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Spatiotemporal Observation of Electron-Impact Dynamics in Photovoltaic Materials Using 4D Electron Microscopy Basamat S. Shaheen, Jingya Sun, Ding-Shyue Yang, and Omar F. Mohammed J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 17 May 2017 Downloaded from http://pubs.acs.org on May 18, 2017
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Spatiotemporal Observation of Electron-impact Dynamics in Photovoltaic Materials using 4D Electron Microscopy Basamat S. Shaheen †, Jingya Sun †, Ding-Shyue Yang ‡*, and Omar F. Mohammed †* †
King Abdullah University of Science and Technology, KAUST Solar Center, Thuwal 23955-
6900, Saudi Arabia ‡
Department of Chemistry, University of Houston, Houston, Texas 77204 United States
AUTHOR INFORMATION Corresponding Author *
[email protected] *
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ABSTRACT: Understanding light-triggered charge carrier dynamics near photovoltaicmaterial surfaces and at interfaces has been a key element and one of the major challenges for the development of real-world energy devices. Visualization of such dynamics information can be obtained using the one-of-a-kind methodology of scanning ultrafast electron microscopy (SUEM). Here, we address the fundamental issue of how the thickness of the absorber layer may significantly affect the charge carrier dynamics on material surfaces. Time-resolved snapshots indicate that the dynamics of charge carriers generated by electron impact in the electron‒photon dynamical probing regime is highly sensitive to the thickness of the absorber layer, as demonstrated using CdSe films of different thicknesses as a model system. This finding not only provides the foundation for potential applications of S-UEM to a wide range of devices in the fields of chemical and materials research, but also has impact on the use and interpretation of electron beam-induced current for optimization of photoactive materials in these devices. TOC GRAPHICS
KEYWORDS Photovoltaic materials, Surface dynamics, 4D electron microscopy, electron impact dynamics, energy loss, CdSe thin films.
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Filling the gap between energy demand and supply with clean, reliable, and inexpensive resources is one of the main challenges of the twenty-first century.1 Solar energy has long been considered a versatile and appealing choice, but an efficient conversion into electric, thermal, or chemical energy is the fundamental scientific issue to be solved.2 For photovoltaics and photoelectrochemical cells, many parameters including the materials and designs still require thorough studies to reach the theoretical limit of efficiency.3 Thin-film technologies may have the advantage of lower costs and weights for easier transportation, installation, and application of consumer products. However, a number of studies showed that the thickness of the active materials, which can vary from several nanometers to tens of micrometers, may play an important role in overall efficiency4-7; ongoing research aims to find the optimum thickness required to reach the highest performance8, 9. Hence, it is essential to experimentally measure carrier dynamics and reach a clear understanding, especially about the role of surfaces and interfaces of materials in the operation of real-world energy devices. For decades, steady-state characterizations such as optical, voltage, and electron beaminduced current (EBIC)10,
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analysis have been the traditional methods. Ultrafast laser
spectroscopy techniques, including one- and two-photon time-resolved photoluminescence to differentiate the surface and bulk contributions12, have been used to study the non-equilibrium behavior of materials and the factors that affect carrier excitation, localization, and transport13. However, despite the ultrashort temporal resolution by time-resolved methods and the submicrometer spatial resolution by steady-state EBIC, a direct observation of carrier dynamics under non-equilibrium conditions at simultaneous ultrashort temporal and non-averaged nanoscale spatial resolutions remains as an open challenge. The method of ultrafast transient absorption microscopy may have the capability to study charge carrier dynamics with good
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spatiotemporal resolutions (still limited by the diffraction limit of light)14-17, but the large penetration depths of photon pulses used make the technique less adequate for surface-specific probing. The invention of four-dimensional ultrafast electron microscopy (4D-UEM), pioneered by Zewail and co-workers at Caltech, is a novel methodology that adds the fourth dimension of ultrashort time to versatile 3D-imaging electron microscopy, allowing for the visualization of matter in both space and time at the atomic level.18, 19 Since its emergence, various ultrafast phenomena and fundamental mechanisms of light-matter interactions have been successfully accessed and imaged.20-30 An ultimate goal of these 4D-UEM studies is to reach the present spatial resolution record of a transmission electron microscope (TEM) at the sub-atomic scale with a femtosecond (fs) temporal resolution. However, a new kind of 4D-UEM that integrates an optical setup with a scanning electron microscope (SEM), so-called scanning ultrafast electron microscopy (S-UEM), has emerged for real-space imaging of ultrafast dynamical processes occurring at materials surfaces and interfaces, which are often the active sites in energy devices31. The ultimate development is to achieve selective probing with nanometer spatial and subpicosecond temporal resolutions. Compared to 4D-UEM in the transmission mode, S-UEM allows simpler sample preparation and the usage of thicker samples, which enables better energy dissipation for stroboscopic studies of photoinduced dynamics and reduction of radiation damage31. Furthermore, S-UEM is a highly surface-sensitive method32 for studying photoactive materials and devices, compared to the aforementioned time-resolved optical techniques33. A brief overview of the mechanisms involved in S-UEM is as follows. In conventional SEM , the most common image formation involves the detection of secondary electrons (SEs) emitted mostly from the first few nanometers of the sample surface region with a most probable
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energy of a few eV in the range of 0‒50 eV, using a positively biased Everhart‒Thornley (E‒T) detector. In S-UEM, a laser pulse passing through an adjustable optical path enters the microscope and photoexcites the sample for dynamics initiation; a primary electron (PE) pulse is photogenerated from a cooled Schottky field-emitter using an ultrashort laser pulse and then utilized as the probe in the photon‒electron dynamical probing regime for scan imaging at positive delay times. Shown in Figure 1 are the experimental schematic and the mechanism for a bright contrast seen in difference images at positive times. In semiconductor materials, an interband electronic transition takes place through the absorption of photons across the band gap. Since a higher probability of SE emission is expected, compared to an unexcited specimen, from those transient energetic electrons upon being scattered by the pulsed PEs, a time-dependent enhancement in the image intensity may be observed in this energy-gain process. However, the pump−probe scheme employed in S-UEM measurements offers another intriguing scenario for probing dynamical processes. In addition to the aforementioned photon‒electron dynamical probing, there is another regime of experiment—the electron‒photon dynamical probing at negative times—where the electron pulse arrives at the specimen earlier than the optical pulse and non-negligible dynamics may still be found. This is in stark contrast with the typical absence of dynamics at negative times using all-optical methods, where a much weaker optical probe is used. As a result of the electron impact by pulsed PEs, a cascade of scattering events will take place in the specimen, leading to nonequilibrium dynamics regardless of the number of electrons used. The time-dependent signals in the SE emission can then be observed on a specimen through clocking by late-arriving photon pulses. Such information cannot be accessed by timeresolved spectroscopy or by 4D imaging in the transmission mode, which highlights a distinct
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advantage of S-UEM to study surface-sensitive SE dynamics of condensed matter at localized regions in real time. More specifically, the SE emission from the surface of a specimen may contain two components: an immediate peak originating mainly within the escape depth of the SEs upon the impact of PEs and a noninstantaneous diminishing component following the main peak. The time scale of the former component is expected to be on the order of 1−10 fs because of the fast speed of escape and thus not resolvable in the current S-UEM design. The noninstantaneous SE component, however, may be observed and will depend on the material’s properties, thickness, and the penetration depth of the PE beam. To date, only a dark contrast was observed in the SE images obtained in the electron‒photon dynamical probing regime, which was explained considering an energy-loss process of SEs in various studies.33-37 However, further experimental and theoretical efforts are needed to elucidate the mechanisms that lead to such observations.37, 38 From a broader perspective, a clear understanding of electron-impact dynamics may connect closely with the use and interpretation of S-UEM results in device development. Conventional EBIC imaging collects the high-energy electrons generated via inelastic scatterings but without the ultrafast temporal information beyond the characteristic carrier lifetime and diffusion length.10 Time-resolved cathodoluminescence with a 10-picosecond (ps) time resolution has been developed, where the observable is the time-dependent emission of photons from the recombination dynamics of carriers generated by pulsed electrons.39 In S-UEM, the use of an optical pulse provides an opportunity via the pump-probe scheme to examine the dynamics and movements of electron-beam-induced carriers generated in the impact volume. More understanding about the electron‒photon dynamical probing regime may reveal further dynamics
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information buried in time-integrated EBIC data and allow studies of real-world devices with covered or nanoscale structures at higher spatiotemporal resolution. In this contribution, CdSe films, whose applications are of considerable interest40-43, were employed as a prototype system. Compared to the dark contrast seen on bulk CdSe single crystals at negative times using a landing energy of 30 keV33, 36, here we report the opposite observation of bright contrast on CdSe thin films at negative times using similar experimental conditions. To further confirm the origin of such dynamics, we performed two types of experiment by varying the thickness of CdSe films as well as the landing energy of the electron beam, both of which suggest that the rich observations in the electron‒photon probing regime strongly depend on the balance among the locations, energy contents, and movements of carriers generated by electron-beam impact as well as their interactions with lower-energy electron-hole pairs photogenerated through an interband transition. Despite that the central concern of this study is to examine the origin of the dark contrast in S-UEM experiments at negative time delays, studies of the influence of photoactive materials thickness on carrier dynamics provide insights on the performance and the design of semiconductor devices.
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Figure 1. (a) Mechanism for the dynamics observed in the photon‒electron probing regime where the valence band electrons are promoted to the conduction band upon optical excitation. Difference images at selected times are displayed to indicate the bright contrast due to the energy gain. The dashed ellipse indicates the location of the laser on the specimen. (b) A close-up view of the probe region and schematic for the pixel-by-pixel image construction. The axis of time is defined by adjusting the arrival time of the laser excitation pulse relative to that of the electron probe pulse using a controllable optical delay line. (c) At 8 MHz, multiple light pulses and PE pulses arrive at the specimen during the dwell time at each pixel. Changes induced in the SE signals from the excited region are recorded and compared to the unexcited regions.
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Figure 2a shows the x-ray diffraction (XRD) patterns of the CdSe films with different thicknesses of 100 nm, 250 nm, 500 nm, 750 nm, and 1000 nm. The main peak from all of the films was found to be at 2θ = 25.5⁰ with the (0002) indices. Two minor peaks were observed at 2θ = 35.3⁰ and 45.9⁰ with the (101̅2) and (101̅3) indices, respectively (Figure S1). Therefore, the CdSe films are polycrystalline with the hexagonal wurtzite structure and a highly preferred (0001) orientation along the surface normal direction44. From the steady-state absorption spectra and the corresponding Tauc plots, the bandgap of the CdSe films were found to be 1.69 eV (Figure 2b), which resembles the bulk value of 1.73 eV. Standard SEM images showed almost the same morphology for the films of different thicknesses (Figure S2). Hence, it was confirmed that these films were of good crystallinity with the same structure and optical properties. The main difference among them is only the film thickness.
Figure 2. Properties of CdSe films with different thicknesses. (a) XRD patterns showing the main peak, (0002). (b) Tauc plots and the bandgap of CdSe films of thicknesses 100 and 750 nm. Insets: steady-state absorption spectra.
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Figure 3 shows the dynamical changes in the SE images of CdSe films with different thicknesses. Low magnification images are needed to observe the laser footprint (approximately 40 m) and the unexcited region despite the higher spatial resolution of S-UEM. The difference images shown in Figure 3 were obtained from an average of 8 rounds of 64 frames acquired from negative to positive times and back-tracked from positive to negative times. The observations found were not affected by the dwell time used at each pixel or by frame averaging excluding the artifact interpretation as a result of impingement of a series of electron pulses. No change is seen at large negative delay times (e.g., ‒450 ps, referring to the arrival of the electron pulse at the specimen being earlier than that of the clocking laser pulse by 450 ps), which is a clear indication of complete recovery of the specimen to its initial equilibrium state before the next stroboscopic probing event begins at a repetition rate of 2–8 MHz. At positive times, a bright contrast appears for all of the CdSe films immediately after the arrival of the optical pulse within the region of laser irradiation. It was found that the thickness of the sample does not affect the carrier dynamics at positive times. This observation in CdSe is consistent with the energy-gain mechanism depicted in Figure 1a, given that a nearly identical profile of the carrier density is photoinjected from the top 100-nm region of each film measured, as the penetration depth of 515-nm photons in CdSe is ~100 nm and most SEs emit from the first couple of nanometers of the top surface. At the apparent excitation fluence of 10 µJ/cm2, an average density of 1.6 interband electron-hole pair per (10 nm)3 exists near the specimen surface, which is much larger than the density of 0.06 probing PEs over the same volume (calculated using the area of the electron-beam footprint at the specimen and the total mean-free-path length of ~20 nm in CdSe at 30 keV). Such a scenario coincides with the typical pump-probe scheme for ultrafast timeresolved studies.
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However, an unexpected contrast inversion is observed when the electron pulse arrives at the specimen earlier than the laser pulse. A bright contrast is seen for the thinner CdSe films (100 nm and 250 nm). Increasing the CdSe film thickness does not yield a brighter signal in the electron−photon dynamical probing. In particular, there is no contrast change in the negativetime difference images for 500-nm CdSe films. A dark contrast emerges when the film thickness is further increased to 750 nm and 1000 nm, which begins to resemble the observation seen on bulk CdSe33, 36.
Figure 3. Time-resolved difference images of CdSe films with thicknesses of 100 nm, 250 nm, 500 nm, 750 nm, and 1000 nm, at selected times referenced to -450 ps frames. The wavelength of the optical pulse was 515 nm and the landing energy of the pulsed primary electrons was 30 keV.
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The transition of “opposite” signals detected by the E‒T detector as a result of an increase in the CdSe film thickness reveals the mechanisms at work in the electron‒photon probing regime. Due to the high speed of the PEs, electron-impact processes may be considered instantaneous for all of the films measured in this study. Generally speaking, the following signals in conventional SEM experiments require consideration: secondary, backscattered, and Auger electrons, characteristic x-rays, and low-energy photons. However, contributions from most of them can be ruled out based on the following reasons. First, due to their large velocities, backscattered electrons cannot be responsible for the observed contrast changes on a ps time scale. The energy loss of a PE in CdSe can be reasonably estimated using the measured energydissipation depth profile for RbI45 and a linear scaling based on the density and average atomic number of materials46. A 30-keV PE will have an average energy of ~15.6 keV after passing through 1-μm CdSe. However, even with only an energy of 1 keV, electrons can pass a distance of 1 μm in ~50 fs, which is shorter than the instrumental response time. Second, contributions from x-rays and Auger electrons may also be excluded because their emissions from core-excited atoms are typically on the few-fs or attosecond time scale47. Furthermore, x-rays cannot be detected by the E‒T detector, and Auger electrons from a deeper region will experience inelastic scattering47 and hence convert to a minor fraction of the electron-impact SE dynamics. Third, near-gap photons of cathodoluminescence at ~1.8 eV49 cannot be detected by the E‒T detector either, and they may be reabsorbed by CdSe to generate low-energy electron-hole pairs that mix with the photogenerated charge carriers. Thus, it can be concluded that the observed negative-time signals on a ps time scale in the electron‒photon probing regime originate solely from SE-related processes, which have direct connection with carrier dynamics in photoactive materials. To escape the materials surface, SEs
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need to have an energy larger than the work function of CdSe, i.e., ~5 eV50. Previous experiments showed that an energy of ~5 eV is required to create an electron-hole pair in CdSe by impact of high-energy particles.51 Therefore, any statistically significant perturbations of the nonequilibrium distribution (in energy and space) of the impact-generated electron-hole pairs will lead to changes in the SE signals. Two mechanisms may be involved: 1. Absorption of a 2.41-eV photon from the optical pulse can further elevate high-energy electrons. Such an energy-gain mechanism will lead to a higher SE yield and hence a bright contrast; here, the optical pulse plays the role of an actual probe. This may be analogous to the dynamical processes observed using time-resolved two-photon photoelectron spectroscopy.52 However, a limiting factor is the attenuation of light in CdSe. 2. Upon their diffusion toward the materials surface, high-energy electrons from a deeper region may experience scatterings by the low-energy carriers generated by the latearriving optical pulse (Figure 4a). Such an energy-loss mechanism will lead to a reduction of SE signals (compared to those observed without photoexcitation) and hence a dark contrast can be obtained. Instead of active probing, here the optical pulse serves more as a clocking one.
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Figure 4. Electron-Impact dynamics. (a) Schematic for the observation of electron-impact dynamics on CdSe using S-UEM with 30-keV electrons. High-energy electrons are generated in the pear-shaped volume (a contour plot with decreasing densities from red to blue regions), whereas near-gap electronhole pairs are photoinjected in the upper region (pink). Arrows indicate the directions of carrier diffusion for different regions. (b) Normalized time-dependent SE intensities obtained from 100 and 1000-nm CdSe films. The red solid lines are the results of a single exponential fit.
Consequently, the contrast inversion in Figure 3 can be understood. The energy-gain mechanism for a bright contrast is most prominent in thinner CdSe films (i.e., 100 nm and 250 nm) and outweighs the energy-loss mechanism. With an increase in the CdSe film thickness, reduction of the SE yield due to energy loss becomes significant and cancels the gain from the upper region of a film, as seen in the difference images for 500-nm CdSe films with negative delay times. Further increase of the film thickness allows more generation of high-energy electrons in a pear-shaped impact volume, which enhances the importance of the energy-loss mechanism and hence leads to a dark image contrast for 750-nm and 1000-nm CdSe films in the electron−photon dynamical probing. It is important to note that at positive times in the photon‒ electron probing regime, the contrast is not affected by the thickness of the films as opposed to what happens at negative times. This is because at positive times, the excitation by 515-nm photons creates low-energy electron‒hole pairs near the surface whereas at negative times the
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impact by 30-keV electrons is able to generated high-energy electrons at deeper regions although the density is not high. Figure 4b shows the dynamical changes of the SE signals in the center of the laserilluminated region for CdSe films of different thicknesses. From a single-exponential fit, a similar time constant of ~40 ps is obtained for the thinnest and thickest films measured. Such a time scale is reasonable considering a similar characteristic time for the downward and upward diffusion of upper- and deeper-region electrons, respectively (Figure 4a), even though the image contrast is opposite. A diffusion constant of the order of 10 cm2/s can be estimated, which may be appreciably higher than the ambipolar diffusion constant for low-energy carriers generated by above-gap photoexcitation or by injection.53 As for intermediate thicknesses, especially for 250nm films, the competing mechanisms result in more complex dynamics and therefore a simple exponential fit becomes inadequate. Further support for the aforementioned mechanisms is found from experiments using PEs with a low landing energy. Figure 5a shows the time-resolved SE images observed on a CdSe (0001) single crystal at different delay times in response to the 515-nm excitation pulse. A bright contrast is seen in the laser-illuminated region even when the specimen is thick. However, at 1 keV, PEs have an impact range of ~10 μg/cm2 in the unit of mass-thickness,48 or ~20 nm of CdSe. Hence, high-energy electrons are created only near the surface region and the energy-gain mechanism is dominant. Since the bulk sample is equivalent to a very thin film with tens of nm in thickness (Figure 5b, 100 nm CdSe), a bright contrast opposite to that observed using 30-keV PEs is resulted (Figure 5b, 1 µm CdSe).
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Figure 5. CdSe dynamics at different experimental conditions. (a) Time-resolved difference images for CdSe (0001) single crystal at selected time frames obtained with 1-keV pulsed primary electrons. (b) Time-resolved difference images obtained with 30-keV pulsed primary electrons from 100-nm and 1-mthick CdSe films.
In conclusion, the present study may open up investigations of devices that use, for example, nanoscale structures of different materials and compositions. Given the tunability of the landing energy of the electron pulse, it is possible to study surface-related (photo) chemical phenomena as well as photo-physical dynamics underneath the surface region. Using the one-ofa-kind S-UEM, we address the fundamental issue of how the thickness of an absorber layer may influence charge carrier dynamics near the surface and in the bulk. More specifically, our timeresolved images indicate that the energy-gain mechanism for the SEs is prominent in thinner CdSe films (i.e., 100 nm and 250 nm). With an increase in the CdSe film thickness, reduction of the SE yield due to the energy-loss mechanism becomes significant and cancels the gain from the upper region of a film. How the locations and energy contents of charge carriers affect their transport properties, time-dependent interactions with other carriers, and ultimate fate may be further answered using this real-space, time-resolved imaging methodology, which could provide a key element to find the optimum absorber thickness required to reach highest performance in a wide variety of solar cell and optoelectronic devices.
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Experimental Section CdSe films were deposited on silicon and glass substrates by sputtering deposition (Angstrom Engineering Evovac) from a CdSe target (minimum purity of 99.999%). The substrates were cleaned before deposition by acetone and isopropyl alcohol. The chamber was kept at a pressure of 20 mTorr of argon during deposition. The power used was 90 watt and the argon flow rate was 20 sccm. The duration of the depositions was adjusted accordingly to reach the different thicknesses (100, 250, 500, 750 and 1000 nm). The films were annealed at 350°C for 30 minutes for better crystallinity. The thickness of the CdSe films was measured by a surface profiler (KLA Tencor P-6). The structures of the CdSe films were characterized using x-ray diffraction (Bruker D8 ADVANCE). A plain silicon substrate was used as a reference to calibrate the peaks of the CdSe films. A UV-visible-NIR spectrophotometer (Cary 6000) was used to measure the optical absorbance of CdSe films deposited on glass (750 and 100 nm). The general experimental setup of 4D S-UEM comprises of a fs laser system integrated with a modified scanning electron microscopy (SEM). Figure 1 shows the general concept for the second-generation 4D S-UEM, where a femtosecond fiber laser (Clark-MXR) operates at a central wavelength of 1030 nm with a pulse width of 270 fs. The fundamental laser output was divided by a beam splitter and directed to two independent harmonic generators (HGs) to produce the second and third harmonic pulses at 515 and 343 nm, respectively. The output of the first HG (515 or 343 nm) was directed with precision through a pyrometric quartz window and tightly focused on a cooled Schottky field-emitter tip (zirconium oxide-coated tungsten) to generate the pulsed electrons for imaging. The output of the second HG (515 nm, excitation clocking pulse) entered the microscope at an angle of 50° relative to the surface normal through
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a viewport and is focused onto the specimen surface to initiate or clock the dynamics. Finally, a computer-controlled optical delay line was used to vary the relative clocking between the electron and photon pulses. The scanning process of the electron beam took place across the surface of the sample, over both the laser-excited and unexcited regions in the raster pattern, and the SEs emitted from the sample were detected by a positively biased Everhart‒Thornley detector. All experiments were conducted at a laser repetition rate of 2–8 MHz. To enhance the signal-to-noise ratio, the SE images were obtained as an integration of 64 frames with a dwell time of 300 ns at each pixel.
ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: Figure S1. XRD patterns for CdSe thin films with different thicknesses (PDF). Figure S2. Standard SEM images for CdSe films. (a) 500 nm and (b) 1000 nm thickness (PDF). AUTHOR INFORMATION Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. B. S. S. and J. S.: Contributed equally to this work. Notes The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work reported here was supported by King Abdullah University of Science and Technology (KAUST). DY acknowledges the support from the R. A. Welch Foundation (Grant No. E-1860). The authors acknowledge B. Murali for providing standard SEM images for the CdSe films. REFERENCES (1) Smith, C. L. The Energy Challenge. Appl. Petrochem. Res. 2012, 2, 3-6. (2) Crabtree, G. W.; Lewis, N. S. Solar Energy Conversion. Physics Today 2007, 37-42. (3) Granqvist, C. G. Solar Energy Materials. Adv. Mater. 2003, 15, 1789-1803. (4) Purohit, A.; Chander, S.; Nehra, S. P.; Lal, C.; Dhakaa, M. S. Efect of Thickness on Structural, Optical, Electrical and Morphological Properties of Nanocrystalline CdSe Thin Films for Optoelectronic Applications. Opt. Mater. 2015, 47, 345-353. (5) Kang, M. G.; Ryu, K. S.; Chang, S. H.; Park, N. G.; Hong, J. S.; Kim, K.-J. Dependence of TiO2 Film Thickness on Photocurrent-Voltage Characteristics of Dye-Sensitized Solar Cells. Bull. Korean Chem. Soc. 2004, 25, 742-744. (6) Ju, T.; Yang, L.; Cartera, S. Thickness Dependence Study of Inorganic CdTe/CdSe Solar Cells Fabricated from Colloidal Nanoparticle Solutions. J. Appl. Phys. 2010, 107, 104311. (7) Ye, C.; Bando, Y.; Shen, G.; Golberg, D. Thickness-Dependent Photocatalytic Performance of ZnO Nanoplatelets. J. Phys. Chem. B 2006, 110, 15146-15151. (8) Tamang, A.; Sai, H.; Jovanov, V.; Hossain, M. I.; Matsubara, K.; Knipp, D. On the Interplay of Cell Thickness and Optimum Period of Silicon Thin‐Film Solar Cells: Light Trapping and Plasmonic Losses. Prog. Photovolt: Res. Appl. 2016, 24, 379-388. (9) Koval, R. J.; Koh, J.; Lu, Z.; Jiao, L.; Collins, R. W.; Wronski, C. R. Performance and Stability of Si: H p–i–n Solar Cells with i Layers Prepared at the Thickness-Dependent Amorphous-to-Microcrystalline Phase Boundary. Appl. Phys. Lett. 1999, 75, 1553-1555. (10) Leamy, H. J. J. Charge Collection Scanning Electron Microscopy. Appl. Phys. 1982, 53, R51-R80. (11) Edri, E.; Kirmayer, S.; Henning, A.; Mukhopadhyay, S.; Gartsman, K.; Rosenwaks, Y.; Hodes, G.; Cahen, D. Why Lead Methylammonium Tri-Iodide Perovskite-Base Solar Cells Require a Mesoporous Electron Transporting Scaffold (But Not Necessarily a Hole Conductor). Nano Lett. 2014, 14, 1000−1004. (12) Barnard, E. S.; Hoke, E. T.; Connor, S. T.; Groves, J. R.; Kuykendall, T.; Yan, Z.; Samulon, E. C.; Bourret-Courchesne, E. D.; Aloni, S.; Schuck, P. J.; Peters, C. H.; Hardin, B. E. Probing Carrier Lifetimes in Photovoltaic Materials Using Subsurface Two-Photon Microscopy. Sci. Rep. 2013, 3, 2098. (13) Alfano, R. R. Semiconductors Probed by Ultrafast Laser Spectroscopy; Harcourt Brace Jovanovich: New York, 1984; Vol. II.
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