Quantifying energy losses in planar perovskite solar cells

Solar Energy Materials and Solar Cells 174 (2018) 206–213

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Solar Energy Materials and Solar Cells journal homepage: www.elsevier.com/locate/solmat

Quantifying energy losses in planar perovskite solar cells a

Yun Da , Yimin Xuan a b

a,b,⁎

MARK

a

, Qiang Li

School of Energy and Power Engineering, Nanjing University of Science & Technology, Nanjing 210094, China School of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Perovskite solar cells Loss analysis Optical absorption Electrical recombination Coupled optical and electrical modeling

Perovskite solar cells are considered as an up-and-coming substitute for the next generation solar cells. Despite of significant increase of its photon-electric conversion efficiency, a definitive direction for further increment remains ambiguous. In this paper, we quantitatively assess the energy losses in planar perovskite solar cells in terms of the underlying physical mechanisms. The coupled optical and electrical modeling is developed to explore the working principle of the perovskite solar cells. A comparison between simulation results and experimental data under different operating conditions is investigated to elucidate the reliability of the device modeling. With the aid of the accurate device modeling, we explore the energy loss mechanisms in planar perovskite solar cells. Five energy loss mechanisms are quantified, such as thermalization loss, below bandgap loss, optical loss, recombination loss, and spatial relaxation loss. The effects of the optical properties, carrier diffusion length, surface recombination velocity, and series resistance on the performance of the perovskite solar cells are analyzed to identify the dominant loss contributors limiting the power conversion efficiency of the perovskite solar cells. Our results indicate that more efforts should be paid to enhance the optical absorption of the perovskite layer, improve the surface passivation, and reduce the series resistance. Based on the theoretical analysis, a roadmap to promote the device performance of the perovskite solar cells is summarized. Our work provides a detail guideline for design and innovation of perovskite-based device.

1. Introduction The development of inorganic-organic halide perovskite solar cells is booming in the past several years since it was firstly announced by Kojima et al. in 2006 [1]. The first hybrid lead halide perovskite solar cells appeared in the form of dye-sensitized solar cells (DSSCs) with the power conversion efficiency (PCE) of 2.2%. Three years later, the same group of Kojima et al. improved the PCE to the level of 3.8% [2]. Their work gained much attention and greatly promoted fascinating progresses in perovskite solar cells and resulted in an unprecedented rise rate of PCE. Currently, the record efficiency of perovskite solar cells reached to 22.1% [3]. The perovskite materials possess excellent optical and electrical characteristics, such as direct band-gap, high light absorption coefficient, high charge carrier mobility, long charge carrier diffusion length, and long electron-hole recombination lifetime [4–8], making them desirable for high efficiency thin-film solar cells. Hence, depending on these properties, perovskite solar cells become a star in the photovoltaic realm and attract tremendous research interests. It has been experimentally demonstrated that the PCE of the perovskite solar cells depends on the morphology of film, device configuration, interface losses, and crystal quality [9–15]. However, the key factors affecting

⁎

the performance of the perovskite solar cells remain challenging. The theoretical model to clarify these influencing factors is still lacking. Thus, there is an urgent requirement to develop an accurate theoretical model to describe the working mechanisms of the perovskite solar cells and to examine the extent of the impact of these factors. To correctly establish the device modeling, it is necessary to understand the operation principle of the perovskite solar cells. It is well known that the perovskite solar cells were initially derived from the DSSCs. The working mechanism may be similar to DSSCs or bulk heterojunction organic solar cells at first impression. But the subsequent investigations denied this conjecture [16,17]. Hu et al. provided the direct evidence to reveal the non-excitonic nature of the perovskites by comparing the exciton dissociation behavior of perovskite materials to conventional excitonic semiconductors [18]. Additionally, the small exciton binding energy of the perovskite crystal further confirmed the fact that the free charge carriers are formed in perovskite solar cells under operation conditions [19]. Therefore, the perovskite solar cells can be modeled as inorganic photovoltaic devices [20]. It is reasonable to apply the device physics modeling of inorganic cells to perovskite solar cells. Recently, many researchers have established one-dimensional (1D) device modeling and successfully explained the

Corresponding author at: School of Energy and Power Engineering, Nanjing University of Science & Technology, Nanjing 210094, China. E-mail address: [email protected] (Y. Xuan).

http://dx.doi.org/10.1016/j.solmat.2017.09.002 Received 24 June 2017; Received in revised form 22 August 2017; Accepted 4 September 2017 0927-0248/ © 2017 Elsevier B.V. All rights reserved.

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⎯→ ⎯ ⎯ ∂D ⎧ ∇ × ⎯→ H = ∂t ⎪ ⎯→ ⎯ ⎯→ ⎯ ⎪ ∂B ∇ × E = − ∂t ⎨ ⎯→ ⎯ ⎯→ ⎯ ⎪ D = εE ⎪ ⎯→ ⎯ ⎯→ ⎯ (1) ⎩ B = μH ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯ where H is the magnetic field, D is the electric displacement field, E ⎯→ ⎯ is the electric field, B is the magnetic flux density, ε is the complex permittivity, and μ is the complex permeability. The optical performance of the perovskite solar cells can be obtained via the Finite Difference Time Domain (FDTD) algorithm, which is a rigorous electromagnetic calculation for solving the Maxwell's equations. By assuming that each absorbed photon with energy greater than the bandgap of the semiconductor can generate an electron-hole pair, the photogeneration rate can be presented as

fundamental role of the influencing factors in perovskite solar cells [21–24]. Unfortunately, 1D simulation is restricted by its simplified process, such as lacking the ability to entirely characterize the optical properties, failing to consider the influence of microstructure in the solar cells. Thus, it is required to develop an sufficiently accurate device modeling for the perovskite solar cells. Meanwhile, energy loss analysis is an impressive procedure to understand the working principle of the solar cells as well. It can help us to comprehend where the lost energy went and how to improve the PCE of the photovoltaic cell. At present, two typical device architectures including mesoporous scaffold structure and planar junction configuration have already succeeded in obtaining high efficiency for perovskite solar cells. In terms of the simple structure and facile reproducibility, planar heterojunction configuration is preferred to mesoporous scaffold structure because it has prospect of industrial application due to roll-toroll production [25]. It is generally known that there exist intrinsic loss and extrinsic loss processes in the solar cells. Due to the non-excitonic nature of the planar perovskite solar cells, five kinds of energy loss processes occurs inside the device including thermalization loss, below bandgap loss, optical loss, recombination loss, and spatial relaxation loss. Nevertheless, till today, the energy loss in planar heterojunction perovskite solar cells is not yet quantified and the dominant energy loss mechanisms remain ambiguous. Of particular note is that the current PCE of the perovskite solar cells is far less than the theoretical maximum value. For example, the radiative efficiency of the CH3NH3PbI3−xClx solar cell, which is a typical perovskite material and has the bandgap of 1.55 eV, is 31.5% according to Shockley-Queisser limit under AM1.5G illumination conditions [26,27]. The energy loss analysis can quantitatively illustrate the gap between the current PCE and the fundamental efficiency limit, pointing out the specific direction for targeted improvement of the performance. In this work, we perform a comprehensive analysis of energy losses affecting the performance of the CH3NH3PbI3−xClx perovskite-based solar cells under standard AM1.5G sunlight irradiance conditions by means of coupled optical and electrical modeling. Our theoretical model is validated by comparing the simulation results with the experimental data. On the basis of the accurate device modeling, each energy loss mechanism is properly considered in the planar perovskite solar cells and the value of each loss is quantitatively given. Extrinsic losses including optical losses and electrical losses, which can be determined by the cell configuration and the fabrication process, have been carried out in detail. Firstly, the device modeling is described in brief and the simulation results are compared with the experimental data to validate the device modeling. Then, the category of the energy losses is clarified and the corresponding analytical expression is presented. Subsequently, each energy loss mechanism is visibly visualized in a novel graphic representation, which involves all the incident solar radiation energy. We systematically analyze the extrinsic energy loss mechanisms in perovskite solar cells, finding out the dominant energy loss channel. Finally, we issue the guidelines on how to design and optimize for realization of the high efficiency perovskite solar cells and promote a roadmap to extend the PCE to 23%.

G (r ) =

∫E

∞

g

2 ⎯→ ⎯ ωIm(ε ) E (r , Eλ ) PFDAM1.5 (Eλ ) dEλ 2

(2)

where Eg is the bandgap of the photovoltaic material, ω is the angular frequency of the incident photon, Im(ε ) is the imaginary part of the permittivity, Eλ is the photon energy, and PFDAM1.5 is the photon flux density under AM1.5G conditions. For the electrical simulation, the device characteristics are governed by the semiconductor equations including Poisson, continuity, and drift-diffusion equations.

⎧− ∇•(ε∇ϕ) = q (p − n + ND − NA) ∂n 1 ⎪ = q ∇• Jn + G − R ∂t ⎪ ⎪ ∂p 1 = − q ∇• Jp + G − R ∂t ⎨ ⎪ Jn = −qμn n∇ϕ + qDn ∇n ⎪ ⎪ Jp = −qμp p∇ϕ − qDp ∇p ⎩

(3)

where ϕ is the electrostatic potential, ε is the dielectric constant of the semiconductor, n (p) is the electron (hole) concentration, ND (NA) is the donor (acceptor) doping concentration, q is the elementary charge, Jn (Jp) is the current density of electron (hole), μn (μp ) is the electron (hole) mobility, Dn (Dp) is the electron (hole) diffusion coefficient, G is the photogeneration rate extracted from optical simulation, and R is the total carrier recombination. There are four types of recombination mechanisms considered in the electrical simulation with the expression of

⎧ R = Rrad + RAug + RSRH + Rsurf ⎪ Rrad = B (np − n 2) i ⎪ 2 ⎪ ⎪ RAug = (Cn n + Cp p)(np − ni ) np − ni2 ⎨ RSRH = τp (n + nt ) + τn (p + pt ) ⎪ np − ni2 ⎪ ⎪ Rsurf = 1 (n + n ) + 1 (p + p ) ts ts ⎪ Sp Sn ⎩

(4)

where Rrad is the radiative recombination, B is the radiative recombination coefficient, RAug is the Auger recombination, Cn (Cp) is the electron (hole) Auger recombination coefficient, RSRH is the ShockleyRead-Hall recombination, τn (τp) is the electron (hole) lifetime, Rsurf is the surface recombination, Sn (Sp) is the surface recombination velocity of electron (hole), and ni is the intrinsic carrier concentration. Therefore, the coupled optical and electrical modeling can accurately elucidate the device performance of the solar cells. In order to validate our theoretical model, the experimental data reported by Liu et al. [31] was used as a comparison. The device configuration reported by Liu et al. is a planar heterojunction p-i-n structure with thin film stacks composed of glass/FTO(fluorinedoped tin oxide, 500 nm)/ compact TiO2(titanium dioxide, 50 nm)/ CH3NH3PbI3−xClx(methylammonium lead tri-iodide perovskite with

2. Device modeling and validation In this work, the coupled optical and electrical modeling is carried out to investigate the optical and electrical performance of the perovskite solar cells. This numerical method intends to separately address the optical and electrical properties of the solar cells. More details about this method can be found in our previous publications [28–30]. For the optical simulation, Maxwell's equations are the foundation to describe the light-matter interaction and enable to calculate the spectral features.

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Fig. 1. (a) Schematic diagram of the perovskite solar cells, (b) energy band structure of the device. Fig. 2. Comparison of J-V characteristics between simulation results and experimental data from reference [30] under illumination and dark conditions.

a mixed halide, 330 nm)/Spiro-OMeTAD(2,2',7,7'-tetrakis(N,N-p-dimethoxy-phenylamino)-9,9'-spirobifluorene, 350 nm)/Ag(silver, 200 nm). Because the thickness of the glass is much larger than that of the other layers, the glass is assumed to be perfectly transparent and the refractive index is taken as 1.5. Fig. 1(a) shows the simulated structure of the perovskite solar cells and the corresponding energy band diagram of the device is displayed in Fig. 1(b). It can be seen from the energy band structure that the photogenerated carriers can be effectively separated. The TiO2 layer and the Spiro-OMeTAD layer are often called electron transport material (ETM) and hole transport material (HTM) respectively. For optical calculation, the standard AM1.5 G spectrum is utilized as an incident light source. The optical parameters including wavelength-dependent refractive index (n) and extinction coefficient (k) for FTO, TiO2, CH3NH3PbI3−xClx, SpiroOMeTAD, and Ag are taken from literature [32,33]. Table 1 summaries the key parameters for electrical simulation [34,35]. The effect of surface recombination mainly occurs at the front interface (ETM/Perovskite) and the back interface (Perovskite/HTM). It is noticeable that the surface recombination velocity and the minority carrier lifetimes are the fitting parameters, which depends on the quality of the material and fabrication process. The surface recombination velocity we take is comparable to the literature [36]. Based on the physical parameters, the values of electron diffusion k T constants ( Dn = bq μn ) and electron diffusion lengths ( Ln = Dn τn )

and dark conditions. It is evident that the simulated results fit well with the experimental data under both light and dark conditions. Consequently, the remarkable match between simulations and experiments validates that our device modeling is reliable and feasible. 3. Description of energy loss mechanism in perovskite solar cells It is imperative to identify the energy loss mechanisms in perovskite solar cells and to take targeted strategy to improve the efficiency. According to the energy conservation law, solar radiation energy is composed of extracted power and the energy loss of the photovoltaic cell. The energy loss mechanisms mainly include below bandgap loss, thermalization loss, optical loss, recombination loss, and spatial relaxation loss. All the energy transfer processes in the photovoltaic cells are described in detail in the following. 3.1. Extracted power The PCE of the solar cells is defined as the ratio of the power extracted at the maximum output condition to the incident solar radiation power. It can be expressed as

are 0.052 cm2 s−1 and 1188 nm, which are similar to those used in the reference [37]. Fig. 2 shows the comparison of current-voltage (J-V) curves for the simulated results and the experimental data under both illumination

η=

ETM TiO2

Perovskite CH3NH3PbI3-xClx

HTM Spiro-OMeTAD

Thickness (nm) NA (cm−3) ND (cm−3) ε Eg (eV)

50 _ 1×1016 9 3.2

330 _ 1 × 1013 6.5 1.55

350 2 × 1018 _ 3 3

μn (cm2/V/s) μp (cm2/V/s)

0.017 2.11

2 2

1.64 4e-5

NC (cm−3) NV (cm−3) τn (s) τp (s) Radiative coefficient (cm3/s) Auger coefficient (cm6/s) Other parameters

1 1 1 1

2.2 × 1018 1.8 × 1019 2.73 × 10−7 2.73 × 10−7

1 1 1 1

× × × ×

1019 1016 10−5 10−6

−10

× × × ×

_ _

1.1 × 10 2.3 × 10–29

_ _

Series resistance (Ω cm2 )

3.5 2 × 104

Sn (cm/s) Sp (cm/s)

650

Shunt resistance (Ω cm2 )

Pin

=

Jsc Voc FF Pin

(5)

where Jmpp stands for the current density at the maximum output condition, Vmpp is for the voltage at the maximum power point, Pin is the incident solar radiation power, Jsc is the short-circuit current density, Voc is the open-circuit voltage, and FF is the fill factor. In general, the electrical power output of solar cells occurs at the maximum power point and can be expressed as

Table 1 Electrical simulation parameters of the perovskite solar cells. Material

Jmpp Vmpp

Pmpp = Pin η = Jmpp Vmpp

(6)

3.2. Below bandgap loss Photons with energy below the bandgap of the photovoltaic material do not have enough energy to excite an electron-hole pair. These photons either leave the cell or are absorbed to generate heat. In a word, these photons make no contribution to generate electricity for a photovoltaic cell. The below bandgap loss can be presented as

1020 1020 10−5 10−6

QbelowEg =

∫0

Eg

Eλ PFDAM1.5 (Eλ ) dEλ

(7)

3.3. Thermalization loss

650

Based on the principle of one photon generating an electron-hole 208

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pair, photons with energy above the bandgap of the photovoltaic material can generate charge carriers with high kinetic energy. However, these photoexcited carriers will decay from initial excited states to the band edges very quickly to reach their thermal equilibrium states and release their excess energy through interaction with crystal lattice. This process is called thermalization. The thermalization loss is the relaxed energy during the thermalization process and can be presented as

∫E

Qthermalization =

∞

g

Eλ PFDAM1.5 (Eλ ) A (Eλ )(Eλ − Eg ) dEλ

(8)

where A (Eλ ) is the energy-dependent absorption of the photovoltaic material. 3.4. Optical loss Photons with energy larger than the bandgap of the photovoltaic material are useful to be utilized by the photovoltaic cell. Since the existence of the optical loss, these photons can not be completely absorbed by the solar cells. The optical loss originates from the reflection, transmission, and parasitic absorption, reducing the photon absorption inside the device. It is worthy noticing that only the photons absorbed by the photovoltaic material can be used to generate electron-hole pairs. Therefore, the optical loss refers to the photons with energy above the bandgap not effectively absorbed by the photovoltaic material and can be expressed as

Qoptical =

∫E

∞

g

Eλ PFDAM1.5 (Eλ )(1 − A (Eλ )) dEλ

Fig. 3. Energy loss occurring in the perovskite solar cells. Different colors represent different energy loss mechanisms.

Qrecombination =

Qspatialrelaxation =

∫E

∞

g

PFDAM1.5 (Eλ ) dEλ

(10)

(11)

where Aave is the average absorption of the photovoltaic cell. The average absorption is a convenient representation for solar cells and is defined as

Aave =

∞ ∫Eg A (Eλ ) PFDAM1.5 (Eλ ) dEλ ∞ ∫Eg PFDAM1.5 (Eλ ) dEλ

(13)

Jmpp (Eg − qVmpp) q

(14)

On the basis of the theoretical device modeling, the energy loss of the perovskite solar cells is quantitatively discussed in the following. It is convenient to represent the energy losses via drawing a dual axis plot showing the cumulated incident photon flux density times electrical elementary charge as a function of photon energy and also cell current density as a function of cell voltage. Because all the incident solar radiation power is accounted for, the energy loss mechanisms are fully described. As depicted in Fig. 3, the total area represents all the incident solar radiation power. The areas with different tinted regions represent the energy loss attributed to different loss mechanisms. It is evident to identify each energy loss mechanism of the incident radiation power in the photo-electric conversion process of the perovskite solar cells. The quantification of different energy loss mechanisms is presented in Fig. 4. From the perspective of the total energy loss, the below bandgap loss is the dominant energy loss process for perovskite solar cells. This is because the large bandgap of the perovskite material (Eg = 1.55 eV ) limits the number of photons that can be effectively utilized. On the other hand, it also demonstrates that the single-junction perovskite solar cells are unable to utilize the full solar spectrum energy. This weakness is a major obstacle limiting the PCE of the single-junction perovskite solar

Actually, a fraction of incident photons will inevitably escape from the cell. The optical short-circuit current density refers to the photons absorbed by the photovoltaic cell generating the photocurrent and can be expressed as

Jopt = Jmax Aave

q

4. Results and discussion

(9)

Several key parameters should be mentioned in the discussion of the optical process. Under short-circuit conditions, if all the photons with energy above the bandgap of the photovoltaic material are absorbed to generate current, the maximum short-circuit current density can be presented as

Jmax = q

(Jopt − Jmpp) Eg

(12)

3.5. Recombination loss and Spatial relaxation loss The origin of both recombination loss and spatial relaxation loss is attributed to the internal carrier annihilation during the electrical transport process. Thus, both of them belong to electrical loss. A portion of photogenerated carriers may recombine when they are separated and collected in the transport process, resulting in recombination loss. Spatial relaxation loss refers to the photogenerated carriers losing potential energy jumping from band-edges to the contacts [38]. It should be noted that these two loss mechanisms strongly depend on the bias voltage of the solar cells. The proportion of these two energy losses changes once the bias voltage of the solar cells varies. Here we take into account four typical recombination mechanisms including radiative, Auger, Shockley-Read-Hall (SRH), and surface recombination. Simultaneously, series and shunt resistance effects are considered as well. The energy loss mechanisms associated to the bias voltage at maximum power point can be expressed as

Fig. 4. Quantification of energy loss occurring in the perovskite solar cells under AM1.5 illumination.

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cells. Based on the quantitative analysis of the energy losses in perovskite solar cells, it motivates us to develop a high efficient perovskite-based energy device. For the purpose of reducing the below bandgap loss, photon upconversion technique is an efficient strategy to be adopted in perovskite solar cells [39]. In order to improve the solar energy utilization efficiency, broadening the absorption spectrum or utilizing the full solar spectrum energy is an available way. For the former, the perovskitebased tandem solar cells, such as perovskite/silicon tandem cells and perovskite-perovsikte tandem photovoltaic cells, become a research hotpot [40–43]. For the latter, we can combine the perovskite solar cells with thermoelectric device to form photovoltaic-thermoelectric hybrid system, enabling full spectrum utilization of solar energy [44]. Therefore, it is natural to think of integrating the novel advanced techniques to perovskite solar cells for designing a high efficient hybrid energy system via analysis of energy losses. These advanced approaches not only are beneficial to utilize more solar spectrum energy for perovskite-based device but also offer the direction towards for the design of highly efficient perovskite-based energy device. From the viewpoint of improving the PCE of a single-junction perovskite solar cell, below bandgap loss and thermalization loss belong to intrinsic loss, which is unavoidable. In reality, reducing the extrinsic loss may become a feasible way. Hence, it is essential to carry on a detail investigation on analysis of the optical and electrical loss. The dominant factors limiting the PCE of the perovskite solar cells can be carried out through a careful analysis, enabling us to adopt appropriate strategies. Optical loss in perovskite solar cells includes reflection loss and parasitic absorption loss. It can reduce the photons absorption inside the device, resulting in a considerable decrease of Jopt . As a result, the short-circuit current density ( Jsc ) and the PCE of the perovskite solar cells will decrease as well. It can be found in Fig. 4 that optical loss in perovskite solar cells accounts for 11.3% of the total incident solar radiative energy. It is promising to reduce optical loss to improve the PCE of the perovskite solar cells. Fig. 5 shows the spectral absorption of the perovskite solar cells obtained from optical calculation. In this figure, the reflection loss and parasitic absorption of the solar cells are also depicted. We focus on the optical loss in the wavelength range of 300–800 nm, which is determined by the bandgap of the perovskite material (1.55 eV). As seen in Fig. 5, although the perovskite absorption occupies the primary part of the total incident light, there is still much room to enhance absorption of the perovskite solar cells. The reflection loss and parasitic absorption of FTO occur in the total wavelength range. The presence of TiO2 leads to a reduction of absorption in the short wavelength range of λ < 360 nm due to its optical parameters. In contrast, the parasitic absorption caused by Spiro-OMeTAD occurs in the long wavelength range of λ > 650 nm . The light absorption of Ag is negligible.

Fig. 6. Quantification of the optical loss in the perovskite solar cells.

Fig. 6 shows a quantitative optical loss in the perovskite solar cells. These values are calculated from absorption spectrum. The reflection loss and parasitic absorption in FTO, TiO2, Spiro-OMeTAD, and Ag layers are represented as an equivalent current density if these lost photons could be converted into photocurrent. The bandgap of perovskite layer is 1.55 eV, so the maximum short-circuit current density Jm is 27.23 mA/cm2 under the AM1.5 G conditions. As shown in Fig. 6, the effective optical absorption in the perovskite layer, which is the same as the optical short-circuit current density, is 21.61 mA/cm2. Moreover, the reflection loss is 2.48 mA/cm2 whereas the total parasitic absorption is 3.14 mA/cm2. The value of the parasitic absorption occurring in the FTO, TiO2, Spiro-OMeTAD, and Ag layers is 2.38, 0.12, 0.52, and 0.12 mA/cm2, respectively. It is obvious that the major parasitic light absorption is induced by the FTO and Spiro-OMeTAD layers. The parasitic light absorption in the TiO2 and Ag layers is quite small and can be neglected. Overall, reflection loss and parasitic absorption in FTO and Spiro-OMeTAD layers are the dominant factors in optical loss limiting the absorption of the perovskite solar cells. This suggests that optical optimization design is an effective approach to improve the performance of the perovskite solar cells. In order to decrease the reflection, an alternative way is anti-reflection coating or nanostructures. For the sake of reducing the parasitic absorption, we can reduce the thickness of the FTO and Spiro-OMeTAD layers. Electrical loss in perovskite solar cells includes recombination loss and spatial relaxation loss. It originates from radiative recombination, Auger recombination, Shockley-Read-Hall (SRH) recombination, surface recombination, and series and shunt resistance effects. As seen in Fig. 4, electrical loss accounts for 17.7% in perovskite solar cells. During the transport process of the photogenerated carries, there are many factors affecting the electrical loss in perovskite solar cells. These factors come from different loss mechanisms and are extremely complex, meaning that the cumulative impact from each recombination mechanism is not a simple and additive process. Therefore, we emphasize the individual effect of each mechanism to identify the key factors affecting the performance of perovskite solar cells. Fig. 7 shows the energy conversion efficiency of the perovskite solar cell after taking into account the individual effect of each loss mechanism. On the one hand, we exclude the concerned loss mechanism after considering all the recombination mechanisms. As seen from Fig. 7, the PCE of the perovskite solar cells is hardly changed when eliminating the radiative recombination and Auger recombination. Once the SRH recombination, surface recombination, and resistive effects are removed, the PCE of the perovskite solar cells is improved, particularly for surface recombination. This indicates that SRH recombination, surface recombination and resistive effects are the dominant loss mechanisms in electrical loss limiting the PCE of the perovskite solar cells. When the surface recombination is excluded, the PCE of the perovskite solar cells increases to the maximal value, meaning that surface recombination has the greatest impact on the performance among them. On the other hand, we only consider one kind of recombination mechanisms. As shown in

Fig. 5. Spectral absorption of each layer in the perovskite solar cells.

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Fig. 7. Energy conversion efficiency at different loss mechanisms.

Fig. 7, the PCE of the perovskite solar cells decreases to the minimum value when the surface recombination is merely considered. The effects of different recombination mechanisms affecting the PCE of the perovskite solar cells can be sorted as follows: Surface > SRH > Radiative > Auger. This phenomenon also demonstrates that surface recombination plays the most critical role in determining the device performance of the perovskite solar cells. There are three dominant factors including SRH recombination, surface recombination, and resistive effects that contribute to decrease the PCE of the perovskite solar cells. It is necessary to examine the extent of these factors on the PCE of the perovskite solar cells. It is well known that SRH recombination is induced via traps or defects of the crystal and depends on the quality of the material. In order to make it easier to compare with experimental data, here we use carrier diffusion length (Ln ) to represent the absorber quality. Fig. 8(a) shows the PCE of the perovskite solar cells as a function of the diffusion length. Apparently, with the increase of the diffusion length, namely improving the quality of the perovskite film, the PCE of the perovskite solar cells increases. When the diffusion length is less than the thickness of the perovskite thin film, the PCE significantly increases by improving the quality of the perovskite film. However, once the diffusion length is larger than the thickness of the perovskite thin film, the PCE increases slowly with increasing the diffusion length. Therefore, we infer that when the diffusion length is larger enough, the PCE will saturate to a maximum value and grow in a small-amplitude. In other words, the simulation results indicates that the experimental data of Ln = 1180 nm is long enough for highly efficient perovskite solar cells. Further improvement in perovskite material quality results in less benefits for improving the PCE. Thus, the material quality with diffusion length of 1180 nm is suitable for highly efficient perovskite solar cells with thickness of 330 nm. Fig. 8(b) illustrates the PCE of the perovskite solar cells as a function of the surface recombination velocity. As the surface recombination velocity increases, the PCE slowly decreases at first and then a significant drop occurs. When the surface recombination velocity is larger than 10 cm/s, the PCE of the perovskite solar cells jumps significantly. This demonstrates that the PCE of the perovskite solar cells is sensitive to the value of the surface recombination velocity. The surface recombination is a critical factor in achieving high efficiency of the perovskite solar cells. The surface passivation or interfacial engineering introduces an explicit direction for boosting the PCE of the perovskite solar cells. Fig. 8(c) shows the PCE of the perovskite solar cells as a function of the series resistance. As shown in Fig. 8(c), the PCE of the perovskite solar cells linearly decreases with the increment of the series resistance. A high series resistance seriously restricts the device performance. The slope of the descendent curve is 0.4%, meaning that the reduction of the series resistance can evidently improve the PCE of

Fig. 8. Energy conversion efficiency as a function of (a) diffusion length, (b) surface recombination velocity, (c) series resistance.

the perovskite solar cells. The series resistance stems from several aspects of contributions, such as the contact resistance, bulk resistance of the ETM, absorber and HTM as well as their interface resistance. Improving the conductivity of the ETM, perovskite, and HTM or reducing the interface resistance is an effective way to reduce the series resistance, thereby leading to improve the PCE of the perovskite solar cells. The metal ion doped ETM or HTM is a promising way to improve the conductivity and has been widely used [45–47]. In addition, interfacial engineering can also optimize the interface resistance [48]. In summary, surface recombination and resistive effects are directly attributable to electrical loss, limiting the PCE of the perovskite solar cells. It is urgent to both mitigate the surface recombination and diminish the series resistance to reduce the electrical loss for the improvement of the PCE in the perovskite solar cells. It should be pointed out that the interfacial engineering can not only mitigate the surface recombination via passivation but also reduce the series resistance by optimizing the interface resistance. The interfacial engineering may be 211

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dominant loss process for perovskite solar cells, which accounts for 41.1%. The weakness of the single-junction perovskite solar cells has been totally revealed. This suggests that novel advanced techniques should be integrated to the perovskites solar cells to form hybrid energy devices. For example, the perovskite solar cell is a reasonable selection for tandem solar cell or photovoltaic-thermoelectric hybrid system. Simultaneously, photon upconversion technique is an efficient strategy to be employed in perovskite solar cells. Moreover, we also investigate the roles of optical loss and electrical loss in detail from the perspective of boosting the PCE of the perovskite solar cells. Based on the coupled optical and electrical modeling, we identify that three factors, such as insufficient light absorption in perovskite layer, surface recombination, and series resistance, are the dominant loss contributors limiting the PCE of the perovskite solar cells. Our results suggest that more attention should be paid to enhance the optical absorption in perovskite layer, mitigate the surface recombination by passivation, and reduce the resistance in the future. Based on these guidelines, we simply design and optimize the CH3NH3PbI3−xClx solar cell with thickness of 330 nm, of which the PCE can facilely reach to 23%. A better strategy may further increase the performance of the perovskite solar cells. Our work not only indicates the feasibility of the perovskite-based hybrid energy system but also designates an unambiguous direction for the improvement of the PCE of the perovskite solar cells.

Fig. 9. Roadmap for improving the PCE of the perovskite solar cells to 23%.

a paramount approach to improve the PCE of the perovskite solar cells in the future. From the thorough analysis of the optical and electrical loss mechanisms, we have shown that the main loss mechanisms for the perovskite solar cells are: i) reflection loss and parasitic absorption in FTO and Spiro-OMeTAD layers, namely insufficient efficient light absorption in perovskite layer, ii) surface recombination, iii) series resistance. Aimed at solving these problems, a series of optimization designs are proposed. Fig. 9 indicates the roadmap for improving the PCE of the perovskite solar cells. When the thickness of the FTO and SpiroOMeTAD layers are declined to 100 nm, the parasitic absorption in FTO and Spiro-OMeTAD layers can be reduced significantly, which makes the PCE of the perovskite solar cells rise from 15.8% to 17.8%. Light trapping is proved to be beneficial for boosting the PCE of the solar cells by capturing more light into the active layers. Here we propose a light trapping structure with top dielectric grating and back metallic grating to promote the light absorption in the perovskite layer. The period ( p ) of the grating is 500 nm and the width (w ) of the grating is 250 nm. Noticeably, the perovskite layer is flat in our light trapping structure, meaning that no surface area is increased in photocurrent-generating layer, thereby not affecting the recombination properties of the cell. The PCE of the perovskite solar cells reaches to 18.9% by the light trapping structure. If an efficient surface passivation strategy is introduced to suppress the surface recombination velocity to 10 cm/s, the PCE of the perovskite solar cells can reach to 21.3%. By the same token, once the series resistance is reduced from 3.5 to 0.42 Ω cm2 , which is identical to GaAs solar cells, the PCE of the perovskite solar cells can approach to 23%. It should be noted that the thickness of the 23% efficient perovskite solar cells is 330 nm and the light trapping structure is not completely optimized. Increasing the thickness of the perovskite absorber and optimizing the light trapping structure can further improve the PCE of the perovskite solar cells. Therefore, it is expected that the PCE of the perovskite solar cells can be further increased to the Shockley-Queisser limit with a better light trapping structure, a more effective the surface passivation method, and a smaller the series resistance.

Acknowledgment We are grateful to the financial support from the National Natural Science Foundation of China (Grant N0. 51336003). References [1] A. Kojima, K. Teshima, T. Miyasaka, Y. Shirai, Novel photoelectrochemical cell with mesoscopic electrodes sensitized by lead-halide compounds, in: Proceedings of the 210th ESC Meeting Abstracts, 2006, p. 397. [2] A. Kojima, K. Teshima, Y. Shirai, T. Miyasaka, Organometal halide perovskites as visible-light sensitizers for photovoltaic cells, J. Am. Chem. Soc. 131 (17) (2009) 6050–6051. [3] M.A. Green, Y. Hishikawa, W. Warta, E.D. Dunlop, D.H. Levi, J. Hohl-Ebinger, A.W.Y. Ho-Baillie, Solar cell efficiency tables (version 50), Prog. Photovolt.: Res. Appl. 25 (7) (2017) 668–676. [4] Z. Xiao, Q. Dong, C. Bi, Y. Shao, Y. Yuan, J. Huang, Solvent annealing of perovskiteinduced crystal growth for photovoltaic-device efficiency enhancement, Adv. Mater. 26 (37) (2014) 6503–6509. [5] Y. Takahashi, H. Hasegawa, Y. Takahashi, T. Inabe, Hall mobility in tin iodide perovskite CH3NH3SnI3: evidence for a doped semiconductor, J. Solid State Chem. 205 (2013) 39–43. [6] L.J. Phillips, A.M. Rashed, R.E. Treharne, J. Kay, P. Yates, I.Z. Mitrovic, A. Weerakkody, S. Hall, K. Durose, Maximizing the optical performance of planar CH3NH3PbI3 hybrid perovskite heterojunction stacks, Sol. Energy Mater. Sol. Cells 147 (2016) 327–333. [7] C.S. Ponseca Jr., T.J. Savenije, M. Abdellah, K. Zheng, A. Yartsev, T. Pascher, T. Harlang, P. Chabera, T. Pullerits, A. Stepanov, J.P. Wolf, V. Sundstrom, Organometal halide perovskite solar cell materials rationalized: ultrafast charge generation, high and microsecond-long balanced mobilities, and slow recombination, J. Am. Chem. Soc. 136 (2014) 5189–5192. [8] Z. Lin, J. Chang, J. Xiao, H. Zhu, Q.H. Xu, C. Zhang, J. Ouyang, Y. Hao, Interface studies of the planar heterojunction perovskite solar cells, Sol. Energy Mater. Sol. Cells 157 (2016) 783–790. [9] H.H. Fang, F. Wang, S. Adjokatse, N. Zhao, J. Even, M.A. Loi, Photoexcitation dynamics in solutin-processed formamidinium lead iodide perovskite thin films for solar cell applications, Light Sci. Appl. 5 (2016) e16056. [10] G. Adam, M. Kaltenbrunner, E.D. Glowacki, D.H. Apaydin, M.S. White, H. Heilbrunner, S. Tombe, P. Stadler, B. Ernecker, C.W. Klampfl, N.S. Sariciftci, M.C. Scharber, Solution processed perovskite solar cells using highly conductive PEDOT:PSS interfacial layer, Sol. Energy Mater. Sol. Cells 157 (2016) 318–325. [11] J. Seo, J.H. Noh, S.I. Seok, Rational strategies for efficient perovskite solar cells, Acc. Chem. Res. 49 (2016) 562–572. [12] Y. Hou, W. Chen, D. Baran, T. Stubhan, N.A. Luechinger, B. Hartmeier, N. Li, Overcoming the interface losses in planar heterojunction perovskite-based solar cells, Adv. Mater. 28 (2016) 5112–5120. [13] M.A. Green, A. Ho-Baillie, H.J. Snaith, The emergence of perovskite solar cells, Nat. Photonics 8 (2014) 506–514. [14] H.S. Jung, N.G. Park, Perovskite solar cells: from materials to device, Small 11 (2015) 10–25. [15] H.D. Kim, H. Ohkita, H. Benten, S. Ito, Photovoltaic performance of perovskite solar cells with different grain sizes, Adv. Mater. 28 (2016) 917–922.

5. Conclusions In conclusion, a quantitative energy loss analysis for planar perovskite solar cells has been performed by means of the coupled optical and electrical modeling. The device modeling is validated by comparing the simulation results with the experimental data. The intrinsic and extrinsic losses occurring in single-junction perovskite solar cells have been taken into account. Accounted for all the incident solar radiation energy, we explore five energy loss mechanisms including thermalization loss, below bandgap loss, optical loss, recombination loss, and spatial relaxation loss. From the perspective of the total energy losses, the results have demonstrated that the below bandgap loss is the 212

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4115–4121. [35] C. Wehrenfennig, M. Liu, H.J. Snaith, M.B. Johnston, L.M. Herz, Charge-carrier dynamics in vapour-deposited films of the organolead halide perovskite CH3NH3PbI3−xClx, Energy Environ. Sci. 7 (7) (2014) 2269–2275. [36] Y. Yang, M. Yang, D.T. Moore, Y. Yan, E.M. Miller, K. Zhu, M.C. Beard, Top and bottom surface limit carrier lifetime in lead iodide perovskite films, Nat. Energy 2 (2017) 16207. [37] S.D. Stranks, G.E. Eperon, G. Grancini, C. Menelaou, M.J.P. Alcocer, T. Leijtens, L.M. Herz, A. Petrozza, H.J. Snaith, Electron-hole diffusion lengths exceeding 1 μm in an organomental trihalide perovskite absorber, Science 342 (6156) (2013) 341–344. [38] D. Ding, S.R. Johnson, S.Q. Yu, S.N. Wu, Y.H. Zhang, A semi-analytical model for semiconductor solar cells, J. Appl. Phys. 110 (2011) 123104. [39] X. Chen, W. Xu, H. Song, C. Chen, H. Xia, Y. Zhu, D. Zhou, S. Cui, Q. Dai, J. Zhang, Highly efficient LiYF4:Yb3+, Er3+ upconversion single crystal under solar cell spectrum excitation and photovoltaic application, ACS Appl. Mater. Interfaces 8 (2016) 9071–9079. [40] J. Werner, L. Barraud, A. Walter, M. Brauninger, F. Sahli, D. Sacchetto, N. Tetreault, B. Paviet-Salomon, S.J. Moon, C. Allebe, M. Despeisse, S. Nicolay, S.D. Wolf, B. Niesen, C. Ballif, Efficient near-infrared-transparent perovskite solar cells enabling direct comparison of 4-terminal and monolithic perovskite/silicon tandem cells, ACS Energy Lett. 1 (2) (2016) 474–480. [41] K.A. Bush, A.F. Palmstrom, Z.J. Yu, M. Boccard, R. Cheacharoen, J.P. Mailoa, D.P. McMeekin, R.L.Z. Hoye, C.D. Bailie, T. Leijtens, I.M. Peters, M.C. Minichetti, N. Rolston, R. Prasanna, S. Sofia, D. Harwood, W. Ma, F. Moghadam, H.J. Snaith, T. Buonassisi, Z.C. Holman, S.F. Bent, M.D. McGehee, 23.6%-efficient monolithic perovskite/silicon tandem solar cells with improved stability, Nat. Energy 2 (2017) 17009. [42] B. Chen, Y. Bai, Z. Yu, T. Li, X. Zheng, Q. Dong, L. Shen, M. Boccard, A. Cruverman, Z. Holman, J. Huang, Efficient semitransparent perovskite solar cells for 23.0%efficiency perovskite/silicon four-terminal tandem cells, Adv. Energy Mater. 6 (2016) 1601128. [43] G.E. Eperon, T. Leijtens, K.A. Bush, R. Prasanna, T. Green, J.T.W. Wang, D.P. McMeekin, G. Volonakis, R.L. Milot, R. May, A. Palmstrom, D.J. Slotcavage, R.A. Belisle, J.B. Patel, E.S. Parrott, R.J. Sutton, W. Ma, F. Moghadam, B. Conings, A. Babayigit, H.G. Boyen, S. Bent, F. Giustino, L.M. Herz, M.B. Johnston, M.D. McGehee, H.J. Snaith, Perovskite-perovskite tandem photovoltaics with optimized band gaps, Science 354 (6314) (2016) 861–865. [44] J. Zhang, Y. Xuan, L. Yang, A novel choice for the photovoltaic-thermoelectric hybrid system: the perovskite solar cells, Int. J. Energy Res. 40 (10) (2016) 1400–1409. [45] H. Zhang, J. Shi, X. Xu, L. Zhu, Y. Luo, D. Li, Q. Meng, Mg-doped TiO2 boosts the efficiency of planar perovskite solar cells to exceed 19%, J. Mater. Chem. A 4 (40) (2016) 15383–15389. [46] D. Liu, S. Li, P. Zhang, Y. Wang, R. Zhang, H. Sarvari, F. Wang, J. Wu, Z. Wang, Z.D. Chen, Efficient planar heterojunction perovskite solar cells with Li-doped compact TiO2 layer, Nano Energy 31 (2017) 462–468. [47] P. Wang, J. Zhang, Z. Zeng, R. Chen, X. Huang, L. Wang, J. Xu, Z. Hu, Y. Zhu, Copper iodide as a potential low-cost dopant for spiroMeOTAD in perovskite solar cells, J. Mater. Chem. C 4 (38) (2016) 9003–9008. [48] H. Zhou, Q. Chen, G. Li, S. Luo, T. Song, H.S. Duan, Z. Hong, J. You, Y. Liu, Y. Yang, Interface engineering of highly efficient perovskite solar cells, Science 345 (6196) (2014) 542–546.

[16] H.S. Kim, I. Mora-Sero, V. Gonzalez-Pedro, F. Fabregat-Santiago, E.J. Juarez-Perez, N.G. Park, J. Bisquert, Mechanism of carrier accumulation in perovskite thin-absorber solar cells, Nat. Commun. 4 (2013) 2242. [17] E. Edri, S. Kirmayer, S. Mukhopadhyay, K. Gartsman, G. Hodes, D. Cahen, Elucidating the charge carrier separation and working mechanism of CH3NH3PbI3−xClx perovskite solar cells, Nat. Commun. 5 (2014) 3461. [18] M. Hu, C. Bi, Y. Yuan, Z. Xiao, Q. Dong, Y. Shao, J. Huang, Distinct exciton dissociation behavior of organolead trihalide perovskite and excitonic semiconductors studied in the same system, Small 11 (2015) 2164–2169. [19] V. D'Innocenzo, G. Grancini, M.J. Alcocer, A.R.S. Kandada, S.D. Stranks, M.M. Lee, G. Lanzani, H.J. Snaith, A. Petrozza, Excitons versus free charges in organo-lead trihalide perovskites, Nat. Commun. 5 (2015) 3586. [20] S. Collavini, S.F. Volker, J.L. Delgado, Understanding the outstanding power conversion efficiency of perovskite-based solar cells, Angew. Chem. Int. Ed. 54 (2015) 9757–9759. [21] 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. [22] T. Minemoto, M. Murata, Theoretical analysis on effect of band offsets in perovskite solar cells, Sol. Energy Mater. Sol. Cells 133 (2015) 8–14. [23] T.S. Sherkar, C. Momblona, L. Gil-Escrig, H.J. Bolink, L.J.A. Koster, Improving perovskite solar cells: insights from a validated device model, Adv. Energy Mater. (2017) 1602432, http://dx.doi.org/10.1002/aenm.201602432. [24] L. Huang, X. Sun, C. Li, R. Xu, J. Xu, Y. Du, Y. Wu, J. Ni, H. Cai, J. Li, Z. Hu, J. Zhang, Electron transport layer-free planar perovskite solar cells: further performance enhancement perspective from device simulation, Sol. Energy Mater. Sol. Cells 157 (2016) 1038–1047. [25] K. Hwang, Y.S. Jung, Y.J. Heo, F.H. Scholes, S.E. Watkins, J. Subbiah, D.J. Jones, D.Y. Kim, D. Vak, Toward large scale roll-to-roll production of fully printed perovskite solar cells, Adv. Mater. 27 (2015) 1241–1247. [26] W. Shockley, H.J. Queisser, Detailed balance limit of efficiency of p-n junction solar cells, J. Appl. Phys. 32 (1961) 510–519. [27] S. Ruhle, Tabulated values of the Shockley-Queisser limit for single junction solar cells, Sol. Energy 130 (2016) 139–147. [28] Y. Da, Y. Xuan, Role of surface recombination in affecting the efficiency of nanostructured thin-film solar cells, Opt. Express 21 (106) (2013) A1065–A1077. [29] Y. Da, Y. Xuan, Effect of temperature on performance of nanostructured silicon thinfilm solar cells, Sol. Energy 115 (2015) 109–119. [30] Y. Da, Y. Xuan, Q. Li, From light trapping to solar energy utilization: a novel photovoltaic-thermoelectric hybrid system to fully utilize solar spectrum, Energy 95 (2016) 200–210. [31] M. Liu, M.B. Johnston, H.J. Snaith, Efficient planar heterojunction perovskite solar cells by vapour deposition, Nature 501 (7467) (2013) 395–398. [32] J.M. Ball, S.D. Stranks, M.T. Horantner, S. Huttner, W. Zhang, E.J.W. Crossland, I. Ramirez, M. Riede, M.B. Johnston, R.H. Friend, H.J. Snaith, Optical properties and limiting photocurrent of thin-film perovskite solar cells, Energy Environ. Sci. 8 (2) (2015) 602–609. [33] C.W. Chen, S.Y. Hsiao, C.Y. Chen, H.W. Kang, Z.Y. Huang, H.W. Lin, Optical properties of organometal halide perovskite thin films and general device structure design rules for perovskite single and tandem solar cells, J. Mater. Chem. A 3 (17) (2015) 9152–9159. [34] S. Agarwal, M. Seetharaman, N.K. Kumawat, A.S. Subbiah, S.K. Sarkar, D. Kabra, M.A.G. Namboothiry, P.R. Nair, On the uniqueness of ideality factor and voltage exponent of perovskite-based solar cells, J. Phys. Chem. Lett. 5 (23) (2014)

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