Comprehensive Insights into Charge Dynamics and Improved

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Comprehensive Insights into Charge Dynamics and Improved Photoelectric Properties of Well-Designed Solar Cells Xiangyang Liu, Shun Wang, Haiwu Zheng, Xiuying Cheng, and Yuzong Gu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b05204 • Publication Date (Web): 25 Jul 2016 Downloaded from http://pubs.acs.org on July 31, 2016

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ACS Applied Materials & Interfaces

Comprehensive Insights into Charge Dynamics and Improved Photoelectric Properties of Well-Designed Solar Cells Xiangyang Liu,* Shun Wang, Haiwu Zheng, Xiuying Cheng, and Yuzong Gu

Institue of Microsystems Physics and School of Physics & Electronics, Henan University, Kaifeng 475004, P.R. China

ABSTRACT: Here, Zn2SnO4 nanorods/Cu4Bi4S9 (ZTO/CBS) and ZTO nanorods/CBS-graphene nanosheets (ZTO/CBS-GNs), as well as two types of bulk heterojunction (BHJ) solar cells with high flexibility were fabricated on stainless steel meshes (SSMs). The excellent photovoltaic responses of CBS-GNs and ZTO/CBS-GNs with incorporation of GNs were determined using surface photovoltage spectroscopy (SPS). The signals of time-resolved fluorescence response (TFR) and transient surface photovoltage (TPV) provide more detailed information for transition, separation and transport of photoinduced carriers. Besides, the ZTO nanorods/CBS-GNs cell exhibits the superior performance and the highest efficiency is 11.2%. The multichannel separation process from the TPVs indicates that the macro-photoelectric signals can be attributed to the photogenerated charges separated at the interface of CBS/GNs, rather than CBS/ZTO. The multi-interfacial recombination is the major carrier loss with electrical impedance spectroscopy (EIS) and the hole selective NiO can efficiently accelerate the charge extraction to the external circuit. The comprehensive signals of SPS, EIS, TFR and TPV provide insights into transition, separation, recombination and shifting of carriers. Importantly, the BHJ flexible solar cells with high efficiency and facile, scalable production present a potential for application.

KEYWORDS: multichannel transport, charge dynamics, interface recombination, time-resolved fluorescence spectroscopy, transient surface photovoltage 1

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1. INTRODUCTION In the past twenty years, some thorough and comprehensive researches have been carried out to improve the photoelectric conversion efficiency of bulk heterojunction (BHJ) solar cells. Here, several superior performances were reported over 8.0%,1,2 such as 9.2%,3 8.94%,4 11.7%,5 and achievement of 0.80 fill factor.6 For the electron transport layer, some binary oxides including ZnO,7 SnO28 and In2O39 were reported. However, multi-cation oxides have been scarcely investigated in BHJ solar cells. Up to now, only two ternary oxides of SrTiO310 and Zn2SnO411 were used as the electron transport layer in solar cells. Zinc stannate (Zn2SnO4) as a ternary oxide exhibits superior electrical properties and high optical stability.12 Recently, an efficiency of 3.8% for Zn2SnO4 (ZTO) application was reported in dye-sensitized solar cells.11 Besides, ZTO as electron transport material has better stability than ZnO and SnO2 for acidic donors,13 and higher open-circuit potential and lower sensitivity to UV-Vis light than standard TiO2 cells.14 Recently, flexible solar cells owning lightweight, foldable, portable, wearable, and cheap advantages have attracted much academic interest and industrial attention with extensive applications.15-17 Traditional plastic and polymer substrates do not withstand a high temperature sintering process. Here, the stainless steel mesh (SSM) is an ideal substrate for weave-based solar cells due to its low cost, high strength, good electrical conductivity, excellent temperature-resistance, and corrosion resistance. The key of SSM-based solar cells is to construct an optimal architecture with suitable materials to achieve the superior performance.18 For application as photoelectric device, it is reported that Cu4Bi4S9 (CBS) presents excellent photoconductivity and electron transfer properties.19 The thin film of CBS nanoribbons also exhibits a wide photovoltaic response.20 Recently, some BHJ solar

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cells with CBS as donor were reported, indicating the potential application of CBS nanoribbons.21 However, the high recombination rate of photogenerated electron-hole pairs in pure CBS only generates a weak photoelectric property. Graphene possesses a typical two-dimensional (2D) structure. With superior properties, such as remarkably high electron mobility, high thermal conductivity, high surface area, and excellent mechanic strength,22 graphene, especially for graphene nanosheets (GNs), has attracted extensive research interest and industrial application in solar cells, electron device, energy conversion and storage device, etc.23 With some factors changing of ZTO/CBS and ZTO/CBS-GNs on SSM, qualitative and quantitative analysis from the photoelectric signals can provide some insights into the thermodynamic model and the basis of systematic studies on the photochemical charges transport process using surface photovoltage spectroscopy (see Figures S1 and 2a). Here, the transition, separation, recombination, transport and collection of photoinduced carrires can all affect the photoelectric properties. With the combination of detecting methods, we aim to further explore the inherent transfer process and the charge dynamics.21,24-27

2. EXPERIMENTAL SECTION 2.1. Preparation of samples. All reagents are analytical grade or better without further purification. The deionized water used in our work has an electrical resistivity of 18 MΩ·cm. After cleaned and degreased with several cleaning steps and sonicated successively in acetone, absolute ethanol, and deionized water, the clean SSMs were obtained. Finally, the SSMs were blown dry with a nitrogen gas stream. Here, the SSMs of 316L were purchased from the Hua-xin hardware factory with thickness of 0.16 mm (Shanghai, China). The device areas of SSMs selected in our work are from 2.16 to 19.2 cm2 as shown in Figures S3 and 4.

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For preparation of ZTO nanorods arrays on SSM, 0.21 g of SnCl4·4H2O and 0.263 g of Zn(CH3COO)2·2H2O were added into a solvent with 10 mL ethylenediamine (En) and 10 mL H2O in a 50-mL flask. The solution was stirred for 30 min and then added 0.29 g NaOH slowly. After stirring for a few minutes, the obtained slurry was quickly transferred to a stainless Teflon-lined autoclave with a 50 mL inner volume. Soon, the SSMs as flexible substrate were put into the autoclave and leaned against the inner wall. This process was performed under an auto-generated pressure at 200 °C for 20 h in an oven and cooled naturally to room temperature. After cleaned with deionized water, the ZTO nanorods with high crystallinity were obtained. The fabrication process of CBS nanoribbons was reported in our previous work.21 Several CBS electrodes were prepared with thickness of 2.5, 3, 3.5, 4, 4.5, 5 and 5.5 µm, respectively. Here, the graphene nanosheets were purchased from the Biological Technology Co. of Zhenzhun (Shanghai, China) For fabrication of heterojunction and BHJ flexible solar cells, first, the different amounts of GNs were added into several colloids of CBS (with GNs of 0.4, 0.8, 1.2, 1.6, 2.0 and 2.4 wt.%). After dispersed by ultrasonication and stirring continuously for 12 h, the homogeneous, dispersed solutions of CBS-GNs were obtained. Secondly, the CBS-GNs with GNs of 1.6 wt.% was spin-coated onto ZTO substrate, which was put into a glove box for 0.5 h and dried naturally. After repeated five times, the SSM was placed into an autoclave of keeping 30 h at 180 °C and the ZTO/CBS-GNs with well-crystallized CBS can be obtained. Here, the film thickness of heterojunction is about 4.5 µm. Other thicknesses of 2.5, 3, 3.5, 4, 5 and 5.5 µm by changing the spin-coating times of CBS-GNs can be fabricated. Using a magnetron sputtering technique, NiO was deposited onto CBS-GNs with various thicknesses (10, 20, 25, 30, 35 and 40 nm) as the hole transport layer. For a fair comparison, the ZTO/CBS

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heterojunctions and BHJ flexible solar cells were also provided. In order to improve the photovoltaic response of ZTO/CBS and ZTO/CBS-GNs, a thin mica sheet was placed on CBS-GNs (or CBS) with Pt screen electrode directly on mica sheet as seen in Figures S2b and 2c. 2.2. Characterization of materials. Utilizing a Philips X’ Pert Pro X-ray diffractometer of a CuKα radiation (wavelength = 0.154 nm), the XRD patterns of as-prepared materials were measured. The surface morphologies of CBS, CBS-GNs and ZTO nanorods were determined on a field-emission scanning electron microscopy system (SEM, JSM-7001F). The microstructure of CBS-GNs was observed via a high-resolution transmission electron microscopy (HRTEM, JEM-2100UHR). The thickness of heterojunction was obtained by a profilometry (Dektak 3 profilometer, Veeco). Utilizing a scanning Kelvin probe system (SKP370), the surface potential and electronic work function of as-prepared materials were measured. The electron mobility of ZTO was obtained via a Hall-effect measurement system (HMS-3000). The photovoltaic response of two types of heterojunctions was evaluated using surface photovoltage spectroscopy (SPS), and the detailed information can be seen in our work.21 The sandwich structure with two electrodes is supplied in Figures S1 and 2a. The emission lifetime of CBS-GNs and heterojunctions was monitored using a time-resolved fluorescence spectroscopy (TFS). The materials were excited at 360 nm by a frequency doubled Ti:sapphire laser (pulse width of 120 fs; Mira 900F, Coherent). The time-resolved data were collected with a synchroscan streak camera (Hamamatsu, C5680). There are two temporal scanning ranges and the instrument response function (IRF) of 16 ps corresponds to 2.2 ns range and 4 ps to 160 ps range with a deconvolution technique. The decay of photovoltaic response was monitored using transient surface photovoltage spectroscopy. A third harmonic Nd:YAG laser (Polaris

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II, New Wave Research, Inc.) with a laser radiation pulse (pulse width of 5 ns, wavelength of 355 nm) was used to illuminate heterojunction. The time-resolved data were collected by a 500 MHz digital phosphor oscilloscope (TDS 5054, Tektronix) with a preamplifier. The electrical impedance spectroscopy measurements were measured using the PGSTAT302N frequency analyzer together with the frequency response analyzer module, providing the voltage modulation in a desired frequency range. 2.3. Characterization of BHJ flexible solar cells. The incident photon to current conversion efficiency (IPCE) of BHJ flexible solar cells was determined using a quantum efficiency measurement system (QTest Station 1000ADI). The I-V measurement was carried out with a cell active area of 0.132 cm2 (battery plate of 2×2 cm2) via a photoelectric measurement system (Newport-94043A). The open-circuit photovoltage (Voc) and short-circuit current density (Jsc) were obtained via a digital source-meter (Keithley 2400). Besides, the overall conversion efficiency (η) can be calculated as follows: η = VocJsc FF/Pin

(1)

In Eq. (1), Voc and Jsc are the open-circuit photovoltage and short-circuit current per unit area. Pin represents the incident light power (AM 1.5G, 100 mW/cm2). As shown below, the fill factor (FF) can be obtained by FF = VmaxJmax/VocJsc

(2)

In Eq. (2), Jmax and Vmax are the current and voltage per unit area with the maximum output values, respectively.

3. RESULTS AND DISCUSSION 3.1. XRD patterns and SEM image. The XRD patterns of CBS nanoribbons and ZTO nanorods arrays are shown in Figures 1a and 1b, respectively. As seen, CBS has

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an orthorhombic-phase structure and ZTO nanorods growing vertically on SSM match well with the cubic phase structure. As shown in Figure S5a, ZTO nanorods arrays exhibit a highly ordered structure and the average diameter is about 40-120 nm. For CBS-GNs (GNs 1.6 wt.%) supplied in Figure 2a, the GNs can completely incorporate with CBS and a densely interfacial contact between two components has been formed. The SEM image of pure CBS is also provided in Figure S5b. The TEM image of CBS-GNs (GNs 1.6 wt.%) is shown in Figure 2b, suggested that the GNs walls are very thin with stacked GNs and many corrugations. Besides, the HRTEM image of CBS is supplied in Figure 2c. The (10,11) planes have a lattice spacing of 0.24 nm and the (12,00) planes with a lattice spacing of 0.26 nm. As seen in Figure 2d, there is also a selected area electron diffraction (SAED) image of CBS. 3.2. Surface photovoltaic response. As seen in Figure 3a, the pure CBS film with thickness of 4.5 µm exhibits a broad surface photovoltage (SPV). For some traditional donor materials, CBS nanoribbons possess superior properties as inorganic donor to prepare BHJ solar cells.18,21 However, the majority of photogenerated charges are not separated prior to recombination in pure CBS film.21,26,27 With GNs wt.% changing, the SPVs of CBS-GNs having the same thickness are shown in Figure 3a. Here, the SPV increases gradually as GNs from 0.4 to 1.6 wt.%. Above 1.6 wt.%, the SPV decreases and the separation between two response regions becomes clearly as pure CBS again. For GNs 1.6 wt.%, there is the highest SPV (633 µV ca. 485 nm) with an obvious amalgamation between two SPV regions relative to pure CBS. From Table S1, there is an energy level matching between CBS and GNs. The photogenerated electrons can easily transfer to GNs and holes in CBS. With GNs wt.% increasing, more electrons transport to GNs. Due to the high electron mobility

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of GNs,22 the accumulated electrons in GNs quickly transfer to the electron collector, which can improve the collection efficiency and generate a higher SPV. For the low SPV with further adding GNs, graphene is an almost transparent material. The optical absorption of CBS and photogenerated carriers will decrease due to the transmission of GNs. The high electron mobility in GNs can promote the electrons to diffuse to the interface of Pt electrode/CBS-GNs and improve the recombination rate. Besides, there is not an electron blocking layer to impede the recombination. The decreasing SPV can be attributed to such factors. For ZTO/CBS and ZTO/CBS-GNs, the photovoltaic responses all exhibit a trend from rise to decline with thickness increasing. Here, the SPV peaks with changing thickness are shown in Figure S6. As seen, the peaks increase linearly from 2.5 to 4.5 µm (or 4 µm) and then decrease slowly. The SPVs of ZTO/CBS and ZTO/CBS-GNs illumination from Pt electrode are shown in Figure 3b. The ZTO/CBS-GNs exhibits a higher SPV than that of ZTO/CBS with a distinct amalgamation between two regions. For ZTO/CBS-GNs, the photogenerated electrons in CBS firstly transport to GNs. The accumulated electrons can raise the Fermi level of GNs and enhance the transfer dynamics between GNs and ZTO. Then, lots of free electrons shifting from GNs to ZTO with an energy level matching can be seen in Table S1. Incorporation of GNs in CBS can improve the separation efficiency of photogenerated electron-hole pairs and result in a higher SPV than that of ZTO/CBS. The highest SPVs of two types of heterojunctions under illumination from two electrodes are provided in Figure S7. As seen in Figure 3c, there is a diagram of energy band structure with several energy level matchings. For CBS and ZTO, the direct-contact exhibits a high contact barrier. Importantly, there are not the adequate interfaces between CBS and ZTO. The majority of photogenerated electron-hole pairs are split at the interface of CBS/GNs,

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and the electrons transfer to GNs and then to ZTO. Incorporation of GNs can supply more interfaces and improve the separation efficiency of photogenerated charges. The SPVs can be attributed to the comprehensive effect of adequate interfaces, energy level matching, GNs conductive network, etc. About the energy level matching, its effect can be explained with an “inverted region effect”. From the fundamental quantum uncertainty and energy band theory, the wave function of the photoexcited state is a delocalized coherent superposition of the eigenfunctions of the Schroedinger equation. When two nanocrystallines are getting closer, the different wave functions can overlap each other. With further shortening the distance, the overlapping area further increase, which can improve the immediate probability amplitude of mobile electrons in different regions and facilitate the electronic sharing movement. Here, the larger overlapping area of two wave functions can promote the separation of photogenerated charges and generate a higher SPV signal.21,24-28 3.3. Time-resolved fluorescence spectroscopy. Using time-resolved fluorescence spectroscopy, the emission lifetimes of as-prepared materials were monitored with different scanning ranges. The detailed information of temporal scanning ranges can be seen in our work.25 In order to confirm the inherent transition mechanism of photogenerated carriers, CBS-GNs and ZTO nanorods/CBS were measured firstly and the fluorescence decay curves with two scanning ranges are provided in Figures 4a and 4b. Here, there are two decay components for CBS-GNs and ZTO nanorods/CBS. The two larger time constants of 83 and 88 ps for CBS-GNs and ZTO nanorods/CBS can be assigned to the faster components due to the surface defects or/and deep defect levels.29,30 Besides, the ultrafast components of CBS-GNs and ZTO nanorods/CBS exhibit two time constants of 6 and 9 ps, respectively. The two ultrafast processes can be attributed to the transition of photogenerated electrons from the excited CBS to

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GNs and CBS to ZTO nanorods.29,30 ZTO nanorods/CBS-GNs was also measured and the fluorescence decay curves with two scanning ranges are shown in Figure 4c. As a result, there are three decay curves, which can be fitted with three decay components. The two faster components exhibit two time constants of 90 and 46 ps, respectively. The larger time constant can be attributed to the deep defect levels or/and surface defects and the smaller results from the transition of photogenerated electrons from GNs to ZTO. Here, it can be seen that there is an ultrafast decay curve with a time constant of 11 ps. However, there are two ultrafast transition processes from the excited CBS to GNs and CBS to ZTO nanorods.29,30 Due to the limitation of our equipment, the two ultrafast processes are not distinguished with amalgamation. The signals of TFS confirmed the different transition processes of photogenerated electrons. 3.4. Transient surface photovoltaic response. Here, the energy band-gaps of CBS and ZTO are about 0.88 and 3.5 eV, respectively. The detailed information of pulse laser and the sign of transient surface photovoltage (TPV) are shown in our work.27 For ZTO nanorods/CBS-GNs, the illumination by a pulse laser from Pt screen electrode can be seen in Figure S2b. Two different separation and transfer processes of photoinduced carriers are shown in Figures 5a and 5c. The first positive sign process has a time constant of 5.2 × 10-6 s, and the second with a time constant of 3.8 × 10-5 s. From the shifting process of photogenerated carriers, the fast can be attributed to the direct separation at the interface of CBS/ZTO and the slow to the separation at the interface of CBS/GNs.31-33 With a media of mica sheet, the interface effect between CBS-GNs and Pt electrode can be ignored. Besides, the ZTO substrate was directly spin-coated with CBS-GNs solution and the state densities are very similar for the bulk and the surface in CBS-GNs layer. This weak separation process

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of photoinduced carriers due to surface defect state and surface adsorption can also be neglected. Under illumination, some excitons can diffuse to the interface of CBS/ZTO where they are split, forming charge carriers; holes in the donor side of CBS and electrons in the transport layer of ZTO. Then the electrons transfer to SSM, and holes to Pt screen electrode. Considering the inadequate interfaces, only a small part of photoinduced charges can be separated and collected by bilateral current collectors. Compared to some reports, a weaker and slower TPV signal was obtained for the first process.31-33 However, the majority of excitons diffuse to the interface of CBS/GNs where they are split, electrons in GNs and holes in CBS. The free electrons and holes can be achieved with further diffusion and actual separation. Then lots of electrons transport from GNs to ZTO (then to SSM) and holes in CBS to Pt electrode, inducing the second process as shown in Figure 5c.31-33 Meanwhile, the illumination by a pulse laser from SSM electrode can be seen in Figure S2c, and three different separation and shifting processes of photogenerated carriers are shown in Figures 5b and 5d. The first negative sign process has a time constant of 3.2 × 10-7 s, the second of 5.3 × 10-6 s, and the third of 3.9 × 10-5 s. Generally, the drift process is quicker for several orders than diffusion.31-33 Here, a built-in electric field at the interface of ZTO/SSM is established with direction from SSM to ZTO, promoting the electrons to transport to SSM and holes to the bulk of ZTO for the first process. Similarly, some excitons can diffuse to the interface of CBS/ZTO, and the separated electrons transfer to SSM and holes to Pt electrode. As seen, there is a weak TPV signal for the second process. The majority of excitons can easily diffuse to the interface of CBS/GNs, and the separated electrons transport from GNs to ZTO (then to SSM) and holes in CBS to Pt electrode with the third process. It can be seen that the TPV signal illuminated from SSM is lower than that from Pt electrode. The majority of photogenerated charges are from

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the CBS-GNs layer. The changing optical absorption and photoinduced carriers result in the different TPVs. For ZTO nanorods/CBS, the illumination by a pulse laser from Pt electrode can be seen in Figure S2b, and the separation and transfer process of photoinduced carriers is supplied in Figure 5e. This positive sign process has a time constant of 5.2 × 10-6 s. The surface and interface effects can also be ignored as the interpretation in Figure 5c. Here, the excitons only split at the interface of CBS/ZTO, holes in CBS and electrons in ZTO. Then the electrons transfer to SSM and holes to Pt electrode with a low TPV signal. Besides, the illumination by a pulse laser from SSM can be seen in Figure S2c, and two different separation and transfer processes of photoinduced carriers are shown in Figure 5f. The first negative sign process has a time constant of 3.3 × 10-7 s, and the second of 5.3× 10-6 s. Similarly, the first can be attributed to the drift process and the second to diffusion. It can be seen that there are different separation and shifting mechanisms, as well as the charge dynamics for two types of heterojunctions. Incorporation of GNs, the adequate interfaces of CBS/GNs can promote the separation of photogenerated electron-hole pairs. The ultrafast electron transmission channel in GNs can improve the collection efficiency. With regard to TFS, the TPV signals provided insights into the separation and transfer process of carries, as well as the comprehensive effect of main factors. 3.5. I-V characteristics and IPCE spectra of cells. The incident photoelectric conversion efficiency of BHJ solar cell is shown in Figure 6a. At 485 nm, the IPCE values of ZTO/CBS and ZTO/CBS-GNs cells are 38.5% and 75%, respectively. The IPCE spectra of two types of solar cells with changing thickness are also provided in Figure S8. Using a Hall-effect system, the electron mobility of ZTO nanorods was measured of 56 cm2V-1s-1. The ZTO nanorods can also promote the electrons shifting

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and improve the photoelectric conversion efficiency. As seen in Figure S9, the overall photoelectric conversion efficiency of cells with various film thicknesses was firstly measured. There is a same changing trend as the SPVs to film thickness. Here, two types of solar cells have the best performance under the hole transfer layer of 30 nm. For a fair comparison, the I-V characteristics and I-V curves of two types of solar cells with the same film thickness are shown in Table 1 and Figure 6b, respectively. As seen, the ZTO/CBS-GNs cell presents an overall light-to-electricity efficiency (η) and a short-circuit current density (Jsc) of 11.2% and 18.8, and ZTO/CBS cell with η and Jsc of 3.3 % and 6.6. It can be seen that there is an identical feature as shown in Figure S9. In contrast, the ZTO/CBS-GNs cell exhibits a higher efficiency (η) than that of ZTO/CBS. Moreover, the highest η of 11.2% in our work is remarkably higher than the report of 1.15%.34 After incorporation of GNs, it is mainly due to the adequate interfaces of CBS/GNs, GNs conductive network, energy level matching and other factors. The majority of photogenerated electron-hole pairs can split to electrons and holes at the interface of CBS/GNs. Then the separated electrons and holes can be collected quickly by bilateral current collectors. As seen in Figures S3a-3f, there are some different circumferences of 1.88, 2.53, 2.66, 2.72, 4.7 and 5.38 cm, and the corresponding circle radii are 0.3, 0.4, 0.42, 0.43, 0.75 and 0.86 cm as shown in Figures S4a-4f. After bent with tweezers for 1000 times, the SSMs still exhibit a high durability with fine flexibility and bendability. Here, the original SSMs present an electrical resistivity of 0.03 Ω·cm and the resistivity is 0.05 Ω·cm under strong alkaline solution (pH >13) of 200 °C or higher processing temperature. Besides, the SSMs also show a high resistance to strong acid (pH < 2) with the designed experiment. Other parameters of allowable stress for SSM are supplied with factory (T ≤ 150 °C, (σ) = 117 MPa；T = 200 °C, (σ) = 108 MPa；T = 250 °C, (σ) = 100

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MPa；T = 300 °C, (σ) = 95 MPa). 3.6. Electrical impedance spectroscopy measurements. Electrical impedance spectroscopy (EIS) measurements were conducted to investigate the internal electrical properties of BHJ flexible solar cells. Figures 7a and 7b show the Nyquist plots and the corresponding Bode phase plots in the frequency range from 1 MHz to 10 mHz for ZTO/CBS and ZTO/CBS-GNs cells under illumination at a bias of -0.75 V. The frequency analysis indicates that there are five separated semicircles for ZTO/CBS-GNs and three semicircles for ZTO/CBS in the Nyquist diagram. From the Nyquist plots, the peaks in the high frequency regime (104 to 106 Hz) can be attributed to the electron transfer process on the Pt electrode surface.35-38 However, these responses in intermediate (104 to 10 Hz) and low frequencies (

Comprehensive Insights into Charge Dynamics and Improved

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