Modeling of optical losses in perovskite solar cells

Accepted Manuscript Modeling of optical losses in perovskite solar cells Mohammad Houshmand, M. Hossein Zandi, Nima E. Gorji

PII:

S0749-6036(16)30287-7

DOI:

10.1016/j.spmi.2016.06.031

Reference:

YSPMI 4392

To appear in:

Superlattices and Microstructures

Received Date: 25 March 2016 Revised Date:

13 May 2016

Accepted Date: 13 June 2016

Please cite this article as: M. Houshmand, M.H. Zandi, N.E. Gorji, Modeling of optical losses in perovskite solar cells, Superlattices and Microstructures (2016), doi: 10.1016/j.spmi.2016.06.031. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Modeling of Optical Losses in Perovskite Solar Cells Mohammad Houshmanda , M. Hossein Zandia , Nima E. Gorjib,∗ a Department

of Physics, Shahid Bahonar University of Kerman, Kerman 75429, Iran of New Technologies, University of Tabriz, Tabriz 51566, Iran

RI PT

b Department

Abstract

M AN U

SC

The optical losses in the structure of hybrid perovskite-based solar cells are investigated using only the optical properties of each layer e.g. refractive index and extinction coefficient. This model allows calculating the transmission/reflection rates at the interfaces and absorption loss within any layer. Then, the short circuit current density and it’s loss are calculated versus the perovskite layer’s thickness and several TiO2 thicknesses from 50 nm to 150 nm. To make our calculations closer to reality, we extracted the optical properties of each device component from literature reports for glass/TCO/TiO2 /perovskite/metal. The simulations results were fitted with the experimental results of some relevant references. Our simulations show that ITO transmits the light better than SnO2 as the TCO front electrode, and the light reflection at both sides of the perovskite layer, e.g. at TiO2 /perovskite and perovskite/Spiro-OMeTAD , is lower than 25%. The light interference and multiple reflections have been accounted in our calculations and finally we showed that a thicker TiO2 and perovskite cause more optical loss in current density due to stronger absorption. Keywords: Modeling, Optical loss, Perovskite, Solar cell.

1. Introduction

AC C

EP

TE

D

The optical and electrical properties of hybrid organic/inorganic methylammonium lead iodide CH3NH3PbI3 perovskite solar cells have been extensively studied in the last recent years [1, 2]. Many research groups are now investigating these materials applications in solar cells. The main issues are with materials engineering to find a proper partner for perovskite layer [3], performance enhancement [4], and stability over time of such devices [5]. Perovskites have a proper energy bandgap, are simple to deposit, strong light absorption, low defect activity, and good carrier mobilities. However, they suffer from moisture sensitivity and instability decomposition under either high temperatures, high-intensity, and have finite mobility, and Pb toxicity. Modeling the device physics of such devices are extremely required for refining the device design and obtaining an insight into recombination/generation and carrier collection mechanism. However, this is not easy since the perovskites behave odd and unknown and it seems a specific device physics runs the photo-absorption and photo-generation. To avoid dealing with the complicated recombination mechanisms, an optical approach is used which considers only the absorption coefficient, α, refractive index, n and extinction coefficient, κ of any device component and their relation to device parameters e.g. the short circuit current density, J sc [6, 7]. This relation is via the Transmission/Reflection rates (T & R). We have recently developed such an approach for modeling the optical losses in CdTe and CIGS devices with a graphene electrode [8, 9] and will apply this model to hybrid planar perovskite-based solar cells using the optical data given in literature especially in Ref. [10]. There are only a few publications in the literature on the optical modeling of perovskite solar cells [11, 12, 13]. They all developed a rigorous theoretical model based on the transfer matrix formalism which allows us to calculate the electric field intensity within each device component. However, we used a quite simpler model which does not require a rigorous modeling and computing calculation but can also calculate the reflection and transmision of the light from every interface in the device and the light absorption in any layer. ∗ +39

05120 93578 Email address: [email protected] (Nima E. Gorji)

Preprint submitted to ...

June 14, 2016

RI PT

ACCEPTED MANUSCRIPT

SC

Figure 1: a. schematic structure of a perovskite solar cell, b. refractive index and, c. extinction coefficient of every layer.

2. II. Modeling Approach

AC C

EP

TE

D

M AN U

The schematic structure of a perovskite solar cell and the optical constants of every layer have been presented in Fig. 1a and Fig. 1(b,c), respectively. The heterostructure is made of glass/TCO/TiO2 /Perovskite/HTM/back-contact where HTM is Spiro-OMeTAD and the back contact can be Au, C or any metallic alloy [14, 15]. The values of n and κ were taken within λ=150-1000 nm from the relevant references e.g. for TCO/ITO from [9], for TiO2 from [7], for perovskite from [10] and for HTM layer from [16, 17], respectively. n varies slowly for a wide range of wavelengths and κ changes significantly only within a small range and ends to zero for longer λ almost for all the layers. The perovskite layer shows extinction coefficient peaks at 350-730 nm with κ values of 0.5-1.7 respectively, and the refractive index is ≥2.5 in the visible to near-infrared wavelength range in agreement with data presented in Ref. [18]. The κ values of the perovskite are slightly higher than those of inorganic materials such as CIGS, GaAs and CdTe in the wavelength range of 450 nm to 750 nm. The perovskite layer exhibits a lower refractive index than that of CIGS, GaAs and CdTe, which will result in lower reflection at the perovskite interfaces and thus a higher absorption in the respective layer and higher J sc values. Ziang et al., demonstrated that n(λ) for CH3NH3PbI3 materials is a little smaller than, but very close to that of GaAs and much larger than that of c-Si in all wavelengths [19]. The thickness of the TiO2, perovskite, and HTM layers are quite thinner than the one of Si and chalcogenide materials too (nm versus µm). Therefore, optimized optical losses will assist in increasing the J sc and reducing the recombination, reflection and absorption rates within the device components and at the interfaces. The device parameters of a few perovskite-based devices reported in literature such as the ones given in Ref. [15] are used in our simulations and are compared with our modeling results. The input data of our modeling are the thickness and the experimentally derived complex refractive index spectra for each layer. For the present report, we have analyzed the simple pin planar heterojunction stack although in principle the method and data could be used as a building block for the analysis of the many structures variation currently being explored in perovskite solar cells including mesoporous architectures, by employing an effective medium approximation. To calculate J sc , and ∆J sc , (due to light reflection and absorption in every layer before the light being absorbed in perovskite layer), the reader is referenced to our recently published papers [7, 8, 9]. The modeling approach is identical to previous ones. However, we briefly describe it here. First we obtain the Reflection, R12 from the interface of two different materials n1 and n2 [9]. This coefficient calculation maybe different if one of the two layers cause interference in light reflection [9, 20]. In our case, the reflection coefficient at TiO2 /perovskite and perovskite/HTM was calculated using, R45,56 (λ) =

r12 + r22 + 2r1 r2 cos(2β(λ)) 1 + r12 + r22 + 2r1 r2 cos(2β(λ))

(1)

where r1,2 are reflection coefficients at both perovskite sides by β is given by β(λ)=2π ndG /λ where n and d are the perovskite layer’s refractive index and thickness, respectively. The reflection coefficient at the other interfaces are obtained normally. In addition of the reflection, the photoabsorption cause a loss in TiO2 and HTM layers. The total 2

RI PT

ACCEPTED MANUSCRIPT

SC

Figure 2: a. Reflection at the interfaces of SnO2 /TiO2 , ITO/TiO2 , TiO2 /perovskite, perovskite/Spiro-OMeTAD ; b. Transmission rate through several stacked layers separately for SnO2 and ITO front contact; c. Reflection and Transmission rate at every stage of considering normal reflection without interference and with interference.

M AN U

j=2:6 transmission rate, T , is obtained using: T (λ) = Σi=1:5 (1 − Ri j ) × exp(−αi .di ). This means that the transmission rate, T(λ), includes both reflection (at 12, 23, 34, 45, 56) and absorption in previous layers with the absorption coefficient given by α(λ)= 4π λ κ(λ). This allows calculation of J sc for a device irradiated with Φin density of photons with energy hυ, with incident photon flux Φin /hυ for every single photon [6, 9],

J sc (λ) = q

X

T (λ)

i

Φin (λ) ∆λi . hυi

(2)

where ∆λ is the interval between the adjacent wavelengths in the spectrum. The integral is over λ=150-1000 nm. The loss percentage of short-circuit current density is given by ∆J sc , due to light reflection/absorption is given by, J sc (d) ) ∗ 100% ◦ J sc

(3)

D

∆J sc (d) = (1 −

EP

TE

◦ where J sc is the primary measured value reported in literature for a typical device given in Ref. [15]. Note that in our simulations which is an optical approach, no carrier recombination loss is assumed after the conversion of photons into free carriers. Unfortunately, some inter-layers are quite thin in the design of perovskite devices which makes it difficult to consider their role in the calculations. Also, the optical properties of some inter-layers are not available and we couldn’t bring them in the model. Nevertheless, this will not affect the generality of the model and presented results.

3. Simulation of Reflection & Transmission

AC C

The reflection rate at several interfaces of the adjacent layers has been calculated in Fig. 2a. The reflection at the interface of SnO2 /TiO2 is higher than ITO/TiO2 for λ<300 nm and λ>800 nm. Within 300 nm<λ< 800 nm ITO cause a higher reflection. Overall, the ITO shows a better match for TiO2 and thus we use this for the rest of our simulations. The interface reflection has been calculated using Eq. (1). The reflection at the other two interfaces of TiO2 /perovskite and pervskite/Spiro-OMeTAD show a similar trend for a wide range of wavelengths. Since perovskite shows interference of light reflections as of TiO2 layer, we correctly used the same equation for all the interfaces here. We obtained R<25% for reflection at both sides of perovskite layer, while it is less than 10% for TiO2 interfaces for λ<320 nm. Such a low reflection losses at the interfaces are explained by the relatively small difference between the optical constants of the optically contacting materials. Fig. 2b represents the transmission rate through several interfaces before the light arrives in TiO2 , perovskite, and Spiro-OMeTAD layer where it may be absorbed and lost. Since the multiple reflections may have a significant effect in these materials, we also plotted the transmission rate by calculating multiple reflection rate (T=1-R, R with interference). Also we calculated the reflection from the same device structure replacing the ITO with SnO2 . Except the interface of perovskite/Spiro-OMeTAD , the rest of the interfaces show a better transmission with ITO constant. 3

ACCEPTED MANUSCRIPT

T (λ)

=

−

(1

R12 )(1

−

R23 )(1

−

R34 )(1

RI PT

This might be because of a better match between the refractive index of SnO2 and Spiro-OMeTAD materials. However, this is not of interest to the absorption in perovskite layer since, we want the light to be reflected to the perovskite thickness from the perovskite/Spiro-OMeTAD which is better for the device with ITO contact. We used the following formula to calculate the transmission rate,

−

R45 )(1

−

R56 )

(4)

SC

In above equation, we neglected the effect of absorption and focused on reflection effect. To calculate the effect of absorption as well, we used the following equation which considers that the light can be partially absorbed when going through a thickness as following,

T (λ) = (1 − R12 )(1 − R23 )(1 − R34 )(1 − R45 )(1 − R56 )× exp(−αIT O .dIT O )exp(−αT iO2 .dT iO2 )exp(−α p .d p )

(5)

M AN U

In above equations, the reflection and absorption of every interface and thickness of every device component was taken into account by R and exponential function, respectively. Fig. 2c shows the effect of absorption loss on the transmission rate. The effect of interference was considered in some cases in order to show the difference between the normal reflection and multiple reflection. Interference and multiple reflection were also compared for several interfaces. It is observed that the multiple reflection reduces the transmission and cause a sinusoidal curves within a range of wavelengths. This is of course closer to reality and similar to perovskite materials properties. Note that in above simulations, one can take into account that the absorption is doubled by considering the reflection from the metallic back contact and being re-absorbed in perovskite layer again.

D

4. Simulation of J sc and ∆J sc

AC C

EP

TE

Now we can obtain J sc versus the thickness of perovskite and TiO2 layers as shown in Fig. 3a and the inset of Fig. 3b using Eq. (2). For the first case, we plotted the J sc against the perovskite thickness for several T iO2 thicknesses, dT iO2 , and fitted the simulations with the experimental data given in Ref. [21]. The simulation results fit well with the experiment when dT iO2 =120 nm. There is an optimum thickness of perovskite layer in the range of d p =250-300 µm which unfortunately was not considered in the experiments most probably because of the lake of modeling in that work. Kim et al. have considered only 3 TiO2 thicknesses where the last one is much thicker than the first two TiO2 layers. However, our optical modeling results in an optimum around d p =300 nm which is well within a reasonable range according to the thickness reported in literature as well [10, 15]. Please note that we ignored to optimize the efficiency for this work since the aim of this modeling is to investigate the effect of perovskite and TiO2 layers and the loss by reflection and transmission. Fig. 3a also shows that a thinner TiO2 layer enhances J sc by a lower absorption in that layer and a better transmission rate to the perovskite layer. Differently, TiO2 thickness was in favor of J sc if we calculate the current density given by TiO2 layer. This layer must be considered since it is not yet clear in literature that if TiO2 contributes significantly in the total current density of the cell. Fig. 3b shows that TiO2 thickness enhances the J sc consistently with data given in Ref. [21]. The reason raise in J sc is that TiO2 layer contributes slightly in current. Note that we calculated this J sc similar to previous case of perovskite layer where the absorption was considered to be origin of this thickness dependency. A small difference between the simulation and experimental data at dT iO2 =0 nm is probably because of an error in the value of the optical parameters at some λs which depends on the fabrication details. Finally, we plotted ∆J sc versus the TiO2 and perovskite layer’s thicknesses in Fig. 3b. ∆J sc starts from a higher value for thicker TiO2 and increases for a thicker perovskite layer as is expected due to stronger photo-absorption within a thicker TiO2 layer. The noticeable peak at thicker perovskite is due to a higher absorption which is in agreement with increased J sc in (a). However, it doesn’t suggest that a thicker perovskite layer in the device structure since a lower materials consumption is preferred.

4

SC

RI PT

ACCEPTED MANUSCRIPT

Figure 3: a. J sc and b. ∆J sc vs. perovskite thickness for a variety of TiO2 thicknesses. The simulation (a) is consistent with data of Ref. [21]. It also shows an optimum value for the thickness at around d p =300 nm

M AN U

.

5. Conclusion

6. Acknowledgments

TE

D

The optical and electrical properties of perovskite materials are similar to chalcogenide polycrystallines. Therefore, we applied a previously developed optical modeling to a stack of TiO2 /perovskite/Spiro-OMeTAD heterojunction solar cell to calculate the optical loss due to reflection at the interface and absorption in any layer. It is shown that ITO transmits the light better than SnO2 and thus is preferred TCO layer for perovskite devices. The multiple reflection fits better with the reflection loss data reported in literature. This is consistent with the normally believed that perovskite materials cause light reflection interference inside their thickness. Finally, we calculated the ∆J sc versus the perovskite thickness and for several TiO2 thicknesses. It was shown that both thicker TiO2 and perovskite increase the optical loss by stronger absorption. The simulation results were fitted by the literature data reported in Ref. [21].

7. References

EP

We gratefully acknowledge the Senior Research Fellowship of Iran Nanotechnology Initiative Council, 2016, Grant No. 97577.

AC C

[1] G. E. Eperon, S. N. Habisreutinger, T. Leijtens, et al., ‘’The Importance of Moisture in Hybrid Lead Halide Perovskite Thin Film Fabrication ‘’, ACS Nano, 9:9 (2015) 9380-9393. [2] M. C. Tathavadekar, Sh. A. Agarkar, et al., ‘’Enhancing efficiency of perovskite solar cell via surface microstructuring: Superior grain growth and light harvesting effect”, Solar Energy, 112 (2015) 12-19. [3] M. Bag, Z. Jiang, L. Renna, S. Jeong, V. Rotello, D. Venkataraman, ‘’Rapid combinatorial screening of inkjet-printed alkyl-ammonium cations in perovskite solar cells‘’, Materials Letters 164:1 (2016) 472-475. [4] Y. Zhao, J. Liu, et al., ‘’Improving the efficiency of perovskite solar cells through optimization of the CH3NH3PbI3 film growth in solution process method”, Appl. Surf. Sciences, 359 (2015) 560-566. [5] T. Leijtens, G. Eperon, et al., ‘’Stability of metal halide perovskite solar cells”, Advanced Energy Materials, 5:20, (2015) 1500963. [6] L.A. Kosyachenko, E.V. Grushko, X. Mathew, ‘’Quantitative assessment of optical losses in thin film CdS/CdTe solar cells”, Solar Energy Materials & Solar Cells, 96 (2012) 231237. [7] N.E. Gorji, ‘’Quantitative analysis of the optical losses in CZTS thin film semiconductors”, IEEE Transactions on Nanotechnology, 13:4 (2014) 743-748. [8] M. Aldosari, N. E. Gorji, ‘’Optical Analysis of Graphene Contacted CIGS Thin Film Devices”, Physica E, (2016) in press. [9] M. Houshmand, M. H. Zandi, N. E. Gorji, ‘’Modeling of optical losses in graphene contacted thin film solar cells”, Materials Letters 164 (2016) 493-497. [10] Ph. Loper, M. Stuckelberger, et al., ‘’Complex Refractive Index Spectra of CH3NH3PbI3 Perovskite Thin Films Determined by Spectroscopic Ellipsometry and Spectrophotometry”, J. Phys. Chem. Lett., 6 (2015) 66-71.

5

ACCEPTED MANUSCRIPT

[21]

RI PT

[20]

SC

[19]

M AN U

[18]

D

[17]

TE

[16]

EP

[15]

M. Anaya, G. Lozano, M. E. Calvo, W. Zhang, M. Johnston, H. Snaith, J. Phys. Chem. Lett., 6 (2015) 48-53. A. Leguy, P. Azarhoosh, M. Alonso, et al., Nanoscale, (2016) DOI: 10.1039/C5NR05435D, in press. Y. Jiang, M. A. Green, R. Sheng, A. H. Baillie, Solar Energy Materials & Solar Cells, 137 (2015) 253-257. M. Aldosari, L. Grigoriu, N. E. Gorji, ‘’Modeling of Depletion Width Variation Over Time in Thin Film Photovoltaics”, Modern Phys. Lett. B, in press 2016. T. Minemoto, M. Murata, ‘’Device modeling of perovskite solar cells based on structural similarity with thin film inorganic semiconductor solar cells”, J. Appl. Phys., 116 (2014) 054505. M. Filipic, Ph. Loper, B. Niesen, S. De Wolf, J. Krc, Ch. Ballif, M. Topic , ‘’CH3NH3PbI3 perovskite / silicon tandem solar cells: characterization based optical simulations”, OPTICS EXPRESS, 23:7 (2015) A263-A278. D. Shi, Y. Zeng, W. Shen, ‘’Perovskite/c-Si tandem solar cell with inverted nanopyramids: realizing high efficiency by controllable light trapping”, Scientific Reports, 5:16504 (2014) 1-10. Ch.-W. Chen, Sh.-Y. Hsiao, et al., ‘’Optical properties of organometal halide perovskite thin films and general device structure design rules for perovskite single and tandem solar cells”, Journal of Materials Chemistry A, 3 (2015) 9152-9159. X. Ziang, L. Shifeng, Q. Laixiang, et al., ‘’Refractive index and extinction coefficient of CH3NH3PbI3 studied by spectroscopic ellipsometry”, Optical Materials Express, 5:1 (2015) 29-43. L. Kosyachenko, X. Mathew, et al.,‘’Optical and recombination losses in thin-film Cu(In,Ga)Se2 solar cells”, Solar Energy Materials & Solar Cells, 130 (2014) 291-302. H.S. Kim, N.G. Park, ‘’Parameters Affecting IV Hysteresis of CH3NH3PbI3 Perovskite Solar Cells: Effects of Perovskite Crystal Size and Mesoporous TiO2 Layer”, J. Phys. Chem. Lett., 5 (2014) 2927-2934.

AC C

[11] [12] [13] [14]

6

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

First time simulating the optical loss of perovskite solar cells Light transmission from ITO/TiO2 interface is more than FTO/TiO2 The optical loss increases by increasing the TiO2 and perovskite thicknesses.