Halide Perovskites for Tandem Solar Cells - The ... - ACS Publications

Apr 19, 2017 - Biography. Jin-Wook Lee is a postdoctoral researcher in Prof. Yang Yang's group at the University of California Los Angeles (UCLA). He ...
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Halide Perovskites for Tandem Solar Cells Jin-Wook Lee,† Yao-Tsung Hsieh,† Nicholas De Marco,† Sang-Hoon Bae,† Qifeng Han, and Yang Yang* Department of Materials Science and Engineering and California NanoSystems Institute, University of California, Los Angeles, California 90095, United States ABSTRACT: Perovskite solar cells have become one of the strongest candidates for nextgeneration solar energy technologies. A myriad of beneficial optoelectronic properties of the perovskite materials have enabled superb power conversion efficiencies (PCE) exceeding 22% for a single-junction device. The high PCE achievable via low processing costs and relatively high variability in optical properties have opened new possibilities for perovskites in tandem solar cells. In this Perspective, we will discuss current research trends in fabricating tandem perovskite-based solar cells in combination with a variety of mature photovoltaic devices such as organic, silicon, and Cu(In,Ga)(S,Se)2 (CIGS) solar cells. Characteristic features and present limitations of each tandem cell will be discussed and elaborated upon. Finally, key issues for further improvement and the future outlook will be discussed.

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hotovoltaic technologies began attracting remarkable attention when William Shockley and Hans J. Queisser calculated the theoretical efficiency limit of the single p−n junction solar cell, coined the Shockley−Queisser limit or detailed balance limit.1 Assuming the sun as a blackbody (6000 K) and the absence of nonradiative recombination, a maximum power conversion efficiency (PCE) was calculated to be approximately 33% based on a single p−n junction with bandgap (Eg) of 1.1−1.4 eV. This indicated that ca. 77% of the energy coming from the sun cannot be utilized. The PCE is a combination of current (short-circuit current) and voltage (open-circuit voltage) from a cell; both of them are correlated with the bandgap of the material. A major part of the loss was attributed to spectral losses,1 which is caused by fundamental optical responses of semiconducting absorbers. Photons with lower energy than that of the absorber bandgap (Eg) cannot be absorbed, while photons with higher energy than Eg ultimately produce charge carriers having the same energy as the Eg. Persistent research efforts have been devoted to surpassing the Shockley−Queisser limit, from which several advanced concepts have been devised to reduce spectral losses, including hot carriers,2 multiple exciton generation (MEG)3 and tandem designs.4 So far, however, only the tandem solar cells have shown practical efficiencies higher than the Shockley−Queisser limit among them.5 Tandem solar cells were devised to minimize spectral losses. As seen in Figure 1a, in single-junction devices, photons with energy lower than Eg will not be absorbed by the absorber, whereas photons with energy higher than Eg will produce hot carriers, which will be thermalized to band edge by phonon interaction while emitting excessive energy as a heat. As a result, more than 50% of the energy losses arise by the spectral losses.1 To reduce the spectral losses, tandem solar cells incorporate multiple junctions (Figure 1b). The tandem devices consist of two junctions having one relatively larger and one smaller Eg, such that the higher energy photon will be absorbed by the top © 2017 American Chemical Society

Figure 1. (a) Schematic illustration showing light absorption in single and multijunction solar cells. (b) Typical spectral response of top (high Eg ∼ 1.9 eV) and bottom (low Eg ∼ 1.0 eV) devices.

absorber with higher Eg, and the lower-energy photons will pass through the high Eg cell and become absorbed by the bottom lower Eg cell. This will utilize a broader range of the solar spectrum to maximize absorption with minimized energy losses (Figure 1b). For tandem solar cells based on two junctions under standard light intensity (1 sun), the optimal combination of bandgaps was calculated to be ca. 1.9 and 1.0 eV, which can Received: February 15, 2017 Accepted: April 19, 2017 Published: April 19, 2017 1999

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has shown high VOC with small potential loss (∼0.39 V).10,15 Furthermore, it can be processed via low temperature solution processes (1.5 eV) compared to typical inorganic light absorbers such as silicon (1.1 eV) and CuInGaSe2 (1.02−1.68 eV).14 The Eg of the PVSK materials can be easily tuned by controlling halide composition over the whole visible wavelength region, and it

An understanding of organic material properties is a necessary first step in designing OSC/PVSK tandem cells. The absorption range of halide PVSK materials ranges from approximately 300 to 800 nm, depending on the composition of the PVSK material.23−25 The synthetic variability of organic materials makes them strong candidates as a supplementary absorber layer to PVSK.21 Since the electrical properties of organic materials depend on the electronic structure of molecular and polymeric materials, introducing small changes into the molecular structure or composition remarkably changes the electrical properties and enables Eg engineering of organic materials. Thus, we can design organic molecules with an optimal absorption spectrum for light harvesting with halide PVSK materials. In general, the electron-donating group elevates the HOMO energy level, whereas the electronwithdrawing group lowers the LUMO energy level. Also, the 2000

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Figure 3. Approaches to make low Eg polymers. (a) Aromatic and quinoid resonance structure. (b) Stabilized quinoid resonance structure. (c) Donor−acceptor copolymer by Yamamoto. (d) Donor−acceptor copolymer by Havinga. (e) Eg lowering by donor−acceptor interaction. (f) Approach to combine the electron-accepting and stabilizing of the quinoid resonance structure. Reprinted with permission from ref 26. Copyright 2015 American Chemical Society.

Figure 4. OPV/PVSK monolithic tandem solar cells (a) The solid lines indicate the external quantum efficiency of the OPV and the PVSK cells in the tandem cells. Dashed lines are for the single-junction reference devices. (b) J−V characteristics of tandem devices using different conditions. (c) The band alignment of OPV/PVSK tandem cells. (d) The structure of low Eg polymer, PBSeDTEG8. Reprinted with permission from ref 31. Copyright 2015 Royal Society of Chemistry.

deposit or facilitate bonding between organic materials. Instead, the molecules and polymers can be easily dissolved in solvents, per their polarity, and form into a solid state thin film. However, due to such a low formation energy, stability issues can arise since the lower activation energy leads to the organic materials being more susceptible to their bonding being interrupted. This can accelerate degradation of the active layer during processing and under device operation. There is another limitation with OSC/PVSK tandems due to the tightly bound electron−hole pair, or Frenkel exciton, of organic semiconductors. The exciton is a molecular excited state that can hop from molecule to molecule or from chain to chain, which is the same mechanism of charge carrier transport in organic materials. Thus, the excitonic state determines the optoelectronic properties of organic semiconductors. The

energy difference between the HOMO and LUMO increases as a result of the decrease of the length of conjugation.27 For example, the so-called push−pull effect stabilizes the quinoid resonance structure and can enable the design of a polymer having a Eg as low as 1 eV.26 (Figure 3) The formation energy of PVSK is low compared to other inorganic solar absorbers, where most inorganic solar materials require high energy to form a suitable phase for photovoltaics.14 The OSC is an appealing choice in terms of its low temperature processing requirements, since organic materials need similar levels of formation energy as halide PVSK materials. Organic materials are bound by intermolecular forces, such as hydrogen bonding, dipole−dipole interactions, and dispersion forces, which are not strong compared to materials with ionic or covalent bonding.28 Therefore, we do not need high energies to 2001

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Figure 5. Integration of PVSK and BHJ. (a) Schematic energy level diagrams of the integrated PVSK/(DOR3T-TBDT:PC71BM) device and (b) External quantum efficiency (EQE) curves of corresponding devices. (c) Schematic energy level diagrams of the integrated PVSK/M3 or M4 device and (d) EQE curves of corresponding devices. Reprinted with permission from refs 32 (Copyright 2015 American Chemical Society) and 34 (Copyright 2016 American Chemical Society).

additional near-infrared (NIR) light to current, which lead to an improvement in short-circuit current density (JSC) from 19.3 mA/cm2 to 21.2 mA/cm2 (Figure 5b). They claimed that the BHJ layer can function as an absorption layer as well as a charge transporting layer. In 2016, J. Kim et al. reported a similar concept work based on the integration of PVSK materials and BHJ to harvest the long wavelength region.33 They integrated a diketopyrrolopyrrole (DPP)-based low Eg polymer (LBP) DTPDPP2T-TT (TT) and [6,6]-phenyl C71 butyric acid methyl ester (PC71BM) as the BHJ layer with MAPbI3. They claimed that high electron transport from the BHJ can play an important role for high FF and VOC. Later, M. Cheng et al. also showed an integrated structure by using other small molecules based on benzo[1,2b:4,5b′]-dithiophene (BDT) flanked by phenoxazine (POZ) units.34 (FAPbI3)0.85(MAPbBr3)0.15, was used for more optimal band alignment (Figure 5c), and the integration helped to extend the long wavelength light harvesting up to 900 nm (Figure 5d). The BHJ was composed of small molecules and PC70BM, which enables exciton dissociation in organic materials. The PCE was enhanced from 15.0% to 16.2% by utilizing a PVSK/ BHJ system with improved JSC from 20 mA/cm2 to 24 mA/ cm.2 Considering the limitation of single-junction OSC devices, the PVSK/BHJ system might be a promising approach to enhance the efficiency of PVSK solar cells. Silicon/PVSK Tandem Cells: A Promising Approach to Reduce the Cost-per-Kilowatt of Silicon-Based Solar Cells. Silicon, the current photovoltaic material of choice due to its wellestablished industry and relatively high efficiencies (∼25.6% PCE), is the current standard for terrestrial photovoltaic applications. However, its efficiency has largely plateaued over the past several years. Thus, reducing the cost-per-kilowatt of silicon-based solar relies majorly on manufacturing rather than device performance improvements. One promising approach to overcome these limitations is to construct a tandem device composed of a silicon and another material with complementary absorption, which is tandem solar cells. Silicon has a Eg

Frenkel exciton is the primary species of organic semiconductors with a binding energy of ∼1 eV. This is a result of a low dielectric constant (εr = 2−4), since the Coulombic interaction between the electron and hole is strong.29 Accordingly, charge carrier transport is quite slow compared with other inorganic semiconductors due to the strong interaction. In general, while the mobility of inorganic materials ranges from 102 to 104 cm2/(V s) at room temperature, organic materials show ∼1 cm2/(V s), which eventually limits the performance of organic based solar cells.30 Thus, tandem cells with OSCs are always accompanied by slow charge carrier transport from organic materials. It is critical that we find answers to these issues generated by the tightly bound electron−hole pair to remove restrictions on the potential of organic materials as tandem solar cells with PVSK solar cells. Chen et al. demonstrated a good example of organic/PVSK monolithic tandem cells31 utilizing CH3NH3PbI3 (MAPbI3), an IR-sensitive block copolymer, and PBSeDTEG8, to increase the absorption range up to 950 nm (Figure 4). They designed an interconnecting layer to facilitate recombination between cells consisting of PFN/TiO2/PEDOT:PSS PH500/PEDOT:PSS AI 4083 double hole and double electron transporting layers. PCEs of 9.08% for the MAPbI3 single junction and 6.62% for the PBSeDTEG8 single junction were obtained, while a PCE of 10.23% was demonstrated for a two terminal OSC/PVSK tandem solar cell. However, the PCE demonstrated is lower than that of recently reported single PVSK cells, which was due to limitation in process temperature and solvents. The Organic/PVSK Bilayer System: Toward an Enhanced Absorption Range. While conventional tandem cells consist of two or more subcells, the bilayer system is essentially one cell with two stacked absorber materials (organic and PVSK). In 2014, Y. Liu et al. first reported the concept of a PVSK/bulkheterojunction (BHJ) integration to extend the absorption range.32 They utilized MAPbI3 and the small molecule DOR3T-TBDT as a donor in the BHJ (Figure 5a). This contributed the overall device photocurrent by converting 2002

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of ∼1.1 eV, absorbing lower energy photons, which means that the second absorber material ought to have a higher Eg to efficiently collect higher energy photons. Because of the wellestablished silicon industries, relatively active research works have been done for the development of silicon/PVSK tandem solar cells.

Reducing the cost-per-kilowatt of silicon-based solar relies majorly on manufacturing rather than device performance improvements.

For monolithic two-terminal tandem cells, there is a required current matching between the subcells for the device to operate effectively. In addition, the processing temperature of the PVSK subcell atop silicon must be 500 °C. This monolithic integration provides the challenge of producing a mechanism of electrical coupling between subcells that is simultaneously optically transparent to long wavelength (infrared) light to the bottom cell. Mailoa et al. were the first to demonstrate a two-terminal silicon/PVSK tandem device using a silicon tunnel junction.36 Using silicon, with an indirect Eg, allows for electrical coupling of the subcells with minimal parasitic absorption loss. Moreover, the band alignment of the PVSK subcell TiO2 selective contact and silicon conduction band alleviates the necessity for use of a transparent conducting oxide as a recombination layer (e.g., ITO). Charge neutrality is established via tunneling of the electrons and holes through the tunnel junction to n-type silicon base and p-type emitter, where recombination can readily occur. The device and band structures are shown in Figure 6a. The MAPbI3-based siliconPVSK tandem could achieve an efficiency of 13.7% with an open-circuit voltage of 1.65 V using the silicon tunnel junction monolithic integration (Figure 6b). The authors claim that the lower efficiency is due to use of materials that are not of the highest quality, both for PVSK and silicon subcells, and that by using higher quality materials the device has the potential to achieve efficiencies up to 29%. Moreover, Albrecht et al. introduced low-temperature monolithic devices employing a SnO2 layer deposited via atomic layer deposition (ALD) to achieve a stabilized efficiency of 18% (Figure 6c,d).35 The authors claim this low-temperature process to be compatible with the low-temperature requirements of the highest performing crystalline silicon single-junction devices. Werner and co-workers have recently shown higher efficiency monolithic tandem cells using a low-temperature process consisting of a sputtered indium−zinc-oxide (IZO) recombination layer and inorganic PC61BM/PEIE and SpiroOMeTAD selective contacts.37 These devices yielded efficiencies up to 21.2 and 19.2% for 0.17 and 1.22 cm2 device areas, respectively, with no hysteresis, for an architecture of IZO/ PEIE/PCBM/MAPbI3/Spiro-OMeTAD/MoOx/IO:H/ITO. Werner et al. later built upon this work by introducing rear side texturing to the silicon bottom cell to increase light harvesting capability in the NIR region.38 This was accomplished via a standard double-sided texturization in a KOH-based solution.

Figure 6. (a) The device structure of a two-terminal monolithically grown PVSK/Si multijunction solar cell with an n-type Si base. The polished SEM image (500 nm scale bar) and corresponding band diagram of the PVSK/silicon cell interface. (b) J−V curve of the twoterminal PVSK/silicon multijunction solar cell under AM1.5G illumination. (c) J−V curves of single-junction and monolithic tandem solar cells. Inset shows cross-sectional SEM image of the tandem device. (d) External quantum efficiency of the individual subcell in the monolithic tandem device with AR coating. Reprinted with permission from refs 36 (Copyright 2015 AIP Publishing LLC) and 35 (Copyright 2015 Royal Society of Chemistry).

Furthermore, the electron selective contact of the PVSK subcell was improved upon through use of sputtered SnO2 between the PVSK and PCBM/PEIE layers to enhance uniformity and further prevent shunting pathways. Ultimately, a higher quality PVSK subcell was achieved with a steady-state efficiency of 16.4% (compared to 14.5% in the previous work). Along with the rear-side texturization, an efficiency for the monolithic tandem device of 20.5% was achieved, compared to a previous 19.2% for polished surfaces and unoptimized top cell. Recently, McGehee’s group at Stanford has announced a monolithic two-terminal silicon-PVSK tandem reaching an efficiency of 23.6% for 1 cm2 active area.39 The device consists of a c-Si bottom cell from Holman group at ASU, a NiO hole contact, ITO/LiF transparent top contact, and PVSK film with composition FA0.83Cs0.17Pb(I0.83Br0.17)3. The authors claim that this device to be very stable, and we are awaiting formal publication of this work. Bailie and co-workers demonstrated mechanically stacked silicon-PVSK tandem devices (four terminal) using lower quality multicrystalline silicon (mc-Si) as the bottom cell.40 The lower quality mc-Si was used in an effort to reduce costs of the expensive single-crystalline silicon (sc-Si), and supplementing the poor efficiency with use of the PVSK addition in tandem cells. Constructing a mc-Si-PVSK tandem device improved the performance of the stand-alone mc-Si device from 11.4% to 17% PCE for the tandem cell. The PVSK top cell consisted of mesoporous (mp)-TiO2/MAPbI3/Spiro-OMeTAD/AgNW, where a silver nanowire (AgNW) mesh was used as the transparent top electrode. The AgNW mesh provided a low sheet resistance of 12.4 Ω-cm2 with 90% transmission between the 530−730 nm range of the spectrum, and falls to 87% up to 1000 nm. In addition, the electrode must be applied without damaging the sensitive PVSK and Spiro-OMeTAD layers, 2003

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Figure 7. Device structure and corresponding J−V curves and external quantum efficiency spectra of four terminal tandem solar cells reported by (a−c) Chen et al.41 and (d−f) Wener et al.37 Reprinted with permission from refs 41 (Copyright 2016 John Wiley and Sons) and 37 (Copyright 2016 American Chemical Society).

application of the approach in the commercial field is still under debate due to use of the expensive dichroic mirror. The optimal Eg of the PVSK subcell ought to be around 1.8 eV for optimal efficiency.40 Surprisingly, most the PVSK compositions discussed in the above tandem devices utilize the traditional MAPbI3 PVSK composition, which possesses an Eg of ∼1.55−1.6 eV. This is likely due to photosegregation of mixed halide PVSK that occurs readily in mixed I and Br PVSKs.44 Several studies have been conducted to obtain a more optimal PVSK Eg for tandem cells. Beal et al. demonstrated PVSKs with composition CsPbBrI2 with an Eg of 1.9 eV and enhanced photo- and thermal stability against phase separation.45 However, this material was only able to achieve a stabilized efficiency of 6.5%, which requires further work to boost efficiency while stabilizing the large Eg PVSK. McMeekin and co-workers demonstrated the potential of mixed compositions for tandem cells using a composition of FA0.83Cs0.17Pb(I0.6Br0.4)3 with an optical Eg of approximately 1.74 eV,46 which is close to the ideal top-cell Eg of 1.8 eV. Solar cells employing this PVSK absorber composition achieved open circuit voltages up to 1.2 V and a PCE of 17% on small areas. By considering the individual efficiencies of the subcells, the authors suggest that by combining the 17% PVSK cell with a 19% efficient silicon cell, a tandem device has the potential to achieve >25% PCE in an ideal four-terminal configuration. A similar composition was recently demonstrated by McGehee group, as discussed in the previous section, consisting of the PVSK absorber composition FA0.83Cs0.17Pb(I0.83Br0.17)3. It will be of paramount importance to develop a stable PVSK composition with a near-optimal Eg to achieve high performance tandem devices. CIGS/PVSK Tandem Cells: Another Promising Branch of Tandem Solar Cells. Chalcopyrite (CIGS) compounds have proven to be a promising material for photovoltaics. Currently, the highest efficiency of CIGS solar cells has reached 22.6%.6 CIGS is still one of the photovoltaic technologies providing commercialized high-efficiency products that can compete with the prevalent silicon wafer-based photovoltaics.6 CIGS compounds are stable inorganic quaternary alloys with direct Eg. To achieve superior photovoltaic performance requires the ratio of Ga/(Ga+In) to be finely controlled between 0.25 and

which was achieved by a spray deposition technique. Later, Chen et al. demonstrated the potential of obtaining an efficiency of 23% for a silicon-PVSK four-terminal tandem by filtering light through a PVSK top cell onto a silicon bottom cell (Figure 7a−c).41 The PVSK subcell used a thin semitransparent 1 nm Cu/7 nm Au transparent electrode, providing a sheet resistance of 23 Ω-cm2. A 40 nm-thick layer of BCP was also added to improve transmittance (by ∼10%) in the NIR region. The PVSK subcell achieved a single-junction efficiency of 16.5% with a device area of 0.075 cm2 and architecture of ITO/PTAA/MAPbI3/PCBM/C60/BCP/Cu/ Au. The silicon subcell was enhanced by applying a doublelayer antireflection coating at the front side, a MgF2 back reflector layer at the rear side, and replacing ITO with the higher carrier mobility IZO. The authors ultimately demonstrated a summed 23% efficiency for a silicon-PVSK and a 6.5% efficient silicon cell after filtering light using the PVSK cell onto silicon. Werner and collaborators achieved efficiencies of 23% and 25.2% for 4-terminal PVSK/SHJ tandem cells with device areas of 1.015 cm2 and 0.25 cm2 PVSK top cell aperture areas, respectively, using the same SnO2-based low temperature semitransparent PVSK subcell (Figure 7d-f).38 Because the same top cell was used for both the monolithic and mechanically stacked tandem cells, a direct comparison between tandem cell architectures could be made in terms of parasitic absorption and light management requirements. The authors note that for the monolithic tandem cell, a larger Eg top cell is necessary to achieve optimal performance, as it is currentlimited by the bottom cell. Another promising approach has been demonstrated using an optical splitting system. Uzu et al. used a dichroic mirror to split and guide the light to two separate solar cells responding to corresponding wavelength regions.42 They combined a monocrystalline silicon heterojunction solar cell and MAPbI3 PVSK solar cell, in which short wavelength light (550 nm) was incident to the silicon solar cell. They achieved total PCE of 28%, which is the highest PCE reported for four terminal tandem solar cell incorporating PVSK. Takumi et al. used a similar approach, where an infrared dye-sensitized solar cell was used instead of the silicon solar cell and achieved PCE of 21.5%.43 However, 2004

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0.35, corresponding to a Eg of 1.1 to 1.24 eV. With its excellent absorption coefficient, only approximately 2 μm of the CIGS thin film is needed to absorb most of the incident sunlight, which significantly decreases the demand of absorbing materials. Another promising feature of CIGS is that it can be integrated onto flexible substrates without a significant efficiency loss.47 This capability can theoretically lower production costs by using techniques such as roll-to-roll manufacturing, thus offering the possibility for commercialized large-scale applications. In past years, many efforts have been devoted to improving the efficiency of CIGS solar cells, especially CIGS absorber materials development. However, the progress in enhancing device efficiency has not been significant.6 In order to boost the efficiency of CIGS solar cells beyond their practical limit, one promising approach is to combine CIGS solar cells with suitable absorbers to form a tandem device. According to calculations, the optimum Eg for bottom cells in a double junction is 0.9−1.2 eV.4,48 With the capability to adjust the Eg by tuning Ga/(Ga+In) and S/(S+Se) ratios, CIGS becomes an ideal candidate to work as the bottom cell in tandem structure. By operating with PVSK solar cells, a CIGS/PVSK tandem device can extend the absorption range further into the spectrum for more light harvesting. The advantage of combining CIGS and PVSK photovoltaic technologies has been realized for many years. Nonetheless, in contrast to several encouraging results of silicon/PVSK tandem devices, the CIGS/PVSK tandem solar cells still have not demonstrated their superiority over single-junction solar cells.

Figure 8. (a) Schematic device structure and SEM cross-sectional image of the photovoltaic device. (b) J−V curve and (c) external quantum efficiency of top illuminated PVSK, CIGS, and CIGS cell under the PVSK device. Reprinted with permission from ref 50. Copyright 2015 American Chemical Society.

On the other hand, the high-performance transparent conducting oxides (ITO, AZO, and In2O3:H) deposited through sputtering processes have been introduced and commonly applied on semitransparent PVSK solar cells.51−54 In order to adopt this approach, it is inevitable to deposit additional buffer layers (e.g., zinc oxide nanoparticles or MoO3), which serve as sacrificial layers to prevent mechanical destruction during sputtering. Optimization of the buffer layer becomes necessary to minimize optical and electrical losses. To date, the highest efficiency of 4-terminal CIGS/PVSK tandem solar cells is 22.1%, which was achieved in 2016.53 In the same year, McGehee and co-workers proposed an alternative approach to laminate a silver nanowire mesh as the top electrode, as applied to a silicon-PVSK tandem cell described above.40 This advanced process can be conducted in room temperature without any solvents involved. The auuthors reported an efficiency of 18.6% for the four-terminal CIGS/ PVSK tandem device. However, the sophisticated transferring process would affect the reproducibility, resulting in a variation of device efficiency. To date, the development of the monolithic CIGS/PVSK tandem structure has been retarded for some time. Compared with the mechanically stacking architecture, the monolithic design on a single substrate would be gifted with better device efficiency because of the minimum number of ancillary layers for optical and parasitic resistance losses. Yet, the lack of appropriate recombination layers and a fully compatible fabrication sequence for all layers becomes the major hindrance in realizing high performance monolithic CIGS/PVSK tandem solar cells. In the work done by the IBM research group, which is the only published work successfully demonstrating a monolithic CIGS/PVSK tandem device, the intrinsic ZnO layer was removed from the CIGS solar cell since it can cause a chemical instability of PVSK materials at processing temperatures above 60 °C.49 It is understandable that the ZnO-free

A CIGS/PVSK tandem device can extend the absorption range further into the spectrum for more light harvesting. A typical tandem structure of the CIGS/PVSK solar cell is the same as for the silicon/PVSK tandem devices. It consists of one wide-Eg PVSK solar cell upon a low-Eg CIGS solar cell, and these two single-junction devices are connected either by monolithic integration (two-terminal) or mechanically stacking (four-terminal). The incident solar light first passes through the PVSK top cell and then reaches the bottom CIGS cell. Regarding the realization of high efficiency CIGS/PVSK tandem solar cells, the top PVSK cell plays an essential role. The key aspect of this subject is to achieve the high performance near-infrared transparent PVSK solar cells. Reducing the thickness of the metal electrode is a simple and straightforward route to increase optical transmission, even if it has to compensate for higher resistance. The first monolithic CIGS/PVSK tandem solar cell with a 10.9% efficiency was published by an IBM research group in 2015.49 A Ca-based top electrode was employed, composed of thermally evaporated Ca (10−15 nm) and bathocuproine (5 nm), that contributed the serious parasitic optical losses. The authors claimed that the device efficiency could be augmented to 25% once state-of-art CIGS and PVSK technologies are integrated together perfectly. Later, Yang and co-workers first exhibited the dielectric/metal/ dielectric (MoOx/Ag/MoOx) structure (DMD structure) in transparent electrode for PVSK solar cells (Figure 8).50 Based on the thermal evaporation technique for DMD electrode fabrication, they demonstrated a four-terminal CIGS/PVSK tandem device, showing a device efficiency of 15.5%. 2005

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enormous potential for large-scale commercialization over other PVSK-based tandem technologies. In late 2015, researchers were able to demonstrate all-PVSK tandem solar cells with high open circuit voltage (>1.8 V).59,60 At that early stage, however, the device efficiency was limited by the inferior current density because two subcells can only use analogous absorbers. A major challenge to deliver high efficiency all-PVSK tandem devices comes from the difficulty of synthesizing stable low-Eg PVSKs for highly efficient photonto-electron conversion. Pb-based PVSKs are relatively stable with halide atoms, but the corresponding Eg can merely be adjusted downward to ∼1.48 eV. The theoretical Eg’s are located between 1.57 and 2.29 eV for MAPbX3, and 1.48−2.23 eV for FAPbX3 (X = Cl−, Br−, and I−). So far, the most effective and widely adopted approach to lower PVSK Eg is to replace Pb with Sn in PVSK compounds. This method is rationally accessible since Sn and Pb are both from IVA group and they have the similar ionic radii (Sn2+ 1.35 Å and Pb2+ 1.49 Å), which allows for easy substitution without large lattice distortion. Several works have been published on Sn-based PVSK solar cells. In 2014, Snaith and co-workers first demonstrated a leadfree organic−inorganic tin halide PVSK (MASnI3).61 Their results confirmed that a pure tin-based PVSK with a Eg of 1.23 eV was able to deliver an efficiency over 6% on a mesoporous TiO2 scaffold. After that, Kanatzidis and co-workers reported a systematic investment for the anomalous Eg behavior in mixed Sn and Pb PVSKs (Figure 9).62 The authors claimed that the PVSK Eg could be successfully reduced to 1.17 eV with a device efficiency over 7% by varying the Pb-to-Sn ratio in MA(Pb,Sn)I3. Later, Jen and co-workers improved the PCE to 10.1% based on Pb/Sn alloy PVSKs (MAPb1−aSnaI3−‑xClx) with an Eg of 1.38 eV, which was grown on the planar heterojunction architecture.63 The superior efficiency was credited to a good film quality and better coverage of PVSKs. In 2016, Jen’s group demonstrated higher efficiency and stable Pb−Sn binary PVSK solar cells, and further realized highperformance all-PVSK tandem solar cells in a four-terminal structure.64 By incorporating formamidium cations, the stable mixed cation Sn-based PVSK (MA0.5FA0.5Pb0.75Sn0.25I3) presented a stabilized PCE of 14.19% with an Eg of 1.33 eV. The PCE of a four-terminal all-PVSK tandem solar cell was pushed to 19.08%, which consisted of a 1.33 eV low-Eg PVSK with a semitransparent MAPbI3 solar cell. Very recently, Snaith and co-workers revealed a notable result by accomplishing a

CIGS structure would ensure the tandem device from damage; however, it also ruined the entirety of the CIGS solar cell, which is a large trade-off with the high efficiency of CIGS. As a result, while the top PVSK performance is noteworthy, it is also crucial to preserve the merits of CIGS solar cells within the tandem structure. Especially for the monolithic device architecture, the overall device performance might be limited by the reduced efficiency of the bottom cells for current matching. To prevent this condition, the low temperature processing for PVSK solar cell fabrication and the careful design for chemically stable recombination layers are essential. Once high-quality transparent top electrodes, suitable recombination layers, and compatible fabrication sequences become reachable, all achievements from the state-of-the-art PVSK and CIGS solar cells, such as Eg engineering, materials stability, and efficiency enhancement, can be transferred to the CIGS/PVSK monolithic tandem solar cells. All-PVSK Tandem Solar Cells: An Emerging Technology. To date, the high-efficiencies of single-junction PVSK devices mainly stem from methylammonium lead iodide and its relatives, with substitution of formamidium, cesium, and/or bromide. As this group of PVSK, with a Eg range between 1.5 and 1.7 eV, exhibits excellent optoelectronic properties, it is instinctive to pair them with low-Eg solar cells for tandem devices, as we have discussed in previous sections. Recently, the range of PVSK Eg has been extended due to noteworthy progress on compositional engineering and advanced deposition techniques.46,55−58 These developments have opened up an opportunity for researchers to explore all-PVSK tandem solar cells. Recently, considerable research works have been conducted for low-Eg as well as wide-Eg PVSK materials. With

With rewards of facile solution processability and low materials cost, all-PVSK tandem solar cells are considered to possess enormous potential for large-scale commercialization over other PVSK-based tandem technologies. rewards of facile solution processability and low materials cost, all-PVSK tandem solar cells are considered to possess

Figure 9. Absorption spectra and schematic energy level diagram of the MASn1−xPbxI3 solid solution PVSKs. (a) Absorption spectra and (b) schematic energy level diagram of the MASn1−xPbxI3 solid solution PVSKs. Reprinted with permission from ref 62. Copyright 2014 American Chemical Society. 2006

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monolithic all-PVSK tandem solar cell.65 They successfully developed a FA0.75Cs0.25Pb0.5Sn0.5I3 absorber with an Eg of 1.2 eV. This PVSK device alone showed a PCE of 14.8% with excellent stability. By applying this infrared−absorbing PVSK with a 1.8 eV FA0.83Cs0.17Pb(I0.5Br0.5)3 film, they eventually established a current-matched monolithic all-PVSK tandem solar cell. The monolithic and four-terminal tandem devices upgraded the PCE to 17% and 20.3%, respectively (Figure 10).

using doped organic semiconductors.70 The main advantage of using organic semiconductors is that it can be deposited by a simple vacuum technique at low fabrication temperature, which prevents chemical and physical interactions with the underlying layers. By using the doped organic semiconductors as charged recombination layers, the high efficiency all-PVSK monolithic tandem device composed of Cs0.15FA0.85Pb(I0.3Br0.7)3 and MAPbI3 has been achieved with average PCE of 15%. Considering the high production cost of conventional inorganic solar cells, the all-PVSK tandem solar cells might be a promising approach for development of low cost and superhigh efficient tandem solar cells. However, as mentioned above, stabilization of low Eg PVSK and design of proper device architecture and process might be prerequisite for the development of high efficiency all-PVSK tandem solar cells. We expect that incremental research works on all-PVSK tandem solar cells will deliver another striking breakthrough for tandem solar cells in the near future. Breaking the Barrier: Achieving Market Competitive PVSKBased Tandem Solar Cells. The PCE of a PVSK-based tandem device is still lower than the highest reported PCE of a singlejunction PVSK solar cell. We believe this is a result of device architecture and the constituent materials of PVSK solar cells that have been optimized for single junction use, but not for tandem application. So far, most of the PVSK-based tandem solar cells incorporate similar device architecture and materials used for single-junction PVSK solar cells. For the case of tandem application, however, one should consider different design rules, which require development of new materials and processes specialized for tandem application. In this section, we describe the key issues in device design and material properties for PVSK-based tandem solar cells. The keys to reaching high efficiencies rely on (i) reducing parasitic absorption, (ii) optical management, (iii) using electrode(s) with high transparency in the NIR that can be processed without damaging the underlying PVSK layers, and (iv) improving PVSK single-junction performances for larger device areas with optimal Eg’s. Reducing Parasitic Absorption: Parasitic absorption from the necessary selective contacts of the PVSK subcell poses the first issue for obtaining high tandem cell efficiencies. The top selective contact must possess an Eg as large as possible so as not to absorb any light before entering the PVSK film. The bottom selective contact would ideally have an Eg identical to that of PVSK, and may be larger but not smaller, so as not to absorb any light passing through the PVSK cell that is to be collected by the bottom subcell. Common selective contacts include TiO2 (Eg = 3.2 eV), Spiro-OMeTAD (Eg = 3.1 eV), PCBM (Eg = 1.9 eV), and PEDOT:PSS. Of these, TiO2 and Spiro-OMeTAD both have Eg’s large enough to prevent parasitic absorption; however, Spiro-OMeTAD is commonly doped with Li-based salts, which allows it to absorb largely throughout the UV to IR regions of the spectrum. For the case of a two-terminal device, according to the optical simulation by Filipič et al., in which light was incident to spiro-MeOTAD on top of a PVSK layer, 2.4 mA/cm2 of JSC loss was found to occur by the spiro-MeOTAD layer.18 Albrecht et al. also pointed out that not only the optimization of thickness and Eg of PVSK layer but also the elimination of parasitic absorption by spiroMeOTAD are key to achieve efficiency higher than 30%.19 For

Figure 10. (a) Schematics showing two-terminal tandem PVSK solar cell concepts. (b) Scanning electron micrograph of the two-terminal PVSK−PVSK tandem. (c) Scanned current−voltage characteristics under AM 1.5G illumination of the two-terminal PVSK−PVSK tandem, of the 1.2 eV solar cell, and the ITO-capped 1.8 eV solar cell. (d) External quantum efficiency spectra for the subcells. Reprinted with permission from ref 65. Copyright 2016 American Association for the Advancement of Science.

While the performance of low-Eg Sn-based PVSK devices is progressing, there is still a discernible gap compared with the Pb-based PVSK devices. The nature of the stable Sn oxidation state is the root of the problem. When Sn exists within the PVSK compounds as Sn2+ cation, it can be easily oxidized to Sn4+, as that is its most stable state. This proclivity to oxidize would induce a thermodynamic instability of crystal, and consequently device degradation becomes inevitable. As a result, it is critical to overcome the stability issue brought by the Sn incorporation. It has been confirmed that by hybridizing with Cs and formamidium cations, degradation from photo and moisture effects can be alleviated.66,67 In another work, by using hydrazine to create a reducing atmosphere, researchers have successfully suppressed the formation of Sn4+ species during the preparation of a Sn-based PVSK device.68 Recently, an antioxidant, ascorbic acid, has also been introduced as an additive to increase the stability and efficiency of Sn-based PVSK solar cells in which the antioxidant can impede the oxidation of a Sn-containing precursor solution.69 Besides the stability issue, the charge recombination layers might limit further progress of tandem device performance. A suitable design for band alignment and compatible fabrication sequences is essential. High optical transparent conducting oxides (such as ITO) are commonly used as the charge recombination layer in tandem solar cells;65 however, people have to pay more attention to the compromise between the deposition processes and the underlying layers since the materials for PVSK solar cell are not as rigid as materials for inorganic subcells. An alternative strategy has been proposed 2007

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used to protect the underlying layers as mentioned above.37 It will be of great importance to develop techniques to utilize materials with high transparency and high mobility that do not compromise the Jsc, Voc, or FF of a PVSK device. PVSK Single Junction: Improving the PVSK single-junction cell efficiency, with favorable Egs near 1.8 eV, over larger wafersized device areas will be an important factor for further development of PVSK-based tandem solar cells. So far, the Eg tuning has mainly been done for single-junction use, which, however, will need more delicate tuning for tandem use. Furthermore, stability of the large (mixed halide) and low Eg (Sn-containg) PVSK is a crucial issue for realistic commercialization of PVSK-based tandem solar cells. Currently, the highest single-junction PVSK devices are based on mixedcomposition PVSKs and mesoporous titania scaffolds. Ultimately, mixed-compositions must be fine-tuned in terms of efficiency, Eg, and processing considerations. The high temperatures of mesoporous scaffolds will prevent their use in tandem devices. Therefore, new low temperature processing techniques, potentially utilizing different materials, must be developed. Larger device areas must also be developed to reduce complexity in module design, and may be accomplished using alternative solution-processing techniques such as printing, doctor-blading, and more. Finally, incorporation of state-of-the-art technologies for management of crystal growth and charge carrier manipulation in single-junction PVSK solar cells will enable higher quality of PVSK top cells.25,76−78 Regardless of the remarkable progresses in PVSK singlejunction devices in recent years, relatively less attention has been paid to their application in tandem solar cells. Although the PVSK single-junction solar cell itself has shown competitiveness against other presenting photovoltaics, its combination with well-established industries will open up new businesses that can penetrate into the market over a short period to provide highly efficient and cost-effective energy sources. Recent progress on PVSK-based tandem solar cells has shown noteworthy potential in terms of both PCE and manufacturing costs. With consideration of the aforementioned issues and incorporation of state-of-the-art single-junction PVSK technologies, we believe that a PCE of 30% is a realistic goal for the near future.

this reason, similarly PCBMs, which are typical top selective contacts in inverted PVSK solar cells, are poor candidates for top selective contacts in tandem architectures. Ideally these materials ought to be minimized or replaced altogether with more appropriate Eg materials to dispose of all parasitic absorption. Potential candidates may include CuSCN, SnO2, and NiO.71−73 However, careful attention must be paid to the processing techniques employed for these materials so as not to damage the underlying layers. Optical Management: Light management is another critical component to achieving high efficiency tandem devices. The absorption depth of a material provides the distance that light may penetrate the material for which its intensity drops by 1/e (∼36%) of its original intensity. Typically, the thickness of the optimized PVSK film is lower than that of its absorption depth, especially in the long wavelength region. As such, not all the light can be effectively absorbed. For instance, MAPbI3 has an absorption depth of 398 nm for λ = 750 nm, but increases to 855 nm for a wavelength increase of only 20 nm to λ = 770 nm.7 In single-junction PVSK devices, metallic counterelectrodes such as Ag act as rear reflectors to reflect and recycle the light through the material a second time to enhance absorption. However, these metals cannot be incorporated on the bottom of the PVSK subcell, as light must still be able to pass through toward the bottom silicon subcell. Furthermore, with a flat top PVSK subcell, JSC of around 4−7 mA/cm2 is typically lost by light reflection.19,74,75 Several computational simulation results demonstrated that the absolute efficiency of 2−4% can be enhanced with improved light reflection by texturing the front surface.71,74,75 The surface texturing of the silicon subcell would be an effective technique to create lighttrapping capabilities within the device. In general, high efficiency inorganic bottom cells incorporate a textured surface to enhance the light trapping, which, however, can cause difficulty in forming a uniform and compact layer on it using a solution process (typically spin-coating process). Optical modeling with consideration of practical process should be performed to solve the light management issue. Electrode Transparency: In traditional single-junction PVSK solar cells, the absorber grows on the transparent FTO (or ITO) glass substrate with an opaque metal back contact (considered as the superstrate configuration). For application in tandem solar cells, it becomes a primary requirement for top PVSK cells that the opaque metal back contact has to be replaced with the transparent conducting electrode. Such transparent electrodes with low sheet resistance and high transmittance are designated to allow the penetration of long wavelength photons (typically 700−1200 nm) as much as possible. Moreover, it has to be designed carefully so that the fabrication process for the top electrode would not impair functional layers within the PVSK cell, as underlying PVSK materials and adjacent charge transporting layers usually contain organic components that are not as concrete as inorganic layers. Implementing electrodes with high transparency and high mobility that do not damage the underlying layers during processing is a large challenge for obtaining high efficiencies. For example, sputtering of the common ITO transparent electrode can damage the underlying hole-transporting and PVSK layer, and its high annealing temperatures would further damage the device. AgNWs, also discussed above, have been shown to be effective, but present the potential issue of forming silver halide complexes, such as AgI, by reacting with ions migrated from the PVSK layer. In general, a MoOx layer is



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yang Yang: 0000-0001-8833-7641 Author Contributions †

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest. Biographies Jin-Wook Lee is a postdoctoral researcher in Prof. Yang Yang’s group at the University of California Los Angeles (UCLA). He got his Ph.D. in Energy Science from Sungkyunkwan University (SKKU), Korea, in 2016 under the supervision of Prof. Nam-Gyu Park. His research has been focused on the development of highly efficient and stable perovskite solar cells by materials and process engineering. Yao-Tsung Hsieh is a Ph.D. candidate at the University of California Los Angeles (UCLA) in Prof. Yang Yang’s group. He received his B.S. degree in materials science and engineering from National Cheng 2008

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(9) Zhou, H.; Chen, Q.; Li, G.; Luo, S.; Song, T.-b.; Duan, H.-S.; Hong, Z.; You, J.; Liu, Y.; Yang, Y. Interface engineering of highly efficient perovskite solar cells. Science 2014, 345 (6196), 542−546. (10) Saliba, M.; Matsui, T.; Domanski, K.; Seo, J.-Y.; Ummadisingu, A.; Zakeeruddin, S. M.; Correa-Baena, J.-P.; Tress, W. R.; Abate, A.; Hagfeldt, A.; et al. Incorporation of rubidium cations into perovskite solar cells improves photovoltaic performance. Science 2016, 354 (6309), 206−209. (11) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-range balanced electron-and holetransport lengths in organic-inorganic CH3NH3PbI3. Science 2013, 342 (6156), 344−347. (12) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-hole diffusion lengths exceeding 1 micrometer in an organometal trihalide perovskite absorber. Science 2013, 342 (6156), 341−344. (13) Lee, J. W.; Seol, D. J.; Cho, A. N.; Park, N. G. High-Efficiency Perovskite Solar Cells Based on the Black Polymorph of HC(NH2)2PbI3. Adv. Mater. 2014, 26 (29), 4991−4998. (14) Bae, S.-H.; Zhao, H.; Hsieh, Y.-T.; Zuo, L.; De Marco, N.; Rim, Y. S.; Li, G.; Yang, Y. Printable Solar Cells from Advanced SolutionProcessible Materials. Chem. 2016, 1 (2), 197−219. (15) Noh, J. H.; Im, S. H.; Heo, J. H.; Mandal, T. N.; Seok, S. I. Chemical management for colorful, efficient, and stable inorganic− organic hybrid nanostructured solar cells. Nano Lett. 2013, 13 (4), 1764−1769. (16) Chen, Q.; Zhou, H.; Hong, Z.; Luo, S.; Duan, H.-S.; Wang, H.H.; Liu, Y.; Li, G.; Yang, Y. Planar heterojunction perovskite solar cells via vapor-assisted solution process. J. Am. Chem. Soc. 2014, 136 (2), 622−625. (17) Li, Y.; Meng, L.; Yang, Y. M.; Xu, G.; Hong, Z.; Chen, Q.; You, J.; Li, G.; Yang, Y.; Li, Y. High-efficiency robust perovskite solar cells on ultrathin flexible substrates. Nat. Commun. 2016, 7, 10214. (18) Filipič, M.; Löper, P.; Niesen, B.; De Wolf, S.; Krč, J.; Ballif, C.; Topič, M. CH3NH3PbI3 perovskite/silicon tandem solar cells: characterization based optical simulations. Opt. Express 2015, 23 (7), A263−A278. (19) Albrecht, S.; Saliba, M.; Correa-Baena, J.-P.; Jäger, K.; Korte, L.; Hagfeldt, A.; Grätzel, M.; Rech, B. Towards optical optimization of planar monolithic perovskite/silicon-heterojunction tandem solar cells. J. Opt. 2016, 18 (6), 064012. (20) Pope, M.; Swenberg, C. E. Electronic Processes in Organic Crystals and Polymers; Oxford University Press: Oxford, U.K., 1999. (21) Scharber, M. C.; Mühlbacher, D.; Koppe, M.; Denk, P.; Waldauf, C.; Heeger, A. J.; Brabec, C. J. Design rules for donors in bulk-heterojunction solar cellsTowards 10% energy-conversion efficiency. Adv. Mater. 2006, 18 (6), 789−794. (22) Yu, Z.; Smith, D.; Saxena, A.; Martin, R.; Bishop, A. Molecular geometry fluctuation model for the mobility of conjugated polymers. Phys. Rev. Lett. 2000, 84 (4), 721. (23) Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric engineering of metal-halide perovskites with tunable optical band gaps. Nat. Commun. 2014, 5, 5757. (24) Chen, Q.; De Marco, N.; Yang, Y. M.; Song, T.-B.; Chen, C.-C.; Zhao, H.; Hong, Z.; Zhou, H.; Yang, Y. Under the spotlight: The organic−inorganic hybrid halide perovskite for optoelectronic applications. Nano Today 2015, 10 (3), 355−396. (25) Zuo, L.; Chen, Q.; De Marco, N.; Hsieh, Y.-T.; Chen, H.; Sun, P.; Chang, S.-Y.; Zhao, H.; Dong, S.; Yang, Y. Tailoring the interfacial chemical interaction for high efficiency perovskite solar cells. Nano Lett. 2017, 17, 269. (26) Dou, L.; Liu, Y.; Hong, Z.; Li, G.; Yang, Y. Low-bandgap nearIR conjugated polymers/molecules for organic electronics. Chem. Rev. 2015, 115 (23), 12633−12665. (27) Pei, Q.; Zuccarello, G.; Ahlskog, M.; Inganäs, O. Electrochromic and highly stable poly (3, 4-ethylenedioxythiophene) switches between opaque blue-black and transparent sky blue. Polymer 1994, 35 (7), 1347−1351.

Kung University, Tainan, Taiwan. His research focuses on solutionprocessed thin-film solar cells. Nicholas De Marco is a Ph.D. candidate in Materials Science & Engineering at the University of California, Los Angeles (UCLA) under Prof. Yang Yang. He received his B.S. in Mechanical Engineering from the University of California, Merced (UCM) in 2013. His research focuses on hybrid perovskite thin film growth for highly efficient solar cells. His overall interests lie in energy harvesting, storage, and other optoelectronic applications. Sang-Hoon Bae is a Ph.D. candidate in Materials Science and Engineering at the University of California, Los Angeles (UCLA) under the supervision of Prof. Yang Yang. He received his B.S. degree from Sungkyunkwan University (SKKU), Korea, in 2011, and his M.S. from Sungkyunkwan University, Korea, in 2013 under the supervision of Prof. Jong-Hyun Ahn, both in Materials Science and Engineering. Qifeng Han received his Ph.D. in Condensed Matter Physics from the Institute of Solid Physics, Chinese Academy of Sciences in 2008. Now he is an associate professor of Shanghai Normal University and a visiting associate researcher in Prof. Yang Yang’s group at the University of California Los Angeles (UCLA). His research focus on solution-processed thin-film solar cells and single crystal growth. Yang Yang received his M.S. and Ph.D. in Physics and Applied Physics from the University of Massachusetts, Lowell, in 1988 and 1992, respectively. Before he joined UCLA in 1997, he served as a research staff member at UNIAX (now DuPont Display) from 1992 to 1996. Yang is now the Carol and Lawrence E. Tannas Jr. Endowed Chair Professor of Materials Science at UCLA. He is also the Fellow of MRS, SPIE, RSC and the Electromagnetic (EM) Academy. He is an expert in the fields of organic, inorganic, and organic/inorganic hybrid electronics and the development and fabrication of related devices, such as photovoltaic cells, LEDs, transistors, and memory devices.



ACKNOWLEDGMENTS This work is supported by the Air Force Office of Scientific Research (AFOSR, Grant No. FA9550-15-1-0610), the Office of Naval Research (ONR, Grant No. N00014-04-1-0434), and the National Science Foundation (NSF, Grant Nos. DMR1210893 and ECCS-EPMD-1509955).



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