Towards nanostructured perovskite solar cells with enhanced efficiency: Coupled optical and electrical modeling

Solar Energy 137 (2016) 364–370

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Towards nanostructured perovskite solar cells with enhanced efficiency: Coupled optical and electrical modeling Omar A.M. Abdelraouf, Nageh K. Allam ⇑ Energy Materials Laboratory (EML), School of Sciences and Engineering, The American University in Cairo, New Cairo 11835, Egypt

a r t i c l e

i n f o

Article history: Received 4 July 2016 Received in revised form 18 August 2016 Accepted 24 August 2016

Keywords: Perovskite Solar cell CuSCN CH3NH3PbI3 Carrier generation Light trapping

a b s t r a c t Third generation photovoltaic technologies based on perovskites have demonstrated an exceptional progress in solar energy conversion since their first use in 2009. Herein, we investigated the effect of using light trapping nanostructures on the absorption, carrier collection, and overall efficiency of perovskite (CH3NH3PbI3) solar cells using three dimensional (3D) finite element method (FEM) technique. A combined optical-electrical model was constructed to full characterize the proposed devices. Upon the use of nanotubular architecture, the optimized active area absorption enhanced by 6% and the total generation rate increased by 7% compared to the planar architecture. Under one sunlight illumination (AM1.5G), with normal incident angle, the solar cells containing nanostructured light trapping architecture showed a drastic enhancement in the short circuit current (Jsc), the quantum efficiency (EQE), and the overall efficiency compared to the planar film-based solar cell. The obtained enhancements would open a new route for integrating light trapping nanostructures in CH3NH3PbI3 perovskite-based solar cells for better efficiency. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Third generation photovoltaic technologies based on perovskites have demonstrated an exceptional progress in solar energy conversion since their first use in 2009 (Kojima et al., 2009). These promising results have made perovskites one of the most attractive light absorbing materials for solar energy conversion applications (Im et al., 2011; Etgar et al., 2012). Devices based on CH3NH3PbI3 perovskite have large absorption coefficient, high charge carrier mobility and diffusion length (Zhumekenov et al., 2016; Lee et al., 2012; He et al., 2014). In 2014, Grätzel and co-workers reported power conversion efficiency of 12.4% using an effective and cheap inorganic p-type hole-transporting material, copper thiocyanate CuSCN, on lead halide perovskite-based devices using low-temperature solution-process deposition method (Qin et al., 2014). Herein, we propose a new approach to increase the efficiency of CH3NH3PbI3 perovskite-based solar cells. Specifically, we investigated the effect of using nanostructures with different shapes and dimensions on light absorption, carrier generation, and carrier collection. To this end, light trapping nanostructures with thin absorbing layer would increase the optical absorption in the active layer and enhance charge carriers collection. Introduc-

⇑ Corresponding author. E-mail address: [email protected] (N.K. Allam). http://dx.doi.org/10.1016/j.solener.2016.08.039 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.

ing nanostructures would enable the efficient use of many materials with short diffusion length. Moreover, they would reduce time and cost of production due to the use of thin absorbing layers (He et al., 2014). The integration of light trapping nanostructures in photovoltaics changes the mechanism of light absorption. In bulk semiconductor, light is absorbed exponentially from front to back. In a thin film with a back reflector, incompletely absorbed light can reflect off each interface several times, making multiple light paths through the semiconductor. Optical models are based on the interaction between electromagnetic waves and photovoltaic solar cell materials. Maxwell’s equations of light propagation can be used to describe the optical properties:

@H 1 ¼ rE @t l

e

@E ¼  r  H  rE @t

ð1Þ

ð2Þ

Here, H is the magnetic field, E is the electric field, l is the permeability, e is the permittivity, and r is the electric conductivity. The optical generation rate (Goptical) of electrons per wavelength (k) can be calculated using Eq. (3) (Deceglie et al., 2012). The optical generation rate is proportional to the intensity of the electric field in the active layer, and the imaginary part of the permittivity (e00 ).

O.A.M. Abdelraouf, N.K. Allam / Solar Energy 137 (2016) 364–370

Gopt ðkÞ ¼

e00 jEj2 2h

ð3Þ

Electrical modeling of photovoltaic solar cells is important to calculate the electrical performance of devices. The currentvoltage (J-V) characteristics of any photovoltaic solar cell can be described using Eq. (4), where Jsc is the short circuit current that is proportional to the generation rate of electrons (GTotal), diffusion length of the perovskite material (Ln), and diffusion length of the hole transport material (HTM) (Lp). The term Jdark represents the current of photovoltaic cell in the absence of sunlight illumination and it does not depend on the generation rate of electrons. (n) is an ideality factor and it depends on the type of material, (J0) is the saturation current of the photovoltaic solar cell and can be calculated using Eq. (5), where (ND) is the donor concentration in perovskite, (NP) is the hole concentration in HTM, (ni) is the intrinsic carrier concentration in perovskite and HTM, (sn) is the electron lifetime, (sp) is the hole lifetime, (Dn) is the diffusion coefficient of electrons, and (Dp) is the diffusion coefficient of holes.



  eV  1  qGTotal ðLn þ Lp Þ JðVÞ ¼ J dark  J sc ¼ J 0 exp nKT

J0 ¼

sffiffiffiffiffiffi ! sffiffiffiffiffiffi Dp n2i Dn n2i þ sp ND sn NA

ð4Þ

ð5Þ

In our mode, the effect of external series (Rs) and shunt (Rsh) resistance was considered, as shown in Eq. (6). These parasitic resistances degrade the performance of any solar cell device as will be described later.



  eV þ J sc Rs V þ Jsc Rs 1  JðVÞ ¼ J sc  J 0 exp nKT Rsh

ð6Þ

Therefore, to enhance the efficiency of any solar cell, the generation rate of electrons should be enhanced by increasing the absorption of incident sunlight in the active layer. Also, it is necessary to enhance the carrier collection of these electrons by increasing the built in electric field inside the active layer and reducing the carriers recombination. Herein, the optical modeling of perovskite solar cells was performed using different light trapping structures inside the active layer such as thin film, nanotube, nanopyramid, nanorod, and nanocone. In this part, the nanostructure with the largest absorption enhancement and electron-hole pair generation rate enhancement in the active area of solar cell was identified. Then, the calculated generation rate of electrons was used as an input in the electrical model to estimate the enhancement in the overall efficiency of each nanostructured solar cell. 2. Modeling details The design of the proposed nanostructures is based on photonic and electronic design considerations. Two photonic design considerations were applied on the proposed nanostructures: First, to achieve light trapping by making the photon propagation and carrier transport orthogonal, which could be possible if the propagation of incident photon is normally above the active layer, where nanostructuring may result in CH3NH3PbI3/HTM interface being in the normal direction above the active layer, thus transport of carriers between interfaces should be orthogonal to the photon propagation. Light trapping depends also on the distance between repeating patterns of nanostructures. Therefore, to enhance absorption, the nanostructures in the array would be closely packed while increasing the aspect ratio. The second photonic consideration is to increase antireflection. A graded index for optical impedance matching has proven to be an effective antireflection

365

strategy (Wang et al., 2012). There are two geometric requirements for effective antireflection. First, the periodicity of nanostructures needs to be much smaller than the wavelength of incoming light to result in an effectively averaged refractive index. Second, the height of nanostructures needs to be large enough for a smooth transition. Achieving these two requirements should result in enhanced absorption over broad range of wavelengths. On the other hand, the two separate electronic considerations in designing the nanostructures are: First, is to maximize the collection of generated electron-hole pairs. This could be achieved by using nanostructures with dimensions less than their diffusion length. The electron diffusion length in CH3NH3PbI3 perovskite is greater than 1 lm, which is more than four orders of magnitude of the light intensity (Zhao et al., 2014). The second electronic consideration in our approach is to increase the built-in electric field aiming to increase the rate of carrier collection. Therefore, the thickness of our nanostructures should not be less than the thickness of space charge region and should be large enough for increasing the optical absorption. To construct the model, we started with the optical modeling of the different nanostructures. We calculated optical absorption and generation profiles of electrons within the nanostructures, then we calculated the generation rate of electrons, followed by optimization of the thickness and length of the nanostructures to satisfy the optical considerations mentioned above. The generation rates of electrons obtained from the optical model were used as an input to the electrical model to calculate the short circuit current and carrier collection rates in all nanostructures. Finally, we made another optimization in thickness and length of the nanostructures to satisfy both the optical and electronic considerations at the same time. The modeled perovskite solar cell consists of (up-to-bottom) air, fluorine-doped tin oxide (FTO) and titanium dioxide (TiO2) as a transparent conducting oxide, perovskite (CH3NH3PbI3) as an ntype layer, holes transport material (CuSCN) as a p-type layer, and silver (Ag) as a back reflector. Five designs have been modeled where different nanostructured light trapping architecture of the perovskite (CH3NH3PbI3) layer were simulated: (I) planar, (II) nanotube, (III) nanopyramid, (IV) nanorod, and (IV) nanocone. The theoretical investigation on the optical and electrical performances of perovskite solar cell has been reported by several groups using transfer-matrix method (Ball et al., 2015) or finite difference time domain method (Zhang and Xuan, 2016). Our optical model simulation was done in three dimension (3D) using finite element method (FEM) simulator COMSOL 4.3b. A plan wave source is placed above air and used as a source of sunlight. AM1.5G was used as the input power of the plan wave, with normal incident angle only. The wavelength simulation range was 300–800 nm with 10 nm resolution. Note that this wavelength range is chosen based on the fact that the investigated perovskite material (CH3NH3PbI3) has a band gap of 1.6 eV (Butler et al., 2015) and its extinction coefficient reduces to zero at a wavelength of 800 nm (Lin et al., 2015). Also, AM1.5G spectrum showed a higher incident sunlight energy on the earth surface starting from a wavelength of 300 nm. To reduce simulation time, we modeled a small unit of solar cell and used periodic boundary condition (PBC) on side of all simulated layers except silver. For silver, we used different boundary condition, which is perfect electric conductor (PEC), silver acts as a back reflector and reflects back most of unabsorbed incident sunlight. The used mesh size is ten times smaller than the smallest incident wavelength of the sunlight. The complex refractive indices of Ag, CuSCN, CH3NH3PbI3, TiO2, and FTO were taken from previously measured data (Xing et al., 2014; Pattanasattayavong et al., 2013; Rakhshani et al., 1998; Wang et al., 2013; Rakic´ et al., 1998). Using the optical model, we calculated the absorption of incident sunlight into the active layer,

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Eq. (7). The generation profile of electrons for each wavelength was calculated using Eq. (3) and the generation rate of electrons was calculated using Eq. (8).

Absorption ðkÞ ¼

area ðkÞj 2 jETotal ðkÞj

jEactiv e

2

ð7Þ

Total Geneation Rate ðs1 m3 Þ Total Generated electrons in dev ice ¼ Volume of dev ice

ð8Þ

Using the generation profile of electrons as an input into the electrical model, we were able to calculate the J-V output of the solar cell. The electrical model was built only for the HTM and Perovskite regions, where the contacts were assumed series Ohmic contacts (10 X/cm2), and considering direct recombination only as perovskite has a direct band gap (Kanhere et al., 2015). The electrical parameters for perovskite (CH3NH3PbI3) and HTM (CuSCN) were taken from measured data in Zhao et al. (2014), Butler et al. (2015), Lin et al. (2015), Brivio et al. (2013, 2014) and Kumaraa et al. (2001), Cheng et al. (2015), respectively. 3. Results and discussion To validate our proposed optical and electronic considerations, we started by modeling a previously published work (Qin et al., 2014) to investigate the effect of our assumptions on enhancing the power conversion efficiency of the device, as will discussed later. Fig. 1 shows the five modeled perovskite solar cells, which have a width of 300 nm and a depth of 300 nm, with the thickness of Ag, CuSCN, CH3NH3PbI3, FTO, and TiO2 layers are 100 nm, 600 nm, 200 nm, 50 nm, and 50 nm, respectively. The nanotube has a wall thickness of 25 nm, the inner and outer radius of each nanotube are 25 nm and 50 nm, respectively, with the pitch between each nanotube is 150 nm. The nanopyramid has a square base with a length of 150 nm and the distance between tips of each nanopyramid is 150 nm. The nanorod has a circular cross section with a radius of 25 nm and spacing between each rod is 150 nm. The nanocone has a circular base with a radius of 75 nm with no

spacing between bases, pitch between tips of each nanocone is 150 nm. The length of each nanostructured light trapping architecture is denoted as: T for nanotube, P for nanopyramid, R for nanorod, and C for nanocone. The length of each nanostructure was changed (keeping the same thickness of the solar cell) and the enhancements in generation rate and absorption were calculated using Eqs. (9) and (10), respectively.

Normalized Geneation Rate ðkÞ ¼

Normalized Absorption ¼

Generation rate of nanostructure film Generation rate of planar film ð9Þ

Absorption of nanostructure film Absorption of planar film

ð10Þ

Fig. 2 shows the normalized light absorption profiles inside the active area of the modeled solar cells. Fig. 2a shows absorption enhancement over planar perovskite solar cell upon the use of nanotubular architecture with different lengths starting from 60 nm to 140 nm. The absorption increased by increasing the length of the nanotube, reaching 6% at a wavelength of 500 nm. Fig. 2b illustrates the absorption enhancement upon using nanopyramid architecture with lengths between 60 nm and 140 nm, achieving a maximum enhancement of 3.5% at a wavelength of 520 nm. Fig. 2c shows the absorption enhancement upon using nanorod architecture with lengths from 60 to 140 nm, resulting in a maximum absorption enhancement of 2% at a wavelength of 510 nm. Fig. 2d illustrates the enhancement in absorption upon using nanocone architecture, showing an absorption enhancement of 2.5% at 520 nm. According to the four simulated nanostructures, absorption showed the highest enhancement around 500 nm. This may be related to the fact that the incident sun light has the highest intensity at this wavelength. As sun light energy is proportional to square of the electric field intensity, the absorption will be parabolic and similar to AM1.5G, because the refractive index of perovskite is approximately constant (2.5) over the simulated wavelength range. As a result, the highest absorption enhancement was obtained upon the use of nanotube architecture, and the lowest absorption enhancement was obtained for the nanorod architecture.

Fig. 1. (I) Perovskite solar cell structure consisting of silver (Ag) as a back reflector, HTM (CuSCN) as a p-type layer, perovskite (CH3NH3PbI3) as an n-type layer, and fluorinedoped tin oxide (FTO)/compact TiO2 combination is replaced by indium tin oxide as a transparent conducting oxide. Perovskite solar cell with (II) nanotube structure, the length of nanotube is given by T, (III) nanopyramid structure, the length of nanopyramid is given by P, (IV) nanorod structure, the length of nanorod is given by R, and (V) nanocone structure, the length of nanocone is given by C. All simulated cells have the same dimensions.

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Fig. 2. Normalized light absorption profiles in the active area of the proposed solar cells with changing the length of the nanostructure: (a) perovskite nanotube, (b) perovskite nanopyramid, (c) perovskite nanorod, and (d) perovskite nanocone.

Fig. 3. Carriers generation profiles of the proposed solar cell designs with (I) perovskite thin film, (II) perovskite nanotube, (III) perovskite nanopyramid, (IV) perovskite nanorod, and (V) perovskite nanocone under AM1.5G illumination at a wavelength of (a) 300 nm and (b) 800 nm.

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Fig. 4. Normalized total generation rate of electrons (m3 s1) in perovskite and HTM layer in the proposed solar cells for different lengths of simulated nanostructures: (a) perovskite nanotube, (b) perovskite nanopyramid, (c) perovskite nanorod, and (d) perovskite nanocone.

Table 1 Generation rates (m3 s1) of electrons in the perovskite layer with different lengths. Structurensize

60 nm

80 nm

100 nm

120 nm

140 nm

Nanocone Nanopyramid Nanotube Nanorod Planar

6.25  1029 6.36  1029 6.46  1029 5.97  1029 5.8  1029

6.39  1029 6.55  1029 6.67  1029 6.02  1029 5.8  1029

6.54  1029 6.75  1029 6.88  1029 6.03  1029 5.8  1029

6.68  1029 6.94  1029 7.12  1029 6.04  1029 5.8  1029

6.81  1029 7.14  1029 7.46  1029 6.05  1029 5.8  1029

Table 2 Generation rates (m3 s1) of electrons in the hole transport material (HTM) layer with different lengths. StructurenSize

60 nm

80 nm

100 nm

120 nm

140 nm

Nanocone Nanopyramid Nanotube Nanorod Planar

3.22  1028 3.15  1028 2.59  1028 2.86  1028 2.79  1028

3.19  1028 3.32  1028 2.54  1028 2.91  1028 2.79  1028

3.34  1028 3.54  1028 2.48  1028 2.98  1028 2.79  1028

3.51  1028 3.75  1028 2.44  1028 3.09  1028 2.79  1028

3.69  1028 3.96  1028 2.44  1028 3.26  1028 2.79  1028

Fig. 3 shows the calculated electrons generation profiles at two different incident wavelegnths; 300 nm (Fig. 3a) and 800 nm (Fig. 3b). The generation rate was found to be maximum at the interface due to the possible multiple reflection of light with the nanostructure inside active area. Generation rate decreased too much as we go down inside the active area, as most of the incident light is absorbed in the perovskite layer and trapped between nanostructures. Fig. 4 shows the generation rate enhancement for all simulated nanostructures upon changing the length from

60 nm to 140 nm. While the nanotube showed a maximum enhancement of 7% at 530 nm (Fig. 4a), the nanopyramid showed 6% at 800 nm (Fig. 4b). On the other hand, the nanorod showed a maximum enhancement of 2% at 800 nm (Fig. 4c) and the nanocone showed a maximum enhancement of 5% at 800 nm (Fig. 4d). Therefore, the highest enhancement in generation rate is 7% and achieved upon using the nanotubular architecture, while the lowest enhancement rate is 2% upon using the nanorod architecture. Overall generation rate in perovskite layer for each simulated

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Fig. 6. Variation of the short circuit current (Jsc) of the proposed solar cells with the length of the nanoarchitectued layer.

Fig. 5. (a) Comparison between the I-V characteristics of previously measured and simulated planar perovskite solar cells, and (b) the I-V characteristics of proposed nanostructured perovskite solar cells.

Table 3 The semiconductor parameters of CH3NH3PbI3 and CuSCN used to construct the electrical model.

Thickness (nm) Band gap (eV) Electron affinity (eV) CB density of state Nc (cm3) VB density of state Nv (cm3) Donor density ND (cm3) Acceptor density NA (cm3) Diffusion length Ln (nm) Diffusion length Lp (nm)

CuSCN

CH3NH3PbI3

200 3.6 1.5 1  1016 5  1015 – 1  1017 – 97

600 1.6 5.7 1  1016 5  1015 1  1017 – 100 –

Table 4 The electrical performance parameters of the proposed solar cells. Structure

Jsc (mA/ cm2)

Series resistant (X)

Voc (mV)

Shunt resistant (X)

FF

Efficiency (%)

Nanocone Nanopyramid Nanotube Nanorod Planar

22.64 23.76 24.29 20.09 19.20

10 10 10 10 10

1000 1000 1000 1000 1000

400 400 400 400 400

0.627 0.627 0.627 0.627 0.627

14.20 14.90 15.23 12.60 12.04

Fig. 7. The external quantum efficiency of the proposed nanostructured perovskite solar cells.

nanostructure with different length is calculated by integrating all generated electrons over the wavelength range 300–800 nm as listed in Table 1, while overall generation rate of the hole transport material (HTM) is listed in Table 2. The electrical model was constructed to evaluate the electrical parameters of perovskite solar cells upon the use of nanostructured layers. The simulated planar perovskite was compared to previously reported solar cells (Qin et al., 2014) as shown in Fig. 5a. A very good matching was achieved, while considering a series resistance of 10 X/cm2 and a shunt resistance of 400 X/cm2. The semiconductor parameters of CuSCN and CH3NH3PbI3 used in the simulation are listed in Table 3. Fig. 5b shows the J-V characteristics of each simulated nanostructure with a length of 140 nm. The highest efficiency was found to be 15.23% for the solar cell with the nanotubular architecture, while the planar film solar cell showed an efficiency of 12.04%. The solar cells containing nanopyramid, nanocone, and nanorod showed efficiencies of 14.9%, 14.2% and 12.6%, respectively. The electrical parameters of all simulated architectures are listed in Table 4. These enhancements in efficiency, compared to the planar film solar cell, confirm that using nanostructures in perovskite solar cells would facilitate carriers transport and increase the absorption of incident sunlight.

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Fig. 6 shows the variation of the short circuit current (Jsc) for the solar cells made using the simulated nanostructures as a function of the length of each nanostructure. Note that Jsc increases with increasing the length. The highest Jsc is obtained for the solar cell containing the nanotube architecture, reaching 24.29 mA/cm2 that is about 5 mA/cm2 enhancement over the planar perovskite solar cell, while the lowest Jsc achieved upon using nanorod architecture, reaching 20.09 mA/cm2 that is 0.8 mA/cm2 higher than that of planar perovskite solar cell. Fig. 7 shows the external quantum efficiency of each nanostructured soar cell. Note that the internal quantum efficiency (IQE) was considered as unity over he whole simulated wavelength range, therefore the enhancement in EQE is proportional to the enhancement in the absorption of incident sunlight.

EQE ¼ IQE  Absorption

ð11Þ

The nanotubular-based solar cell showed EQE that is 5% higher than that of the planar film-based solar cell over the wavelength range 400–550 nm. However, the nanorod-based solar cell showed only 1–2% enhancement in the EQE compared to that of the planar film. Most of the enhancements occurred at smaller wavelengths (below 600 nm), probably due to the fact that smaller wavelengths can be easily trapped compared to longer wavelengths (Abdelraouf and Allam, 2016; Alshal and Allam, 2016).

4. Conclusion In conclusion, the effect of using nanostructured light trapping architectures on enhancing the perovskite solar cells performance was investigated. Four different nanostructures (nanotubes, nanorods, nanocones, and nanopyramids) of perovskite solar cells were designed and optimized for enhancing the overall efficiency. Many different dimensions of the proposed nanostructures were simulated to study the effect of nanostructure dimensions on the solar cell performance. The results showed that the active area absorption can be increased and accordingly the short-circuit current by increasing the length of nanostructure. Under certain lengths of nanostructures, the active area absorption enhanced up to 6% over planar perovskite solar cell, while total generation rate increased up to 7%. The nanotubular and nanopyramidal nanostructures showed higher short circuit current for small dimensions. The nanotubular structure (140 nm in length) showed the highest short circuit current (24.29 mA/cm2) with an overall efficiency of 15.23%. The proposed nanostructures in this study could be fabricated using open nanofluidic channels (Spina et al., 2016) for growth of nanowires, hydrothermal method (Peng et al., 2016) for fabricating nanocones, and free standing TiO2 (Gao et al., 2014) for creating nanotubes. These enhancements would open a new route for integrating light trapping nanostructures in CH3NH3PbI3 perovskite-based solar cells for better efficiency. References Abdelraouf, O.A.M., Allam, N.K., 2016. Nanostructuring for enhanced absorption and carrier collection in CZTS-based solar cells: coupled optical and electrical modeling. Opt. Mater. 54, 84–88. Alshal, M.A., Allam, N.K., 2016. Broadband absorption enhancement in thin film solar cells using asymmetric double-sided pyramid gratings. J. Electr. Mater. http://dx.doi.org/10.1007/s11664-016-4735-7. Ball, James M. et al., 2015. Optical properties and limiting photocurrent of thin-film perovskite solar cells. Energy Environ. Sci. 8, 602–609.

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