrad. According to the calculation, when the temperature rises by 5 K, the ΔVrad would increase by about 0.01 V.

In addition to the loss caused by radiative recombination, the loss caused by nonradiative recombination (ΔVnon-rad) is also critical. The ΔVnon-rad can be calculated by the following equation^[33,34]: ΔVnon-rad=−nkTeln(EQEEL),(3)where the EQEEL represents electroluminescent quantum efficiency of the device and suggests the proportion of radiative recombination to the total recombination. As shown in Fig. 3, increasing the EQEEL can effectively reduce the ΔVnon-rad, resulting in the improvement of the VOC. The ΔVnon-rad is reduced to 60 meV when the EQEEL increases by one order of magnitude. Table S1 (Supplementary Material 1) shows the values of ΔVnon-rad when the EQEEL changes from 10−1 to 10−5. At present, the outstanding organic active layer materials can achieve EQEEL of around 10−3 (such as PBDB-TF:GS-ISO^[9]), which results in a small ΔVnon-rad of 0.17 V. For perovskite solar cells, the EQEEL can be much higher, in the range of about 10−2−10−1^[12,35]. Thus, the ΔVnon-rad of the perovskite PVs is lower than that of the organic PVs. The calculation of ΔVrad and ΔVnon-rad is based on the step function of the EQEPV with a value of 1 when E≥Eg. In reality, the EQEPV generally has a sloped tail rather than a step function, and the EQEPV value is not constantly 1. That will cause additional voltage loss. Based on the experimental data, this voltage loss can be as low as 0.066 V for organic^[28] and perovskite^[11] PVs. Thus, we do not include this part of the voltage loss into the Fig. 3.

For the realistic loss of the FF, the FF is influenced by the series resistance (Rs) and the shunt resistance (Rsh). In the calculation of the efficiency limit, the Rs is zero and the Rsh is infinity. In reality, the drop of the FF as a function of the Rs and the Rsh is shown in Fig. 4(a). The FF of the IPVs is very sensitive to the Rsh. When the Rsh is high, 104kΩcm2, the FF monotonically increases as a function of Eg. When the Rsh is lower, the trend of the FF as a function of Eg is changed, and the value of the FF is lower. This is because the current under indoor illumination is low, on the order of µA/cm2. If the Rsh is not high enough, then the shunt current will be high and significantly reduce the output power (Pout). The behavior of the FF (as a function of Rs and Rsh) under indoor illumination is different from that under one-sun illumination. As shown in Figs. 4(b) and 4(c), the FF of the device under one-sun illumination is quite constant when the Rsh changes from 20 to 300kΩcm2, while the FF of the device under indoor illumination increases rapidly from 0.4 to 0.86. On the contrary, the FF of the device under one-sun illumination is sensitive to the Rs, which drops from 0.87 down to 0.64 when the Rs changes from 0.1 to 20Ωcm2, while the FF of the device under indoor illumination is constantly high, 0.87, when the Rs changes from 0.1 to 20Ωcm2 [Fig. 4(c)]. In addition, the nonradiative recombination (EQEEL) also slightly influences the FF. When the EQEEL increases from 10−5 to 1, the FF increases from 0.87 to 0.90 when the Rs is 1Ωcm2 and the Rsh is 104kΩcm2. Thus, a large Rsh is important for the FF of IPVs.

Figure 5(a) shows the comparison of the J-V characteristics between the theoretical limit (VOC=1.356V, JSC=139.53µA/cm2, FF=0.907, and PCE=55.33% at the Eg of 1.77 eV) and the realistic organic^[28] (VOC=0.943V, JSC=123.8µA/cm2, FF=0.811, and PCE=30.2% at Eg of 1.72 eV) and perovskite^[12] (VOC=1.23V, JSC=94.54µA/cm2, FF=0.84, and PCE=32.41% at Eg of 1.86 eV) IPVs. The JSC, the VOC, and the FF are all lower than the theoretical limit, which caused the large gap between the realistic efficiencies and the theoretical limit. Based on the above discussion, it can be known that the efficiency loss is due to the loss of the EQEPV, the EQEEL, and the Rsh. Figure 5(b) shows the plots of the PCE as a function of Eg with different EQEPV and EQEEL. The Rsh was set as 104kΩcm2 since the FF saturates at this value, as shown in Fig. 4(b). The following information can be obtained: (1) the optimum Eg is 1.77–1.80 eV to achieve the highest PCE for IPVs, and (2) the EQEPV and the EQEEL could significantly change the PCE of the IPVs. When the EQEPV=0.9 and the EQEEL=10−1, the PCE can reach a high value of 47.39% at 1.77 eV (VOC=1.299V, JSC=125.33µA/cm2, and FF=0.903, Table 2). When the EQEPV=0.8 and the EQEEL=10−5, the PCE is lower of 33.86% (VOC=1.080V, JSC=109.45µA/cm2, and FF=0.888). The asterisk and triangle in the figure correspond to the PCE values of the reported organic^[28] and perovskite^[12] IPVs.

To improve the PCE of the realistic IPVs, it is important to increase the EQEPV and the EQEEL, while maintaining the Rsh over 104kΩcm2. The JSC (EQEPV) could be improved by choosing high-performance active layers, reducing the light reflection, and increasing the transmittance of transparent electrode. The VOC (EQEEL) could be enhanced by suppressing the nonradiative recombination via defect passivation or improving the crystallinity of the active layer. Currently, the maximum EQEEL reported in the literature is around 10−3 for organic PVs^[9,28] and 10−2−10−1 for perovskite PVs^[12,35]. In the future, it is desirable for the EQEEL to be enhanced to over 10−1. As a result, it is feasible for the PCE to reach a high value of 47.39% with an EQEPV of 0.9 and an EQEEL of 10−1 at the Eg of 1.77 eV.

In this work, we have discussed the theoretical efficiency limit and realistic losses of indoor photovoltaics. The power conversion efficiency limit of indoor photovoltaics is 55.33% (indoor condition: 1000 lux, 2700 K light) when the Eg of the active layer is 1.77 eV. The efficiency limit is based on assuming 100% EQEPV when E≥Eg, no nonradiative recombination (EQEEL=1), infinity shunt resistance, and zero series resistance. In reality, the losses of the EQEPV, the EQEEL, and the shunt resistance cause the large gap between the efficiency of the realistic devices and the theoretical limit. The efficiency of the PV devices under indoor illumination is sensitive to the Rsh, while being sensitive to the Rs under one-sun illumination. Combining the highest parameters reported in the literature of Rsh=104kΩcm2, EQEPV=0.9, and EQEEL=10−1, it could be feasible that the PCE reaches a value of 47.39% at 1.77 eV for organic and perovskite IPVs. To realize this value, it is important to reduce the optical loss and nonradiative recombination and increase the Rsh by reducing the leakage current.