鋰離子電池硅薄膜電極充電膨脹的有限元仿真及其實驗驗證①

季家磊,朱孔軍*, 劉鵬程, 錢國明, 王 裕, 劉勁松

(1.南京航空航天大學 航空宇航學院， 江蘇 南京 210016;2.廣州大學 機械與電子工程學院，廣東 廣州 510006， 3.南京航空航天大學 材料科學與工程學院，江蘇 南京 210016)

1 Introduction

Due to their advantages of high energy density, long life, low toxicity and environmental friendliness, lithium-ion batteries(LIBs) have become the most promising and widely applied rechargeable batteries.[1]LIBs have been widely used in portable electronics such as mobile phone, digital camera, DV, laptop, and (hybrid) electrical vehicles. The theoretical capacity of commercial graphite (used as anode) is only 372mAh/g[2], and can not meet the increasing demands for lithium-ion batteries with high energy density and long cycling life. In recent years, the development of new high capacity anode material has attracted significant interest. It is well known that some elements can electrochemical react with Li with high capacity. Some alloying elements with high theoretical capacities, such as Si, Sn, Ge Al[3-6], and conversion electrodes such as NiO, and Co3O4[7-8],have been studied extensively. Among these material, Si has high theoretical capacity,4100mAh/g, ten times of graphite[9]. However, Si shows a massive volume expansion/contraction during Li+insertion/extraction, larger than 300% after fullly lithium insertion[10]. This causes the pulverization of Si particle and loose contacts between Si particles and current collector, which will further result in mechanical in mechanical instability and poor cyclability[11-13]. To solve such problems, combine Si and inert metal materials which can relieve the huge volume change of Si thin films during lithiation and delithiation. Researchers have made attempts to improve the electrochemical performance of Si thin films as anode material, among which, the introduction of a secondary material is an effective way[14-16].

In this study, choose secondary materials which have good conductivity and ductility and act as buffer to alleviate the particle pulverization. Use Abaqus to compare the stree and strain in three different thin films(Si, Si-Mn, Si-Zr) during Li+insertion/extraction and analyse the role of the inert metal. Then, fabricate above Si thin films by magnetron supttering. The electrochemical performance of Si film was investgated by cyclic voltammetry and constant current charge/discharge test. The experimental results consist with the simulation. The use of metal material is useful for the cycling performance and Mn is more useful.

2 Finite Element Model

Li+insertion will result in a distorted lattice, volumetric expansion, mechanical stresss occures because of the constraint of Cu substrate. The size and stiffness of the substrate(Cu foil) is much lower than Si thin film, the deformation of Cu foil is then much lower than Si thin film and can be neglected, we assume the substrate to be rigid. Cracking and interface debonding are not considered, body force and inertia effects are neglected. Mechaniacl deformaion is thought to be quasi-static because it is much slower than diffusion process.

An axisymetric finite element model under a cylindrical polar coordinate system(r,θ,z) is used in Abaqus. Si thin film is assumed to be homogeneous and isotropic and be firmly bonded to the rigid substate. Because mechanical stress and diffusion process influence each other, fully coupled thermal-mechanical transient analysis procedure is used. First-order elements are used for the highly nonliner problem, finite element size is set to 1% of the height of Si thin film and fine mesh is used due to stress concentration. To improve convergence of the nonliner problem, liner search algorithm and maximum 5 interations are used.

There is no diffusion-stress aanalysis in Abaqus,use the method proposed by Prussin[17]as convention. Mechanical response under concetration loading is analogous to that under temperature loading, stress caused by diffusion is analogous to thermal stress.

Extending the 1D relation given by Prussin[17]to 3D, the constitutive equation for diffudsion-induced deformation of an elastic solid can be expressed

(1)

Fig.1 Structure of thin film

where εij(i,j=1,2,3) are componts of strain tensor; σij(i,j=1,2,3) are componts of stress tensor; c(mol m3) is concentration of diffusion componts; Ω is partial molar volume representing volume expansion caused by diffusion of Li+; E is elastic modulus; υ is posson’s ratio. Stress caused by diffusion is analogous to that caused by temperature gradient, Ω/3 plays the same role as thermal expansion coefficient in thermal stress analysis.

2.1 Structure and Material

The model of anode is based on the 2016-type cell which is used to be tested later. The anode of 2016-type cell is wafer thin film The thickness and radius of the Si thin film is D and R, the thickness of transition metal material is d. According to 2016-type cell, R is set to be 6μm. Bourderau S[18]fabricated the Si thin film with 1.2μm which had bad cycling performance, while thin film with 275nm[19]had better cycling performance, thus D is set to be 500nm. Transition metal just works as buffer layer and not participate in LI+insertion/extraction, d is smaller than Si and set to be 200nm(Fig. 1.).

Based on volumes of lithiated silicon at different Li-Si alloy phases[20], and linear relations between Li fraction and elastic constants[21- 22], dependence of elastic constants on concentration c (fmol mm-3) is expressed.

E=E0+k1c，υ=υ0+k2c.

(2)

Where E0=130Gpa, V0=0.22[23]. k1= -0.13Gpa.μm3fmol-1，k2=-0.00047μm3fmol-1(minus k1、k2represents the soften of Si electrode during lithium intercalation.)

The choice of transition metal must have good ductility, it acts as the buffer to alleviate the huge expansion, at the same time, it doesn’t act with Li+. Metal choosed here is Mn and Zr.

2.2 Boundary Condition

As metioned previous,the structure of the electrode is wafer type and symmetry, also the electrode is surrounded by invariant Li-ion concentration,the electrod can be treated as a symmetric finite model, and for simplify, we choose a section for analysis.

The initial condition is

when t=0, c=0.

(3)

In potentiostatic operation,the electrode surfaces are surrounded by an invariant Li-ion concentration, cs, so the concentration of Li-ion on the top surface and edge surface is fixed.

when 0

(4)

when 0

(5)

Cu foil is rigid substrate and doesn’t take part in Li+diffusion,

(6)

Under the cylindrical polar coordinate system, the structure, boundary conditions and loading conditions are all axisymmetric.

when t>0,r=0, ur=0.

(7)

Volume change consistsin stress because of the constraint of substrate. Because the film is firmly adherent to the substrate, there is no lateral displacements occures on the interface.

when t>0,z=0,ur=uθ=uz=0.

(8)

There is no mechanical loading applied on the top surface and side sur face.

when t>0,在z=h處,σz=0.

(9)

when t>0, r=R, z>0, σr=0.

(10)

3 Simulation Results

3.1 Concentratin, Displacement and Stress Fields

The concentration field before fully insertion is showed in Fig. 2a. Due to the edge diffusion, concention is dependent on radial coordinate. For the central region of the electrode, concentration is dependent on axial displacement.

The displacement and stress field after fully insertion is showed in Fig. 2b-e. Fig. 2d-e. shows the expansion caused by lithium-ion insertion includes radial extension and bending.

The radial displacement is concentrated at the edge of the top surface and the maximum radial displacement occures at the edge on the top surface, also there is little radial displacement in the central region of the film.

The maximum axial displacement occures at the center of the top surface. Axial displacement in the central region can be regarded to be independent of radial coordinate. Due to the fixed constraint of the rigid substrate, negative axial displacement is possible near the edge on the interface. A dome-like morphology is formed due to the axial and lateral expansions.

Fig.2 Concentration, displacemt and stress fields (a.concentration field, b.stress field, c, d, e. displacement field in equilibrium state) Fig.2b shows the stress caused by lithium-ion insertion mainly occures at the center of the top surface and the edge of the bottom surface.

3.2 ComparasionofDisplacement/StressFieldsinDifferentSi-MThinFilms

The displacement after fully insertion is showed in Fig.3. The distribution of displacement in different Si-M electrode is similar. No matter the total displacement or vertional/radial displacement declines while the metal is used.

Same conclusion can be achieved in the stress fields (Fig. 4). The maximun of von mises of Si-M thin film is less than Si thin film. Both the results of displacement and stress comparasion fields reveals that use of metal is beneficial to the Si anode to experience less destroy during insertion.

Fig.3 Comparasion of displacement fields (a.total, b.radial, c.axial displacement)

Fig. 4 Comparasion of stress fields(a.Si, b.Si-Mn,c.Si-Zr)

4 Experimental Results

4.1 Experimental

Si thin films were prepared in an PVD 75 multi-target magnetron sputtering system(KJLC, Co.). The samples were deposited on both Si wafer for thickness measurement and Cu foil for electrochemical measurements. The target was N-type monocrystalline Si with 2 inch diameters and 99.999% purity, Mn with 99.9% purity and Zr with 99.5% purity. The target-substrate distance of the sputtering system was set to be 50mm. After the base pressure reached 8.3×10-4Pa, Ar (99.999%) was introduced into the chamber. The working pressure was kept at 8mtorr. Si thin films were deposited using a constant radio frequency power supply of 100W.The film thickness was controlled by deposition time.The amount of deposited Si was calculated assuming a density of 2.33g·cm-3for the Si thin film.

The morphology and accurate thickness of Si thin films were measured by the field emission scanning electron microscopy (FSEM, SIGMA, Germany). The phase structure of was analyzed by X-ray diffraction (XRD, Bruker D8 Advance, Germany).

To evaluate the electrochemical properties of the Si thin film anode, 2025-type half-cells were assembled in an argon-filled glove box with H2O and O2concentrations of less than 1ppm. A lithium metal foil was used as a counter electrode, and Celgard2400 was used as a separator. The electrolyte solution was 1.0 M LiPF6in EC/DEC (1∶1 vol/vol). Cyclic voltammetry measurements were performed using an electrochemical workstation (Princeton PARSTAT MC) at a scan rate of 0.01 mV in the potential range 0V～1.5V.Galvanostatic charge/discharge measurement was carried out using a Land battery test system (LAND CT2001A) with the cut off potentials being 0V versus Li/Li+for discharge and 1.5V versus Li/Li+for charge.

4.2 Results and Discussion

Fig.5 SEM images(a.cross-ssection, subface of b.Si, c. Si-Mn, d. Si-Zr)

The cross-sectional SEM image of Si thin film deposited on a Si wafer is presented in Fig. 5a. The thickness of the dense Si、Mn、Zr can be observed,and the corresponding growth rate can be calculated,finally actual operating time was obtained accoring to the target thickness(Tab 1).

Table1 SputteringParameter

Fig.6. shows the XRD pattern of Si thin film deposited on Cu foil. All the diffraction peaks are attributed to the Cu foil, and no peak of Si appears, especially the typical peak for crystal Si at 28°. This indicates that the Si thin film is amorphous.

Fig.6 XRD patterns of Si thin films

The L+insertion/extraction reactions of Si thin film were studied by cyclic voltammetry. For all of the three thin films, three cyclic voltammetric curves of the Si thin film are shown in Fig. 7. In the first scanning cycle, there is a cathodic peak at 0.32V, which disappears from the second cycle. This cathodic peak is attributed to the formation of a solid electrolyte interphase (SEI) layer due to decomposition of electrolyte on the film surface. Two cathodic peaks at 0.20V and 0.05V, as well as two anodic peaks at 0.50V and 0.33V, are observed on all three cyclic voltammograms; these are ascribed to the electrochemical reactions of Li+insertion and extraction in the Si thin film. The slight difference in the intensity and the potential for each peak can be attributed to the kinetic effect involved in the cyclic voltammetry measurement.

Fig.7 Cyclic voltammetry plots (scanning rate 0.1Mv/s，potential range 0V～1.5V, a. Si; b.Si-Mn; c.Si-Zr)

Fig.8.shows the first three times of the discharge/charge curves. The first discharge capacity of the Si, Si-Mn, Si-Zr thin film is 2045.0mAh·g-1, 2203.1mAh·g-1, 2505.0mAh·g-1, and initial coulombic efficiency is 101.76%, 103.98%, 102.89%. The first and second reversible capacity of the Si-Mn thin film is 1900.3mAh·g-1and 1976.0mAh g-1，for Si-Zr, 1997.0mAh·g-1, 2054.7mAh·g-1,which is much larger than that of a graphite anode(1662.9mAh·g-1, 1692.3mAh· g-1,respectively). The irreversible capacity is attributed to the formation of a SEI layer in the first cycle. In evidence, a SEI-formation voltage plateau is observed near 0.32V, which disappears in the second cycle. This observation is also in good agreement with CV results.

Fig.8 Discharge/charge curves (a. Si; b.Si-Mn; c.Si-Zr)

Cycling performance of the Si thin films are shown in Fig. 9 a-c. The first reversible capacity 100mA/g for Si, Si/Mn, Si/Zr is 1692.3mAh/g, 1830.8mAh/g, 1955.6mAh/g respectively, and 71.2%, 83.9%, 88.2% capacity remained after 50 cycles.The introduce of transition metal can enhance both the first reversible capacity and the capacity retention effectively, which proves that the metal can improve the cycling performance of Si thin films. Rate performance of the Si thin films are shown in Fig. 9 d-f.

Fig.9 Eletronical performance of Si thin films (Cycling performance of a.Si, b. Si-Mn, c. Si-Zr, rate performance of d. Si, e. Si-Mn, f. Si-Zr)

To further evaluate the performance of Si thin films, the rate capability measurements (Fig. 9d-f) at the quickly increased current density from 0.1A/g to 1A/g were carried out. For Si thin films, the discharge capacity of 2045.3mAh/g, 1413.2mAh/g, 1128.8mAh/g, 919.5mAh/g, 732.7mAh/g can be obtained at 0.1A/g, 0.2A/g, 0.3A/g, 0.5A/g, 1.0A/g, 0.1A/g. For Si-Mn, 2203.1mAh/g, 1718.9mAh/g, 1535.7mAh/g, 1329.6mAh/g, 1044.3mAh/g can be obtained, and for Si/Zr, 2505.0mAh/g, 1859.4mAh/g, 1661.2mAh/g, 1500.6mAh/g, 1117.8mAh/g can be delievered. Although suffering from the rapid change of the current density, the cell can still exhibit a stable cycling at each current. Importantly, 80% of the first reversible capacity can be remained for Si thin film when the current density is turned back to 1A/g, and for Si-Mn, Si-Zr, 89.0% and 92.9% can be remained.It proved that use of metal is beneficial to the electrocal performance again.

5 Conclusion

In this article, Si and inert metal is combined to relieve the expansion during Li+insertion/ extraction. Use Abaqus to compare three different Si thin films (Si, Si-Mn, Si-Zr).we found that the use of inert metal reduces the displacement and stress induced during the Li+insertion. Also, Si-M thin film used as anode material.was deposited by magnetron supttering The morphology of the Si-M thin films are similar, and XRD results reveals that the structure of Si thin films is amorphous. The electrochemical performance of Si thin films consistents with the simulation, use of metal can relieve the expansion and result in better cycling and rate performance. Among Mn and Zr, Mn is more useful.

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