Electric energy storage (EES) systems can minimize the deterioration of the environment by integrating various sustainable and environmentally-safe energy sources into smart grids, thereby decreasing the risk of exhaustion of nonsustainable energy sources.1–5 Lithium-ion batteries (LIBs), the most widely used EES system, have been responsible for the growth of portable electronic gadgets owing to their high specific capacity and extended cycling lifetime.6–10 Unfortunately, the radically-increasing requirement of energy storage devices in bulk has slowed down because of irregular allocation and a global scarcity of lithium sources (only 0.0017 wt.%).11 Given their abundance, low-cost reserves, and analogous chemical qualities, potassium-ion batteries (PIBs) have great potential to be a promising alternatives to LIBs.12–14 Specifically, as the redox potential of K/K+ is closer to that of Li/Li+, PIBs can potentially provide high operating voltages.15–23 Besides, the cost and weight of the current collector are lower in PIBs owing to the employment of Al foil rather than Cu foil, which offers additional advantages.22,24–30 Despite these virtues, PIBs currently face limitations resulting from the unavailability of high-performance anode materials. Developing suitable electrode materials capable of accommodating significant volume variations during the insertion or extraction of K+ ions remains challenging owing to their relatively large ionic radius (the ionic radius of K+, Na+, and Li+ ions are 1.38, 1.02, and 0.76 Å, respectively). Besides, the high performance of PIBs benefit from suitable electrodes size, reliable mechanical properties as well as stable solid-electrolyte interphase (SEI) layer, in which stable SEI might alleviate electrolyte disintegration and buffer the large volume variations during long cycle.31–33 Moreover, previous studies have proved that using the incorrect size of electrode materials results in a huge capacity loss during cycling.34 Hence, it is an urgent requirement and a challenging proposition to search for practicable PIB anode materials of the correct size that can facilitate the diffusion of K+ and provide an exceptionally stable structure for buffering volume change.
Current research on PIBs anode materials has focused on carbonaceous materials, transition-metal carbides and oxides, sulfides, and simple substances such as P, Sn, Sb, and Bi.35–42 Among them, transition metal chalcogenides have been reported to be suitable electrode materials for PIBs owing to their good thermal strength, strong redox reversibility, and superior electrical conductivity.43–45 Interestingly, the conductivity of Se (1 × 10−5 S m−1), a group VI element, is several orders of magnitude higher than that of S (5 × 10−30 S m−1).46 Considering the low cost, nontoxic nature, and abundance of reserves in the earth, anode materials based on iron selenides like FeSe2 and FeSe have been found to deliver stable capacities in PIBs.47,48 Deng et al. prepared an interconnected three-dimensional (3D) porous carbon skeleton with FeSe nanoparticles, which helped buffer volume expansion and promoted fast and efficient ionic transport, resulting in improved performance. They also regarded K2Se as a product of the potassiation reaction.49 Zhang et al. explored FeSe nanoparticles confined in a carbon matrix as an anode material for PIBs. According to them, the K5Se3 phase is formed after complete discharge.50 Although the performance of this material has been validated, ionic migration and atomic reorganization-induced microstructural transformations that are dynamic and necessary for the stability and performance of the battery remain elusive. The size-dependent effect and cycling mechanism have not been identified for the cyclic performance. Hence, fundamentally understanding the genuine nature of the behavior and reaction mechanisms of the FeSe anode for PIBs requires thorough investigation of the interplay between FeSe and K+ during the live potassiation/depotassiation process.
Real-time atomic-scale observations of the potassiation/depotassiation of FeSe are crucial for clarifying the structural and phase evolution and reaction mechanisms. Herein, we report the first high-resolution transmission electron microscopy (TEM) observation of the dynamic evolution of the material structure, morphology, and chemistry during live potassiation/depotassiation of FeSe nanoflakes of different sizes at the atomic scale. In addition, the basic atomic structure of FeSe was revealed using spherical aberration-corrected scanning transmission electron microscopy (Cs-STEM). We found that the FeSe nanoflakes successively underwent intercalation and conversion reactions, and the potassiation pathways of the intercalation process varied with different nanoflake sizes. Small-sized FeSe nanoflakes exhibited evident volume expansion induced by the intercalation of K+, whereas for large-sized nanoflakes, atomic-scale cracks were formed along the direction of ionic diffusion, which could be attributed to significant stress accumulation caused by ionic diffusion, as confirmed by geometric phase analysis (GPA) and finite-element analysis (FEA). The products of full potassiation, Fe, and K2Se, were identified using selected area electron diffraction (SAED), and the latter phase was discovered for the first time using in situ technology.46 Remarkably, small-sized FeSe nanoflakes exhibited a higher cyclability performance with well-maintained structural integrity. This work is expected to offer essential guidelines for optimizing the sizes of electrode materials and may also be helpful in elucidating the reaction and degradation mechanisms of transition-metal selenides, thus allowing for the design of batteries with improved performance.
RESULTSThe typical morphological and structural characteristics of the FeSe nanoflakes are shown in Figure 1. The x-ray diffraction (XRD) pattern shows the major diffraction peaks of the nanoflakes that can be indexed to the tetragonal phase of FeSe (PDF card no. 85-0735) in Figure 1A. The sharp diffraction peaks at 16.0, 28.6, 32.4, 37.4, and 47.4° correspond to the (001), (101), (002), (111), and (112) planes, respectively. The chemical composition analysis of the sample via x-ray photoelectron spectroscopy (XPS) (Figure 2B) shows the primary components of Fe and Se in the FeSe nanoflakes. The characteristic peaks of FeSe indicate Fe 2p3/2 and 2p1/2 orbitals in Figure S1A at 710.0 and 723.9 eV, respectively. In addition, Figure S1B shows the presence of Se 3d based on the peaks at 54.5 and 55.7 eV indexed to Se 3d5/2 and Se 3d3/2, respectively. Further investigation of the morphology and structure of FeSe was carried out using TEM and scanning electron microscopy (SEM) (Figure S2). The lattice fringes of 0.55 nm in Figure 1C correspond to the (001) planes of tetragonal FeSe. The corresponding fast Fourier transform (FFT) image (Figure 1D) reveals that the tetragonal FeSe sample was monocrystalline. The atomic-resolution HAADF-STEM images in Figure 1E,F show that iron and selenium atoms are alternately arranged (iron and selenium indicated by brown and green dots, respectively) perpendicular to the FeSe layer. The corresponding atomistic structure models of FeSe along the [010] and [001] directions correspond well with the observations from the atomic-resolution HAADF-STEM, as illustrated in Figures 1G,H. Energy dispersive spectroscopy (EDS) elemental mapping images (Figure 1I−L) confirm the two-dimensional (2D) structure in a detailed manner, showing uniform dispersion of Fe and Se throughout the nanoflake.
FIGURE 1. (A) XRD pattern of FeSe powder. (B) XPS survey spectra of the FeSe nanoflakes. (C,D) HRTEM of FeSe samples and the corresponding fast Fourier transform (FFT). (E) Atomically-resolved HAADF-STEM image of FeSe viewed along the [010] zone axis. (F) The magnified HAADF-STEM image of (E). (G,H) Atomic structure model of FeSe viewed along [010] and [001] axis. (I–L) HAADF-STEM image and EDS elemental mappings of FeSe
FIGURE 2. (A) Schematic illustration of in situ electrochemical potassiation and depotassiation. (B–G) Time-sequenced TEM images of a small-sized FeSe nanoflake during the first potassiation. (H) The reaction front rates of the intercalation and conversion as a function of potassiation time. (I–L) HAADF-STEM image of a small-sized potassiated FeSe nanoflake and EDS mappings of K, Fe, and Se
To clarify the potassiation behavior and underlying reaction mechanisms of FeSe nanoflakes during the live potassiation/depotassiation process, a functioning solid-state nanosized PIB capable of real-time in situ monitoring of (de)potassiation was assembled inside the TEM (schematic illustration is shown in Figure 2A). In this study, we compared the kinetic behaviors of small-sized (less than ~25 nm) and large-sized (more than ~200 nm) FeSe nanoflakes using in situ TEM. Small-sized FeSe nanoflakes were fabricated using a liquid-phase exfoliation technique involving micro-sized FeSe powder grinding and subsequent ultrasound probe sonication in a low-temperature environment. The detailed methods and a schematic illustration of the liquid-phase exfoliation operation are presented in Figure S3. Real-time observation of the morphological evolution of a small-sized FeSe nanoflake during the first potassiation is displayed in the time-sequenced TEM images in Figure 2B−G (Movie S1). The corresponding TEM image of a nano-battery consisting of an FeSe anode is displayed in Figure 2B, where the yellow arrow indicates the transport direction of K+ ions. During potassiation, a gradual microstructural change along the diffusion direction of K+ ions was observed. A “hump” region, with radial and longitudinal lengths of 20.32 and 32.85 nm, respectively, was observed at the top of the FeSe nanoflake. Upon applying a potential, two distinct potassiation reaction fronts (RFs) were observed at the boundary of the “hump” (RF-I marked with blue and RF-II with green dashed lines, Figure 2C), which propagated along the diffusion direction of K+. This indicated the simultaneous occurrence of two different reactions. In the RF-I region (blue dashed line), the slight imaging contrast and residual lattice fringes suggest intercalation of K+ into the FeSe interlayers without causing the collapse of the crystal structure. Identical behavior was also observed in Bi, Fe2O3, and Cu2S nanoplates, in which mild contrast changes occurred owing to the intercalation of Na+ or Li+ ions.51 RF-II, indicated by the green dotted line, closely followed. The lattice fringes of FeSe vanished completely after RF-II. Noticeable expansions of approximately 14.27% in the radial direction and 13.21% in the longitudinal direction (from 20.32 to 23.22 nm and from 32.85 to 37.19 nm, respectively) were observed, implying emergence of the conversion reaction in the FeSe nanoflake.
Subsequently, the RFs advanced continuously, as shown in Figure 2D−F. For quantitative analysis of the potassiation dynamics of small-sized FeSe nanoflakes, the migration speeds of RF-I and RF-II were measured from time-lapse high-resolution transmission electron microscopy (HRTEM) images, as shown in Figure 2H. Based on statistical results, the calculated migration speeds of RF-I and RF-II were found to be approximately 89 and 42 nm s−1, respectively, both of which were faster in comparison to analogous ion systems such as K-Sb2S3 (9.8 nm s−1) and Na-FeS2 (6–11 nm s−1).44 This suggests that the potassiation kinetics for FeSe is relatively efficient, despite the larger radius and higher mass of the K+ ion than those of Na+ ion. The initial intercalation rate was double that of the conversion reaction. However, with the movement of the intercalation front, there was a dramatic reduction in the velocity of the intercalation reaction because the potassium was rapidly consumed by the fast-moving RF corresponding to the conversion reaction. Although the axial length increased from 32.85 to 39.25 nm (≈19% expansion) after complete potassiation, no apparent cracks and pulverization were observed for small-sized FeSe nanoflakes, implying reliable mechanical stability. The HAADF-STEM image and the corresponding EDS mapping of the fully potassiated nanoflakes in Figure 2I−L show that Fe, Se, and K were evenly distributed throughout the nanoflakes, indicating the same degree of potassiation at the single-nanoflake level. The repeated in situ experiment of such small-sized nanoflakes during the first potassiation was presented in Figure S4.
Large-sized FeSe nanoflakes were fabricated from the micro-sized FeSe sample using the focused ion beam method (Figure S5, detailed operations provided in the Supporting Information). The potassiation behavior and phase evolution in a large-sized FeSe nanoflake during the first potassiation were investigated by HRTEM imaging, using which the corresponding FFT patterns were obtained (Figure 3). Before the reaction, the low-magnification morphology of the as-prepared FeSe nanoflakes was characterized (Figure S6). The large FeSe nanoflake has a width of 200 nm, and the lattice fringe of 0.22 nm corresponds with the (102) plane of tetragonal FeSe. Once potassiation began, we detected two different RFs (Figure 3B, Movie S2), consistent with the results shown in Figure 2. In this state, the interlayer spacing of the (102) planes was expanded by the inserted K+ ions and the gradual distortion (Figure 3B). Interestingly, tiny structural cracks with low contrast were first identified in the reaction boundary in Figure 3C, which gradually grew larger along the potassium diffusion direction and finally evolved into larger cracks, as indicated in Figure 3D. Splitting the (102) plane into two spots (Figure 3B inset) indicated that the KxFeSe phase expanded but remained in the same crystal orientation as the pristine FeSe phase. It is speculated that because of the insertion of K+ into the open positions of the interlayer, there is a slight expansion of the lattice; however, the structural integrity of the original 2D framework was maintained.52 With an increase in K+-intercalation, the KxFeSe phase gradually disappeared (Figure 3C), together with the formation of a new phase, K2Se. Moreover, the electrochemically-reduced Fe species began to agglomerate after excess K+ was inserted (Figure 3D). In the electrochemical reactions indicated below, there are possibly two K+ ions stored per unit cell at most during the overall potassiation process:[Image Omitted. See PDF] [Image Omitted. See PDF]To obtain a more detailed understanding of the formation of cracks in large-sized FeSe nanoflakes, atomic-scale structural evolution was directly visualized by in situ HRTEM imaging, as shown in Figure 4. We found a strong coupling between the electrochemical process and mechanical effect. As illustrated in Figure 4A, three cracks, roughly parallel to the (102) plane, were detected. The corresponding GPA identified an insertion interface in which potassium ion diffusion led to the accumulation of significant stress, which was primarily released by the initiation of cracking (Figure 4B). In addition, it is speculated that some defects emerge at the interface between the FeSe nanoflakes and potassium sources. The insertion of K+ ions promoted the movement of defects, which further led to the extension of cracks, as shown in Figure 4A. Notably, the rapid evolution of cracks also prompted the diffusion of K+ and accelerated the electrochemical intercalation reaction. Such crack generation was undoubtedly due to the potassiation of FeSe, as verified by repeated in situ experiments (Figure S7). Local EELS measurements from the in situ potassiated nanoflakes were in the order of the potassium diffusion direction (Figures 4C,D). A cursory increase in the intensity of the K–K edge was observed as potassiation progressed. However, the spectrum labeled “V” began to decrease, implying the inhomogeneity of the K+ concentration across the crack region. This led to internal strain continuity that sustained the continuous cracking formation. In addition, using finite element analysis (FEA), we conduct electrochemo-mechanical modeling to simulate potassium ion diffusion-induced reaction interface advance and stress distribution, as shown in Figure 4E. A three-dimensional (3D) model allowing potassium diffusion through bulk and surface paths was conducted by applying a constant concentration boundary condition.53 As the potassiation diffused, distinct reaction boundaries were acquired in the simulation, as shown in Figure 4F. The reaction-induced stress distribution corresponding to the concentration profiles is also shown in Figure 4G, which shows a convex geometry for the RF. The corresponding stress concentrations in the convex RF can drive crack generation at the phase boundary and further facilitate the diffusion of potassium ions in the continued reaction.54
FIGURE 3. Structure evolution of a large-sized FeSe nanoflake during the first potassiation at 0 s (A), 3 s (B), 10 s (C), and 16 s (D) (Movie S2). TEM images (top), corresponding FFT patterns (middle), and HRTEM images (bottom). The inset HRTEM image in (D) depicts the enlargement of the blue box. Scale bar: 0.5 nm
FIGURE 4. (A) Atomic-scale image of a large-sized partially-potassiated FeSe nanoflake. The yellow dotted lines represent “crack”. (B) Geometric phase analysis (GPA) showing the generation of the crack during potassium-ion intercalation. (C) HAADF-STEM image of a large-sized potassiated FeSe nanoflake. The yellow dashed arrow shows the direction of electron energy loss spectroscopy (EELS) collection. (D) STEM-EELS in the order of K+ diffusion captured from (C). (E−G) Electrochemo-mechanical finite element analysis (FEA) results showing stress generation during the reaction. (H−K) Selected area electron diffraction (SAED) patterns corresponding to the dashed box in (C)
Coupled with in situ TEM and FFT-based determination of the phase transformation, real-time phase evolution during potassiation was also monitored via in situ SAED. The phase identification obtained from in situ SAED patterns is more precise and has better statistical validation because it sequentially captures structural information. These two stages can be clearly identified during the potassiation of FeSe: (i) formation of the KxFeSe phase with an expanded lattice (indicated by the (002) plane in Figure 4I) and (ii) formations of K2Se and Fe via the conversion reaction, as shown in Figure 4J. Representative SAED patterns collected at each stage show a coherent crystallographic relationship among pristine FeSe, potassiated KxFeSe, and the converted K2Se phase, consistent with the FFT analyses in Figure 3A−D. Therefore, we confirmed that the phase transformations occurring during potassiation reactions were identical by combining the in situ SAED and in situ HRTEM results and validating the reliability of HRTEM and FFT analyses for precise phase identification.
For the practical application of FeSe as an anode in rechargeable PIBs, an essential precondition is the reversible extraction of K+. Thus, the electrochemical potassiation and depotassiation cycles were investigated to further demonstrate whether the structure of the FeSe electrode could be restored upon cycling. As shown in Figure 5A,B, the insertion of K+ led to the expansion of FeSe. After the extraction of K+, although the left region of FeSe was not directly connected to the K source, the diameter of the FeSe nanoflakes decreased, demonstrating that K+ could still be extracted across the contact interface, as indicated in Figure 5C. Remarkably, even after multiple insertions and extractions of K+ (Figure 5A−G), the volume expansion and contraction of the FeSe nanoflakes remained reversible. Figure 5H further shows the change in diameter for each cycle. The results demonstrate the viability of FeSe nanoflakes as electrode materials for recyclable PIBs. The SAED patterns of the FeSe nanoflakes during the first two cycles are presented in Figure 5I−M. The potassiated products were always K2Se and Fe that can be further converted into FeSe after the first depotassiation process. Moreover, the SAED patterns of the second potassiated and depotassiated products indicate the reversibility of the subsequent electrochemical cycles between the FeSe and Fe phases, as illustrated in Figure 6A. The discharging–charging curves of two FeSe/C composites of different sizes (less than ~25 nm and more than ~200 nm) are shown in Figure 6B,C, demonstrating obvious discrimination of specific capacity at a rate of 0.1 A g−1. Interestingly, the initial discharge/charge capacity of small-sized FeSe/C composites is significantly higher than that of the large sized composites. More remarkably, it can be clearly observed that large-sized FeSe/C composites present rapid capacity loss whereas small-sized FeSe/C composites still display the high specific capacity at 100th cycles (Figure 6D), suggesting that small-sized FeSe/C composites show better cyclic stability than large-sized FeSe/C composites, which is in agreement with the above in situ TEM observations. Figure S8 shows an attractive rate performance of small-sized FeSe/C composites from 0.1 to 2 A g−1. These results may be attributed to the good conductivity and strong mechanical resilience of small-sized FeSe/C nanocomposites, further suggesting the great potential of the small-sized FeSe as a promising anode material for PIBs.
FIGURE 5. (A−G) The first three potassiation–depotassiation TEM image of FeSe nanoflakes. (H) The measured diameters of the FeSe nanoflake as a function of electrochemical cycling times. (I−M) SAED patterns of the first (J,K) and the second (L,M) potassiation–depotassiation products
FIGURE 6. (A) Schematic illustration of the FeSe nanoflake during electrochemical potassiation–depotassiation cycles. (B) Discharge–charge curves of large-sized FeSe/C composites at 0.1 A g−1. (C) Discharge–charge curves of small-sized FeSe/C composites at 0.1 A g−1. (D) Cycling performance of small-sized and large-sized FeSe/C composites at 0.2 and 0.1 A g−1, respectively
In summary, thorough understanding and contrastive investigations of FeSe nanoflakes of different sizes during live potassiation–depotassiation processes, including the dynamic migration behaviors of K+, detailed phase transformations, and the corresponding cyclic properties, were carried out through the in situ TEM approach down to the atomic scale. We demonstrated that small-sized FeSe nanoflakes exhibited noticeable volume expansion induced by the intercalation of K+ at the intercalation stage, whereas visible cracks with low contrast along the direction of K+ diffusion were observed in large-sized FeSe nanoflakes. GPA and FEA were used to elucidate the significant stress generation and crack extension originating from the synergistic effect of mechanical and electrochemical interactions. In situ FFT and SAED results show that FeSe experienced stepwise reactions during potassiation, namely, intercalation and conversion (FeSe → KxFeSe → K2Se + Fe). Furthermore, a reversible phase transformation between the FeSe and Fe phases was observed after multiple cycles. In particular, small-sized FeSe nanoflakes exhibited better cyclability and well-maintained structural integrity. The findings of this study provide important guidelines for optimizing FeSe materials with appropriate dimensionality and insight into the underlying K+ storage mechanism of transition-metal selenides, which would also be beneficial for developing high-performance PIBs.
EXPERIMENTAL SECTIONXRD pattern of FeSe sample was recorded by a Bruker D8 Advance diffractometer. XPS was collected using PHI 5000 VersaProbe III with a monochromatic-anode Al Kα X-ray source. To capture atomic-scale high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of FeSe nanoflakes, an aberration-corrected FEI (Titan Cubed Themis Z) were used. A Talos-F200 transmission electron microscope (TEM) at 200 kV was used to obtain detailed structures and elemental mappings of the products.
The FeSe nanoflakes were mounted onto a half-copper grid as the active electrode. A needle tip of tungsten, using which the K metal was scratched, was used as source of potassium. The naturally-formed layer of KOx served as the solid electrolyte, which allowed the transport of K+ ions. The KOx/K electrode approached the FeSe electrode by driving the mobile piezo-probe with caution. After establishing contact, a bias of −1.5 V was applied to the FeSe nanoflakes to induce the electrochemical potassiation reaction by driving the electrons and K+ ions to run across the circuit. For depotassiation, the bias was reversed, and a voltage of +1.5 V was applied to extract K+ from the potassiated FeSe nanoflakes.
ACKNOWLEDGMENTSThis work was supported by the National Key R&D Program of China (Grant No. 2018YFB1304902); the National Natural Science Foundation of China (Grant Nos. 12004034, U1813211, 22005247, 11904372, 51502007, 52072323, 52122211, 12174019, and 51972058), the General Research Fund of Hong Kong (Project No. 11217221), China Postdoctoral Science Foundation Funded Project (Grant No. 2021M690386). The authors acknowledge the Analysis & Testing Center in Beijing Institute of Technology for using in situ TEM platform.
CONFLICT OF INTERESTThe authors declare no conflict of interest.
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Abstract
Potassium-ion batteries (PIBs) are considered promising alternatives to lithium-ion batteries owing to cost-effective potassium resources and a suitable redox potential of −2.93 V (vs. −3.04 V for Li+/Li). However, the exploration of appropriate electrode materials with the correct size for reversibly accommodating large K+ ions presents a significant challenge. In addition, the reaction mechanisms and origins of enhanced performance remain elusive. Here, tetragonal FeSe nanoflakes of different sizes are designed to serve as an anode for PIBs, and their live and atomic-scale potassiation/depotassiation mechanisms are revealed for the first time through in situ high-resolution transmission electron microscopy. We found that FeSe undergoes two distinct structural evolutions, sequentially characterized by intercalation and conversion reactions, and the initial intercalation behavior is size-dependent. Apparent expansion induced by the intercalation of K+ ions is observed in small-sized FeSe nanoflakes, whereas unexpected cracks are formed along the direction of ionic diffusion in large-sized nanoflakes. The significant stress generation and crack extension originating from the combined effect of mechanical and electrochemical interactions are elucidated by geometric phase analysis and finite-element analysis. Despite the different intercalation behaviors, the formed products of Fe and K2Se after full potassiation can be converted back into the original FeSe phase upon depotassiation. In particular, small-sized nanoflakes exhibit better cycling performance with well-maintained structural integrity. This article presents the first successful demonstration of atomic-scale visualization that can reveal size-dependent potassiation dynamics. Moreover, it provides valuable guidelines for optimizing the dimensions of electrode materials for advanced PIBs.
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Details
; Xu, Feng 8 ; Dong, Lixin 3 1 Beijing Advanced Innovation Center for Intelligent Robots and Systems, School of Medical Technology, Beijing Institute of Technology, Beijing, People's Republic of China
2 Analysis & Testing Center, Beijing Institute of Technology, Beijing, People's Republic of China
3 Department of Biomedical Engineering, City University of Hong Kong, Hong Kong, People's Republic of China
4 Shaanxi Materials Analysis and Research Center, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, People's Republic of China
5 School of Environmental and Safety Engineering, North University of China, Taiyuan, People's Republic of China
6 Department of Materials Science and Engineering, College of Materials, Xiamen University, Xiamen, Fujian, People's Republic of China
7 Department of Nanoengineering, University of California San Diego, La Jolla, California, USA
8 SEU-FEI Nano-Pico Center, Key Laboratory of MEMS of Ministry of Education, Southeast University, Nanjing, People's Republic of China




