Permeation, solubility, diffusion and segregation of lithium in

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Permeation, solubility, diffusion and segregation of lithium in amorphous silicon layers Erwin Hüger, Lars Dörrer, and Harald Schmidt Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b00186 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on April 24, 2018

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Chemistry of Materials

Permeation, solubility, diffusion and segregation of lithium in amorphous silicon layers Erwin Hüger*,a, Lars Dörrera, and Harald Schmidta,b a. Institut für Metallurgie, Abteilung Mikrokinetik, Technische Universität Clausthal, Robert-Koch-Str. 42, 38678 Clausthal Zellerfeld, Germany b. Clausthaler Zentrum für Materialtechnik (CZM), Technische Universität Clausthal, Leibnizstraße 9, 38678 Clausthal-Zellerfeld, Germany 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 density2) 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) P=S·D.

(1)

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 (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 analysed 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

Results Li permeation measurements

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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 Fig. 1(a). A sequence of two (6LiNbO3/Si/7LiNbO3/Si) structural 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

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The 6Li and 7Li isotope fractions, f6Li and f7Li, were obtained from SIMS signals (see SI) by f

6Li

6Li SIMS = 6Li 7Li I +I SIMS SIMS I

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 Fig. 1 (b-e) and (g-j). The logarithmic scaling illustrates the high dynamic range of extremely strong Li signals. The Si signal (Fig. 1(d)) 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.

f

7Li SIMS = 6Li 7Li I +I SIMS SIMS I

(2)

where ISIMS6Li and ISIMS7Li are the SIMS intensities measured at 6Li and 7Li masses, respectively. The isotope fractions for the as-deposited ML are presented in Fig. 2(a).

6

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

;

7Li

7

Figure 2: Li (red curves) and Li (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.

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Chemistry of Materials 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 asdeposited ML to 30 nm for the ML annealed at 240°C for 52 h and at 500°C for 6 min (Fig. 4(a,b,c)) assuming the same sputter rates. The horizontal arrows in Fig. 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.

6

7

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

In order to induce Li permeation, the ML were annealed at four temperatures of 240°C, 360°C, 420°C and 500°C at different annealing times between 1 min and 3450 h. Fig. 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 6LiNbO3 reservoir layers. The reverse effect is found for the 7LiNbO3 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 (Figure S4 and S5 in SI)32. From Fig. 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 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°C and 500°C, respectively. It can be observed that the depth profiles of Li, Nb and Si resulting

Figure 4: SIMS depth profiles close to the surface of (a,d) the 6 7 93 28 sum of Li and Li signals, (b,e) Nb and (c,f) Si 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 minutes (d,e,f), respectively. The horizontal arrows point out the shift of the profile to larger depths due to growth of a surface layer.

Li permeability determination For further analysis, we calculate the 6Li contrast (K), which is defined as

K (t ) =

f (t ) − f min  t − t0  = exp  − f max − f min  τ 

(3)

where fmax and fmin are the 6Li fractions in the 6LiNbO3 reservoirs in the as-deposited state and after complete Li isotope intermixing (see e. g. Fig. 2 (a) and (h)). Further, f(t) is the 6Li 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 SI.



6

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

Figure 5 presents the annealing time dependence of the contrast K(t) in the two different types of Li reservoirs (surface and middle) measured at different temperatures. The contrast decrease of the first 6LiNbO3 layer at the surface is presented in Fig. 5(a) 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 Fig. 1(a)) is presented in Fig. 5(b). 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 Fig. 5. Figure 5 shows clearly that the decrease of the isotope contrast K(t) of the middle 6LiNbO3 layer (Fig. 5(b)) is slower than that of the surface 6LiNbO3 layer (Fig. 5(a)). 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 (SI) ρ d ⋅d 1 M Si τ= ⋅ ⋅ LiNbO3 ⋅ Si LiNbO3 4 M LiNbO3 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 asdeposited 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 (Fig. 5) determines the time constant and from eq. (4) the Li permeability is calculated.

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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 34 33 of solubility and diffusivity. The open circle is an experimental value for 5 nm amorphous Si layers from ref. [19]. Table 1: Activation enthalpy, ∆Hx, and pre-exponential factor, X0, for the Arrhenius behaviour (see eq. (5)) of Li transport parameters in silicon as determined from the experimental data in Figs. 6, 9, 10. 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 it is referred to the text. Parameter

Material

∆Ηx (eV)

log10X0

Permeability

a-Si, fast

0.9 ± 0.2

-12 ± 0.3

Permeability

a-Si, slow

1.9 ± 0.2

-6 ± 0.4

Permeability

c-Si from [34,33]

1.2 ± 0.2

-7 ± 0.4

Solubility

a-Si

0.5 ± 0.1

-0.2 ± 0.1

Solubility

c-Si [33]

0.6 ± 0.1

-0.6 ± 0.2

Diffusivity

a-Si, slow, time-lag

1.3 ± 0.2

-7 ± 0.4

Diffusivity

a-Si, slow, P/S

1.5 ± 0.2

-5 ± 0.3

The temperature dependence of the Li permeability for the fast Li permeation process governing segregation (Fig. 5(a)) is plotted in Fig. 6 as stars. In order to simplify the extraction of these Li permeabilities, we assumed that the Li flux to the ML at the surface comes from the neighbouring 7LiNbO3 layer only. Consequently, the factor of one 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 X = X0 exp(-∆Hx/kT)


(5)

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where X is the Li transport parameter (X = P, D or S). X0 and ∆Hx are the pre-exponential factor and the activation enthalpy of each process. Concerning the segregation process, the resulting activation enthalpy of Li permeation of ∆HPa-Si, fast= (0.9 ± 0.2) eV and the preexponential factor are listed in Tab. 1. The temperature dependence of the Li permeability corresponding to the slow Li permeation process is depicted in Fig. 6 with filled squares. The data show also an Arrhenius behaviour with a higher activation enthalpy of Li permeation of ∆HPa-Si,slow = (1.9 ± 0.2) eV (Tab. 1). The permeability at 240 °C is not shown due to the rather incomplete measurement of the Li isotope contrast decrease (Fig. 5(b)) 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 the third Si layer in higher resolution which should be less affected by Li segregation towards the ML surfaces. The intensity ratio between the total Li signal (the sum of 6Li and 7Li 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=

(I

7 Li + I SIMS ) ⋅ RSF Li 1 RSF Si 28 Si I SIMS ⋅ 0.9223

6

7

Figure 7: SIMS depth profiles of the total Li signal ( Li + Li 28 signal) (red curve), of the Si signal (blue curve) and of the 28 ratio of the total Li signal to the Si 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.

6 Li SIMS

(6)

where ISIMS6Li, ISIMS7Li and ISIMS28Si are SIMS intensities measured at 6Li, 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 = 2E-5. Due to SIMS ion beam mixing effects, this value can be considered as an upper limit.37 After annealing, the solubility increases (Fig. 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 Fig. 7 (b)). The annealing time dependence of the solubility is presented in Fig. 8. A 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 Fig. 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 ∆HSa-Si = (0.5 ± 0.1) eV (Tab. 1).



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enthalpy of Li diffusion in amorphous silicon of ∆HDa-Si, slow, time-lag = (1.3 ± 0.2) eV (Tab. 1). Additional Li 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 activation enthalpy of ∆HDa-Si, slow, P/S = (1.5 ± 0.2) eV.

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.

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 literature. The open triangles and squares are only for a better discrimination of each curve. For details, see text. 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].

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

D=

d Si2 2⋅ t0

(7)

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

Discussion The main results of the study are illustrated in Figs. 6, 9 and 10: The Arrhenius behaviour of the permeabilities, solubilities and diffusivities of Li in amorphous silicon layers. These results are now discussed with respect to literature. Permeabilities In addition to the experimental results obtained in this study, Fig. 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 Pell33, respectively. An activation enthalpy of ∆HPc-Si (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 Li permeation process, ∆HPa-Si, fast. The slow permeation process (Fig. 5(b)) has a considerably higher activation enthalpy (Fig. 6 and Tab. 1). Hence, the fast Li permeation process (Fig. 5(a)) in amorphous silicon should show a similar Li transport mechanism as Li in crystalline silicon, while the slow process (Fig. 5(b)) is different. The energy barrier which


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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 two orders of magnitude. Solubilities According to eq. (1), a discussion of Li solubility will give more information on transport mechanisms. In 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 Fig. 9. Literature values of Li solubility in crystalline Si from ref. [34] are presented also in Fig. 9. In both cases the Li solubility obeys the Arrhenius law in good approximation and show the same activation enthalpy of about 0.5 eV (∆HSa-Si ≈ ∆HSc-Si). 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-vapour 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 behaviour found in this work (Fig. 9) indicates low acceptor impurities in the amorphous silicon layers with Li acting as donor type impurity.40 Despite of 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: Since P, D and S all follow the Arrhenius law, it can be concluded from eqs. (1, 5) that ∆HP = ∆HD + ∆HS. 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 crystalline (∆HPc-Si = (1.2 ± 0.2) eV) and amorphous Si (∆HPa-Si, slow = (1.9 ± 0.2) eV) have to stem from the activation enthalpy of Li diffusion ∆HD. Lithium segregation (fast process) As mentioned above and further discussed in SI32 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 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 analysing 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 percent 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 (Fig. 5 (a)) to the surface and a slower process (Fig. 5 (b)) 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 (Tab. 1) and consequently those of diffusion. According to ∆HDa-Si, fast = ∆HPa-Si, fast ∆HS, we can calculate an expected activation enthalpy of diffusion of about 0.4 eV. Experiments found an activation enthalpy for interstitial Li diffusion in crystalline silicon of ∆HDc-Si = (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 (Fig. 6). Li permeation in the interior of the ML seems to be less affected by the Li segregation phenomenon. In 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 Fig. 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. 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 Fig. 10) are identical within error limits with the Li diffusivities obtained from D=P/S (squares in Fig. 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 Fig. 11). Trap-limited diffusion was observed also for 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

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.

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

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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 Tab. 1). The temperature dependence of trap-controlled Li diffusivities in silicon (with 0.1 % Li content) from ref. [4144] 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 analysed by Fink et al.4144 . Moreover, calculations 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 reported69 and are presented also in Figure 10 for a reason of 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 one 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 reference [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 Fig. 10 by a dotted line. They are also higher. The open circle plotted in Fig. 10 at 320 °C corresponds to Li diffusion in Si with 2.4 percent 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


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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 Fig. 11). Consequently, during the Li segregation process the traps have to be all occupied/saturated. This can be achieved by Li and only surplus non-trapped Li is moving. Li segregation takes place until the surface energy is minimized and/or until all excess Li is segregated.47 Afterwards 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 literature4-6,17,24,28,64-68,70: 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 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

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.

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 non-lithiated (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. Tab. 2 presents Li permeabilities, solubilities and diffusivities extrapolated to room temperature using the activation enthalpy and the pre-exponential factor of the corresponding processes listed in Tab. 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 x 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. Table 2: Li transport parameters in amorphous silicon layers extrapolated to room temperature (300 K) for the processes listed in Tab. 1. Parameter

at room temperature

Permeability (fast)

8 × E-28 (m /s)

Permeability (slow)

1 × E-38 (m /s)

Solubility

3 × E-9

Diffusivity (lag-time)

1 × E-29 (m /s)

Diffusivity (D = P / S)

2

2

2

2

7 × E-31 (m /s)

Lithium tracer diffusion experiments performed on lithiated silicon electrodes at room temperature are also given in 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 > E-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 > E-15 m2/s. Consequently, we obtain a ratio of the Li permeabilities of PLi2.5Si / PSi > E23. 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 non-lithiated 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 ratelimiting 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 of 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 Fig. 10, a growing Li concentration enhances diffusion and permeation. Also pores and micro-cracks 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 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 films70 gave room temperature Li diffusivities between E-17 and E-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 > E-15) performed on lithiated silicon electrodes as already mentioned.70 The drastic difference between these diffusivities and those found in our study

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on pure a-Si evidences 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 non-lithiated phase (blue area of Figure 12) were presented in this work. As a final remark note that a straightforward step towards 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.

Experimental Multilayer films as sketched in Fig. 1 (a) were deposited using an ion-beam 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 SI.32

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.


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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 trap-limited 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 one order of magnitude higher than in crystalline silicon. This evidences 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. In 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 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 Supporting Information. It contains 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. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * e-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. / All authors have given approval to the final version of the manuscript.

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

ACKNOWLEDGMENT 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.

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Permeation, solubility, diffusion and segregation of lithium in

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