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Direct Mapping of Charge Distribution during Lithiation of Ge Nanowires Using Off-axis Electron Holography Zhaofeng Gan, Meng Gu, Jianshi Tang, Chiu-Yen Wang, Yang He, Kang L Wang, Chongmin Wang, David J. Smith, and Martha R. McCartney Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b01099 • Publication Date (Web): 18 May 2016 Downloaded from http://pubs.acs.org on May 20, 2016

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Direct Mapping of Charge Distribution during Lithiation of Ge Nanowires Using Off-axis Electron Holography

Zhaofeng Gan,1,a,* Meng Gu,2,* Jianshi Tang,3 Chin-Yen Wang,3,4 , Yang He,5 Kang L. Wang,3 ChongMin Wang, 2,a David J. Smith,1 and Martha R. McCartney1,a

1

Department of Physics, Arizona State University, Tempe, AZ 85287, USA 

2

Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory,

Richland, WA 99352, USA 3

Device Research Laboratory, Department of Electrical Engineering, University of California,

Los Angeles, CA 90095, USA 4

Department of Materials Science and Engineering, National Taiwan University of Science and

Technology, Taipei City, Taiwan 10607, Republic of China 5

Department of Mechanical Engineering and Materials Science, University of Pittsburgh,

Pittsburgh, PA 15261, USA

* These authors contributed equally to this work.

a

Corresponding authors: [email protected] [email protected] [email protected]

Key Words: lithium ion battery, charge distribution, in situ TEM, electron holography

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Abstract The successful operation of rechargeable batteries relies on reliable insertion/extraction of ions into/from the electrodes. The battery performance and the response of the electrodes to such ion insertion and extraction are directly related to the spatial distribution of the charge and its dynamic evolution. However, it remains unclear how charge is distributed in the electrodes during normal battery operation. In this work, we have used off-axis electron holography to measure charge distribution during lithium ion insertion into a Ge nanowire (NW) under dynamic operating conditions. We discovered that the surface region of the Ge core is negatively charged during the core-shell lithiation of the Ge NW, which is counterbalanced by positive charge on the inner surface of the lithiated LixGe shell. The remainder of the lithiated LixGe shell is free from net charge, consistent with its metallic characteristics. The present work provides a vivid picture of charge distribution and dynamic evolution during Ge NW lithiation, and should form the basis for tackling the response of these and related materials under real electrochemical conditions. -4

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Lithium ion batteries (LIBs) are indispensable nowadays for powering portable electronics and electric vehicles, and they are emerging, in combination with other multi-valence ion batteries, as a means for storing renewable energy such as wind and solar.1, 2 The LIB recharging process is rather simple in physical and chemical terms, relying on insertion/extraction of ions into/from a host lattice (the electrode) with concurrent flow of electrons to compensate the charge balance. The materials used as cathode and anode for the rechargeable battery range from metal to semiconductor and insulator. It has been well documented that the electrochemically driven insertion of lithium ions into a semiconductor or insulator will lead to amorphization (typically Li into Si, Ge, ZnO2, and SnO2),3-6 a process that is not attainable with other known solid-state or wet-chemistry synthesis methods. Some materials, instead of being subject to solidstate amorphization, alloy directly with the inserted ions to form new crystalline phases (typically Li with Al or Sn).7, 8 The distinctively different responses of these materials to ion insertion and retraction appear to be related to the local charge distribution. Based on computational modeling,9 it has been proposed that the local electron enrichment contributes to the solid-state amophization of the materials upon lithium ion insertion into silicon and germanium (semiconductor), while for metals (conductor) the ion insertion leads to alloying. Furthermore, the charge and discharge rates of a battery critically depend on the rate of ion mobility in the electrode, which has been found to be closely related to the electronic conducting characteristics of the electrode.10,11 Apparently, during the functioning of a rechargeable battery, the local charges show dynamic evolution, which critically governs the response of the electrode to ion insertion/extraction and ultimately determines the battery performance. However, associated with the dynamic, evolving nature of the electrode, direct observation of charge distribution under battery operating conditions has never been possible, although some attempts have been reported.12 In this work, we use a combination of in situ transmission electron microscopy (TEM) and off-axis electron holography to directly map the charge distribution across a Ge/LixGe core/shell nanowire (NW) formed during the lithiation of the Ge NW under dynamic battery operating conditions. We discovered that during the core-shell lithiation of the Ge NW, the outer part of the Ge core is negatively charged, which is counterbalanced by positive charge on the inner surface of the lithiated LixGe shell. The remaining lithiated LixGe shell is free from net charge, indicating its metallic characteristics. The present work provides a vivid picture of charge 3 ACS Paragon Plus Environment

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distribution and dynamic evolution during Ge NW lithiation, and should form the basis for tackling the response of these materials under real electrochemical conditions. Off-axis electron holography is an electron-microscopy-based interferometric technique.13,14 By using interference between the reference wave which has passed only through vacuum, and the object wave, which has passed through the sample, an electron hologram is formed. Phase and amplitude images of the sample can then be reconstructed. In the absence of any magnetic field, the projected phase shift of the electron wave caused by electrostatic fields within the sample, can be simply expressed as: ∆߮ሺ‫ݔ‬, ‫ݕ‬ሻ = ‫ܥ‬ா ∙ ‫׬‬ሺܸ଴ ሺ‫ݔ‬, ‫ݕ‬, ‫ݖ‬ሻ + ܸ௕௜ ሺ‫ݔ‬, ‫ݕ‬, ‫ݖ‬ሻሻ dz

(1)

where CE is an electron-energy-dependent interaction constant with the value of 0.00653 rad V-1 nm-1 for 300-keV electrons, V0 is the mean inner potential (MIP) of the sample, and Vbi is the built-in potential due to any charge distribution. By using this equation, the phase shift measured by holography can be directly related to the electrostatic potential distribution of the sample. The single-crystal Ge NWs studied here were grown along [111] directions on Si(001) substrates, as described in detail elsewhere.15 After growth, one Ge NW was detached from the substrate and attached to a Pt tip using silver glue while Li metal was attached to a second Pt tip. Both electrodes were then installed in a NanofactoryTM STM holder for the in situ lithiation experiments. Before insertion into the TEM lens column, the STM holder was exposed to air for a few seconds, and a Li2O layer was formed on the Li metal surface during this short period, which then serves as the solid electrolyte during lithiation. The Ge NW was moved to make physical contact with the Li source, forming an open cell battery structure, as illustrated in Figure 1. A bias of ~ -2V was then applied to the Ge NW, while the Li metal was kept grounded during the lithiation process. The off-axis electron holography experiments were performed using an FEI Titan 80-300 electron microscope, which was operated at 300keV and equipped with field emission gun, probe corrector, electrostatic biprism, Lorentz mini-lens and Gatan Imaging Filter (Quantum 965). For the holography experiments, the objective lens was switched off, and the Lorentz mini-lens was used to obtain a larger field of view. The typical biprism voltage was 120V, the fringe spacing was ~3.4nm, and the hologram exposure time was 2s.


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Based on in situ TEM studies, it has been well established that lithiation of the Ge NW proceeds in two phases, leading initially to the formation of an LixGe shell that surrounds the remaining core of the Ge.6 This process is also demonstrated for the present case, as shown by the in situ TEM movie included with the Supplementary Material (Movie S1).10,16,17 Figure 2 shows TEM images of the Ge NW taken during lithiation. Figure 2a shows the Ge NW in contact with the Li metal. Application of -2V bias causes Li2O to diffuse onto the Ge NW surface as a solid electrolyte. Figure 2b indicates that Li ions have diffused into the surface of the Ge NW, forming a crystalline Ge/amorphous LixGe core/shell structure. As lithiation continued, the shell became thicker, while the core region shrank. The total volume of the NW increased, as clearly visible in Figure 2c, while the core size decreased further. At the completion of lithiation, the Ge core had completely disappeared and the NW became polycrystalline, as shown in Figure 2d. Figure 3 shows STEM HAADF and EELS mapping of the Ge/LixGe core/shell structure, which were recorded immediately after Figure 2b. In the HAADF image, the intensity of the NW shell is lower, compared to the core, which means that the shell has lower average atomic number. The Li ionization edge arrowed in Figure 3b was used to map the distribution of Li across the NW, as shown by Figure 3c. The intensity distribution in the mapping indicates that the Li was distributed homogeneously in the NW shell. Electron holography observations were made during the lithiation process. Figures 4a, 4d and 4g show holograms taken at almost the same times as the corresponding images shown in Figures 2b, 2c and 2d, respectively. Figures 4b, 4e and 4h are the corresponding reconstructed phase images, using pseudo-color to emphasize the local changes of phase. The color scale bars are shown at top right. The center part of the NW has higher phase compared to the outer parts, which is due to the combination of greater thickness and higher mean inner potential of crystalline Ge, compared to LixGe. Phase profiles were extracted along the white arrows in the reconstructed phase images and are shown at the right in Figures 4c, 4f and 4i, respectively. The Ge core in Figure 4c is about half the diameter of the NW, and both the core and shell parts have nearly cylindrical shapes. In Figure 4f, the Ge core has shrunk to a smaller size and appears to be faceted, as suggested by the triangular profile at its center. Meanwhile, the LixGe shell still retains a round cross section. In Figure 4h, the entire Ge NW has been lithiated, the Ge core has disappeared, and the lithiated LixGe (x~3.75) NW again resembles a cylindrical NW shape.


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During this process, the NW diameter has increased from 176nm in Figure 4c, to 258 nm in Figure 4i. The phase profiles across the NW result from superposition of the mean inner potentials of the materials and any built-in potential. As a first step towards interpretation of the phase profiles, it is initially assumed that there are no trapped charges in the NW and that the phase changes are due only to mean inner potential Vshell and the change of thickness. Models that include trapped charges are discussed below. Assuming that the NW has a cylindrical shape, then the phase change due to the shell part can be calculated and compared with the experimental results, as shown by the red curves in Figures 4c, 4f and 4i. From the fitting for the best fitted Vshell, it seems that a cylindrical NW shape fits reasonably well with the experimental results. The best fitted values of Vshell for these three stages of lithiation are shown in Table 1. As the lithiation continued, the mean inner potential of Vshell decreased from 7.6V to 5.1V. This drop indicates that the Li concentration in the LixGe shell has increased during lithiation, which is to be expected since Li is a light element and has a smaller mean inner potential relative to Ge. The bias applied to the NW should not affect this conclusion since the bias was kept fixed at -2V throughout the entire process. Similar fitting was applied for the core part in Figure 4c, as shown by the greencurve. This model also fits closely with the experimental data. However, the best fitted Vcore is only 10.6±0.1V, which is in contrast to the value of 14.3±0.2V for crystalline Ge published in the literature.18 This substantial difference of 3.7+0.3V suggests the likelihood that charges are trapped in the NW during the lithiation process. In order to determine the amount of trapped charge in the NW, a variety of models were considered, including: (a) sheet electrons at the Ge core surface and sheet positive charge at the inner shell surface; (b) bulk electrons in the Ge core and sheet positive charge at the inner shell surface; (c) sheet electrons at the Ge core surface and sheet positive charge at the outer shell surface; (d) bulk electrons in the Ge core and sheet positive charges at the outer shell surface; (e) sheet electrons at the Ge core surface and bulk positive charge in the shell (See additional figures in the Supplementary Materials). The model that provides the closest fit with the experimental results is shown in Figure 5a. This model assumes that Li+ ions have accumulated at the inner surface of the LixGe shell, while electrons are trapped near the outer surface of the Ge core.


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In this model, the LixGe shell is grounded, while the Ge core is negatively biased through the TEM biasing holder. Thus, electrons are distributed near the Ge surface, causing the Ge NW core to become an equipotential, while the Li+ ions are distributed on the inner surface of the LixGe shell and balance the charge of electrons in the Ge core. Thus, an electric field is formed at the core-shell interface, which is attributed to a possible band alignment. The LixGe shell is also an equipotential so that there are no free charges in its bulk, which would be consistent with the idea that the LixGe shell has metallic characteristics. Based on this model, the built-in potential for the Ge core is -3.7V while the LixGe shell remains grounded, so that the potential offset between the core and shell would be ~3.7V. Thus, the lithiation process seems to be associated with local electron enrichment, as predicted by theoretical modeling,9 and suggests that the rate of NW lithiation might be limited by the LixGe/Ge interface reaction, which is consistent with the kinetics studies of Ge and Si reported in the literature.19-21 It is generally appreciated that it is very difficult to quantify the Li concentration, as indicated by the value x of Li in the LixGe, especially by in situ methods as the reaction proceeds. The present measurements of the change in mean inner potential with progression of the lithiation provides a viable means of quantifying x. This can be done from the shell/core volume ratio and the measured mean inner potential using the following expression: ௏ை௅ಸ೐

ሺ‫ܸ ∙ ݔ‬௅௜ + ܸீ௘ ሻ ∙ ൬௏ை௅

ಽ೔ೣ ಸ೐

൰ = ܸ௅௜ೣ ீ௘

(2)

where VGe and VLixGe are the mean inner potentials for crystal Ge and LixGe, respectively, VOLGe and VOLLixGe are the volumes for Ge and LixGe, respectively, and VLi is the mean inner potential changed when one Li atom is added to the Ge unit cell while keeping the total volume unchanged. This equation also assumes that the MIP for Ge does not change while the lithiation process takes place. The measured radius values of the NW core and the complete NW are shown in Table 2, where case A is before lithiation, and cases B, C and D are for almost the same times as when Figures 4a, 4d, and 4g, respectively, were taken. The case D of Figure 4g is used for calculation of the MIP of Li, where x is taken to be 3.75 for the fully lithiated phase, and the volume ratio ௏௢௟ಸ೐

௏௢௟ಽ೔ೣ ಸ೐

was calculated to be 0.13. The value for VLi is then calculated to be 6.34V, using


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Equation 2 and the MIP value for crystalline Ge of 14.3V.18 Since the core has fully disappeared, there should be no trapped charge in the NW, which might otherwise influence the result. After calibration, the concentration of Li in LixGe, as given by the value of x, can be calculated, again using Equation 2. For case B at Figure 4a, the x value in the NW shell is estimated to be 2.4 for the measured MIP of 7.6V, and the effect of trapped charge has been ignored. These results indicate that the intermediate lithiated state for the NW shell is LixGe, where x is significantly lower than 3.75. As the lithiation process continued, more Li diffused into the LixGe shell and thus x increased until it reached 3.75 and NW became fully lithiated. The case A cannot be evaluated to confirm this result because it appears that the core has a faceted shape, meaning that its cross-section area cannot be calculated accurately. Using a combination of in situ TEM and electron holography, we have probed the dynamic evolution of charge distribution during the Ge NW lithiation. With the increase of lithium concentration in the lithiated LixGe shell, the mean inner potential for the LixGe shell decreases. More importantly, during the progress of the Ge core-LixGe shell lithiation, it was also discovered that the Ge core had lower mean inner potential than its theoretical value. This difference was attributed to accumulation of trapped charge near the surface of the Ge core. Moreover, this charge within the Ge core was counterbalanced by positive charge at the very inner surface of the lithiated LixGe shell, which was otherwise an equipotential. The present results provide a direct route to observations of charge distribution and its dynamic evolution during battery charging, and opens up a promising new avenue for studying battery electrode dynamics involving ion insertion and electron transport under battery operating condition.

Supporting Information Available: 1) Different possible models for fitting the experimental results 2) In-situ TEM movie showing the core-shell lithiation of Ge nanowire This information is available free of charge via the Internet at http://pubs.acs.org


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Conflict of Interest Disclosure: The authors declare no competing financial interest.

Acknowledgments The electron holography studies have been supported by DoE Grant DE-FG0204ER46168. The authors acknowledge use of facilities in the John M. Cowley Center for High Resolution Electron Microscopy at Arizona State University. This work at PNNL is supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U. S. Department of Energy under Contract No. DE-AC02-05CH11231, Subcontract No. 18769 and DE-AC-36-08GO28308 under the Advanced Batteries Materials Research.

A portion of the electron holography studies was supported by the Laboratory

Directed Research and Development Program as part of the Chemical Imaging Initiative at Pacific Northwest National Laboratory (PNNL). The work was conducted in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at PNNL. PNNL is operated by Battelle for the DOE under Contract DE-AC05-76RLO1830.


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(12) Yamamoto, K.; Iriyama, Y.; Asaka, T.; Hirayama, T.; Fujita, H.; Fisher, C. A. J.; Nonaka, K.; Sugita, Y.; Ogumi, Z. Angew. Chem., Int. Ed. 2010, 49, 4414-4417. (13) McCartney, M. R.; Smith, D. J. Annu. Rev. Maters. Res. 2007, 37, 729-767. (14) McCartney, M. R.; Agarwal, N.; Chung, S.; Cullen, D. A.; Han, M.-G.; He, K.; Li, L.; Wang, H.; Zhou, L.; Smith, D. J. Ultramicroscopy 2010, 110, 375-382. (15) Tang, J.S.; Wang, C.-Y.; Xiu, F.X.; Lang, M.R.; Chu, L.-W.; Tsai, C.-J.; Chueh, Y.-L.; Chen, L.-J.; Wang, K.L. ACS Nano 2011, 5, 6008-6015. (16) Liu, X. H.; Huang, J. Y. Energy & Environmental Science 2011, 4, 3844-3860. (17) Liu, X. H.; Liu, Y.; Kushima, A.; Zhang, S.; Zhu, T.; Li, J.; Huang, J.Y. Adv. Energy Maters. 2012, 2, 722-741. (18) Li, J.; McCartney, M. R.; Dunin-Borkowski, R. E.; Smith, D. J. Acta Cryst. A 1999, 55, 652-658. (19) Gu, M.; Yang, H.; Perea, D. E.; Zhang, J.-G.; Zhang, S.; Wang, C.-M. Nano Lett. 2014, 14, 4622-4627. (20) McDowell, M. T.; Ryu, I.; Lee, S. W.; Wang, C. M.; Nix, W. D.; Cui, Y. Adv. Mater. 2012, 24, 6034−6041. (21) Yang, H.; Huang, X.; Liang, W.; van Duin, A. C. T.; Raju, M.; Zhang, S. Chem. Phys. Lett. 2013, 563, 58-62.


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Figure Captions Figure. 1. Experimental set-up: Schematic diagram showing experimental setup used for in situ observations of the Ge NW lithiation process. Figure 2. TEM images showing Ge NW during lithiation: (a) Before start of lithiation; (b) Formation of Ge/LixGe core/shell structure; (c) Further growth of LixGe shell as lithiation continues; (d) Higher magnification image taken after completion of lithiation, showing formation of polycrystalline LixGe NW. Figure 3. EELS mapping of Ge/LixGe core/shell structure: (a) STEM HAADF image, where bright contrast corresponds to remaining Ge core; (b) EELS spectrum showing Li ionization edge (arrowed) used to map out the Li distribution. Energy window used for background subtraction also shown; (c) Li spectrum mapping of core/shell structure. Figure 4. Electron holography observations of Ge/LixGe core/shell NW during lithiation: (a), (d) and (g) Holograms of NW; (b), (e) and (h) Corresponding reconstructed phase images, shown in pseudo-color (scale bar shown at top right in units of radian); (c), (f) and (i) Phase profiles along the white arrows in (b), (e) and (h), respectively. Figure 5. Model for trapped charges in Ge/LixGe core/shell structure: (a) Schematic diagram of the model; (b) Experimental data (black), and best fitting results (red).


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Figure 1


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(a)

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(b) Ge LixGe

(c)

(d) Ge LixGe

Figure 2.


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(a)

(b)

C (c) Figure 3


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(a)

(b)

-4

14

(c)

(d)

(e)

-4

14

(f)

(g)

(h)

-4

14

(i)

Figure 4 16 ACS Paragon Plus Environment

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E beam

(a)

LixO LixGe Ge

(b)

+R +- - - + Vs + - VcVr0 - + +- - - + + x0

Figure 5


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Table 1. Measured Potential of the LixGe shell Number

Vshell (V)

1

7.6±0.1

2

6.4±0.1

3

5.1±0.1


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Table 2. Measured radius for NW core and whole NW. Case

Core (nm)

Whole NW (nm)

A

-

66

B

45

88

C

-

110

D

-

129


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