Indoor organic and perovskite photovoltaics (PVs) have been attracting great interest in recent years. The theoretical limit of indoor PVs has been calculated based on the detailed balance method developed by Shockley–Queisser. However, realistic losses of the organic and perovskite PVs under indoor illumination are to be understood for further efficiency improvement. In this work, the efficiency limit of indoor PVs is calculated to 55.33% under indoor illumination (2700 K, 1000 lux) when the bandgap (Eg) of the semiconductor is 1.77 eV. The efficiency limit was obtained on the basis of 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 reported in the literature is 0.80–0.90. The proportion of radiative recombination in realistic devices is only 10-5–10-2, which causes the open-circuit voltage loss (ΔVloss) of 0.12–0.3 V. The fill factor (FF) of the indoor PVs is sensitive to the shunt resistance (Rsh). The realistic losses of EQEPV, nonradiative recombination, and resistance cause the large efficiency gap between the realistic values (excellent perovskite indoor PV, 32.4%; superior organic indoor PV, 30.2%) and the theoretical limit of 55.33%. In reality, it is feasible to reach the efficiency of 47.4% at 1.77 eV for organic and perovskite photovoltaics under indoor light (1000 lux, 2700 K) with VOC = 1.299 V, JSC = 125.33 µA/cm2, and FF = 0.903 when EQEPV = 0.9, EQEEL = 10-1, Rs = 0.5 Ω cm2, and Rsh = 104 kΩ cm2.
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, ), 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 () 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 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 () when , there was no nonradiative recombination, and there were no resistance losses. In reality, the maximum 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 ()] in realistic devices is only [7–9,11,28], which causes the open-circuit voltage loss () of 0.12–0.3 V. In addition, the fill factor (FF) is sensitive to shunt resistance () while being less sensitive to series resistance (). Thus, these realistic losses in the , the , and the 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 , suppressing the nonradiative combination to increase the , and increasing the .
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2. Results and Discussion
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 (), and short-circuit current density () at different 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 , while the light intensity of the 4651 K, 1000 lux LED is . 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 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 is 1.85 eV. The maximum FF and curves at different are almost identical under four different light sources [Figs. 1(b) and 1(c)]. The maximum FF and monotonically increase as the increases. Figure 1(d) shows the maximum of the devices at different . under 1000 lux illumination is twice as high as that under 500 lux illumination. Under 1000 lux, the maximum of the devices is about for 2700 K light and 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 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 of 1.356 V, and a of (Table 1).
Table 1. Theoretical Efficiency Limit and Corresponding Photovoltaic Data of Indoor Photovoltaics under Four Different Illumination Conditions: Two Different Spectra (2700 and 4651 K) and Two Different Light Intensities (500 and 1000 lux)
Table 1. Theoretical Efficiency Limit and Corresponding Photovoltaic Data of Indoor Photovoltaics under Four Different Illumination Conditions: Two Different Spectra (2700 and 4651 K) and Two Different Light Intensities (500 and 1000 lux)
Color Temperature
Irradiance (µW/cm2)
Illuminance (lux)
Eg (eV)
VOC (V)
JSC (µA/cm2)
FF
PCE
2700 K
310.102
1000
1.771
1.356
139.53
0.907
55.33%
155.051
500
1.771
1.338
69.76
0.906
54.54%
4651 K
299.193
1000
1.851
1.430
123.90
0.911
53.93%
149.596
500
1.853
1.415
61.83
0.910
53.20%
Figure 1.Theoretical efficiency limit of indoor photovoltaics. (a)–(d) The theoretical limit of PCE, FF, VOC, and JSC of IPVs as a function of the band gap (Eg) under different indoor conditions at 300 K. (e) The calculated J0 (J0rad, radiative recombination only at 300 K) as a function of Eg. (f) The spectra of indoor light used for the calculation (2700 and 4651 K at 1000 lux).
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 of the semiconductor are fully absorbed, and photons with energy lower than the are not absorbed. The is a step function. The is 1 at , and 0 at . (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 , the , and the FF. Each of the three parameters will cause losses of the PCE.
For the loss of , in the calculation, it is assumed that the is 100% in the spectral region with . In reality, not all photons with energy exceeding can be fully absorbed and converted into free charge carriers. The 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 and . Figure 2(a) shows the of two high-efficiency perovskite[12] and organic[28] IPVs reported in the literature. The perovskite photovoltaics can deliver high of about 90% and be quite constant in the indoor spectral region[11,24,26,27]. The organic IPVs can deliver in the range of 80%–90% but is not constant due to their small film thickness[5,6,28]. That suggests that the practical generally causes 10%–15% loss compared with the theoretical . Figure 2(b) shows that limit of the at different when is 0.7, 0.8, 0.9, and 1.0 under the 2700 K, 1000 lux illumination. Under such illumination, the maximum is 149.3, 134.4, 119.5, and for the of 1.0, 0.9, 0.8, and 0.7 at the of 1.2 eV, respectively. To achieve high PCE of the IPVs, it is important to further enhance the EQEPV to a high value approaching 1 in the entire indoor spectral region.
Figure 2.Realistic loss analysis of JSC. (a) The EQEPV spectra of recently reported high-performance perovskite[12] and organic[28] solar cells. The blue dash lines indicate the positions of the EQEPV of 0.7–1. (b) The integrated JSC as a function of the different EQEPV spectra, where EQEPV is a step function; EQEPV = 0.7, 0.8, 0.9, or 1 (E ≥ Eg); and EQEPV = 0 (E < Eg). The asterisk and triangle represent the JSC of the recently reported high-performance indoor (1000 lux) perovskite[12] and organic[28] photovoltaics, respectively.
For the loss of , the open-circuit voltage loss () mainly includes two parts of radiative and nonradiative recombination, as shown in Eq. (1), where and represent the loss caused by radiative recombination and nonradiative recombination, respectively. is associated with the temperature of the devices and of semiconductors. Every photovoltaic device working under temperatures higher than 0 K will emit and cause the voltage loss. The is calculated with Eq. (2)[32,33], which is correlated with the and the [Fig. 1(e)], where represents the elementary charge; is the ideality factor of the p-n junction, and its value is 1 here; is the Boltzmann constant; is the absolute temperature; and represents the reverse saturation current density caused by radiative recombination. Under indoor illumination, the is the difference between the and the when the and the , included in Fig. 3, which is the larger, in the range of 0.4–0.5 V. It is higher than the under one-sun illumination (typically 0.2–0.3 V[3]). That is because the 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 . According to the calculation, when the temperature rises by 5 K, the would increase by about 0.01 V.
Figure 3.Realistic loss analysis of the VOC. Plots of the VOC limit as a function of Eg, under different nonradiative recombination. The black solid line represents the VOC with the loss caused by only radiative recombination (without nonradiative recombination). The difference between the dash line (slope = 1) and black solid line is the loss caused by radiative recombination (ΔVrad). The asterisk and triangle represent recently reported high-performance indoor (1000 lux) perovskite[12] and organic[28] photovoltaics, respectively.
In addition to the loss caused by radiative recombination, the loss caused by nonradiative recombination () is also critical. The can be calculated by the following equation[33,34]: where the 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 can effectively reduce the , resulting in the improvement of the . The is reduced to 60 meV when the increases by one order of magnitude. Table S1 (Supplementary Material 1) shows the values of when the changes from to . At present, the outstanding organic active layer materials can achieve of around (such as PBDB-TF:GS-ISO[9]), which results in a small of 0.17 V. For perovskite solar cells, the can be much higher, in the range of about [12,35]. Thus, the of the perovskite PVs is lower than that of the organic PVs. The calculation of and is based on the step function of the with a value of 1 when . In reality, the generally has a sloped tail rather than a step function, and the 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 () and the shunt resistance (). In the calculation of the efficiency limit, the is zero and the is infinity. In reality, the drop of the FF as a function of the and the is shown in Fig. 4(a). The FF of the IPVs is very sensitive to the . When the is high, , the FF monotonically increases as a function of . When the is lower, the trend of the FF as a function of is changed, and the value of the FF is lower. This is because the current under indoor illumination is low, on the order of . If the is not high enough, then the shunt current will be high and significantly reduce the output power (). The behavior of the FF (as a function of and ) 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 changes from 20 to , 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 , which drops from 0.87 down to 0.64 when the changes from 0.1 to , while the FF of the device under indoor illumination is constantly high, 0.87, when the changes from 0.1 to [Fig. 4(c)]. In addition, the nonradiative recombination () also slightly influences the FF. When the increases from to 1, the FF increases from 0.87 to 0.90 when the is and the is . Thus, a large is important for the FF of IPVs.
Figure 4.Realistic loss analysis of the FF. (a) The FF of the IPVs as a function of Eg when Rs is 0, 0.5, 1.0, and 2.0 Ω cm2 and Rsh is 50, 100, 103, and 104 kΩ cm2, respectively. The dash lines represent the FF of recently reported high-performance indoor (1000 lux) perovskite[12] (0.84) and organic[28] (0.811) photovoltaics, respectively. (b) The FF as a function of the resistance of the devices under indoor (2700 K, 1000 lux) illumination (Rsh) and (c) one-sun (AM 1.5G, 100 mW cm-2) illumination (Rs). Different EQEEL conditions were considered.
Figure 5(a) shows the comparison of the characteristics between the theoretical limit (, , , and at the of 1.77 eV) and the realistic organic[28] (, , , and at of 1.72 eV) and perovskite[12] (, , , and at of 1.86 eV) IPVs. The , the , 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 , the , and the . Figure 5(b) shows the plots of the PCE as a function of with different and . The was set as since the FF saturates at this value, as shown in Fig. 4(b). The following information can be obtained: (1) the optimum is 1.77–1.80 eV to achieve the highest PCE for IPVs, and (2) the and the could significantly change the PCE of the IPVs. When the and the , the PCE can reach a high value of 47.39% at 1.77 eV (, , and , Table 2). When the and the , the PCE is lower of 33.86% (, , and ). The asterisk and triangle in the figure correspond to the PCE values of the reported organic[28] and perovskite[12] IPVs.
Table 2. Calculated Photovoltaic Parameters of IPVs with Different Values of EQEPV and EQEELa
Table 2. Calculated Photovoltaic Parameters of IPVs with Different Values of EQEPV and EQEELa
EQEPV
EQEEL
Eg (eV)
VOC (V)
JSC (µA/cm2)
FF
PCE
0.8
10-1
1.774
1.299
110.40
0.903
42.12%
0.9
10-1
1.774
1.299
125.33
0.903
47.39%
0.8
10-3
1.784
1.189
110.47
0.896
37.96%
0.9
10-3
1.784
1.189
124.28
0.896
42.71%
0.8
10-5
1.794
1.080
109.45
0.888
33.86%
0.9
10-5
1.794
1.080
123.14
0.888
38.09%
Figure 5.Realistic loss analysis of the PCE. (a) The theoretical and experimental J-V characteristics of the IPVs. The blue line represents the theoretical limit (VOC = 1.356 V, JSC = 139.53 µA/cm2, FF = 0.907, and PCE = 55.33% at Eg of 1.77 eV). The pink and red lines represent the realistic organic[28] (VOC = 0.943 V, JSC = 123.8 µA/cm2, FF = 0.811, and PCE = 30.2% at Eg of 1.72 eV) and perovskite[12] (VOC = 1.23 V, JSC = 94.54 µA/cm2, FF = 0.84, and PCE = 32.4% at Eg of 1.86 eV) solar cells’ curves, respectively. (b) The PCE limit as a function of Eg with different EQEPV and EQEEL (Rs = 0.5 Ω cm2 and Rsh = 104 kΩ cm2). The asterisk and triangle represent recently reported high-performance indoor (1000 lux) perovskite[12] and organic[28] solar cells, respectively.
To improve the PCE of the realistic IPVs, it is important to increase the and the , while maintaining the over . The () could be improved by choosing high-performance active layers, reducing the light reflection, and increasing the transmittance of transparent electrode. The () could be enhanced by suppressing the nonradiative recombination via defect passivation or improving the crystallinity of the active layer. Currently, the maximum reported in the literature is around for organic PVs[9,28] and for perovskite PVs[12,35]. In the future, it is desirable for the to be enhanced to over . As a result, it is feasible for the PCE to reach a high value of 47.39% with an of 0.9 and an of at the of 1.77 eV.
3. Conclusions
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 of the active layer is 1.77 eV. The efficiency limit is based on assuming 100% when , no nonradiative recombination (), infinity shunt resistance, and zero series resistance. In reality, the losses of the , the , 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 , while being sensitive to the under one-sun illumination. Combining the highest parameters reported in the literature of , , and , 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 by reducing the leakage current.