Simulation of Inverted Perovskite Solar Cells

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Oct 10, 2018 - A planar perovskite solar cell (PSC) with p-i-n inverted structure was ..... photodetector on (100) facet of MAPbI3 single crystal. Scientific reports ...

Proceedings of the ASME 2018 12th International Conference on Energy Sustainability ES2018 June 24-28, 2018, Lake Buena Vista, FL, USA

ES2018-7227

SIMULATION OF INVERTED PEROVSKITE SOLAR CELLS Jiawei Gong Department of Mechanical Engineering, Pennsylvania State University Erie, PA 16563

Sumathy Krishnan Department of Mechanical Engineering, North Dakota State University Fargo, ND 58102

demonstrating the excellent capability of perovskite material to transport both electrons and holes. These findings proved the feasibility of a planar device structure to replace a conventional mesoporous TiO2 structure derived from dye-sensitized solar cells (DSSCs) [5]. Although several high efficiency devices were achieved using planar structure, one of the major issues currently holding back the further progress is the presence of anomalous hysteresis. Such hysteresis causes J-V characteristics highly dependent on the prior optical and electrical conditioning, and its magnitude increases with the cell aging as well as materials degradation. This origin of hysteresis has been modeled in a regular n-i-p device structure. Based on a drift-diffusion model, van Reenen et al. [6] found both electronic charge traps and ion migration have to be included to achieve hysteresis in the modeled J-V characteristics. This prediction was confirmed by the experimental observation that the stability of photocurrents and photovoltages in a device can be controlled by changing the interfacial recombination properties, without a change in ion concentration or mobility within the perovskite phase [7]. Recently, an inverted p-i-n device with planar structure has shown minimal J-V hysteresis effects with device efficiency close to 20% [8]. Such hysteresis-free nature will benefit the manufacturing process because of the less requirements in solar cells sealing and solar cell modules packaging. The inverted structure uses intrinsic perovskite sandwiched between p-type (e.g. PEDOT:PSS) and n-type materials (e.g. PCBM) as front and back charge transport layers, respectively. Although this promising structure has attracted much research attention, knowledge of the relevant physical process in inverted PSCs is still lacking. In this work, the p-i-n inverted PSCs were simulated and compared with experimental results in the literature. The optimal thickness of absorber layer was identified, and the effect of energy offset between work function

ABSTRACT A planar perovskite solar cell (PSC) with p-i-n inverted structure was modeled and simulated to determine the power output characteristics under illumination. The performance of inverted PSC device was correlated to the thickness of the absorber layer, band alignment, and electrical properties of the hole transport materials (HTMs). Our simulation indicates that, with an optimized absorber layer thickness ~300 nm, an efficiency of 18% can be achieved. This baseline device was further utilized to investigate the role of band offset between the HTM and absorber layer. Results show that the device efficiency can be improved to 24% when the work function of HTM is reduced to 0.1 eV lower than the valence band edge of perovskite. Parametric studies were carried out to compare the feasibility of five different HTMs including spiro-OMeTAD, Cu2O, CuSCN, NiO, and CuI. Among them, NiO is the most promising candidate with a theoretical efficiency limit up to 27%. This work would serve as a modeling frame to simulate and interpret the performance of inverted PSCs and suggest further device optimization strategies. INTRODUCTION Inorganic-organic hybrid perovskite solar cells have become a rising star of the photovoltaic community and attracted great attention of researchers. Since first introduced, PSCs have demonstrated an exceptional efficiency growth, from 3.8% in 2009 to a certified 22% in 2017 [1]. Those remarkable efficiencies are resulted from (i) an appropriate direct band gap of perovskite near 1.5 eV; (ii) high absorption coefficient of 5.7×104 cm-1 [2]; and (iii) long charge-carrier diffusion lengths in perovskite (~100 nm for CH3NH3PbI3 [2] and ~1000 nm for CH3NH3PbI3-xClx [3]). It was found both electrons and holes in single crystals of CH3NH3PbI3 (MAPbI3) possessed diffusion lengths larger than 175 µm [4],

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of p-type material and absorber layer was investigated. Based on these results, suggestions were made to guide the selection of HTMs.

transport material and electron transport material, respectively. Each material has a different electron affinity, leading to discontinuity energy band diagram. Figure 3 presents the energy level alignment diagram with respect to vacuum.

NOMENCLATURE Chemical Names CH3NH3PbI3 Methylammonium lead chloride CuSCN Copper(I) thiocyanate CuI Copper(I) iodide Cu2O Copper(I) oxide ITO Indium tin oxide NiO Nickel(II) oxide PCBM Phenyl-C61-butyric acid methyl ester Poly(3,4PEDOT:PSS ethylenedioxythiophene):poly(styrenesulfonate) spiro2,2',7,7'-Tetrakis-(N,N-di-4OMeTAD methoxyphenylamino)-9,9'-spirobifluorene Subscripts sc oc

Figure 2. Schematic of the simulated device with stack layer of transparent ITO glass/PEDOT:PSS (30 nm)/CH3NH3PbI3 (300 nm)/PCBM (85 nm)/Ca (20 nm)/Al (100 nm).

Short circuit Open circuit

METHODOLOGY The updated version of AMPS (Analysis of microelectronic and Photonic Structure), wxAMPS, is used for this simulation. The trap-assisted tunneling model was implemented using the Newton-Raphson method, which is capable of solving heavily coupled three basic semiconductor equations (Poisson’s equation and continuity equations for electrons and holes). In this study, we investigated the effects of active layer thickness, energy offset, and hole-transport materials. The univariate optimization of the active layer thickness was first performed to obtain the base case (control device). Based on this control device, the roles of energy offset and hole-transport materials were further examined. Although studied as an independent viable, the energy offset is determined by holetransport materials used. The device simulation was carried out in four major steps as shown in Figure 1.

Figure 3. Band alignment in electronvolts of inverted perovskite solar cells. To validate the proposed model, a device with baseline parameters was first simulated under standard conditions at ambient temperature of 300 K and compared with experimental results. The AM 1.5 solar radiation spectrum and the absorption coefficient of the CH3NH3PbI3 active layer are shown in Figure 4. It was assumed that no optical loss occurs at the front contact and hence reflection coefficient was assumed to be 0. At the back contact, all the incident light is reflected, implying a unit reflection coefficient. Since the hole-transport material (PEDOT:PSS) has a wide band gap, the light absorption is neglected due to the the high transmittance. The work function of ITO front contact was set as -4.7 eV and the Al back contact as -4.2 eV [9]. A boundary condition (Φb0) is determined as the difference between the work function of the front contact metal and electron affinity of the semiconductor. Ideal Ohmic and Schottky contacts were assumed at front and back contacts with a surface recombination of 1×107 cm/s. Electrical properties of each layer in the baseline solar cell are summarized in Table S1.

Model inverted PSCs in wxAMPS Identify base case parameters of the simulation Validate the model with experiments Perform parametric analyses

Figure 1. Major steps in the simulation process. Figure 2 shows a planar PSC with configuration of transparent layer ITO glass/PEDOT:PSS/CH3NH3PbI3/PCBM/Ca/Al metal contact. PEDOT:PSS and PCBM were included as the hole

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smaller built-in voltage in the thicker devices [17, 18]. When the thickness reaches 300 nm, the device efficiency is improved to 18%, a nearly twofold increase compared to the 50 nm thin absorber film. This improvement can be attributed to the more induced photoelectrons due to the enhanced light absorption. The efficiency tends to drop at large thickness beyond 1 um because of the reduced FF.

Figure 4. The spectral irradiance of the AM 1.5G illumination (100 mWcm-2) and the absorption coefficient of CH3NH3PbI3 perovskite thin film. In the simulation, the defect energy levels of CH3NH3PbI3 and PCBM materials were assumed to locate at the center of their bandgap. The energetic distribution was Gaussian type with standard deviation of 0.1 eV. The band tail characteristic energy of perovskite was determined as 0.015 eV and band tail density of states 1×1014 cm-3eV-1 [13]. The band tail characteristic energy of PCBM was 0.01 eV [14]. Since the quality of HTMs is highly dependent on the processing techniques, the their defects were not included for brevity. Other defect parameters are listed in Table S2. The bimolecular electron-hole recombination was set to be 1×10-11 cm3s-1 at room temperature, according to measured values ranging from 6×10-11 to 1.4×10-9 cm3s-1 [15]. Because the band-to-band bimolecular recombination exhibits low dependence on material processing, the set value is also comparable with the recombination rate of 4×10-10 cm3s-1 for the direct inorganic semiconductor GaAs. After the baseline solar cells were simulated, PEDOT:PSS was substituted with HTMs including spiro-OMeTAD, Cu2O, NiO, CuSCN, and CuI. Their electrical properties are summarized in Table S3 [16].

Figure 5. J-V curves of the simulated perovskite solar cells with varied thickness of active layer.

RESULTS AND DISCUSSION The perovskite absorber layer has a great influence on the light absorption and charge collection at terminals. Hence, an appropriate thickness of absorbed layer was determined to optimize the cell performance. Figure 5 shows the J-V curves as a function of the MAPbI3 thickness. It can be seen that, as the thickness increases from 50 nm to 1 µm, the short-circuit current density (Jsc) significantly increases and then gradually saturates to a plateau ~25 mAcm-2. A similar trend of opencircuit voltage (Voc) can be observed in Figure 6. The Voc has a relatively low value for the very thin structure of 50 nm. As the film is thicker than 100 nm, the increase of Voc becomes marginal. On the contrary, the fill factor (FF) drastically decreases with increased thickness, which can be related to a

Figure 6. Effect of the active layer thickness on PV parameters. Our simulated results indicate a possibility to design a thicker absorber layer in the inverted PSCs since it can significantly enhance light harvesting without not causing

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serious recombination. This prediction is in accordance with the experiments; Nie et al. were able to grow millimeter-sized perovskite grains via hot-casting technique, leading to a champion device close to 18% efficiency [19]. It should also be pointed out that the simulated optimal thickness is predicted based on the assumption of high quality perovskite films, which may be challenging to prepare in practice. Pin holes and defects could easily form during spinning thicker perovskite layer. When the perovskite is at optimal thickness ~300 nm, the simulation shows a power conversion efficiency 19%, which is close to 18.1% as observed in the experiments [20]. Since the structure of inverted PSCs was initially derived from polymer solar cells, a 300 nm P3HT/PCBM polymer solar cell was simulated to demonstrate the advantage of perovskite as the active material. The simulated efficiency of the P3HT/PCBM heterojunction solar cell were confirmed with the literature [21]. Figure 7 compares J-V characteristics of the simulated inverted PSCs with experimental results. The overestimated Jsc of simulated results can be attributed to the assumption of no optical loss occurring at the front contact. The underestimated Voc is mainly due to the relatively lower work function of metal back contact (Al) compared with Au in the experiment.

be kept 0.1 eV lower than the valence band edge of perovskite. In practice, the effect of band offset can be mitigated by modifying PEDOT:PSS using polymer materials with deep HOMO levels such as poly-TPD, PCDTBT, and PTAA [22].

Figure 8. The effect of energy offset (ΔEv) on the photovoltaic performance of inverted PSCs. Apart from modified PEDOT:PSS, there are a number of inorganic HTMs that have promising electrical properties. These materials with lower ΔEV would push the device efficiency to the limit. Table 1 listed five inorganic HTMs together with the efficiencies that could be possibly achieved. It shows NiO has the potential to reach a theoretical efficiency up to 28% mainly due to a low ΔEV along with a Φb0 higher than the threshold value of 1.6 eV [23]. Table 1. Simulated PSC performance parameters with different hole-transport materials.

HTMs

Figure 7. Comparison of J-V characteristics of the simulated inverted PSCs with experimental results [20-21]. Note that our simulated device has a Voc around 0.9 V, which is lower than n-i-p regular structure (over 1 V) [22]. This is due to the fact that PEDOT:PSS as HTM has a shallow work function of 5.1 eV compared to the valence band (VB) of perovskite (5.5 eV). The energy offset ΔEV (ΦHTM − VB) creates imperfect ohmic contact, leading to a lower Voc. To quantify this voltage loss, the device was simulated in a range of energy offset from -0.4 to 0.4 eV as shown in Figure 8. It can be seen, the highest Voc of 1.15 V is obtained when ΔEV < 0.1 eV. In this range, although Voc reaches its maximum value, the excess energy barrier reduces the FF. In opposite, when ΔEV > 0.1 eV both Voc and efficiency both simultaneously decrease. The maximum efficiency point occurs at the optimal ΔEV of 0.1 eV, which means the work function of HTM should

Contact parameters

Photovoltaic parameters

Φb0 eV

ΔEV eV

Voc V

Jsc mAcm-2

FF %

η %

PEDOT:PSS

1.1

0.4

0.9

23.4

87.4

18.6

spiroOMeTAD

2.65

0.39

1.3

19.6

89.4

22.8

Cu2O

1.5

0.13

1.3

22.4

85.5

25

CuSCN

3

0.2

1.3

21.6

89.1

25.3

CuI

2.6

0.3

1.3

22.3

90.4

26.3

NiO

3.24

0.24

1.3

23.6

90

27.7

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10.

CONCLUSION The inverted PSC was simulated using the one-dimensional solar cell simulator wxAMPS. Several important factors that influence the device efficiency were studied including absorber thickness, band alignment between the absorber and HTM, as well as substituting inorganic HTMs. The simulation results show that a relative thick absorber layer would be helpful in generating high short-circuit current, which in turn remarkable increases the overall efficiency. It was found the FF and Voc have opposite responses to the increased band offset (ΔEV). Reducing the mismatch of the work function of the HTM and perovskite layer would be a possible route to further enhance the device performance. It is also suggested, using NiO as the HTM, the inverted PSCs can reach a high efficiency up to 27%.

11.

12. 13. 14.

ACKNOWLEDGMENTS The authors acknowledge Prof. Rockett and Dr. Liu at University of Illinois Urbana-Champaign for developing wxAMPS simulation software and Prof. Fonash at Pennsylvania State University for providing AMPS user manual.

15.

16. REFERENCES 1. W. S. Yang et al., Iodide management in formamidiniumlead-halide–based perovskite layers for efficient solar cells. Science 356, 1376-1379 (2017). 2. G. Xing et al., Long-range balanced electron-and holetransport lengths in organic-inorganic CH3NH3PbI3. Science 342, 344-347 (2013). 3. S. D. Stranks et al., Electron-hole diffusion lengths exceeding 1 micrometer in an organometal trihalide perovskite absorber. Science 342, 341-344 (2013). 4. Q. Dong et al., Electron-hole diffusion lengths > 175 μm in solution-grown CH3NH3PbI3 single crystals. Science 347, 967-970 (2015). 5. J. Gong, Z. Zhou, K. Sumathy, H. Yang, Q. Qiao, Activated graphene nanoplatelets as a counter electrode for dye-sensitized solar cells. Journal of Applied Physics 119, 135501 (2016). 6. S. van Reenen, M. Kemerink, H. J. Snaith, Modeling anomalous hysteresis in perovskite solar cells. The journal of physical chemistry letters 6, 3808-3814 (2015). 7. P. Calado et al., Evidence for ion migration in hybrid perovskite solar cells with minimal hysteresis. Nature communications 7, 13831 (2016). 8. S. Ye et al., A Breakthrough Efficiency of 19.9% Obtained in Inverted Perovskite Solar Cells by Using an Efficient Trap State Passivator Cu (Thiourea) I. Journal of the American Chemical Society, (2017). 9. T. Wang, J. Chen, G. Wu, M. Li, Optimal design of efficient hole transporting layer free planar perovskite solar cell. Science China Materials 59, 703-709 (2016).

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22. 23.

E. Unger et al., Hysteresis and transient behavior in current–voltage measurements of hybrid-perovskite absorber solar cells. Energy & Environmental Science 7, 3690-3698 (2014). T. Minemoto, M. Murata, Device modeling of perovskite solar cells based on structural similarity with thin film inorganic semiconductor solar cells. Journal of applied physics 116, 054505 (2014). Z. Lian et al., High-performance planar-type photodetector on (100) facet of MAPbI3 single crystal. Scientific reports 5, 16563 (2015). F. Liu et al., Numerical simulation: toward the design of high-efficiency planar perovskite solar cells. Applied Physics Letters 104, 253508 (2014). Y. Wang et al., Towards printed perovskite solar cells with cuprous oxide hole transporting layers: a theoretical design. Semiconductor Science and Technology 30, 054004 (2015). M. B. Johnston, L. M. Herz, Hybrid perovskites for photovoltaics: Charge-carrier recombination, diffusion, and radiative efficiencies. Accounts of chemical research 49, 146-154 (2015). G. Casas, M. Cappelletti, A. Cédola, B. M. Soucase, E. P. y Blancá, Analysis of the power conversion efficiency of perovskite solar cells with different materials as HoleTransport Layer by numerical simulations. Superlattices and Microstructures 107, 136-143 (2017). M. F. Hossain, M. Faisal, H. Okada, in Electrical, Computer & Telecommunication Engineering (ICECTE), International Conference on. (IEEE, 2016), pp. 1-4. C. Momblona et al., Efficient methylammonium lead iodide perovskite solar cells with active layers from 300 to 900 nm. Apl Materials 2, 081504 (2014). W. Nie et al., High-efficiency solution-processed perovskite solar cells with millimeter-scale grains. Science 347, 522-525 (2015). J. H. Heo et al., Hysteresis-less inverted CH3NH3PbI3 planar perovskite hybrid solar cells with 18.1% power conversion efficiency. Energy & Environmental Science 8, 1602-1608 (2015). B. M. Omer et al., AMPS-1D modeling of P3HT/PCBM bulk-heterojunction solar cell. In Photovoltaic Specialists Conference (PVSC), 2011 37th IEEE, 000734-000743 (2011). L. Meng, J. You, T.-F. Guo, Y. Yang, Recent advances in the inverted planar structure of perovskite solar cells. Accounts of chemical research 49, 155-165 (2015). M. F. Ali, M. F. Hossain, Influence of Front and Back Contacts on Photovoltaic Performances of pn Homojunction Si Solar Cell: Considering an ElectronBlocking Layer. Int J Photoenergy 2017, (2017)

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SUPPORTING INFORMATION Table S1.

Simulation parameters for the baseline solar cells.

Parameters

Symbol

PEDOT:PSS

CH3NH3PbI3

P3HT/PCBM

PCBM

Bandgap (eV)

Eg

1.5

1.6 [10]

2

2

Affinity (eV)

χ

3.6

3.9

3.8

3.9

Relative dielectric Permittivity CB effective density of states (cm-3) VB effective density of states (cm-3) Electron mobility (cm2 V-1 s-1)

ε

10

20 [7]

3.4

3.9

NC

1×1021

2.2×1018 [11]

2.2×1018

2.5×1021

NV

1×1021

1.8×1019 [11]

1.8×1019

2.5×1021

µn

1

20 [12]

0.002

0.2

µp

40

20 [12]

0.0002

2

-1 -1

Hole mobility (cm V s ) -3

17

14

Donor concentration (cm )

ND

0

3×10 [7]

7.38×10

Acceptor concentration (cm-3)

NA

1×1019

3×1017 [7]

1.8×1019

Table S2.

0.2 2.93×1017 0

Defect parameters set for the perovskite solar cells.

Parameters and units

wxAMPS notation

CH3NH3PbI3

PCBM

Gaussian defects donor and acceptor state density (cm-3)

Density

1×1014, 1×1014

1×1014, 1×1014

Gaussian defects donor and acceptor peak energy (eV)

Energy Level

1.2, 1.2

1, 1

Standard deviation (eV)

Deviation

0.1, 0.1

0.1, 0.1

Capture cross section of donorlike Gaussian state for electrons and holes (cm2)

Capture N

1×10-20, 1×10-19

1×10-19, 1×10-18

Capture cross section of acceptor-like Gaussian state for electrons and holes (cm2)

Capture P

1×10-19, 1×10-20

1×10-18, 1×10-19

Characteristic energy for donor and acceptor-like tails (eV)

E

0.015, 0.015

0.01, 0.01

Band tail density of states (cm-3 eV-1)

Go

1×1014, 1×1014

1×1014, 1×1014

Capture cross section for electrons and holes in donor tail states (cm2)

SigN

1×10-15, 1×10-17

1×10-15, 1×10-17

Capture cross section for electrons and holes in acceptor tail states (cm2)

SigP

1×10-17, 1×10-15

1×10-17, 1×10-15

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Table S3. Electrical parameters for hole transport layers. Parameters and units

spiroOMeTAD

Cu2O

NiO

CuSCN

CuI

Eg (eV)

3.06

2.17

3.8

3.6

3.1

χ (eV)

2.05

3.2

1.46

1.7

2.1

ε

3 -3

6.6 20

11.7

6.5 2.5×1020

NV (cm-3)

2.5×1020

2.5×1020

2.5×1020

2.5×1020

2.5×1020

µn (cm2 V-1 s-1)

2×10-4

80

2.8

25

44

µp (cm2 V-1 s-1)

2×10-4

80

2.8

25

44

0

0 18

0

0

NA (cm )

3×10

Φb0 (eV)

2.65

1.5

3.24

3

2.6

Offset (eV)

0.29

0.03

0.14

0.1

0.2

3×10

18

0

-3

3×10

18

2.5×10

20

2.5×10

ND (cm )

2.5×10

5.1 20

NC (cm )

-3

2.5×10

20

3×10

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18

3×1018

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