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Abstract
hv photonics Article Insights of Hysteresis Behaviors in Perovskite Solar Cells from a Mixed Drift-Di usion Model Coupled with Recombination Chongqiu Yang , Xiaobiao Shan and Tao Xie * Harbin Institute of Technology, School of Mechatronics Engineering, Harbin 150001, China; 14B908006@hit.edu.cn (C.Y.); shanxiaobiao@hit.edu.cn (X.S.) * Correspondence: xietao@hit.edu.cn Received: 6 June 2020; Accepted: 2 July 2020; Published: 3 July 2020 Abstract: Hysteresis in perovskite solar cells is a notorious issue limiting its development in stability, reproducibility and eciency. Ions’ migration coupled with charges’ recombination are indispensable factors to generate the hysteretic curves on the basis of experimental and theoretical calculation studies, however, the underlying physical characteristics are rarely clarified. Here, a mixed electronic-ionic drift-di usion model combined with bulk and interfacial recombination is investigated. Positive and negative ion species could drift to and accumulate at interfaces between the perovskite/transport layers, influencing internal electric potential profiles and delaying the charges’ ejection to the transport layers. The charges might recombine spontaneously or trap-assisted, reducing the total amount of electrons and holes collected in the external circuit, leading to a diminished photocurrent. Moreover, our calculations indicate that an appropriate measurement protocol is really essential to evaluate the device performance precisely and to suppress J–V hysteresis. Meanwhile, a negligible hysteretic loop could be obtained by balancing the material properties of the transport layers and restraining the ions mobility in the perovskite layer. Keywords: hysteresis; drift-di usion; recombination; measurement protocol; balanced transportation; ion mobility 1. Introduction Research enthusiasm on organic–inorganic perovskite solar cells (PSCs) has risen tremendously within the last decade, attributed to their remarkable optoelectronic properties, such as high carrier mobility, suitable band gap and excellent economic eciency [1]. Seok et al. [2] published a certified power conversion eciency (PCE) of 23.73% by stabilizing -phase formamidinium lead iodide (FAPbI ) with methylenediammonium dichloride (MDACl ) dopant material, and their lab-measured champion device presented a PCE of 24.66%; meanwhile, the NREL (National Renewable Energy Laboratory, U.S.) best research-cell eciencies presented a record of 25.2% [3]. Moreover, the perovskite/silicon tandem solar cells have achieved a PCE of 26.7% recently [4]. Despite the fact that numerous achievements have been obtained to commercialize the PSCs, one of the major barriers is photocurrent hysteresis, over or underestimating the device performance [5]. The hybrid perovskite materials were reported to be combined conductors of electrons and ions [6]. Experimental and theoretical studies indicated that the iodine (I ) and the methylammonium (MA ) are the major available mobile ion species in the perovskite material of methylammonium lead triiodide (MAPbI ) [7]. Furthermore, it is these ions’ migration combined with trap-assisted recombination that give rise to the anomalous current density–voltage (J–V) hysteresis [8,9]. However, it has yet to be clearly clarified what characteristics inside the PSC are modified if the ions could migrate regularly and what functions of the recombination Photonics 2020, 7, 47; doi:10.3390/photonics7030047 www.mdpi.com/journal/photonics Photonics 2020, 7, 47 2 of 14 act as to induce the hysteretic phenomena. Besides, numerical research work on the improvement of measurement protocols and material properties to suppress J–V hysteresis is rarely performed. A range of approaches have been studied to model the characteristics of the PSCs. Density functional theory (DFT), based on the first principle, is widely used to calculate the microscopic properties of the perovskite materials [10]. Eames et al. [11] estimated the activation energies for di erent ion species using DFT calculation, and the results present 0.58, 0.84 and 2.31 eV for I , MA 2+ and Pb , respectively. A significant limitation for DFT study is the massive computational cost, and it is infeasible to calculate the entire PSC device structure with complicated boundary conditions. In this case, the drift-di usion model is capable of explaining the macroscopic performance based on the microscopic properties, utilizing the conservation of charge carriers coupled with the balance of electric potential. Van Reenen et al. [9] firstly combined the mobile ions into the PSC drift-di usion simulations to reproduce the experimental hysteretic phenomena, assuming an unrealistically high ion mobility and a high scan speed. Richardson et al. [12] implemented an asymptotic analysis of a single perovskite layer including the mobile iodide ion vacancies. Calado et al. [13] investigated the entire PSC layers using the drift-di usion method by simplifying the heterojunctions to homojunctions, neglecting the property di erences between the perovskite layer and the electron and hole transport layers (ETL and HTL). Courtier et al. [14–16] systematically studied the algorithms to solve the drift-di usion equations credibly and fast, while only the positive ions’ migration was concluded in their numerical model. All of the abovementioned calculations require very profound mathematical and programming knowledge, hostile to the non-expert. Shen [17] and Xiang [18] attempted to use a multi-physics platform to define the drift-di usion process of the charge carriers and ion species in the PSC and reproduced the notorious hysteresis J–V curves as occurred in experiments. More deep mechanism study on the working principles of the mobile ions in J–V hysteresis is needed. Hysteresis elimination is the ultimate goal to which the researchers are dedicated. Numerical and theoretical studies could give a general experimental guideline to modify material properties or manufacturing processes to passivate J–V hysteresis. However, research in this area is scarce. Recently, Courtier et al. [16] and Xiang et al. [18] investigated the influences of how the bulk recombination and the interfacial recombination a ect the shape of the J–V hysteresis curves, and put forward a simple diagnosis criterion to determine which kind of recombination was dominantly occurring inside the PSCs, but failed to make a further study on how to eliminate J–V hysteresis. George Alexandru et al. [19] studied how the measurement protocols a ected the normal and inverted J–V hysteresis curves, proposing to reduce the hysteresis by changing the pre-poling conditions. However, the pre-poling treatment could just deal with the superficial issue; the defects and hysteresis still exist inside the PSC. In this work, a well-rounded drift-di usion model combined with the constraints of Shockley Read Hall (SRH) recombination is performed to reveal the underlying factors that support the hysteresis phenomena in the PSCs. We show that both the mobile ions and the SRH recombination are necessary to generate the hysteretic J–V loops. The corresponding variations of electric field and potential during the J–V measurement are proposed to expose the nature of hysteresis. From the point of measurement protocol, a fast J–V scan rate is essential to suppress J–V hysteresis with great photovoltaic eciency. A positive voltage pre-treatment facilitates the PSC to generate a superior eciency performance with reduced hysteresis, while scan direction could significantly a ect the extent and shape of the J–V hysteresis curves. From the point of material properties, in order to passivate J–V hysteresis e ectively, doping concentration and relative permittivity of the ETL and the HTL are supposed to increase equivalently, while no significant e ect to enhance them imbalanced. Furthermore, the ion movement inside the perovskite layer should be limited to further diminish J–V hysteresis. 2. Methods A device configuration of metal contact/ETL (100 nm)/perovskite (400 nm)/HTL (100 nm)/metal contact was adopted to perform the calculations concerning the J–V hysteretic phenomena. The charge Photonics 2020, 7, x FOR PEER REVIEW 3 of 14 Photonics 2020, 7, 47 3 of 14 A device configuration of metal contact/ETL (100 nm)/perovskite (400 nm)/HTL (100 nm)/metal contact was adopted to perform the calculations concerning the J–V hysteretic phenomena. The transport was assumed to be directly across the interfaces in one spatial dimension (x). In addition, charge transport was assumed to be directly across the interfaces in one spatial dimension (x). In the influences of morphology, composition and grain structure of the perovskite layer were neglected. addition, the influences of morphology, composition and grain structure of the perovskite layer were Although these factors could not be calculated in our calculation directly, they determine the neglected. Although these factors could not be calculated in our calculation directly, they determine characteristics of the perovskite layer, such as permittivity, ion concentration and mobility, which are the characteristics of the perovskite layer, such as permittivity, ion concentration and mobility, which analyzed in Section 3.3. As seen in Figure 1, the calculation model defined the motion of the free electrons are analyzed in Section 3.3. As seen in Figure 1, the calculation model defined the motion of the free (n), holes (p), defect negative ions (N) and positive ions (P) using the time-dependent drift-di usion electrons (n), holes (p), defect negative ions (N) and positive ions (P) using the time-dependent drift- equations [14,18], including the bulk recombination (R ) occurring inside the perovskite layer and bulk diffusion equations [14,18], including the bulk recombination (Rbulk) occurring inside the perovskite the interfacial recombination (R and R ) occurring at the ETL/perovskite and the perovskite/HTL ETL HTL layer and the interfacial recombination (RETL and RHTL) occurring at the ETL/perovskite and the interfacial junctions, respectively. Furthermore, all of the recombination mechanisms were ruled by the perovskite/HTL interfacial junctions, respectively. Furthermore, all of the recombination mechanisms Shockley Read Hall (SRH) recombination [20]. The related mathematical equations and calculation were ruled by the Shockley Read Hall (SRH) recombination [20]. The related mathematical equations methods were shown in the Supplementary Materials. At the ETL/perovskite interface, the conduction and calculation methods were shown in the Supplementary Materials. At the ETL/perovskite band (E ) matching facilitated the electrons to flow into the ETL, while the valence band (E ) o set C V interface, the conduction band (EC) matching facilitated the electrons to flow into the ETL, while the prevented the holes from the perovskite layer. However, the electrons from the ETL and the holes valence band (EV) offset prevented the holes from the perovskite layer. However, the electrons from from the perovskite might leak out via the defective ionic trap-assisted recombination, named the the ETL and the holes from the perovskite might leak out via the defective ionic trap-assisted interfacial recombination; the same goes for the perovskite/HTL interface. Inside of the perovskite recombination, named the interfacial recombination; the same goes for the perovskite/HTL interface. material, the electrons and holes could make a non-radiative recombination within a limited transport Inside of the perovskite material, the electrons and holes could make a non-radiative recombination length and lifetime, named the bulk recombination. Additionally, photovoltaic generation (G) and within a limited transport length and lifetime, named the bulk recombination. Additionally, radiative recombination (R) are added to the perovskite layer. photovoltaic generation (G) and radiative recombination (R) are added to the perovskite layer. (a) (b) Figure 1. Figure 1. Sc Schematic hematic o of f the ( the (a a)) work working ing principle and the principle and the co corr rresponding esponding ((b b) cal ) calculation culation m model odel of of the the perovsk perovskite ite sola solar r ce cell ll (PSC (PSC).).The The ion ions s and and char charg ge carriers e carriers we were re equili equilibrated brated at 1.2 at 1.2 V in V the in the l light,ight, an and their d their movement and transport movement and transportationaar tion e indicated are indicated with with the arr the a ows. rrows. In order to highlight the J–V hysteresis loops, an electron/hole pseudo-lifetime of 10 ns for R and In order to highlight the J–V hysteresis loops, an electron/hole pseudo-lifetime of 10 ns for bulk Rbulk 0.2 ns for R and R were chosen, referring to the published work [18]. Moreover, an additional ETL HTL and 0.2 ns for RETL and RHTL were chosen, referring to the published work [18]. Moreover, an radiative recombination was added in the perovskite layer to yield a V of about 1.3 V [21,22]. additional radiative recombination was added in the perovskite layer to yie OCld a VOC of about 1.3 V 27 3 1 27 −3 −1 A uniform electron/hole generation rate of 3.3 10 m s was enabled in the perovskite layer to [21,22]. A uniform electron/hole generation rate of 3.3 × 10 m s was enabled in the perovskite produce a J of about 21 mA cm [9,23 −2 ]. The material parameters used in the model are listed in layer to prod SC uce a JSC of about 21 mA cm [9,23]. The material parameters used in the model are listed Table 1, based on the literature values; since the parameter values varied from the references, a median in Table 1, based on the literature values; since the parameter values varied from the references, a Photonics 2020, 7, 47 4 of 14 or average value was chosen here. The perovskite material was widely regarded as an intrinsic semiconductor [24]; compared to the ETL and the HTL, the concentration of charge carriers was very 9 11 3 low at about 10 ~10 m , and was assumed to be not doped [20]. The doping concentrations in the 24 3 ETL and the HTL were set equally of 10 m to obtain a built-in electric potential (E ) of about 1 V [25], bi and their e ects on the hysteresis are specified in Section 3.3. The influences of permittivities of the ETL, perovskite and HTL on J–V hysteresis were also investigated in the following discussion. The ionic movement and redistribution were only constrained inside the perovskite layer. The ion concentration and mobility in the perovskite layer were studied in Section 3.3 to suppress J–V hysteresis. Speaking of which, the variation of the parameter values in the following calculations might be unrealistic currently for material technology and are just put forward as a guideline for material development. The mobility of electrons and holes were set constant in this work, with the assumption that the scattering defects in the perovskite solar cell were fixed. The boundary conditions at the interfaces were ruled by the heterojunction model with continuous quasi-Fermi levels. The whole cell was defined to connect to an external circuit with an ideal ohmic contact to perform the voltage sweep. For the initial conditions and measurement protocol, the device was generally pre-biased with a positive voltage 1.2 V to reach an equilibrium condition. Then, the external applied voltage swept from 1.2 to 0.2 V (Reverse, R), and turned back to 1.2 V (Forward, F) immediately to fulfill a complete J–V loop. The voltage varied with a step of 20 mV, and the scan rate was 240 mV/s, unless otherwise stated for the specific studies. Table 1. Material parameters adopted in model definition. Parameters ETL(E) Perovskite(P) HTL(H) Reference Permittivity " 31 18 3 [13,18,20,23] E,P,H Bandgap E (eV) 3 1.6 3.2 [13,16,18] 3 24 24 Doping concentration D (m ) 10 —— 10 [13,16,25] E,H 3 26 24 26 E ective density of state in conduction band N (m ) 10 5 10 10 [18] 3 26 24 26 E ective density of state in valence band N (m ) 10 5 10 10 [18] Electron anity (eV) 4.15 3.95 2.15 [13,20] 2 8 4 8 Electron mobility (m /(Vs)) 10 2 10 10 [13,20] 2 8 4 8 Hole mobility (m /(Vs)) 10 2 10 10 [13,20] 3 23 Ion concentration D (m ) —— 5 10 —— [13,16] 2 14 Ion mobility (m /(Vs)) —— 10 —— [13,16] 3. Results and Discussion 3.1. Hysteresis Origin and Generating Principles 3.1.1. Essential Conditions for Hysteresis Reproduction Numerically Firstly, in order to investigate J–V hysteresis in perovskite solar cells, we must reproduce the J–V hysteretic loops as reported experimentally. According to a previous study [26], the mobile ions and the recombination are the two generally accepted factors for the hysteresis phenomena, which were also discussed in our study theoretically, as seen in Figure 2. Consistent with the literature [27], we found that if the recombination (Rec) was not included in the calculation boundary conditions, the J–V curves present hysteresis-free, no matter if the ions were removable or stationary. This result indicates that recombination plays a dominant role in the J–V hysteresis phenomenon. On the other hand, if the calculations cover recombination, open circuit voltage (V ) and short circuit current density (J ) OC SC decreased; only by combining the ion species movement, the distinctive hysteresis curve could be obtained. The current decrease speed and the recombination rate present a large variation between the reverse (R) and the forward (F) scan. However, if no mobile ions are included, a hysteresis-free J–V curve was received. This calculation result is consistent with the published work [13,16], indicating the correctness of our calculation model. Only coupling the mobile ions and the recombination could obtain the hysteretic J–V curves, while no such e ect was found when functionalizing them independently, and the recombination reduced the Voc and J . SC Photonics 2020, 7, x FOR PEER REVIEW 5 of 14 Then, the influences of various combos of different recombination categories were investigated; the mobile ions were always calculated, as seen in Figure 2b,c. Compared to the cases with all of the three recombinations, we found that if the Rbulk was activated alone, the JSC decreased a little bit, while the forward VOC increased. In addition, if only RETL and RHTL were activated, the forward VOC decreased severely, while the JSC increased. This finding indicates that the Rbulk played a reverse role in comparison with the RETL and RHTL. We also investigated the RETL and RHTL independently, as seen in Figure 2c. The results show that the RETL almost had no effect on forward VOC, while reducing the forward JSC severely; the RHTL was the opposite to this effect. This unprecedented calculation result favored the assumption [28] that the imbalanced material properties in the ETL and the HTL could Photonics 2020, 7, 47 5 of 14 lead to an asymmetric transportation of electrons and holes, giving rise to the J–V hysteresis curves. Photonics 2020, 7, x FOR PEER REVIEW 5 of 14 Then, the influences of various combos of different recombination categories were investigated; the mobile ions were always calculated, as seen in Figure 2b,c. Compared to the cases with all of the three recombinations, we found that if the Rbulk was activated alone, the JSC decreased a little bit, while the forward VOC increased. In addition, if only RETL and RHTL were activated, the forward VOC decreased severely, while the JSC increased. This finding indicates that the Rbulk played a reverse role in comparison with the RETL and RHTL. We also investigated the RETL and RHTL independently, as seen in Figure 2c. The results show that the RETL almost had no effect on forward VOC, while reducing the forward JSC severely; the RHTL was the opposite to this effect. This unprecedented calculation result favored the assumption [28] that the imbalanced material properties in the ETL and the HTL could (a) (b) (c) lead to an asymmetric transportation of electrons and holes, giving rise to the J–V hysteresis curves. Figure 2. Influences of the defective ions and various recombinations on J–V hysteresis curves. (a) J– Figure 2. Influences of the defective ions and various recombinations on J–V hysteresis curves. V hysteresis calculation with (Yes) or without (No) ions and recombination (Rec); (b,c) different (a) J–V hysteresis calculation with (Yes) or without (No) ions and recombination (Rec); (b,c) di erent hysteresis loops with various combos of the bulk (Rbulk) and the interfacial (RETL, RHTL) recombination. hysteresis loops with various combos of the bulk (R ) and the interfacial (R , R ) recombination. bulk ETL HTL Then, the influences of various combos of di erent recombination categories were investigated; 3.1.2. Hysteresis Generating Principles the mobile ions were always calculated, as seen in Figure 2b,c. Compared to the cases with all of the The transformation of the charge carriers, ions and the resulting electric field are illustrated in three recombinations, we found that if the R was activated alone, the J decreased a little bit, bulk SC Figure 3. With the pre-bias poling treatment by a positive external potential (Eex) of 1.2 V (>Ebi = 1 V), while the forward V increased. In addition, if only R and R were activated, the forward V OC ETL HTL OC the positive ions drifted and accumulated to the ETL/perovskite interface, while the negative ions decreased severely, while the J increased. This finding indicates that the R played a reverse role SC bulk toward the HTL/perovskite interface, which could generate an ion-induced electric potential (Eion) in comparison with the R and R . We also investigated the R and R independently, as seen ETL HTL ETL HTL across the perovskite layer with the rightward direction. (a) (b) (c) in Figure 2c. The results show that the R almost had no e ect on forward V , while reducing the ETL OC forward J severely; the R was the opposite to this e ect. This unprecedented calculation result SC HTL Figure 2. Influences of the defective ions and various recombinations on J–V hysteresis curves. (a) J– favored the assumption [28] that the imbalanced material properties in the ETL and the HTL could V hysteresis calculation with (Yes) or without (No) ions and recombination (Rec); (b,c) different lead to an asymmetric transportation of electrons and holes, giving rise to the J–V hysteresis curves. hysteresis loops with various combos of the bulk (Rbulk) and the interfacial (RETL, RHTL) recombination. 3.1.2. Hysteresis Generating Principles 3.1.2. Hysteresis Generating Principles The transformation of the charge carriers, ions and the resulting electric field are illustrated in The transformation of the charge carriers, ions and the resulting electric field are illustrated in Figure 3. With the pre-bias poling treatment by a positive external potential (E ) of 1.2 V (>E = 1 V), ex bi Figure 3. With the pre-bias poling treatment by a positive external potential (Eex) of 1.2 V (>Ebi = 1 V), the positive ions drifted and accumulated to the ETL/perovskite interface, while the negative ions the positive ions drifted and accumulated to the ETL/perovskite interface, while the negative ions toward the HTL/perovskite interface, which could generate an ion-induced electric potential (E ) ion toward the HTL/perovskite interface, which could generate an ion-induced electric potential (Eion) (a) (b) (c) across the perovskite layer with the rightward direction. across the perovskite layer with the rightward direction. Figure 3. Schematic of the transformation of the charge carriers, defective ions and electric field during the J–V measurement from reverse to forward (R–F, from 1.2 to −0.2 to 1.2 V) after 1.2 V pre-bias poling, including Rbulk, RETL and RHTL. (a) Reverse-1 (R-1) V; (b) Reverse-0.5 (R-0.5) V and Reverse-0 (R-0) V; and (c) Forward-0 (F-0) V, Forward-0.5 (F-0.5) V and Forward-1 (F-1) V. At the beginning of the reverse scan from 1.2 to 1 V (R-1 V), the energy band structure, charge movement and the possible recombination are presented in Figure 3a. Our calculation displayed an upward energy band with no resistance to the electrons and the holes’ transport to the ETL and the HTL, while preventing them flowing to the opposite layers. However, it might occur that these opposite-migrated charges recombine inside the perovskite layer—that is, the bulk recombination (a) (b) (c) Rbulk or recombine with the intrinsic charges located inside the adjacent transport layers—that is, the Figure 3. Schematic of the transformation of the charge carriers, defective ions and electric field during Figure 3. Schematic of the transformation of the charge carriers, defective ions and electric field during the J–V measurement from reverse to forward (R–F, from 1.2 to −0.2 to 1.2 V) after 1.2 V pre-bias the J–V measurement from reverse to forward (R–F, from 1.2 to 0.2 to 1.2 V) after 1.2 V pre-bias poling, poling, including Rbulk, RETL and RHTL. (a) Reverse-1 (R-1) V; (b) Reverse-0.5 (R-0.5) V and Reverse-0 including R , R and R . (a) Reverse-1 (R-1) V; (b) Reverse-0.5 (R-0.5) V and Reverse-0 (R-0) V; bulk ETL HTL (R-0) V; and ( and (c) Forwar c) Forward-0 (F-0) V, Forward- d-0 (F-0) V, Forward-0.5 (F-0.5) 0.5 (F-0.5) V and Forwar V and Forward-1 (F d-1 (F-1) V. -1) V. At the beginning of the reverse scan from 1.2 to 1 V (R-1 V), the energy band structure, charge At the beginning of the reverse scan from 1.2 to 1 V (R-1 V), the energy band structure, charge movement and the possible recombination are presented in Figure 3a. Our calculation displayed movement and the possible recombination are presented in Figure 3a. Our calculation displayed an an upward energy band with no resistance to the electrons and the holes’ transport to the ETL and upward energy band with no resistance to the electrons and the holes’ transport to the ETL and the the HTL, while preventing them flowing to the opposite layers. However, it might occur that these HTL, while preventing them flowing to the opposite layers. However, it might occur that these opposite-migrated charges recombine inside the perovskite layer—that is, the bulk recombination Rbulk or recombine with the intrinsic charges located inside the adjacent transport layers—that is, the Photonics 2020, 7, x FOR PEER REVIEW 6 of 14 interfacial recombination RETL and the RHTL. In addition, due to the ions equilibration at the relaxation stage, the concentration of positive ions (P) was greater than that of negative ions (N) in the ETL/perovskite interface, as seen in Figure 4b, so the direction of Eion still kept rightward. In this case, Eex < Ebi + Eion, the direction of Etotal was same with the Eion, in agreement with the potential profiles in Figure 4a. The Etotal facilitated the free charges’ ejection to the external transport layers, and meanwhile, the ions began to drift around, following the Etotal. When the reverse scan arrived at 0.5 V (R-0.5 V) and 0 V (R-0 V), as seen in Figure 4b, our Photonics 2020, 7, 47 6 of 14 calculation showed that the amount of N at the ETL/perovskite interface had been larger than that of the P, thus, the direction of Eion inverted compared to that at R-1 V, as shown in Figure 3b. Meanwhile, the potential remained downward, as presented in Figure 4a, indicating the rightward of the Etotal due opposite-migrated charges recombine inside the perovskite layer—that is, the bulk recombination to that Ebi > Eex + Eion. In addition, the potential drop in the perovskite layer at the interfaces also R ; or recombine with the intrinsic charges located inside the adjacent transport layers—that is, bulk enlarged, combined with the more upward energy band structure, promoting the free charges’ the interfacial recombination R and the R . In addition, due to the ions equilibration at the ETL HTL ejection more efficiently [16]. Furthermore, attributing to the extended band offset at the interfaces, relaxation stage, the concentration of positive ions (P) was greater than that of negative ions (N) in the interfacial recombination could be scarce, leaving a small amount of bulk recombination and a the ETL/perovskite interface, as seen in Figure 4b, so the direction of E still kept rightward. In this ion large current density compared to R-1 V. In addition, the gradient of potential profiles at R-0.5 V was case, E < E + E , the direction of E was same with the E , in agreement with the potential ex bi ion total ion larger than that at R-0 V, as seen in Figure 4a, which could favor charge carriers’ transportation more profiles in Figure 4a. The E facilitated the free charges’ ejection to the external transport layers, total efficiently and reduce the recombination lost, resulting in increased current density at R-0.5 V and meanwhile, the ions began to drift around, following the E . total compared to R-0 V in Figure 2. (a) (b) Figure 4. (a) Variation of the electrical potential profile and (b) the corresponding concentration Figure 4. (a) Variation of the electrical potential profile and (b) the corresponding concentration di erence between the negative ions N and the positive ions P during reverse scan (R) and forward difference between the negative ions N and the positive ions P during reverse scan (R) and forward scan (F), including ions migration (Ions) and recombination (Rec). scan (F), including ions migration (Ions) and recombination (Rec). When the reverse scan arrived at 0.5 V (R-0.5 V) and 0 V (R-0 V), as seen in Figure 4b, our calculation When it came to the forward scan at 0, 0.5 and 1 V (F-0, F-0.5 and F-1 V), the calculation result showed that the amount of N at the ETL/perovskite interface had been larger than that of the P, thus, shows that the concentration of N over-weighted that of P at the ETL/perovskite interface through the direction of E inverted compared to that at R-1 V, as shown in Figure 3b. Meanwhile, the potential ion the whole forward scan process, thus, the direction of Eion kept leftward. Combined with the upward remained downward, as presented in Figure 4a, indicating the rightward of the E due to that E potential profiles shown in Figure 4a, Eex + Eion > Ebi, the direction of Etotal was l total eftward and fullbi y > E + E . In addition, the potential drop in the perovskite layer at the interfaces also enlarged, ex ion inverted compared to the reverse scan, as presented in Figure 3c. Combined with the downward combined with the more upward energy band structure, promoting the free charges’ ejection more energy band structure, most of the free charges were drifted and flowed to the wrong transport layers eciently [16]. Furthermore, attributing to the extended band o set at the interfaces, the interfacial (that is, electrons to the HTL, and holes to the ETL), deteriorating the bulk and the interfacial recombination could be scarce, leaving a small amount of bulk recombination and a large current recombination, inducing the small photocurrent at forward scan, as seen in Figure 2. density compared to R-1 V. In addition, the gradient of potential profiles at R-0.5 V was larger than that Above all, our calculation indicated that the recombination is supposed to play a more essential at R-0 V, as seen in Figure 4a, which could favor charge carriers’ transportation more eciently and role than the ionic migration in the hysteresis phenomena. Specifically, it is the ionic movement that reduce the recombination lost, resulting in increased current density at R-0.5 V compared to R-0 V in changes the electric field inside the perovskite layer, delaying the lossless ejection of the free charges, Figure 2. if excluding the recombination. However, it is the recombination that really reduces the number of When it came to the forward scan at 0, 0.5 and 1 V (F-0, F-0.5 and F-1 V), the calculation result electrons and holes to transport from the perovskite layer, causing the decreased photocurrent. shows that the concentration of N over-weighted that of P at the ETL/perovskite interface through the whole forward scan process, thus, the direction of E kept leftward. Combined with the upward 3.2. Measurement Protocols Improvement to Suppress Hysteresis ion potential profiles shown in Figure 4a, E + E > E , the direction of E was leftward and fully ex ion bi total 3. inverted 2.1. Scan Ra compar tes ed to the reverse scan, as presented in Figure 3c. Combined with the downward energy band structure, most of the free charges were drifted and flowed to the wrong transport layers (that is, electrons to the HTL, and holes to the ETL), deteriorating the bulk and the interfacial recombination, inducing the small photocurrent at forward scan, as seen in Figure 2. Above all, our calculation indicated that the recombination is supposed to play a more essential role than the ionic migration in the hysteresis phenomena. Specifically, it is the ionic movement that changes the electric field inside the perovskite layer, delaying the lossless ejection of the free charges, if excluding the recombination. However, it is the recombination that really reduces the number of electrons and holes to transport from the perovskite layer, causing the decreased photocurrent. Photonics 2020, 7, x FOR PEER REVIEW 7 of 14 Voltage scan rate has been reported and widely accepted to modify the hysteresis from the testing point [8,29]. The scan rate was varied through a triangle function, as seen in the Supplementary Materials Figure S1. As seen in Figure 5, the influences of the scan rates of 2.4 V/s, 240 mV/s, 24 mV/s and 4 mV/s were investigated by characterizing the J–V curves and the electric potential profiles across the device. We found that the very fast (>2.4 V/s) and the very slow (≤4 mV/s) scan rate could obtain J–V loops with negligible hysteresis, while the intermediate scan rate enlarged Photonics the gap betw 2020, 7, 47 een the forward and the reverse scan curves. In addition, it is worth mentioning that 7 of 14 compared to the relatively high scan speed of 2.4 V/s and 240 mV/s, when the J–V measurement was conducted under slow scan rates of 24 mV/s and 4 mV/s, the JSC decreased severely, while the 3.2. Measurement Protocols Improvement to Suppress Hysteresis difference of JSC and VOC between the forward scan and reverse scan reduced. The potential distribution at the scan rate of 2.4 V/s is presented in Figure 5b; compared to Figure 3.2.1. Scan Rates 4a at a scan rate of 240 mV/s, we found that the potential profiles kept downward similarly in the stage o Voltage f rever scan se sc rate an, but the gr has been reported adient was and larg widely er here, i accepted ndicati to ng modif that the strength of y the hysteresis Etotal from inside the t testing he perovskite solar cell became stronger, promoting the charge extraction from the perovskite layer to point [8,29]. The scan rate was varied through a triangle function, as seen in the Supplementary the transport layers more efficiently. In this case, the Rbulk, RETL and EHTL could be passivated, and the Materials Figure S1. As seen in Figure 5, the influences of the scan rates of 2.4 V/s, 240 mV/s, 24 mV/s current density kept increasing in the stages of R-0.5 and R-0 V. When it came to the forward scan and 4 mV/s were investigated by characterizing the J–V curves and the electric potential profiles across stage, compared to that of 240 mV/s, the potential profiles still kept downward from F-0 to F-0.5 V, the device. We found that the very fast (>2.4 V/s) and the very slow (4 mV/s) scan rate could obtain and the gradient was similar with that of the reverse scan, indicating the direction of Etotal still drove J–V loops with negligible hysteresis, while the intermediate scan rate enlarged the gap between the the charge carriers to transport efficiently, and the final J–V forward curve almost overlapped the forward and the reverse scan curves. In addition, it is worth mentioning that compared to the relatively reverse curve between F-0 and F-0.5 V with negligible hysteresis. However, from F-0.5 to F-1 V, the high scan speed of 2.4 V/s and 240 mV/s, when the J–V measurement was conducted under slow scan potential profiles changed to be upward gradually, the direction of Etotal reversed to prevent the rates of 24 mV/s and 4 mV/s, the J decreased severely, while the di erence of J and V between SC SC OC charge carriers transport to the correct adjacent layers, increasing the probability of recombination the forward scan and reverse scan reduced. and leading to the sharp reduction in current density between F-0.5 and F-1 V with severe hysteresis. (a) (b) (c) Figure 5. Influences of scan rates on (a) J–V hysteresis; (b,c) potential profiles at the scan rate of 2.4 Figure 5. Influences of scan rates on (a) J–V hysteresis; (b,c) potential profiles at the scan rate of 2.4 V/s V/s and 4 mV/s, respectively. and 4 mV/s, respectively. At the very slow scan rate of 4 mV/s, the corresponding potential profiles are illustrated in Figure The potential distribution at the scan rate of 2.4 V/s is presented in Figure 5b; compared to 5c. In this case, the rate between the ions movement and the external voltage variation were at the Figure 4a at a scan rate of 240 mV/s, we found that the potential profiles kept downward similarly in same level, and the ions could react to the voltage variation immediately. The potential profiles kept the stage of reverse scan, but the gradient was larger here, indicating that the strength of E inside total constant across the perovskite and transport layers during the whole measurement process and the the perovskite solar cell became stronger, promoting the charge extraction from the perovskite layer to gradients were zero, indicating the Etotal was zero through the whole solar cell. In this case, even the transport layers more eciently. In this case, the R , R and E could be passivated, and the bulk ETL HTL though the ions still migrated inside of the perovskite layer, they had no effect on the direction and current density kept increasing in the stages of R-0.5 and R-0 V. When it came to the forward scan stage, strength of Etotal, and no influence on J–V hysteresis. Thus, only the recombination could significantly compared to that of 240 mV/s, the potential profiles still kept downward from F-0 to F-0.5 V, and the influence the hysteresis, but according to above discussion, the recombination alone could generate gradient was similar with that of the reverse scan, indicating the direction of E still drove the charge total a hysteresis-free J–V curve with severely decreased VOC. However, herein, in the case of the scan rate carriers to transport eciently, and the final J–V forward curve almost overlapped the reverse curve of 4 mV/s, the JSC reduced, while the VOC was unchanged. Considering the lifetime limit of the charge between F-0 and F-0.5 V with negligible hysteresis. However, from F-0.5 to F-1 V, the potential profiles carriers, if excluding the drift effect of Etotal, most of the charge carriers might recombine inside of the changed to be upward gradually, the direction of E reversed to prevent the charge carriers transport total perovskite material before reaching the transport interface, leading to the reduced JSC. to the correct adjacent layers, increasing the probability of recombination and leading to the sharp Above all, only if the measurement could be performed with a high enough scan rate (>2.4 V/s), reduction in current density between F-0.5 and F-1 V with severe hysteresis. the perovskite solar cell could obtain a great photovoltaic performance with suppressed J–V At the very slow scan rate of 4 mV/s, the corresponding potential profiles are illustrated in hysteresis. Figure 5c. In this case, the rate between the ions movement and the external voltage variation were at the same level, and the ions could react to the voltage variation immediately. The potential profiles kept constant across the perovskite and transport layers during the whole measurement process and the gradients were zero, indicating the E was zero through the whole solar cell. In this case, total even though the ions still migrated inside of the perovskite layer, they had no e ect on the direction and strength of E , and no influence on J–V hysteresis. Thus, only the recombination could significantly total influence the hysteresis, but according to above discussion, the recombination alone could generate a hysteresis-free J–V curve with severely decreased V . However, herein, in the case of the scan rate of OC 4 mV/s, the J reduced, while the V was unchanged. Considering the lifetime limit of the charge SC OC Photonics 2020, 7, x FOR PEER REVIEW 8 of 14 3.2.2. Scan Direction and Pre-Bias Treatment Scan direction, from reverse to forward (R–F) or from forward to reverse (F–R), combined with a specific voltage pre-bias treatment, has a significant impact on J–V hysteresis according to the experimental reports [30,31]. Here, three different voltages of 1.2, 0 and −1.2 V were adopted for pre- poling the PSC to achieve equilibrated conditions before the J–V test. As seen in Figure 6, we found that the different pre-poling and scan directions could lead to J–V hysteretic loops with varied shapes and extent. Photonics 2020, 7, 47 8 of 14 For the scan direction of R–F, we found that the VOC was severely affected by the voltage pre- treatment, while the JSC remained constant. When perovskite solar cells were pre-relaxed by a positive voltage of 1.2 V, the VOC at the reverse scan was the maximum; a bump current density occurred at carriers, if excluding the drift e ect of E , most of the charge carriers might recombine inside of the total around R-0.7 V. If the pre-bias voltage decreased, the VOC at reverse scan reduced, and the voltage perovskite material before reaching the transport interface, leading to the reduced J . SC where the bump current density occurred also reduced. However, when it came to the forward scan, Above all, only if the measurement could be performed with a high enough scan rate (>2.4 V/s), the J–V loops had no serious difference among the three different voltage pre-bias treatment, except the perovskite solar cell could obtain a great photovoltaic performance with suppressed J–V hysteresis. that the VOC at forward scan of 1.2 V pre-bias was slightly larger than the other two cases. 3.2.2. Scan Direction and Pre-Bias Treatment For the scan direction of F–R, in contrary to the case of R–F, we found that the JSC was severely affected by the voltage pre-treatment, while the VOC remained constant; the reverse scan curves for Scan direction, from reverse to forward (R–F) or from forward to reverse (F–R), combined with the three different voltage pre-bias were almost overlapped with each other, with no obvious a specific voltage pre-bias treatment, has a significant impact on J–V hysteresis according to the difference. However, the forward scan curves were various and complicated. When positive 1.2 V experimental reports [30,31]. Here, three di erent voltages of 1.2, 0 and 1.2 V were adopted for was performed at the pre-bias stage, the obtained forward JSC was even larger than the reverse JSC, pre-poling the PSC to achieve equilibrated conditions before the J–V test. As seen in Figure 6, we found and the forward JSC decreased with the decrease in pre-bias voltage. An anomalous forward curve that the di erent pre-poling and scan directions could lead to J–V hysteretic loops with varied shapes occurred using the negative pre-poling of −1.2 V and obtained a very small JSC of about 4 mA/cm and extent. with a horrible filling factor and hysteresis. (a) (b) Figure 6. Figure 6. Influe Influences nces of of the the volt voltage age pre-bias an pre-bias and d the the scan scan dire direction ction on on J–V hysteresi J–V hysteresis. s. ((a a) S ) Scan can d dir ire ection ction from reverse to forward (R–F); and (b) scan direction from forward to reverse (F–R). from reverse to forward (R–F); and (b) scan direction from forward to reverse (F–R). For the scan direction of R–F, we found that the V was severely a ected by the voltage OC The corresponding potential profiles for 1.2 and −1.2 V pre-poling are illustrated in Figure 7, and pre-treatment, while the J remained constant. When perovskite solar cells were pre-relaxed by a SC note that the potential profiles for 1.2 V pre-bias with R–F scan is shown in Figure 4a. We could see positive voltage of 1.2 V, the V at the reverse scan was the maximum; a bump current density OC that for 1.2 V pre-poling, the whole subsequent potential profiles were located below the initial one, occurred at around R-0.7 V. If the pre-bias voltage decreased, the V at reverse scan reduced, and the OC while above the initial profile for the cases of −1.2 V pre-poling. This indicates that the positive pre- voltage where the bump current density occurred also reduced. However, when it came to the forward bias could increase the internal potential of the perovskite solar cells, while the negative pre-bias scan, the J–V loops had no serious di erence among the three di erent voltage pre-bias treatment, might reduce the internal potential. except that the V at forward scan of 1.2 V pre-bias was slightly larger than the other two cases. OC Compared to Figure 4a of R–F scan with 1.2 V pre-poling, the potential profiles for F–R scan For the scan direction of F–R, in contrary to the case of R–F, we found that the J was severely SC showed distinctively downward at the scan step of F-0 V due to the ions’ accumulation during the a ected by the voltage pre-treatment, while the V remained constant; the reverse scan curves for the OC equilibrium, which could develop a positive electric field to drift the charges flow to the correct three di erent voltage pre-bias were almost overlapped with each other, with no obvious di erence. transport layers, reducing the recombination and leading to a raised JSC. In the case of −1.2 V pre- However, the forward scan curves were various and complicated. When positive 1.2 V was performed equilibrium, the positive ions accumulated at the perovskite/HTL interface and the negative ions at at the pre-bias stage, the obtained forward J was even larger than the reverse J , and the forward SC SC the perovskite/ETL interface, inducing an upward potential profile at the scan step of R-1 V for R–F J decreased with the decrease in pre-bias voltage. An anomalous forward curve occurred using the SC scan, as seen in Figure 7b. This upward potential induced a negative electric field, prompting the negative pre-poling of 1.2 V and obtained a very small J of about 4 mA/cm with a horrible filling SC charges to drift to the wrong transport layers, increasing the possibility of recombination, and factor and hysteresis. resulted in the small VOC. The following forward scan steps were similar with the case of 1.2 V pre- The corresponding potential profiles for 1.2 and 1.2 V pre-poling are illustrated in Figure 7, and note that the potential profiles for 1.2 V pre-bias with R–F scan is shown in Figure 4a. We could see that for 1.2 V pre-poling, the whole subsequent potential profiles were located below the initial one, while above the initial profile for the cases of 1.2 V pre-poling. This indicates that the positive pre-bias could increase the internal potential of the perovskite solar cells, while the negative pre-bias might reduce the internal potential. Photonics 2020, 7, x FOR PEER REVIEW 9 of 14 poling, the upward potential profiles aggravated the recombination, reducing the current in forward scan and leading to the eventual hysteretic J–V loop. In Figure 7c, for F–R scan with −1.2 V pre-poling, the beginning forward scan steps were all performed under the upward potential profiles, Photonics 2020, 7, 47 9 of 14 experiencing the extremely severe recombination across the device and inducing to the diminished forward J–V curve. (a) (b) (c) Figure 7. Potential profiles corresponding to the cases in Figure 6. (a) 1.2 V pre-poling, scan direction Figure 7. Potential profiles corresponding to the cases in Figure 6. (a) 1.2 V pre-poling, scan direction of F–R; of F–R;− 1.2 1.2 V Vpre-bias treatm pre-bias treatment ent for ( for (b b)) R–F R–F scan and ( scan and (c c) F– ) F–R R scan. Note scan. Note th that at the potential profiles for the potential profiles for 1.2 V pre-bia 1.2 V pre-bias s with with R–F scan R–F scan is is shown shown in in Figure 4a. Figure 4a. Compared to Figure 4a of R–F scan with 1.2 V pre-poling, the potential profiles for F–R scan Above all, changing the scan direction and pre-bias treatment could not improve the solar cell showed distinctively downward at the scan step of F-0 V due to the ions’ accumulation during the efficiency or suppress J–V hysteresis distinctively. However, the positive pre-bias treatment favored equilibrium, which could develop a positive electric field to drift the charges flow to the correct the solar cell photovoltaic performance. transport layers, reducing the recombination and leading to a raised J . In the case of 1.2 V SC 3.3. Ma pre-equilibrium, terials Improvem the positive ent to Su ions ppress Hysteresis accumulated at the perovskite/HTL interface and the negative ions at the perovskite/ETL interface, inducing an upward potential profile at the scan step of R-1 V for R–F scan, 3.3.1. Transport Layers Properties as seen in Figure 7b. This upward potential induced a negative electric field, prompting the charges to drift to the wrong transport layers, increasing the possibility of recombination, and resulted in the small As discussed above, hysteresis-free J–V curves might be obtained by optimizing the V . The following forward scan steps were similar with the case of 1.2 V pre-poling, the upward OC measurement protocols; however, the measurement methods just coped with the superficial issues, potential profiles aggravated the recombination, reducing the current in forward scan and leading and the intrinsic defects inside of the perovskite solar cells were not eliminated. The transport layers to the eventual hysteretic J–V loop. In Figure 7c, for F–R scan with 1.2 V pre-poling, the beginning have been verified to have a significant effect on J–V hysteresis experimentally and numerically forward scan steps were all performed under the upward potential profiles, experiencing the extremely [16,32]. Doping concentration and relative permittivity were chosen to investigate how the transport severe recombination across the device and inducing to the diminished forward J–V curve. layers affect the J–V performance in this work. Firstly, the ETL and the HTL were studied Above all, changing the scan direction and pre-bias treatment could not improve the solar cell independently, as seen in Figure 8. We could see that the J–V curves were a little bit more sensitive eciency or suppress J–V hysteresis distinctively. However, the positive pre-bias treatment favored to the HTL properties than that of the ETL. For the case of ETL, in Figure 8a, the J–V curves seemed the solar cell photovoltaic performance. to be similar with each other, except that the forward VOC decreased with the increase in DE and εE; the same as the case of HTL in Figure 8b, with the increase in DH and εH, the forward VOC decreased, 3.3. Materials Improvement to Suppress Hysteresis and the JSC increased a little bit, while J–V hysteresis was not passivated. 3.3.1. Transport Layers Properties As discussed above, hysteresis-free J–V curves might be obtained by optimizing the measurement protocols; however, the measurement methods just coped with the superficial issues, and the intrinsic defects inside of the perovskite solar cells were not eliminated. The transport layers have been verified to have a significant e ect on J–V hysteresis experimentally and numerically [16,32]. Doping concentration and relative permittivity were chosen to investigate how the transport layers a ect the J–V performance in this work. Firstly, the ETL and the HTL were studied independently, as seen in Figure 8. We could see that the J–V curves were a little bit more sensitive to the HTL properties than that of the ETL. For the case of ETL, in Figure 8a, the J–V curves seemed to be similar with each other, except that the forward V decreased with the increase in D and " ; the same as the case of HTL in OC E E Figure 8b, with the increase in D and " , the forward V decreased, and the J increased a little bit, (aH) ( H OC b) SC while J–V hysteresis was not passivated. Figure 8. Effects of the doping concentrations DE and DH and the relative permittivity εE and εH of (a) Increasing the doping concentration and the permittivity were supposed to increase the J and SC ETL and (b) HTL on J–V hysteresis. V by enhancing their conductivity and promoting the charge carrier ’s transportation, while in OC contradiction with our calculation results. After carefully analysis, we found that the material properties between the ETL and the HTL were not equal or balanced, and the corresponding conductivities were di erent. If the conductivity of the ETL or the HTL increases independently, it will aggravate the Photonics 2020, 7, x FOR PEER REVIEW 9 of 14 poling, the upward potential profiles aggravated the recombination, reducing the current in forward scan and leading to the eventual hysteretic J–V loop. In Figure 7c, for F–R scan with −1.2 V pre-poling, the beginning forward scan steps were all performed under the upward potential profiles, experiencing the extremely severe recombination across the device and inducing to the diminished forward J–V curve. (a) (b) (c) Figure 7. Potential profiles corresponding to the cases in Figure 6. (a) 1.2 V pre-poling, scan direction of F–R; −1.2 V pre-bias treatment for (b) R–F scan and (c) F–R scan. Note that the potential profiles for 1.2 V pre-bias with R–F scan is shown in Figure 4a. Above all, changing the scan direction and pre-bias treatment could not improve the solar cell efficiency or suppress J–V hysteresis distinctively. However, the positive pre-bias treatment favored the solar cell photovoltaic performance. 3.3. Materials Improvement to Suppress Hysteresis 3.3.1. Transport Layers Properties As discussed above, hysteresis-free J–V curves might be obtained by optimizing the Photonics 2020, 7, 47 10 of 14 measurement protocols; however, the measurement methods just coped with the superficial issues, and the intrinsic defects inside of the perovskite solar cells were not eliminated. The transport layers have been verified to have a significant effect on J–V hysteresis experimentally and numerically transport imbalance between the electrons and the holes. In this case, even though the electrons (or [16,32]. Doping concentration and relative permittivity were chosen to investigate how the transport holes) could be extracted eciently, the remaining holes (or electrons) in the perovskite material still layers affect the J–V performance in this work. Firstly, the ETL and the HTL were studied promoted the recombination to decrease the photovoltaic performance. It is worth mentioning that the independently, as seen in Figure 8. We could see that the J–V curves were a little bit more sensitive combined e ect [16] did not occur in our calculations, that a fixed product (D " ) or (D " ) could E E H H to the HTL properties than that of the ETL. For the case of ETL, in Figure 8a, the J–V curves seemed obtain identical J–V curves using di erent D , " , or di erent D , " . Furthermore, this combined E E H H to be similar with each other, except that the forward VOC decreased with the increase in DE and εE; e ect might need to be verified by a detailed experiment or a more deeply theoretical study, which is the same as the case of HTL in Figure 8b, with the increase in DH and εH, the forward VOC decreased, beyond the research scope in this work. and the JSC increased a little bit, while J–V hysteresis was not passivated. Photonics 2020, 7, x FOR PEER REVIEW 10 of 14 Increasing the doping concentration and the permittivity were supposed to increase the JSC and VOC by enhancing their conductivity and promoting the charge carrier’s transportation, while in contradiction with our calculation results. After carefully analysis, we found that the material properties between the ETL and the HTL were not equal or balanced, and the corresponding conductivities were different. If the conductivity of the ETL or the HTL increases independently, it will aggravate the transport imbalance between the electrons and the holes. In this case, even though the electrons (or holes) could be extracted efficiently, the remaining holes (or electrons) in the perovskite material still promoted the recombination to decrease the photovoltaic performance. It is worth mentioning that the combined effect [16] did not occur in our calculations, that a fixed product (a) (b) (DE ∙ εE) or (DH ∙ εH) could obtain identical J–V curves using different DE, εE, or different DH, εH. Figure Figure 8. 8. E Effect ects s of the of the doping doping concentrations concentrations D D E and D and D H and the relativ and the relative e pe permittivity rmittivity εE" anand d εH of ( " of a) E H E H Furthermore, this combined effect might need to be verified by a detailed experiment or a more (ETL and a) ETL and (b)( H b)T HTL L on J–V on J–V hysteresis. hysteresis. deeply theoretical study, which is beyond the research scope in this work. Rarely, numerical and experimental research has been focused on the imbalanced transportation Rarely, numerical and experimental research has been focused on the imbalanced transportation between the ETL and the HTL. Here, we attempted to calculate and analyze the influences of the ETL between the ETL and the HTL. Here, we attempted to calculate and analyze the influences of the ETL and HTL balance on J–V hysteresis. The parameters used here might be ridiculous for materials and HTL balance on J–V hysteresis. The parameters used here might be ridiculous for materials design design and engineering and just give a preliminary guideline for material selection in PSC, as seen in and engineering and just give a preliminary guideline for material selection in PSC, as seen in Figure 9. Figure 9. (a) (b) Figure 9. Figure 9. Effe E ects cts of the materials properties ba of the materials properties balance lance on J–V hysteresi on J–V hysteresis. s. (a) The (a) The balance of balanceε of E and " and εH; ("b) ; E H the balance (b) the balance of D of E and D D and H. D . E H Firstly, for the balance of the relative permittivity, a fixed doping concentration of 24 Firstly, for the balance of the relative permittivity, a fixed doping concentration of DE = DH = 10 24 3 −3 D = D = 10 m was adopted, as seen in Figure 9a, set " = " . With the increase in the mE was H adopted, as seen in Figure 9a, set εE = εH. With the in Ecrease H in the permittivity, the J–V permittivity, the J–V performance increased, while the extent of hysteresis increased and decreased; performance increased, while the extent of hysteresis increased and decreased; the JSC raised the J raised gradually, while the V decreased and increased. When " = " = 0.3, the J , V and gradSC ually, while the VOC decreased a OC nd increased. When εE = εH = 0.3, tE he JSC H, VOC and the e SC fficienc OC y the eciency were small, although the extent of J–V hysteresis was moderate. When " = " = 300, were small, although the extent of J–V hysteresis was moderate. When εE = εH = 300, the E photovoltaic H the photovoltaic eciency enhanced, and J–V hysteresis also could be passivated eciently. The same efficiency enhanced, and J–V hysteresis also could be passivated efficiently. The same results for the results for the balance of doping concentration between the ETL and the HTL were seen in Figure 9b, balance of doping concentration between the ETL and the HTL were seen in Figure 9b, here, set εE = 26 3 26 −3 here, set " = " = 30. When D = D = 10 m , the eciency increased, and J–V hysteresis decreased. εH = 30. Whe E n D H E = DH = 10 m E , the effic H iency increased, and J–V hysteresis decreased. Therefore, considering the efficiency and the hysteresis, the permittivity and the doping concentration in the ETL and the HTL should be high enough, which is a great challenge to the material research. Above all, in order to improve the solar cell efficiency and suppress J–V hysteresis, the permittivity and doping properties of the electron and hole transport layers should be balanced and elevated simultaneously, which raises a great challenge to the transport layer materials. 3.3.2. Perovskite Layer Properties The properties of the perovskite layer are supposed to determine the overall performance of the PSC, working as the light absorbing layer and the mixed electronic-ionic conductor. Since the perovskite material was defined as an intrinsic semiconductor without doping additives, thus, just the permittivity εP was analyzed here. As seen in Figure 10a, the J–V curves present no obvious differences. Thus, our calculation indicated that the permittivity εP was not the primary factor Photonics 2020, 7, 47 11 of 14 Therefore, considering the eciency and the hysteresis, the permittivity and the doping concentration Photonics 2020, 7, x FOR PEER REVIEW 11 of 14 in the ETL and the HTL should be high enough, which is a great challenge to the material research. Above all, in order to improve the solar cell eciency and suppress J–V hysteresis, the permittivity influencing J–V hysteresis, and the charge carrier transportation inside of the perovskite layer was and doping properties of the electron and hole transport layers should be balanced and elevated just a representation of the dominant factors—ions’ migration and recombination. simultaneously For the de , which fective ions raises a in t grh eat e perovsk challenge ite lato yer, the astransport discussed a layer bovematerials. , it had been verified to be a necessary element to reproduce hysteretic J–V curves. Here, the ions concentration Di and mobility 3.3.2. Perovskite Layer Properties μi were investigated. The results present that the concentration of the ions had no effect on the J–V loops, as seen in Figure 10b, which indicates the potential of large-area PSC panels for The properties of the perovskite layer are supposed to determine the overall performance of the commercialization, but might affect long-term stability due to ion-assisted decomposition [33,34]. For PSC, working as the light absorbing layer and the mixed electronic-ionic conductor. Since the perovskite the mobility of ions in the perovskite layer, as seen in Figure 10c, the mobility of ions played a material was defined as an intrinsic semiconductor without doping additives, thus, just the permittivity significant role in the hysteretic issue. The very slow-moving ions or the extreme condition with " was analyzed here. As seen in Figure 10a, the J–V curves present no obvious di erences. Thus, immobile ions, the hysteresis could be eliminated thoroughly. For the case of very high ion mobility, −12 2 −1 −1 our calculation 10 m V sindicated , the ionsthat movthe emepermittivity nt could keep" pawas ce winot th or the even primary faster than the vo factor influencing ltage scan r J–V ate. The hyster esis, ions accumulated at the corresponding interfaces immediately following with the internal electric and the charge carrier transportation inside of the perovskite layer was just a representation of the field, and no delay or hysteretic current occurred. However, the rapid-changing Eion could prevent dominant factors—ions’ migration and recombination. the charge carrier’s transportation and deteriorate the recombination, leading to a reduced JSC. (a) (b) (c) Figure 10. Influences of the properties in the perovskite layer on J–V hysteresis. (a) The relative Figure 10. Influences of the properties in the perovskite layer on J–V hysteresis. (a) The relative permittivity εP; (b) the concentration (Di) and (c) the mobility (μi) of the ions. permittivity " ; (b) the concentration (D ) and (c) the mobility ( ) of the ions. P i i Overall, we proposed that restricting ionic movement is a significant approach to passivate the For the defective ions in the perovskite layer, as discussed above, it had been verified to be a hysteresis phenomena in the PSCs, requiring a new stabilized perovskite structure and more stable necessary element to reproduce hysteretic J–V curves. Here, the ions concentration D and mobility i i materials, or attempting to block the ions mobile pathway using effective additives. were investigated. The results present that the concentration of the ions had no e ect on the J–V loops, as seen 4. Con in Figur clusioe ns 10b, which indicates the potential of large-area PSC panels for commercialization, but might a ect long-term stability due to ion-assisted decomposition [33,34]. For the mobility of In summary, a mixed electronic-ionic drift-diffusion model combined with the bulk and ions in the perovskite layer, as seen in Figure 10c, the mobility of ions played a significant role in the interfacial recombination was implemented to uncover the nature characteristics of J–V hysteresis in hysteretic issue. The very slow-moving ions or the extreme condition with immobile ions, the hysteresis the perovskite solar cells. The model was verified via generating the hysteretic J–V loops with the 12 2 1 1 could combined e be eliminated ffect of t thor he oughly ion migr . For ation the and t case he recom of very binat high ion. ion The mobility movement , 10 and var m V iation s of t , the he ions movement charges, ions could and the keep electric potential w pace with or even ere exp faster lored than deeply the voltage to elucidate scan the g rate. eneThe rating ions prinaccumulated ciples of J–V hysteresis. The mobile ions could migrate to the interfaces between the perovskite/transport at the corresponding interfaces immediately following with the internal electric field, and no delay layers, regulating the internal electric potential profiles to influence the charges’ ejection to the or hysteretic current occurred. However, the rapid-changing E could prevent the charge carrier ’s ion transport layers. As long as the charges run out of their lifetimes, the recombination takes place to transportation and deteriorate the recombination, leading to a reduced J . SC reduce the charges transportation, leading to a diminished photocurrent. A proper scan rate and a Overall, we proposed that restricting ionic movement is a significant approach to passivate the favorable voltage pre-bias poling could really obtain a hysteresis-free J–V curve via alleviating the hysteresis phenomena in the PSCs, requiring a new stabilized perovskite structure and more stable adverse effect of the ions’ migration and the recombination. A standard measurement protocol is materials, or attempting to block the ions mobile pathway using e ective additives. essential to evaluate the perovskite solar cells appropriately. In addition, the balancing of the material properties between the electron transport layer and the hole transport layer significantly influenced 4. Conclusions J–V hysteresis; combined with the restriction of the ion’s mobility in the perovskite layer, a negligible hysteresis could be achieved, while possibly raising challenges to the new material development. Our In summary, a mixed electronic-ionic drift-di usion model combined with the bulk and interfacial work reveals the primary rules underlying J–V hysteresis in perovskite solar cells and provides a recombination was implemented to uncover the nature characteristics of J–V hysteresis in the perovskite preliminary guideline for new material research to eliminate the hysteresis. solar cells. The model was verified via generating the hysteretic J–V loops with the combined e ect of the ion migration and the recombination. The movement and variation of the charges, ions and the electric potential were explored deeply to elucidate the generating principles of J–V hysteresis. Photonics 2020, 7, 47 12 of 14 The mobile ions could migrate to the interfaces between the perovskite/transport layers, regulating the internal electric potential profiles to influence the charges’ ejection to the transport layers. As long as the charges run out of their lifetimes, the recombination takes place to reduce the charges transportation, leading to a diminished photocurrent. A proper scan rate and a favorable voltage pre-bias poling could really obtain a hysteresis-free J–V curve via alleviating the adverse e ect of the ions’ migration and the recombination. A standard measurement protocol is essential to evaluate the perovskite solar cells appropriately. In addition, the balancing of the material properties between the electron transport layer and the hole transport layer significantly influenced J–V hysteresis; combined with the restriction of the ion’s mobility in the perovskite layer, a negligible hysteresis could be achieved, while possibly raising challenges to the new material development. Our work reveals the primary rules underlying J–V hysteresis in perovskite solar cells and provides a preliminary guideline for new material research to eliminate the hysteresis. Supplementary Materials: The following are available online at http://www.mdpi.com/2304-6732/7/3/47/s1, Mathematical equations, Calculation method, Figure S1: Scan rate determined by a triangle function. Author Contributions: Conceptualization, C.Y., X.S. and T.X.; methodology, C.Y.; software, C.Y.; validation, C.Y., X.S. and T.X.; formal analysis, C.Y.; investigation, C.Y.; resources, X.S.; data curation, C.Y.; writing—original draft preparation, C.Y.; writing—review and editing, C.Y. and X.S.; visualization, C.Y.; supervision, X.S. and T.X.; project administration, X.S. and T.X.; funding acquisition, X.S. and T.X. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number 51677043. Conflicts of Interest: The authors declare no conflict of interest. References 1. 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Photonics – Multidisciplinary Digital Publishing Institute
Published: Jul 3, 2020