Permeation, Solubility, Diffusion and Segregation of Lithium in

Article Cite This: Chem. Mater. 2018, 30, 3254−3264

pubs.acs.org/cm

Permeation, Solubility, Diffusion and Segregation of Lithium in Amorphous Silicon Layers Erwin Hüger,*,† Lars Dörrer,† and Harald Schmidt†,‡ †

Downloaded via UNIV OF SOUTH DAKOTA on July 1, 2018 at 11:05:29 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Institut für Metallurgie, Abteilung Mikrokinetik, Technische Universität Clausthal, Robert-Koch-Str. 42, 38678 Clausthal Zellerfeld, Germany ‡ Clausthaler Zentrum für Materialtechnik (CZM), Technische Universität Clausthal, Leibnizstraße 9, 38678 Clausthal-Zellerfeld, Germany S Supporting Information *

ABSTRACT: The permeation, solubility, diffusion and segregation of lithium in amorphous silicon layers (∼100 nm) were experimentally determined at temperatures up to 500 °C (773 K). For the experiments, silicon was embedded between 6Li and 7Li enriched solid state Li reservoir layers and the exchange of the isotopes was monitored by secondary ion mass spectrometry. The silicon layers effectively block Li permeation for more than four years at room temperature. At higher temperatures, a fast and a slow Li permeation process can be discriminated. The activation enthalpy for the two processes amounts to (0.9 ± 0.2) and (1.9 ± 0.2) eV, respectively. The first process is based on fast interstitial diffusion leading to Li segregation at the surface and at the substrate interface. The second slower process is due to trap-limited Li diffusion in silicon. An activation enthalpy of Li solubility of (0.5 ± 0.1) eV is found to be identical to that in crystalline silicon, even if absolute values are higher. The activation enthalpy of trap-limited diffusion is determined to be (1.5 ± 0.2) eV. The results are discussed in framework of literature with impact on the lithiation mechanism of silicon electrodes in lithium-ion batteries.

■

INTRODUCTION Lithium diffusion is an important transport process for the performance and failure of (rechargeable) lithium ion batteries (LIB).1−5 Diffusion controlled trapping of Li in electrodes was found responsible for capacity losses in cycled electrodes.1 Further, diffusion in electrodes is crucial for charging/ discharging times, maximum capacity and side reactions. The parameter describing the diffusion process is the diffusion coefficient (diffusivity). In batteries, the knowledge and manipulation of Li flux (i.e., ion current density)2 is sometimes of higher interest than solely diffusion. Li flux takes also into account the amount of Li which is transported during diffusion. In this context, a meaningful parameter is the Li permeability (P) which is the product between Li solubility (S) and diffusivity (D)

(Li21Si6) than carbon (LiC6), the active material of commercial negative electrodes. There is a tendency to use at least small amounts of Si (e.g., as particles or layers) in commercial carbon electrodes.7−10 Amorphous silicon is interesting because it should withstand more properly huge stresses developing during LIB operation.20 It can also routinely be deposited by sputter deposition methods in form of thin films3,8−31 for thin film batteries. The desired advantages are counteracted by a limited structural stability of (pure) Si electrodes during LIB operation. During LIB cycling, the overall capacity of Si is often reduced by delamination from the current collector. Recent investigations11−14 pointed out the importance of Li transport phenomena in thin amorphous Si films such as Li segregation and Li diffusion for this effect. The present work is organized as follows: First, it is presented how Li permeability, solubility and diffusivity in thin amorphous Si layers were obtained from the experiments. In the next section, the results are analyzed and interpreted in context to literature. The penultimate section gives a brief description of the experimental equipment. The results are summarized in the last section. The Supporting Information (SI) accompanying this work presents further details.32

(1)

P = S·D

The solubility expresses the amount of Li ions available for diffusion, whereas the diffusivity takes into account Li movement. The present work reports on Li permeation experiments from which all the quantities of eq 1, i.e., P, S and D, were determined independently. As a model system to probe Li transport, silicon was selected because this material plays an important role for Li storage in high capacity electrodes for the next generation of LIBs.1,3−26 Silicon is naturally abundant in high amounts and can store theoretically 20 times more Li atoms per active host atom © 2018 American Chemical Society

Received: January 14, 2018 Revised: April 23, 2018 Published: April 24, 2018 3254

DOI: 10.1021/acs.chemmater.8b00186 Chem. Mater. 2018, 30, 3254−3264

Article

Chemistry of Materials

■

RESULTS Li Permeation Measurements. Recently, we introduced a new approach that enables the measurement of Li permeability in thin films, especially for materials relevant for LIBs.18,19 This technique is based on multilayers (ML) as sketched in Figure 1a. A sequence of two (6LiNbO3/Si/7LiNbO3/Si) structural

f 6Li =

6Li ISIMS 6Li 7Li ISIMS + ISIMS

;

f 7Li =

7Li ISIMS 6Li 7Li ISIMS + ISIMS

(2)

6 7Li where I6Li SIMS and ISIMS are the SIMS intensities measured at Li and 7Li masses, respectively. The isotope fractions for the asdeposited ML are presented in Figure 2a.

Figure 1. (a,f) Sketch of ML used for the Li permeation experiments: 9.5 nm thin 6LiNbO3 layers (termed 6Li) and 7LiNbO3 layers (termed 7 Li) separated by 95 nm thin Si layers. (b−e,g−j) SIMS depth profiles of (b) 6Li, (c) 7Li, (d) 28Si, (e) 93Nb, (g) 6Li2O, (h) 7Li2O, (i) 6Li7LiO and (j) 16O masses.

units was used for our experiments,32 where 6LiNbO3 is a layer enriched with the 6Li isotope and 7LiNbO3 with the 7Li isotope, respectively. Each of these two isotope enriched LiNbO3 layers are adjacent to a Si layer. The LiNbO3 layers serve solely as solid state Li reservoirs and silicon as the medium to be investigated. Annealing leads to a mutual exchange of Li isotopes through the Si layer and adjacent interfaces by Li permeation modifying the Li isotope fraction in each of the two LiNbO3 layers. In first approximation, the chemical composition of LiNbO3 is not modified because the solubility of Li in silicon is very low. Kinetic parameters are obtained by measuring the relative fraction of 6Li and 7Li isotopes in the lithium reservoirs as a function of annealing time (for details, see SI). As shown by X-ray diffractometry, all materials under investigation are amorphous. The layer thicknesses were determined by X-ray reflectivity measurements to (95 ± 4) nm and (9.5 ± 0.5) nm for the Si and LiNbO3 layers, respectively.32 Lithium isotope fractions were obtained from secondary ion mass spectrometry (SIMS) depth profiling measurements.32 The element (Li, Si, Nb, O) and isotope resolved SIMS depth profiles of an as-deposited ML are presented in Figure 1b−e and g−j. The logarithmic scaling illustrates the high dynamic range of extremely strong Li signals. The Si signal (Figure 1d) shows a strong fluctuation due to a modification of the secondary ion ionization probability at the interface between Si and LiNbO3 layers. Notice that the signal is nearly constant in the middle of all Si layers as expected. The 6Li and 7Li isotope fractions, f6Li and f 7Li, were obtained from SIMS signals (see SI) by the following:

Figure 2. 6Li (red curves) and 7Li (green curves) isotope fraction as a function of sputter depth, obtained from SIMS measurements (a) on as-deposited ML and (b−h) after sequential annealing of the ML at 500 °C (773 K).

Obviously, there is a strong modulation of the isotope fraction in the LiNbO3 layers throughout the ML. Four years of storage of the samples in air at room temperature (300 K) does not modify the Li isotope fraction profile. Silicon layers effectively block Li permeation at room temperature. In order to induce Li permeation, the ML were annealed at four temperatures of 240, 360, 420 and 500 °C at different annealing times between 1 min and 3450 h. Figure 2 presents also typical Li isotope fractions obtained from SIMS depth profiles after sequential annealing performed at 500 °C (773 K). As visible, annealing reduces the 6Li isotope fraction and increases at the same time the 7Li isotope fraction within the 6 LiNbO3 reservoir layers. The reverse effect is found for the 7 LiNbO3 reservoir layers. This is attributed to thermally induced permeation of Li through the silicon layers. During this process, the chemical composition does not change significantly as evidenced by X-ray reflectometry (XRR) (Figure S2 in SI)32 and neutron reflectometry (NR)18,19 (Figures S4 and S5 in SI).32 From Figure 3 (annealing at 240 °C (513 K)), it can also be seen that the permeation process is spatially not homogeneous. The 6Li fraction of the first 6LiNbO3 layer (adjacent to air) and of the last 6LiNbO3 layer (adjacent to the 3255


Article


Figure 4. SIMS depth profiles close to the surface of (a,d) the sum of 6 Li and 7Li signals, (b,e) 93Nb and (c,f) 28Si measured on as-deposited samples and samples annealed at 240 °C for 52 h (a,b,c) as well as at 500 °C for 6 min (d,e,f), respectively. The horizontal arrows point out the shift of the profile to larger depths due to growth of a surface layer.

Figure 5 presents the annealing time dependence of the contrast K(t) in the two different types of Li reservoirs (surface

Figure 3. 6Li (red curves) and 7Li (green curves) isotope fraction as a function of sputter depth, from SIMS measurements (a) on asdeposited ML and (b−h) after sequential annealing of the ML at 240 °C (513 K).

silicon wafer) clearly decrease significantly during annealing. In contrast, the 6Li isotope fraction in the middle layer is nearly unchanged for the same annealing time. A detailed analysis will be given below. Figure 4 presents SIMS depth profiles of Li (6Li plus 7Li), 93 Nb and 28Si for as-deposited samples and samples annealed at 240 and 500 °C, respectively. It can be observed that the depth profiles of Li, Nb and Si resulting from the 6LiNbO3 layer situated next to the surface are changed by the annealing treatment. The thickness of the surface layer grows from initially 10 nm in the as-deposited ML to 30 nm for the ML annealed at 240 °C for 52 h and at 500 °C for 6 min (Figure 4a,b,c) assuming the same sputter rates. The horizontal arrows in Figure 4 indicate this growth. The growing surface layer contains Li but lacks of Si and Nb. This shows that Li moves to the surface and segregates there. Further measurements and elaborations presented in SI32 show additional evidence for Li segregation. Li Permeability Determination. For further analysis, we calculate the 6Li contrast (K), which is defined as follows K (t ) =

f (t ) − fmin fmax − fmin

⎡ t − t0 ⎤ = exp⎢ − ⎥ ⎣ τ ⎦ 6

Figure 5. Annealing time dependence of the 6Li contrast K(t) in (a) the first (close to surface) and (b) the middle 6LiNbO3 layer of the ML at different temperatures. The fit of eq 3 to the measurements is shown by solid lines.

and middle) measured at different temperatures. The contrast decrease of the first 6LiNbO3 layer at the surface is presented in Figure 5a and is similar to that of the last 6LiNbO3 layer at the substrate interface (not shown). As mentioned, this process is attributed to Li segregation at interfaces. The decrease of the contrast of the middle 6LiNbO3 layer (i.e., the third 6LiNbO3 layer in Figure 1a) is presented in Figure 5b. A similar decrease is found for the 7Li contrast in the 7LiNbO3 layers (i.e., the second and fourth LiNbO3 layer). Note the logarithmic scale of the annealing time in Figure 5. Figure 5 shows clearly that the decrease of the isotope contrast K(t) of the middle 6LiNbO3

(3) 6

where f max and f min are the Li fractions in the LiNbO3 reservoirs in the as-deposited state and after complete Li isotope intermixing (see, e.g., Figure 2a,h). Further, f(t) is the 6 Li fraction as a function of annealing time. As shown in ref 18, the contrast K(t) is expected to decrease exponentially with τ as a typical time constant and t0 as a time-lag. The derivation of eq 3 is provided in the SI. 3256


Article


Table 1. Activation Enthalpy, ΔHx, and Pre-exponential Factor, X0, for the Arrhenius Behavior (see eq 5) of Li Transport Parameters in Silicon As Determined from the Experimental Data in Figures 6, 9, 10a

layer (Figure 5b) is slower than that of the surface 6LiNbO3 layer (Figure 5a). The model built up (see SI) to extract Li transport parameters from the 6Li isotope contrast variation K(t) gives an exponential decrease according to eq 3. The time constant of the exponential decay function is given by the following: ρ d ·d MSi 1 · LiNbO3 · Si LiNbO3 τ= · 4 MLiNbO3 ρSi P (4) where MSi = 28.09 g/mol is the molar mass of Si, MLiNbO3 = 147 g/mol is the molar mass of LiNbO3, ρLiNbO3 = 4 g/cm3 is the mass density of the LiNbO3 layer, ρSi = 2 g/cm3 is the mass density of the Si layer, dSi = 95 nm is the thickness of the Si layer, and dLiNbO3 = 9.5 nm is the thickness of the LiNbO3 reservoir layer.32 The mass densities of the as-deposited layers are known from previous experiments.18,19 The parameter P represents the Li permeability in the Si layer (eq 1). A fit of eq 3 to the decrease of the Li isotope contrast (Figure 5) determines the time constant and from eq 4 the Li permeability is calculated. The temperature dependence of the Li permeability for the fast Li permeation process governing segregation (Figure 5a) is plotted in Figure 6 as stars. In order to simplify the extraction

Parameter

Material

Permeability Permeability Permeability Solubility Solubility Diffusivity Diffusivity

a-Si, fast a-Si, slow c-Si33,34 a-Si c-Si33 a-Si, slow, time-lag a-Si, slow, P/S

ΔHx (eV) 0.9 1.9 1.2 0.5 0.6 1.3 1.5

± ± ± ± ± ± ±

0.2 0.2 0.2 0.1 0.1 0.2 0.2

log10X0 −12 −6 −7 −0.2 −0.6 −7 −5

± ± ± ± ± ± ±

0.3 0.4 0.4 0.1 0.2 0.4 0.3

a

a-Si refers to amorphous silicon and c-Si to crystalline silicon. The solubility in c-Si is from ref 33, and the permeability is calculated from diffusivities in ref 34. For details, see text.

The temperature dependence of the Li permeability corresponding to the slow Li permeation process is depicted in Figure 6 with filled squares. The data show also an Arrhenius behavior with a higher activation enthalpy of Li permeation of ΔHPa‑Si,slow = (1.9 ± 0.2) eV (Table 1). The permeability at 240 °C is not shown due to the rather incomplete measurement of the Li isotope contrast decrease (Figure 5b) to only 64%. Complete intermixing would here need total annealing times of several years, which could not be realized experimentally. Lithium Solubility Determination. Figure 7 shows typical SIMS depth profiles recorded from the as-deposited ML and after sequential annealing steps.32 It depicts the region around

Figure 6. Temperature dependence of the Li permeability in amorphous Si layers for the slow and fast process identified (filled symbols). Lines are fits according to the Arrhenius law (eq 5). Open squares are Li permeabilities of crystalline silicon calculated according to eq 1 from literature values of solubility34 and diffusivity.33 The open circle is an experimental value for 5 nm amorphous Si layers from ref 19.

of these Li permeabilities, we assumed that the Li flux to the ML at the surface comes from the neighboring 7LiNbO3 layer only. Consequently, the factor of 1 quarter in eq 4 was replaced by one halve for the calculation (see SI). The temperature dependent permeabilities obey the Arrhenius law. In general, this can be written as follows X = Xoexp( −ΔHx /kT )

(5)

where X is the Li transport parameter (X = P, D or S). X0 and ΔHx are the pre-exponential factor and the activation enthalpy of each process. Concerning the segregation process, the resulting activation enthalpy of Li permeation of ΔHPa‑Si, fast= (0.9 ± 0.2) eV and the pre-exponential factor are listed in Table 1.

Figure 7. SIMS depth profiles of the total Li signal (6Li + 7Li signal) (red curve), of the 28Si signal (blue curve) and of the ratio of the total Li signal to the 28Si signal (black curve). Shown are the results on ML in the as-deposited state and annealed at 500 °C for different times. The red arrow indicates the constant Li/Si ratio in the middle of the Si layer. 3257


Article

Chemistry of Materials the third Si layer in higher resolution which should be less affected by Li segregation toward the ML surfaces. The intensity ratio between the total Li signal (the sum of 6Li and 7 Li signals) and that of 28Si signal is plotted with black lines. This ratio increases within the Si layer (red arrow) after annealing. The solubility (Li per Si atoms) can be determined using the derivation given in SI as S=

6Li 7Li + ISIMS (ISIMS ) RSFLi · 1 28Li RSFSi ISIMS· 0.9223

(6)

7Li 28Si where I6Li SIMS, ISIMS and ISIMS are SIMS intensities measured at 6 Li, 7Li and 28Si masses, respectively. The value of 0.9223 represents the 28Si isotope fraction in silicon. RSFLi and RSFSi are the SIMS relative sensitivity factors for Li and Si in the Si layer, respectively, which are unknown for the concrete system. If we consider tabulated RSF values of Li and Si in crystalline Si for O2+ primary ion beams of RSFLi = 6E20 and RSFSi = 5E22, respectively,35,36 the Li solubility (relative Li concentration) in silicon layers for the present experimental arrangement can be calculated. We detected a very low solubility in as-deposited amorphous silicon of S = 2 × 10−5. Because of SIMS ion beam mixing effects, this value can be considered as an upper limit.37 After annealing, the solubility increases (Figure 7). Here, SIMS induced mixing effects are assumed to be negligible due to the broad plateau of constant Li concentration in the middle of the silicon layer (see red arrow in Figure 7b). The annealing time dependence of the solubility is presented in Figure 8. A

Figure 9. Temperature dependence of the Li solubility in amorphous silicon layers (filled symbols). Lines are fits according to the Arrhenius law (eq 5). Open symbols represent Li solubilities in crystalline silicon taken from ref 34.

of the Si layer and the Li diffusivity can be calculated according to ref 38.

D=

dSi2 2·t0

(7)

The time-lag represents the onset of the Li isotope contrast K(t) decrease in Figure 5. The Li diffusivities determined from the time-lag of the contrast variation K(t) in Figure 5b (middle 6 LiNbO3 layer) is presented with filled red diamonds in Figure 10. The temperature dependence obeys the Arrhenius law with

Figure 8. Lithium solubility in amorphous silicon layers for different annealing times t > t0 at different temperatures. The straight lines indicate the average of the data points for a given temperature.

considerable scatter of the values for different annealing times is observed. This is especially true for 240 °C because the limit of solubility determination with our method is reached. Figure 9 presents the average solubility at each temperature, as indicated in Figure 8 as a straight line. The solubility also follows the Arrhenius law in good approximation in the temperature range investigated. The obtained activation enthalpy is ΔHa‑Si S = (0.5 ± 0.1) eV (Table 1). Lithium Diffusivity Determination. The parameter t0 in eq 3 is termed the time-lag which arises because there is a time interval before a steady state of Li permeation can be approached due to the finite diffusivity of Li in the silicon layer. During this time, a mutual exchange of the isotopes between the two Li reservoirs is not possible. Li is only dissolved and diffusing in silicon, yet not reaching the end of the silicon layer. The time-lag is directly related to the thickness

Figure 10. Temperature dependence of Li diffusivity in amorphous Si layers (filled symbols). Corresponding lines are fits according to the Arrhenius law (eq 5). Open symbols and dashed lines are data from the literature. The open triangles and squares are only for a better discrimination of each curve. For details, see text.

an activation enthalpy of Li diffusion in amorphous silicon of slow, time‑lag = (1.3 ± 0.2) eV (Table 1). Additional Li ΔHa‑Si, D diffusivities were obtained from Li permeability and Li solubility using eq 1, i.e., D = P/S. Figure 10 presents their temperature dependence. They are identical within error limits to those obtained from the time-lag measurements and give an slow, P/S activation enthalpy of ΔHa‑Si, = (1.5 ± 0.2) eV. D 3258


Article


■

slow (ΔHa‑Si, = (1.9 ± 0.2) eV) have to stem from the activation P enthalpy of Li diffusion ΔHD. Lithium Segregation (fast process). As mentioned above and further discussed in the SI,32 the fast Li permeation process is associated with transport of Li to and segregation at the ML interfaces to air and silicon substrate. Such a precipitation of Li at film interfaces is often documented in the literature.37,41−47 Segregation can be explained by a thermodynamically driven process governed by minimization of the surface energy (Gibbs energy minimization) of the material.13,14,48−50 Lithium shows a surface energy which is lower than that of most semiconductors and metals.49,50 Lithium migration toward the surface reduces the surface energy49,50 and can be the driving force of Li segregation. Fink et al.41−44 studied Li implantation and diffusion in various semiconductors and metals by analyzing the thermally induced modification of Li implantation profiles by means of nuclear reaction technique. A fraction of the implanted Li was found to be much more mobile than the majority of the implanted Li. The former gives rise to surface segregation at relatively low temperatures.41−44 It was found that up to 30% of totally implanted Li is mobile and tends to segregate at the surface. Li migration to the surface and the amount of segregated Li increases with temperature, reaching constant values when all the mobile Li supply from the bulk is consumed.41−44 After that, a slower Li diffusion process starts. We assume that exactly such a phenomenon was observed also in this work. A fast permeation process (Figure 5a) to the surface and a slower process (Figure 5b) in the depth of the Si film were found. In addition, our work shows that Li segregation appears also toward the interface between the ML and the Si wafer substrate. Li concentration enrichment at both interfaces, i.e., the sample−air and sample−substrate interfaces, was reported also for amorphous hydrogenated silicon films doped by Li in-diffusion46,47 and for buried interfaces between silicon and carbon materials.37 As stated above, a similar Li diffusion mechanism is expected in crystalline and amorphous silicon (fast segregation process). The activation enthalpies of permeation, and solubility of both types of material are identical within error limits (Table 1) and fast consequently those of diffusion. According to ΔHa‑Si, = D a‑Si, fast − ΔHS, we can calculate an expected activation ΔHP enthalpy of diffusion of about 0.4 eV. Experiments found an activation enthalpy for interstitial Li diffusion in crystalline silicon of ΔHc‑Si D = (0.6 ± 0.1) eV [33]. Calculations show that the energy barrier for Li diffusion pathways in crystalline silicon ranges in between 0.4 and 0.6 eV.51−56 First principle density functional theory calculations53,56 found the energy barrier for interstitial Li diffusion in ultrathin films of crystalline silicon to be identical to that in bulk crystalline silicon. In absolute values, the permeability governing Li segregation (fast process) is higher than that of the slow process in the film interior (Figure 6). Li permeation in the interior of the ML seems to be less affected by the Li segregation phenomenon. In the literature, a Li permeability determined in 5 nm thin amorphous Si layers at 240 °C was published by our group.19 This value is plotted with an open circle in Figure 6. This permeability is in agreement with that of the Li fast process, indicating that for thinner Si layers, this process is dominating. Hence, a systematic investigation of Li permeation through thinner Si films would be of interest in order to elucidate this phenomenon in more detail.

DISCUSSION The main results of the study are illustrated in Figures 6, 9 and 10: The Arrhenius behavior of the permeabilities, solubilities and diffusivities of Li in amorphous silicon layers. These results are now discussed with respect to the literature. Permeabilities. In addition to the experimental results obtained in this study, Figure 6 presents also data on the temperature dependence of Li permeabilities in bulk crystalline Si (open squares) as calculated from eq 1 using the Li solubility and diffusivity given in literature by Reiss et al.34 and Pell,33 respectively. An activation enthalpy of ΔHc‑Si P (1.2 ± 0.2) eV for Li permeation in crystalline Si is identical within error limits to that measured in amorphous Si layers investigated here for the fast . The slow permeation fast Li permeation process, ΔHa‑Si, P process (Figure 5b) has a considerably higher activation enthalpy (Figure 6 and Table 1). Hence, the fast Li permeation process (Figure 5a) in amorphous silicon should show a similar Li transport mechanism as Li in crystalline silicon, while the slow process (Figure 5b) is different. The energy barrier which Li has to overcome during the slow Li permeation process is nearly twice as high as during the fast process. Note that in absolute values the permeabilities in crystalline silicon are higher by 2 orders of magnitude. Solubilities. According to eq 1, a discussion of Li solubility will give more information on transport mechanisms. In the literature, there is a lack of reports on Li solubility in amorphous silicon. The temperature dependence of the averaged Li solubility as determined here in amorphous Si layers is presented in Figure 9. Literature values of Li solubility in crystalline Si from ref 34 are presented also in Figure 9. In both cases, the Li solubility obeys the Arrhenius law in good approximation and show the same activation enthalpy of about ≈ ΔHc‑Si 0.5 eV (ΔHa‑Si S S ). This is a strong hint that the measured Li content represents indeed the Li solubility in the amorphous Si layers investigated here. For solid−solid and solid−vapor equilibria of silicon, the temperature dependence of solubility was reported to obey to the Arrhenius law.39 The acceptor concentration in boron doped crystalline silicon increases Li solubility but annihilates the Arrhenius behavior.39 Consequently, the Arrhenius behavior found in this work (Figure 9) indicates low acceptor impurities in the amorphous silicon layers with Li acting as donor type impurity.40 Despite the same activation enthalpy, the solubility in crystalline silicon is significantly lower than in the amorphous layers if compared at the same temperature. The origin of this difference is very likely the higher free volumes present in the amorphous structure due to a lower packing density of atoms. Consequently, more Li can be dissolved than in interstitial sites of crystalline silicon. In addition, the presence of traps like dangling bonds in amorphous silicon (not present in long-range ordered and high purity crystalline silicon) can help to accommodate a larger amount of Li by the formation of Li− Si bonds. Concerning activation enthalpies, the following can be stated: Because P, D and S all follow the Arrhenius law, it can be concluded from eqs 1, 5 that ΔHP = ΔHD + ΔHS. The identical activation enthalpies of Li solubility in crystalline and amorphous silicon have the consequence that the corresponding different activation enthalpies of Li permeabilities in = (1.2 ± 0.2) eV) and amorphous Si crystalline (ΔHc‑Si P 3259


Article

Chemistry of Materials Trap-Limited Li Diffusion (slow process). Generally, a time-lag analysis represents a straightforward method to determine the averaged chemical diffusivity in a solid and if Li solubility is low (as it is in the present case) the Li tracer diffusivity. The diffusivities obtained with the time-lag method (red diamonds in Figure 10) are identical within error limits with the Li diffusivities obtained from D = P/S (squares in Figure 10). Fink et al.41−44 observed a decrease of the Li diffusivity as a function of annealing time in amorphous silicon over several orders of magnitude. The results were explained by a gradual transition from interstitial Li diffusion to trap-controlled diffusion. In the latter case Li diffuses interstitially over a certain distance until it is trapped by defects. After a certain time it is released from the trap, diffuses again, and so on (see Figure 11). Trap-limited diffusion was observed also for

show that Li diffuses in silicon faster in the vicinity of another Li atom due to electrostatic Li+−Li+ repulsion.51 Consequently, an increased Li content should enhance the Li diffusivity explaining also the higher Li diffusivities measured by Fink et al. Lithium tracer self-diffusion in amorphous [6LixSi (90 nm)/ LixSi (90 nm)] films with low Li concentrations (x ∼ 0.02 and 0.06) (produced in our laboratory) were recently reported,69 and are presented also in Figure 10 for a reason for comparison. However, the method of diffusivity determination is different, not applicable to pure Si. Increasing the Li content in LixSi results in diffusivities that are faster by 1 order of magnitude but still described by an activation energy of (1.42 ± 0.03) eV identical within error limits to the value presented in this work for pure amorphous silicon (i.e., LixSi with x < 0.0001). A trap limited diffusion mechanism was also suggested in ref 69 where faster diffusion with higher Li content is traced back to a lower amount of traps in the sample. This is explained by the fact that traps are saturated by Li atoms, at least partly. The higher Li concentration has the consequence that the number of unsaturated traps is reduced and Li diffusion is accelerated.69 Li diffusivities of Li implanted into hydrogenated silicon37 doped with 1% B2H6 are presented also in Figure 10 by a dotted line. They are also higher. The open circle plotted in Figure 10 at 320 °C corresponds to Li diffusion in Si with 2.4% of Ge.62 The diffusivity is identical to the data of this work. This indicates that the trap density in silicon depends sensitively on the presence of Li and impurity atoms (H, B, Ge) in the percent range. A still open question is: How does the fast interstitial Li diffusion process taking place during the Li segregation process fit into the trap-limited picture? First-principle calculations based on density functional theory52,53 show that Li exists and moves as a Li+ ion in silicon. Li interstitials have a strong tendency to remain isolated and well dispersed in the silicon matrix due to electrostatic Li+−Li+ repulsion.51 Obviously the global minima of the energy landscape for Li diffusion correspond to Li traps (see Figure 11). Consequently, during the Li segregation process the traps have to be all occupied/ saturated. This can be achieved by Li and only surplus nontrapped Li is moving. Li segregation takes place until the surface energy is minimized and/or until all excess Li is segregated.47 Afterward, trap-limited diffusion can be observed. The activation enthalpy for the measured slow Li permeation process of 1.9 eV includes the energy barrier of the traps, whereas that of about 1 eV (Li segregation) includes the mean energy barrier for nontrapped (i.e., trap-saturated, interstitial) Li motion. Implication for Electrochemical Li Storage in Silicon. Our results are also interesting in order to understand mechanisms and kinetics of electrochemical lithiation of silicon electrodes in Li-ion batteries. This process normally takes place at room temperature. For silicon electrodes, a two phase lithiation mechanism is suggested in the literature:4−6,17,24,64−68,70 A LixSi phase penetrates successively into Si during galvanostatic lithiation (Figure 12). The process is characterized by a reaction front, which delimits a highly lithiated phase (red region in Figure 12) from pure silicon66,67 or a poor lithiated Si phase24 (blue region in Figure 12). Transmission electron microscopy observed that lithiation occurs by the movement of a sharp phase boundary between the a-Si reactant and an amorphous LixSi phase with high Li content (x ∼ 2.5).66,67 Such a striking amorphous− amorphous interface exists until the remaining a-Si is

Figure 11. Sketch of potential energy landscape Li has to surpass during diffusion. Between traps the energy barrier for Li migration is lower and governed by interstitial diffusion.

diffusion of hydrogen28,29,57,58 and alkali atoms40 in amorphous Si28,29,40,57,58 and related materials.59−61 Hydrogen is diffusing in undoped single crystalline silicon via an interstitial mechanism with a low activation enthalpy of 0.5 eV which is similar to Li diffusion in crystalline silicon. The activation enthalpy for hydrogen diffusion in amorphous Si is much higher which is characteristic for trap-limited diffusion.61 Defects in Si may act as intrinsic and extrinsic traps. Intrinsic traps are often associated with dangling bonds60 inherent to the material, while extrinsic traps may additionally be introduced in the Si matrix by ion bombardment or impurity doping. The higher the trap density, the lower is the Li diffusivity. Theoretical calculations found that Li may diffuse in amorphous silicon several jumps and gets trapped in some wells.54 Subsequently, Li is then shuttling back and forth among two or more wells. It is predicted that at room temperature Li requires longer than half a year to diffuse out from wells with energy barriers larger than 1.2 eV. Calculations also predict Li diffusion pathways with energy barriers of around 1.5 eV (i.e., trapping sites).55 Identical energy barriers for Li diffusion in amorphous Si are obtained from the experiments performed in this work (see Table 1). The temperature dependence of trap-controlled Li diffusivities in silicon (with 0.1% Li content) from refs 41−44 is presented in Figure 10 as a dashed line. These diffusivities are higher than those found in this work. This indicates that the Si layers of this work possess a higher trap density than the Si material analyzed by Fink et al.41−44 Moreover, calculations 3260


Article


permeabilities of PLi2.5Si/PSi > 1023. The Li flux (permeation) through the highly lithiated material is 23 orders of magnitude higher than through pure silicon. Based on our results, the following statements can be made: The intrinsic Li solubility and Li permeability in silicon are extremely low even in the amorphous phase. This explains why a simple solid solution formation during lithiation of Si is not taking place and lithiation is done by a moving phase boundary. The ability of pure silicon to permeate Li is 23 orders of magnitude lower than the highly lithiated LixSi region. This means, that a large number of Li atoms can easily be transported in the LixSi phase (red region in Figure 12) and stops at the interface to the nonlithiated region of the pure silicon electrode (blue region in Figure 12). Consequently, at the phase boundary elemental Si is converted into a LixSi alloy by a chemical solid state reaction. This phase grows until all Si is consumed. The slow permeation of Li in silicon prevents a homogeneous lithiation of the whole electrode. During electrochemical lithiation the Li current first enhances the Li concentration at the electrolyte/LixSi interface, it decays through Li diffusion inside the LixSi phase65 and Li is piled up at the phase boundary. Hence, depending on the Li diffusivities, on the Li current density and on the LixSi material thickness, the rate-limiting process of lithiation can vary between diffusion controlled and interface reaction controlled. Other effects such as the Li transfer across the electrolyte/ electrode interface (and the solid electrolyte interphase) and formation of mechanical stress during lithiation (including micro and macro cracks) can have also influence on the lithiation mechanism of silicon.6 For reason for completeness, it has to be mentioned that after the first delithiation process, the silicon electrode is in a different state compared to the initial state. Commonly, Li remains irreversibly trapped in the delithiated silicon electrode25 and the overall Li concentration is enhanced to pure Si. As indicated in Figure 10, a growing Li concentration enhances diffusion and permeation. Also, pores and microcracks can be formed which may enhance Li transport parameters. Consequently, the phase boundary mechanism has not to be present during the next lithiation cycles and a more homogeneous lithiation becomes possible as revealed by TEM studies.66,67,6 In the literature, Wang et al.3 and Ozanam et al.17 presented a compilation of Li diffusivities at room temperature in silicon electrodes during lithiation experiments which were estimated by electrochemical methods such as cyclic voltammetry, electrochemical impedance spectroscopy and pulse methods (GITT, PITT). All the values are well above 10−19 m2/s, i.e., significantly higher than found in this work for pure Si. EIS measurements performed in our laboratory during lithiation of amorphous silicon films 70 gave room temperature Li diffusivities between 10−17 and 10−16 m2/s which fits well in the range of diffusivity values reported in literature. These values are also not significantly lower than those found by tracer diffusion experiments (D > 10−15) performed on lithiated silicon electrodes as already mentioned.70 The drastic difference between these diffusivities and those found in our study on pure a-Si evidence that the literature values obtained from electrochemical methods correspond to the lithiated region of the Si electrode (red area of Figure 12). Detailed determination of Li transport parameters in pure Si material which corresponds to the nonlithiated phase (blue area of Figure 12) were presented in this work.

Figure 12. Sketch of a two phase electrochemical lithiation mechanism of amorphous silicon. The current collector is on the far right end of the illustration.

consumed. Indications for a two phase lithiation mechanism was observed also by our group using ex-situ SIMS measurements on lithiation of 600 nm thin amorphous silicon films.24,70 A further important published result70 is that the Li concentration−depth profiles measured in lithiated amorphous silicon electrodes by SIMS (reflecting the phase boundary) are not modified by storing the electrode at room temperature in argon for some weeks. This means that no long-range Li redistribution from the highly lithiated region into the weakly lithiated region is taking place if the lithiation current is removed. The sharp Li concentration gradient (Figure 12) maintains. This can be explained to be a consequence of the low Li permeabilities obtained in this work for pure silicon as it will be further discussed. In this work, Li transport parameters in nonlithiated (pure) silicon are measured (corresponding to the blue region of Figure 12). Li permeabilities and diffusivities are obtained in this study for a temperature of 240 °C and above. Lithium transport at room temperature could not be detected due to the extremely low Li permeation. Table 2 presents Li permeTable 2. Li Transport Parameters in Amorphous Silicon Layers Extrapolated to Room Temperature (300 K) for the Processes Listed in Table 1 Parameter Permeability (fast) Permeability (slow) Solubility Diffusivity (lag-time) Diffusivity (D = P/S)

at room temperature 8 1 3 1 7

× × × × ×

10−28 10−38 10−9 10−29 10−31

(m2/s) (m2/s) (m2/s) (m2/s)

abilities, solubilities and diffusivities extrapolated to room temperature using the activation enthalpy and the preexponential factor of the corresponding processes listed in Table 1. We make the assumption that the activation enthalpies (obtained at higher temperatures) are applicable to the study at room temperature. The extremely low values confirm the experimental result that the Li isotope contrast in ML is not changed even after more than 4 years of ML storage at room temperature. Rahn et al.63 measured a Li diffusivity of 1 × 10−18 m2/s in amorphous LiNbO3 films at room temperature which is several orders of magnitude higher than obtained in this work for Li diffusion in Si layers. Hence, Li mobility inside the Li reservoirs is not responsible for the observed hindered Li isotope intermixing in the ML at room temperature. Lithium tracer diffusion experiments performed on lithiated silicon electrodes at room temperature are also given in the literature.70 They indicate that the diffusion inside the highly lithiated region of the silicon electrode (LixSi with x ∼ 2.5 according to TEM66,67) is very high: D > 10−15 m2/s. If we consider the Li solubility in Li2.5Si to equal the Li content, x = S = 2.5, we obtain a room temperature Li permeability of PLi2.5Si > 10−15 m2/s. Consequently, we obtain a ratio of the Li 3261


Article

Chemistry of Materials As a final remark note that a straightforward step toward high-energy silicon-based thin film lithium ion batteries would be the use of multilayer Si electrodes.15,16 This work shows that the phenomenon of Li segregation at multilayer interfaces has to be taken into consideration.

■

to an explanation why electrochemical lithiation of silicon electrodes in LIB takes place by a moving phase boundary separating a high lithiated Li−Si phase from a poor or none lithiated Si phase.

■

ASSOCIATED CONTENT

S Supporting Information *

EXPERIMENTAL SECTION

Multilayer films as sketched in Figure 1a were deposited using an ionbeam coater. The depositions were performed at room temperature. The MLs were stored in air also at room temperature. Annealing was performed in a commercial rapid thermal annealing setup in argon gas. SIMS was applied to determine the element and isotope depth profile of the ML. Further investigations were done with X-ray reflectometry and grazing incidence X-ray diffraction. All measurements were performed at room temperature. More details are given in the SI.32

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b00186. Details on multilayer preparation, layer thickness determination, neutron reflectometry simulations, SIMS data, detection of Li segregation, derivation of Li isotope fractions and Li solubility from measured SIMS intensity, and derivation of Li permeability from Li permeation experiments (PDF)

■

CONCLUSION Li permeation experiments through amorphous Si were performed using multilayers of alternating 9.5 nm thin 6 LiNbO3 and 7LiNbO3 layers with 95 nm thin Si layers inbetween. Li permeation leads to a mutual exchange of Li isotopes through the Si layer and adjacent interfaces changing the relative Li isotope fraction in the LiNbO3 layers. The modification of the Li isotope fraction was measured by SIMS which enabled the determination of Li permeabilities in amorphous silicon. The Li solubility in amorphous silicon was determined from Si and Li SIMS signals. Li diffusivity was determined from permeability and solubility (D = P/S) and additionally from the time-lag method. It was found that Si layers effectively block Li permeation at room temperature for years. At higher temperatures, Li permeation is measurable within reliable experimental time intervals. A fast and a slow Li permeation process through the Si layers were discerned. The activation enthalpy for the fast Li permeation process amounts to (0.9 ± 0.2) eV which is similar to that calculated for Li permeation in bulk crystalline silicon (1.2 ± 0.2) eV. This result is traced back to the fact that the same mechanism of interstitial Li diffusion is acting in both types of materials. The experiments revealed further that this fast Li permeation process is associated with Li segregation at the surface and at the interface to the Si wafer substrate. The activation enthalpy of fast diffusion was determined to (0.4 ± 0.1) eV. Li permeability of the slow Li permeation process is several orders of magnitude lower than that of the fast Li permeation process. It shows an activation enthalpy of (1.9 ± 0.2) eV which is twice as high. This process can be explained to result from trap-limited diffusion. The activation enthalpy of traplimited diffusion of (1.5 ± 0.2) eV is almost three times larger than that in crystalline Si. This shows that the energy barriers of Li traps are three times higher than that of interstitial Li diffusion in agreement with prediction from first principle calculations. Li solubility in amorphous Si was found to be 1 order of magnitude higher than in crystalline silicon. This evidence that the amorphous structure possesses additional free volumes and defects where a surplus of Li can be accommodated. The activation enthalpy of Li solubility in amorphous silicon of (0.5 ± 0.1) eV was found to be identical to that in crystalline silicon (0.6 ± 0.1) eV within error limits. Overall, extremely low Li permeabilities, solubilities and diffusivities were measured in amorphous silicon at temperatures up to 500 °C. We claim that this result could contribute

■

AUTHOR INFORMATION

Corresponding Author

*E. Hüger, e-mail: [email protected]. ORCID

Erwin Hüger: 0000-0002-1545-1459 Harald Schmidt: 0000-0001-9389-8507 Funding

Deutsche Forschungsgemeinschaft (DFG) under the contract HU 2170/2-1. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the Deutsche Forschungsgemeinschaft (DFG) under the contract HU 2170/2-1 is gratefully acknowledged. Thanks are due to E. Witt and P. Heitjans (U Hannover) for preparing the LiNbO3 sputter targets.

■

REFERENCES

(1) Rehnlund, D.; Lindgren, F.; Bohme, S.; Nordh, T.; Zou, Y.; Pettersson, J.; Bexell, U.; Boman, M.; Edstrom, K.; Nyholm, L. Lithium trapping in alloy forming electrodes and current collectors for lithium based batteries. Energy Environ. Sci. 2017, 10, 1350−1357. (2) Xu, S.; Jacobs, R. M.; Nguyen, H. M.; Hao, S.; Mahanthappa, M.; Wolverton, Ch.; Morgan, D. Lithium transport through lithium-ion battery cathode coatings. J. Mater. Chem. A 2015, 3, 17248−17272. (3) Wang, M.; Xiao, X.; Huang, X. Study of lithium diffusivity in amorphous silicon via finite element analysis. J. Power Sources 2016, 307, 77−85. (4) Wang, M.; Xiao, X.; Huang, X. A multiphysics microstructureresolved model for silicon anode lithium-ion batteries. J. Power Sources 2017, 348, 66−79. (5) Wang, M. Simulation of Amorphous Silicon Anode in Lithium-Ion Batteries. PhD thesis, Michigan State University, East Lansing, MI, 2017. (6) McDowell, M. T.; Lee, S. W.; Nix, W. D.; Cui, Y. 25th Anniversary Article: Understanding the Lithiation of Silicon and Other Alloying Anodes for Lithium-Ion Batteries. Adv. Mater. 2013, 25, 4966−4985. (7) Nguyen, B. P. N.; Chazelle, S.; Cerbelaud, M.; Porcher, W.; Lestriez, B. Manufacturing of industry-relevant silicon negative composite electrodes for lithium ion-cells. J. Power Sources 2014, 262, 112−122. (8) Obrovac, M. N.; Chevrier, V. L. Alloy Negative Electrodes for LiIon Batteries. Chem. Rev. 2014, 114, 11444−11502.

3262


Article

Chemistry of Materials (9) Kasavajjula, U.; Wang, C.; Appleby, A. J. Nano- and bulk-siliconbased insertion anodes for lithium-ion secondary cells. J. Power Sources 2007, 163, 1003−1039. (10) Aifantis, K. E.; Hackney, S. A.; Kumar, R. V. High Energy Density Lithium Batteries. Materials, Engineering, Applications; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, 2010. (11) Ferraresi, G.; Czornomaz, L.; Villevieille, C.; Novak, P.; El Kazzi, M. Elucidating the Surface Reactions of an Amorphous Si Thin Film as a Model Electrode for Li-Ion Batteries. ACS Appl. Mater. Interfaces 2016, 8, 29791−29798. (12) Bordes, A.; Vito, E. D.; Haon, C.; Secouard, C.; Montani, A.; Marcus, P. Investigation of Lithium Insertion Mechanisms of a ThinFilm Si Electrode by Coupling Time-of-Flight Secondary-Ion Mass Spectrometry, X-ray Photoelectron Spectroscopy, and Focused-IonBeam/SEM. ACS Appl. Mater. Interfaces 2015, 7, 27853−27862. (13) Stournara, M. E.; Kumar, R.; Qi, Y.; Sheldon, B. W. Ab initio diffuse-interface model for lithiated electrode interface evolution. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2016, 94, 012802. (14) Stournara, M. E.; Xiao, X.; Qi, Y.; Johari, P.; Lu, P.; Sheldon, B. W.; Gao, H.; Shenoy, V. B. Li Segregation Induces Structure and Strength Changes at the Amorphous Si/Cu Interface. Nano Lett. 2013, 13, 4759−4768. (15) Jimenez, A. R.; Klöpsch, R.; Wagner, R.; Rodehorst, U.; Kolek, M.; Nölle, R.; Winter, M.; Placke, T. A Step Toward High-Energy Silicon-Based Thin Film Lithium Ion Batteries. ACS Nano 2017, 11, 4731−4744. (16) Fister, T. T.; Esbenshade, J.; Chen, X.; Long, B. R.; Shi, B.; Schlepütz, Ch. M.; Gewirth, A. A.; Bedzyk, M. J.; Fenter, P. Lithium Intercalation Behavior in Multilayer Silicon Electrodes. Adv. Energy Mater. 2014, 4, 1301494. (17) Ozanam, F.; Rosso, M. Silicon as anode material for Li-ion batteries. Mater. Sci. Eng., B 2016, 213, 2−11. (18) Hüger, E.; Dörrer, L.; Rahn, J.; Panzner, T.; Stahn, J.; Lilienkamp, G.; Schmidt, H. Lithium Transport through Nanosized Amorphous Silicon Layers. Nano Lett. 2013, 13, 1237−1244. (19) Hüger, E.; Stahn, J.; Schmidt, H. Neutron Reflectometry to Measure In Situ Li Permeation through Ultrathin Silicon Layers and Interfaces. J. Electrochem. Soc. 2015, 162, A7104−A7109. (20) Berla, L. A.; Lee, S. W.; Ryu, I.; Cui, Y.; Nix, W. D. Robustness of amorphous silicon during the initial lithiation/delithiation cycle. J. Power Sources 2014, 258, 253−259. (21) Phan, V. P.; Pecquenard, B.; Le Cras, F. High-Performance AllSolid-State Cells Fabricated with Silicon Electrodes. Adv. Funct. Mater. 2012, 22, 2580−2584. (22) Jerliu, B.; Dörrer, L.; Hüger, E.; Borchardt, G.; Steitz, R.; Geckle, U.; Oberst, V.; Bruns, M.; Schneider, O.; Schmidt, H. Neutron reflectometry studies on the lithiation of amorphous silicon electrodes in lithium-ion batteries. Phys. Chem. Chem. Phys. 2013, 15, 7777−7784. (23) Jerliu, B.; Dörrer, L.; Hüger, E.; Seidlhofer, B.-K.; Steitz, R.; Geckle, U.; Oberst, V.; Bruns, M.; Schmidt, H. Volume Expansion during Lithiation of Amorphous Silicon Thin Film Electrodes Studied by In-Operando Neutron Reflectometry. J. Phys. Chem. C 2014, 118, 9395−9399. (24) Hüger, E.; Jerliu, B.; Dörrer, L.; Bruns, M.; Borchardt, G.; Schmidt, H. A Secondary Ion Mass Spectrometry Study on the Mechanisms of Amorphous Silicon Electrode Lithiation in Li-Ion Batteries. Z. Phys. Chem. 2015, 229, 1375−1385. (25) Jerliu, B.; Hüger, E.; Horisberger, M.; Stahn, J.; Schmidt, H. Irreversible lithium storage during lithiation of amorphous silicon thin film electrodes studied by in-situ neutron reflectometry. J. Power Sources 2017, 359, 415−421. (26) Wang, J. W.; He, Y.; Fan, F.; Liu, X. H.; Xia, S.; Liu, Y.; Harris, C. Th.; Li, H.; Huang, J. Y.; Mao, S. X.; Zhu, T. Two-Phase Electrochemical Lithiation in Amorphous Silicon. Nano Lett. 2013, 13, 709−715. (27) Strauß, F.; Jerliu, B.; Geue, T.; Stahn, J.; Schmidt, H. Short range atomic migration in amorphous silicon. J. Appl. Phys. 2016, 119, 175102.

(28) Beyer, W. Diffusion and evolution of hydrogen in hydrogenated amorphous and microcrystalline silicon. Sol. Energy Mater. Sol. Cells 2003, 78, 235−267. (29) Street, R. A. Hydrogenated amorphous silicon; Cambridge Solid State Sciences Series; Cambridge University Press: Cambridge, U. K., 1991. (30) Weissmantel, C.; Fiedler, O.; Hecht, G.; Reisse, G. Ion beam sputtering and its application for the deposition of semiconducting films. Thin Solid Films 1972, 13, 359−366. (31) Harper, M. E. Ion Beam Deposition. In Thin Film Processes; Vossen, J. L., Kern, W., Eds; Academic Press, New York, 1978; p 194. (32) Further information is presented in the Supporting Information (SI). It contains details on multilayer preparation, layer thickness determination, neutron reflectometry simulations, SIMS data, detection of Li segregation and information on data analysis. (33) Pell, E. M. Diffusion of Li in Si at High T and the Isotope Effect. Phys. Rev. 1960, 119, 1014−1021. (34) Reiss, H.; Fuller, C. S.; Pietruszkiewicz, A. J. Solubility of Lithium in Doped and Undoped Silicon, Evidence for Compound Formation. J. Chem. Phys. 1956, 25, 650−655. (35) Wilson, R. G. SIMS quantification in Si, GaAs, and diamond - an update. Int. J. Mass Spectrom. Ion Processes 1995, 143, 43−49. (36) Stevie, F. A.; Griffis, D. P. Quantification in dynamic SIMS: Current status and future needs. Appl. Surf. Sci. 2008, 255, 1364−1367. (37) Zastrow, U.; Beyer, W.; Herion, J. SIMS depth profile analysis for investigations of the lithium-diffusion in hydrogenated amorphous silicon. Fresenius' J. Anal. Chem. 1993, 346, 92−95. (38) Schmitz, G.; Kesten, Ph.; Kirchheim, R.; Yang, Q. M. Diffusion of hydrogen through metallic multilayers. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 7333−7339. (39) Silicon, solubility, segregation and distribution coefficients of impurities and defects, general. In Impurities and Defects in Group IV Elements, IV-IV and III-V Compounds; Madelung, O., Rössler, U., Schulz, M., Eds.; Landolt-Börnstein - Group III Condensed Matter Series; Springer: Berlin, 2002; Vol. 41A2α, DOI: 10.1007/ 10681604_36. (40) Reinelt, M.; Kalbitzer, S. The diffusion of heavy alkali atoms in amorphous silicon. J. Phys. Colloques 1981, 42, C4-843−C4-847. (41) Schoelch, H. P. Diffusion and drift of Li in amorphous silicon. PhD Thesis, Ruprecht-Karls-University, Heidelberg, Germany, 1986. (42) Fink, D.; Biersack, J. P.; Schoelch, H. P.; Weiser, M.; Kalbitzer, S.; Behar, M.; De Souza, J. P.; Zawislak, F. C.; Mazzone, A. M.; Kranz, H. 5 keV to 2 MeV lithium implantation and diffusion in amorphous silicon. Radiat. Eff. Defects Solids 1989, 108, 185−203. (43) Fink, D.; Kie, T.; Biersack, J. P.; Lihang, W.; Yunru, M. Lithium implantation profiles in metals and semiconductors. Radiat. Eff. Defects Solids 1989, 108, 27−44. (44) Fink, D.; Tjan, K.; Wang, L. On the thermal mobility of lithium in metals and semiconductors. Radiat. Eff. Defects Solids 1990, 114, 21−50. (45) Lagues, M.; Domange, J. L.; Hurault, J. P. Segregation of dissolved Li to the surface of Si: A new activation process. Solid State Commun. 1973, 12, 203−206. (46) Winer, K.; Street, R. A. Interfacial defect creation by interstitial lithium doping of amorphous hydrogenated silicon. Appl. Phys. Lett. 1988, 53, 505−507. (47) Winer, K.; Street, R. A. Interstitial Li doping of a-Si:H. J. Appl. Phys. 1989, 65, 2272−2281. (48) Wang, Z.; Jeurgens, L. P. H.; Sigle, W.; Mittemeijer, E. J. Observation and Origin of Extraordinary Atomic Mobility at MetalSemiconductor Interfaces at Low Temperatures. Phys. Rev. Lett. 2015, 115, 016102-1−016102-5. (49) Skriver, H. L.; Rosengaard, N. M. Surface energy and work function of elemental metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 7157−7168. (50) Tran, R.; Xu, Z.; Radhakrishnan, B.; Winston, D.; Sun, W.; Persson, K. A.; Ong, S. P. Surface energies of elemental crystals. Sci. Data 2016, 3, No. 160080. 3263


Article

Chemistry of Materials (51) Chou, C.-Y.; Kim, H.; Hwang, G. S. A Comparative FirstPrinciples Study of the Structure, Energetics, and Properties of Li−M (M = Si, Ge, Sn) Alloys. J. Phys. Chem. C 2011, 115, 20018−20026. (52) Shenoy, V. B.; Johari, P.; Qi, Y. Elastic softening of amorphous and crystalline Li−Si Phases with increasing Li concentration: A firstprinciples study. J. Power Sources 2010, 195, 6825−6830. (53) Peng, B.; Cheng, F.; Tao, Z.; Chen, J. Lithium transport at silicon thin film: barrier for high-rate capability anode. J. Chem. Phys. 2010, 133, 034701-1−034701-5. (54) Yan, X.; Gouissem, A.; Sharma, P. Atomistic insights into Li-ion diffusion in amorphous silicon. Mech. Mater. 2015, 91, 306−312. (55) Tritsaris, G. A.; Zhao, K.; Okeke, O. U.; Kaxiras, E. Diffusion of Lithium in Bulk Amorphous Silicon: A Theoretical Study. J. Phys. Chem. C 2012, 116, 22212−22216. (56) Tritsaris, G. A.; Kaxiras, E.; Meng, S.; Wang, E. Adsorption and Diffusion of Lithium on Layered Silicon for Li-Ion Storage. Nano Lett. 2013, 13, 2258−2263. (57) Kirchheim, R.; Stolz, U. Modelling tracer diffusion and mobility of interstitials in disordered materials. J. Non-Cryst. Solids 1985, 70, 323−341. (58) Herrero, C. P.; Stutzmann, M.; Breitschwerdt, A.; Santos, P. V. Trap-limited hydrogen diffusion in doped silicon. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41, 1054−1058. (59) Schmidt, H.; Gruber, W.; Borchardt, G.; Bruns, M.; Rudolphi, M.; Baumann, H. The diffusion of ion implanted hydrogen in amorphous Si3N4:H films. J. Phys.: Condens. Matter 2004, 16, 4233− 4244. (60) Schmidt, H.; Borchardt, G.; Geckle, U.; Bruns, M.; Baumann, H. Comparative study of trap-limited hydrogen diffusion in amorphous SiC, Si0.66C0.33N1.33, and SiN1.33 films. J. Phys.: Condens. Matter 2006, 18, 5363−5370. (61) Schmidt, H. Diffusion controlled processes in amorphous Si-C-N and related materials. venia legendi thesis (Habilitationsschrift), TU Clausthal, Germany, 2005, https://dokumente.ub.tu-clausthal.de/ receive/import_mods_00000621. (62) Ruzin, A.; Abrosimov, A.; Litovchenko, P. Study of lithium diffusion into silicon−germanium crystals. Nucl. Instrum. Methods Phys. Res., Sect. A 2010, 617, 588−590. (63) Rahn, J.; Hüger, E.; Dörrer, L.; Ruprecht, B.; Heitjans, P.; Schmidt, H. Self-Diffusion of Lithium in Amorphous Lithium Niobate Layers. Z. Phys. Chem. 2012, 226, 439−448. (64) Liu.; et al. In situ atomic-scale imaging of electrochemical lithiation in silicon. Nat. Nanotechnol. 2012, 7, 749−756. (65) Miao, J.; Thompson, C. V. Kinetic study of the initial lithiation of amorphous silicon thin film anodes. J. Electrochem. Soc. 2018, 165, A650−A656. (66) Wang, J. W.; He, Y.; Fan, F.; Liu, X. H.; Xia, S.; Liu, Y.; Harris, T. C.; Li, H.; Huang, J. Y.; Mao, S. X.; Zhu, T. Two-Phase Electrochemical Lithiation in Amorphous Silicon. Nano Lett. 2013, 13 (2), 709−715. (67) McDowell, M. T.; Lee, S. W.; Harris, J. T.; Korgel, B. A.; Wang, C.; Nix, W. D.; Cui, Y. In Situ TEM of Two-Phase Lithiation of Amorphous Silicon Nanospheres. Nano Lett. 2013, 13 (2), 758−764. (68) Seidlhofer, B.-K.; Jerliu, B.; Trapp, M.; Hüger, E.; Risse, S.; Cubitt, R.; Schmidt, H.; Steitz, R.; Ballauff, M. Lithiation of Crystalline Silicon As Analyzed by Operando Neutron Reflectivity. ACS Nano 2016, 10, 7458−7466. (69) Strauß, F.; Dörrer, L.; Bruns, M.; Schmidt, H. Lithium traces diffusion in amorphous LixSi for low Li concentration. J. Phys. Chem. C 2018, 122, 6508−6513. (70) Jerliu, B.; Dörrer, L.; Hüger, E.; Seidlhofer, B.-K.; Steitz, R.; Borchardt, G.; Schmidt, H. Electrochemical lithiation of silicon electrodes: neutron reflectometry and secondary ion mass spectrometry investigations. Int. J. Mater. Res. 2017, 108, 999−1007.

3264


Permeation, Solubility, Diffusion and Segregation of Lithium in

Recommend Documents