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Lithiation effects on the structural and electronic properties of Si nanowires as a potential anode material
Energy Storage Materials 20 (2019) 438–445
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Lithiation effects on the structural and electronic properties of Si nanowires as a potential anode material F. De Santiago a, J.E. Gonzalez a, A. Miranda a, A. Trejo a, F. Salazar a, *, L.A. Perez b, M. Cruz-Irisson a a b
Instituto Politecnico Nacional, ESIME-Culhuac an, Av. Santa Ana 1000, 04430, Mexico, Ciudad de Mexico, Mexico Instituto de Física, Universidad Nacional Autonoma de Mexico, A.P. 20-364, 01000, Mexico, Ciudad de Mexico, Mexico
A R T I C L E I N F O
A B S T R A C T
Keywords: Silicon nanowires Li batteries Electronic properties Young's modulus
The need for better energy-storage materials has attracted much attention to the development of Li-ion battery electrodes. Si nanowires have been considered as alternative electrodes, however the effects of Li on their electronic band gap and mechanical properties have been scarcely studied. In this work, a density functional study of the electronic and mechanical properties of hydrogen passivated silicon nanowires (H-SiNWs) grown along the [001] direction is presented. The Li atoms are gradually inserted at interstitial positions or replacing surface H atoms. The results show that, for surface-lithiated H-SiNWs, the semiconducting band gap decreases when the concentration of Li atoms increases; whereas the H-SiNWs become metallic even with the addition of only one interstitial Li atom. The formation energy diminishes with the concentration of Li atoms for surface-lithiated HSiNWs, whereas the contrary behavior is found in the interstitial-lithiated H-SiNWs. Furthermore, for the surfacelithiation case, the Li binding energy reveals the existence of Si–Li bonds, whereas for the interstitial-lithiation case, the Li binding energy increases when the Li grows up to a critical concentration, where some Si–Si bonds break. Finally, for the case of surface-lithiation, the Young's modulus (Y) increases with the concentration of Li, whereas for the interstitial-lithiation case, Y suffers a sudden diminution at a certain Li concentration due to the large internal mechanical stresses within the nanowire structure. These results should be considered when regarding H-SiNWs as potential electrodes in Li-ion battery anodes.
1. Introduction
current collector. The bulk Si as anodic materials has higher theoretical capacities for Li storage (4200 mAh/g) [2–4] than the graphite used in commercial batteries (372 mAh/g) [5]. The volumetric expansion during the insertion of Li atoms is around 400% for bulk Si [6,7]. As a result of the crystal structure breakdown by Li atoms, its storage capacity, Li diffusion and electron transport is reduced [6,8]. One possible alternative of anodic materials are arrays of silicon nanowires (SiNWs), grown on metallic substrates, since their great surface/volume aspect ratio allow the storage of more Li atoms than the bulk material [8]. Furthermore, the free space between the nanowires in the array diminishes the internal stress during the Li insertion. Another important issue that can modify the electronic and mechanical properties of SiNWs is the chemical passivation of the nanowire surface. The effects of hydrogen passivation have been widely studied in nanoporous and nanowire structures [9–12] and in two-dimensional systems, such as graphene [13,14]. The hydrogenated graphene or graphane has a non-planar chair-like structure and a semiconducting
Lithium ion batteries have attracted much attention of the scientific community since they offer the best performance for supplying energy to portable electronic devices, and it is expected that their capacity could increase in the next generation of batteries, allowing, for example, energy supply in applications ranging from medical devices working inside the human body, electric vehicles, to the development of great scale energy storage devices for alternative energies. However, in order to increase the scale of the Li-ion battery applications, some problems should be solved before, such as extending the battery useful life, the increment of its gravimetric capacity [1], the reduction of the charging time, the increase of the energy supply under high energy demand, and its safety. In this context, it is necessary to find new materials with low working potential respect to Li/Liþ, high energy storage capacity with high Li diffusion, capable to support internal stresses during the charge/discharge cycles, also warranting an efficient electronic transport from the electrode to the
* Corresponding author.. E-mail addresses: [email protected] (F. Salazar), lperez@fisica.unam.mx (L.A. Perez), [email protected] (M. Cruz-Irisson). https://doi.org/10.1016/j.ensm.2019.04.023 Received 11 November 2018; Received in revised form 18 April 2019; Accepted 18 April 2019 Available online 24 April 2019 2405-8297/© 2019 Elsevier B.V. All rights reserved.
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behavior after the first charge/discharge cycle, in comparison with oxide coated SiNWs [26]. Nowadays, several theoretical methods can be used to study the physical and chemical properties of anodic and cathodic materials, where the system size defines the method to be applied, allowing for a multiscale simulation approach to the development of Li ion batteries [27]. In particular, density functional theory (DFT) has been used to study the structural and electronic properties of those materials. For example, Hubbard-U-corrected DFT in the generalized gradient approximation (GGAþU) accurately predicts the structural and vibrational properties of cathodic materials such as LiMn2O4 [28] and LiFePO4 [29]. On the other hand, previous DFT studies of single Li atom insertion into SiNWs suggest that surface sites are energetically more favorable than interstitial ones [30]. In this work, we present a systematic DFT study of the electronic and mechanical properties of 2.5 nm-diameter H-SiNWs grown along the [001] crystallographic direction, with surface and interstitial Li atoms, in order to understand how the Li intercalation in H-SiNWs could allow the design of electrode materials that could improve the battery performance.
behavior that contrast with the planar structure and zero band gap of pristine graphene. Likewise, the pristine SiNWs can have either metallic or semimetallic behavior [15], while H-SiNWs are semiconductors [10, 16]. On the other hand, it is expected that the SiNWs do not suffer great mechanical stresses during the insertion/detachment of Li atoms, but this problem is still under study [17], however, recent reports indicate that the volumetric expansion in pristine SiNWs is anisotropic [18,19]. According to experimental results, the electronic and optical properties of SiNWs under elastic strain suffer important changes that could lead to new technological applications in the semiconductor industry [20]. Currently, there is no consensus about the optimal location of Li atoms in the nanowire structure and maximum Li concentration that H-SiNWs can store before overcoming their elastic limit. Experimental results reveal Li atoms inside SiNWs up to a distance of 1 nm from the surface [21], as well as an anisotropic swelling of SiNWs attributed to the interfacial processes involving large volumetric strains at the lithiation reaction front that depend on the crystallographic orientation [22]. Moreover, experimental evidence reveals that the axial tensile strength for lithiated pristine SiNWs with diameters greater than 100 nm decreases in comparison with non lithiated pristine ones [23,24]. As stated above, H-SiNWs have semiconductor behavior [10,16,25] however, the effects of the Li atoms on their electronic and mechanical properties have been barely studied. These passivated nanowires have the advantage of being crystalline with no surface dangling bonds, then we expect that the chemical reactions within the electrolyte decrease, thus increasing the useful life of the electrode. Moreover, experimental reports indicate that H passivated SiNWs exhibit superior electrochemical properties such as larger Li storage capacity, higher Coulombic efficiency, and a more stable
2. Theory and model We consider infinitely long H-SiNWs with a diameter of 24.7 Å, and grown along the [001] crystallographic direction as in Ref. [31]. Two cases were considered for the intercalation of Li atoms: the first one, referred as surface-lithiation, where some surface H atoms are replaced by Li ones, as shown in Fig. 1(a). In the second case, referred as interstitial-lithiation, some Li atoms were placed into positions
Fig. 1. Top and side views of non-relaxed unit cells of H-SiNWs. The yellow, white, and violet spheres represent the Si, H, and Li atoms, respectively. The numbers besides the Li atoms indicate the sequence by which (a) the H atoms were replaced by Li ones and (b) the Li atoms were inserted into the nanowire structure. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 439
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error of less than 0.8% [16].
equivalent to those reported as the more energetically stable for bulk silicon [32], and H-SiNWs [30], the so-called Td positions, as illustrated in Fig. 1(b). These Fig. 1(a) and (b) depict the considered non-relaxed initial morphologies for both mentioned cases. The numbers besides the Li atoms indicate the sequence by which the H atoms were replaced by Li ones, as well as the sequence by which the interstitial Li atoms were inserted into the H-SiNWs. The Li concentration for each case is obtained as CLi ¼ ðnLi 100%Þ=Nw where nLi is the number of Li atoms and Nw is the number of atoms in the unit cell of the H-SiNW. All calculations were performed using DFT within the local density approximation (LDA) with standard norm-conserving pseudopotentials [33], in their fully nonlocal form [34], as implemented in the SIESTA code [35]. We also used double-ζ s, p-basis and a single d orbital, as well as an energy cutoff of 150Ry to define the real-space grid for numerical integrations. The Brillouin zone of the H-SiNW unit cell was sampled with 1 1 24 k-points within the Monkhorst–Pack scheme for density of states calculations. All nanowires were free to relax until the Hellmann-Feynman forces were less than 2 meV/Å. The H-SiNWs periodic supercells have a lateral separation of nine times their diameter, enough to consider them as isolated. The suitability of the pseudopotential was tested by calculating the bond lengths and lattice constant for the bulk Si diamond structure; both calculated quantities are in good agreement with the corresponding experimental values [36] within an
3. Results and discussion Fig. 2 shows the relaxed geometries of the unit cell of the H-SiNWs with different number of Li atoms (nLi ) for both surface- and interstitiallithiation cases. Notice how the interstitial Li modifies the crystalline structure of the H-SiNWs, in contrast to the surface case where the Si atoms remain unaltered along the [001] growth direction. It is worth mentioning that when the number of interstitial Li atoms per unit cell is greater than 3, the H-SiNWs suffer structural changes where the Si–Si bonds around the Li atoms change their length due to the electrostatic interaction between Li atoms. This effect increases with the concentration of interstitial Li, leading to broken bonds that cannot be restored when the Li atoms are taken out from the structure, i.e., the nanowire crystalline structure is lost. In contrast, for the surface lithiation case, an even number of Li atoms preserve the nanowire symmetry and the structure only suffers small deformations at the surface, maintaining its internal structure. Fig. 3 shows the electronic band structures and densities of states of the H-SiNWs with different concentrations of surface Li atoms (a) 0%, (b) 0.9%, (c) 5.1% and (d) 10.3%, following the sequence depicted in Fig. 1(a). The band gap (ΔEg ) is direct for all studied Li concentrations,
Fig. 2. Cross views of the relaxed H-SiNWs for the surface- (left) and interstitial-lithiation (right) cases. The number of Li atoms per unit cell (nLi ) is shown at the first column. 440
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Fig. 3. Electronic band structures (left panels) of H-SiNWs with (a) 0 (0%), (b) 1 (0.9%), (c) 6 (5.1%), and (d) 12 (10.3%) surface Li atoms per unit cell, respectively. The corresponding concentrations ðCLi Þ are indicated in parenthesis. Right panels: Total (black line) and partial electronic densities of states per atomic species Si (red line), H (blue line), and Li (green line). The dashed line correspond to the Fermi energy shifted to zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
found for the surface-lithiation case. This behavior can be contrasted with [111]-H-SiNWs, where the Li states have a larger contribution to the conduction band [37]. The relative energetic stability of the lithiated H-SiNWs was obtained from the formation energy (Ef ) per number of atoms in the unit cell (M), which can be calculated as
and the addition of Li atoms leads to new bands within the band gap of the former H-SiNWs. In consequence, ΔEg diminishes when the concentration of surface Li atoms increases, as shown in Fig. 4. Observe that the semiconducting behavior remains even for 12 surface Li atoms per unit cell and the band gaps are still larger than that calculated for the bulk Si within the same theory level. It is worth to mention that all values of ΔEg are lower that for H-SiNWs grown along [111] crystallographic direction [16] whose values range from 1.75 eV to 0.87 eV for 0 and 12 surface Li atoms, respectively. Fig. 5 shows the electronic band structures and densities of states of the H-SiNWs with different concentrations of interstitial Li atoms following the sequence depicted in Fig. 1(b). In contrast to the surface lithiation case, a completely different behavior is observed when the Li atoms occupy interstitial positions (Td ) in the H-SiNW structure. The Fermi energy shifts to the conduction band even with just one interstitial Li atom, resulting in a metallic or semimetallic character. Notice that the number of bands increases with the interstitial Li atom concentration. Moreover, as expected, the main contribution to the electronic states is due to the Si atoms (red lines), whereas the Li atoms (green lines) have a slight contribution to the conduction bands, which is lower than that
Ef ¼
1 1 EðSiNW þ nLi Þ nSi EðSibulk Þ ðnH nLi Þ EðH2 Þ nLi EðLiÞ ; M 2
where EðXÞ is the calculated total energy of system X. Here, SiNW þ nLi denotes the system formed by the H-SiNW unit cell with nLi surface or interstitial Li atoms, EðSibulk Þ, EðH2 Þ, and EðLiÞ is the energy per atom of bulk Si, hydrogen molecule and one isolated Li atom, respectively, while nH and nSi denote the number of H and Si atoms per unit cell, respectively. For the interstitial lithiation case, the coefficient of the third term in the previous equation, (nH nLi ), must be replaced by nH . Fig. 6 shows the formation energy of the lithiated H-SiNWs as a function of the number of Li atoms per unit cell (nLi ), or concentration (CLi ), for both surface and interstitial lithiation cases. A lower Ef value indicates that the system is relatively more stable than another system with a higher value. Notice that the replacement of surface H atoms by Li ones, increases the relative energetic stability of the SiNWs, while the addition of interstitial Li atoms diminishes it. Comparing these results with those previously reported for [111]SiNWs with similar diameters, it is found that the [001]-SiNWs are more energetically stable that [111]-SiNWs for both surface and interstitial cases [37]. On the other hand, we also performed a Hirshfeld population analysis [38] to estimate the electronic charge distribution around each atom of the H-SiNW unit cell. Fig. 7 shows the Hirshfeld average charge (ρXav ðnLi Þ) for each species X as a function of the concentration of surface and interstitial Li atoms. ρXav is given by
ρXav ðnLi Þ ¼
nX 1 X ρX ; nX i¼1 i
where ρXi is the Hirshfeld electronic charge associated to atom i of species X and nX is the number of atoms of species X in the unit cell (X ¼ Si, H, Li). As expected, all H atoms gain electronic charge evidencing that there are Si–H bonds at the nanowire for both studied cases. This charge slightly decreases when the surface Li concentration increases, whereas for the interstitial lithiation case, it stays almost constant. The average charge of the Si atoms for the surface lithiation case decreases (it becomes more negative) when the Li concentration augments, indicating a charge transfer from the Li atoms, which is reflected on the average
Fig. 4. Energy band gap (ΔEg ) as a function of the number of surface Li atoms per unit cell (nLi ) or concentration (CLi ), following the sequence depicted in Fig. 1(a). The dashed line corresponds to the calculated bulk Si band gap. 441
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Fig. 5. Electronic band structures (left panels) of H-SiNWs with (a) 1 (0.9%), (b) 6 (5.1%), (c) 8 (6.8%), and (d) 12 (10.3%) interstitial Li atoms per unit cell, respectively. The corresponding concentrations ðCLi Þ are indicated in parenthesis. Right panels: Total (black lines) and partial electronic densities of states per atomic species, Si (red lines), H (blue lines), and Li (green lines). The dashed line correspond to the Fermi energy shifted to zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 7. Hirshfeld average atomic charge (ρXav ) for species X ¼ Si (black symbols), X ¼ H (red symbols) and X ¼ Li (blue symbols) as a function of surface (open symbols) and interstitial (solid symbols) Li atoms per unit cell (nLi ). The corresponding Li concentration (CLi ) is indicated in the upper horizontal axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 6. Formation energy per atom (Ef ) as a function of the number of Li atoms per unit cell (nLi ). The corresponding concentration (CLi ) is indicated in the upper horizontal axis. Red circles and black squares correspond to the surfaceand interstitial-lithiation cases, respectively. The blue triangles correspond to [111] H-SiNWs with interstitial Li atoms. The data was taken from Ref. [37]. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
calculated adsorption energy of the Li atom (see Eq. (1) in Ref. [39]) which has a value of 3.2 eV, indicating chemisorption [40]. For the interstitial case with one Li atom per unit cell, the δρð! rÞ analysis shows that no Si–Li bond is formed (see Fig. 9(a)), whereas for r Þ analysis shows, that the charge the H-SiNW with 8 Li atoms the δρð! density around Si atoms strongly depends on the position of the Li atoms in the relaxed structure. For example, Fig. 9(b) shows that the charge distribution along the Si–Si bonds is practically not affected by the presence of the Li atom. In contrast, Fig. 9(c) depicts another region of the same H-SiNW with 8 Li atoms, where some Si–Si bonds are broken and Si–Li bonds are formed. As discussed below, these new bonds increase the Li binding energy when the concentration of Li atoms increases. Moreover, the rupture of Si–Si bonds by interstitial Li atoms leads to a diminution of the nanowire mechanical resistance, as shown by the Young's modulus analysis below. To complete the investigation of the effects of interstitial lithiation in H-SiNWs, we also studied the case of an isolated interstitial Li atom. We
positive charge of the surface Li atoms. This indicates that there are Si–Li bonds. For the Li interstitial case, the average charge of the Si atoms decrement is lower than the surface-lithiation case for a concentration larger than four Li atoms. In order to confirm the formation of Si–Li bonds at the surface of the r Þ ¼ ρð! r Þ nanowires, we calculated the charge density difference δρð! ρatom ð! r Þ Δb ðnÞ ¼ EðH SiNWÞ , where ρð! r Þ is the valence pseur Þ is the sum of atomic valence pseudocharge density, and ρatom ð! r Þ for a Si atom docharge densities of each atom species. Fig. 8 shows δρð! in three different environments. For the fully H-passivated nanowire, notice that the four valence bonds show a spherical distribution. For the dangling-bond case, where an H atom is missing, there is a clear charge redistribution along the three valence bonds. Finally, for a Si atom close to a Li one, finite values of δρð! r Þ are observed between them indicating the formation of a chemical bond. This has been corroborated by the
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Fig. 8. Charge density difference distribution, δρð! r Þ, for (a) fully H-passivated Si nanowire, (b) Si nanowire with a dangling bond and (c) Si nanowire with a surface Li atom.
Fig. 9. Charge density difference distribution, δρð! r Þ, for (a) one interstitial Li atom in a hydrogen-passivated SiNW (H-SiNW), as well as for a H-SiNW with 8 interstitial Li atoms, where the displayed Li atoms show (b) no bond formation and (c) a Si–Li bond.
considered a single Li atom, placed at the position 1 depicted in Fig. 1(b), in an H-SiNW of diameter 24.7 Å whose supercell has 351 atoms and it is formed by 3 unit cells. Then, the distance between the periodic images of the Li atom is ~16 Å, which guarantees that there are no interactions between them. The results show that the nanowire geometry does not suffer noticeable changes and the electronic structure analysis reveals a metallic behavior. A similar behavior was obtained when the Li atom is placed at position 8 of Fig. 1(b). These results confirm that the transition from semiconducting to metallic behavior in H-SiNWs is due to the effect of the interstitial Li atoms. A further analysis reveals that one negatively charged Li atom, placed at the center of the H-SiNW (at the Td position), modifies the nanowire structure around it and introduces occupied states into the former empty conduction band and then the nanowire also becomes metallic. Moreover, our calculations indicate that the same behavior occurs when an interstitial Li anion is introduced in bulk silicon. In contrast, when one positively charged Li atom is placed at the same position, there are no noticeable structural changes in the nanowire and the electronic band structure still shows a semiconducting behavior. These results indicate that the charge state of Li atoms also plays an important role in the structural and electronic properties of H-SiNWs. The Li-atom binding energy (Δb ) quantifies how much energy is necessary to extract nLi atoms from the lithiated nanowire and it is relevant for Li storage applications. For the surface-lithiation case, Δb is given by 1 Δb ðnLi Þ ¼ EðH SiNWÞ þ nLi EðLiÞ nLi EðH2 Þ EðSiNW þ nLi Þ; 2
Fig. 10. Normalized lithium binding energy (Δb ) as a function of the number of Li atoms per unit cell (nLi ) for H-SiNWs with surface (red circles) and interstitial (black squares) Li atoms. The corresponding Li concentration (CLi ) is indicated in the upper horizontal axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
where EðH SiNWÞ is the energy of the fully H passivated SiNW. For the interstitial-lithiation case, we use the latter equation without the term concerning the hydrogen molecule energy. Fig. 10 shows the binding energy per Li atom in the unit cell as a function of the Li concentration. Observe that the binding energy of the surface Li atoms is practically independent of the number of Li atoms, remaining close to 2.2 eV. This
value is close to the binding energy found for surface Li atoms on Si layers [41]. On the other hand, the calculated binding energy of a single interstitial Li atom is in good agreement with previous theoretical studies [42]. Also observe that, in general, the binding energy of surface Li atoms 443
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interstitial Li atoms in the electronic and mechanical properties of hydrogen-passivated SiNWs grown along the [001] crystallographic direction with a diameter of 24.7 Å. The electronic band structure of the surface-lithiated H-SiNWs indicates a semiconducting behavior with direct band gap, whose size tends to diminish when the Li concentration increases. In contrast, the H-SiNWs with interstitial Li atoms become metallic, even when just one interstitial Li atom is added to the nanowire. Moreover, the relative energetic stability of the surface-lithiated HSiNWs increases when the Li concentration augments, whereas, for the interstitial-lithiation case, the opposite behavior is found. Also, for the surface-lithiated case, the binding energy and charge density difference analysis indicate that the Si–Li bond energy is almost independent of the Li concentration. On the other hand, the Young's modulus of the surfacelithiated SiNWs increases with the Li concentration, which is very convenient for their potential application as anodic material. In contrast, for the H-SiNWs with interstitial Li, the binding energy per Li atom is lower than the surface case and it grows when the Li concentration increases up to a critical concentration nLi ¼ 8 (CLi ¼ 6:8%), where the binding energy per Li atom has a similar value to the surface case. At nLi ¼ 10 (CLi ¼ 8:5%), the H-SiNW Young's modulus suffers an abrupt decay, indicating a structural instability due to the breaking of Si–Si bonds and the formation of Si–Li bonds. Furthermore, for all the studied Li concentrations, the Young's moduli of the surface lithiated SiNWs are higher than the interstitial lithiated ones. These results indicate that former could be more appropriate than the latter as electrodes in Li ion batteries. Finally, the H-SiNWs studied in this work are very small in comparison with those usually synthetized and then the results obtained cannot be directly compared with current available experimental results, however, they follow the experimental trends.
is larger than that of the interstitial ones for almost all concentrations, indicating that the surface Li atoms are bonded to Si atoms while, for the interstitial case, the Li atoms do not necessarily form bonds with the Si atoms. However, when nLi increases the H-SiNW suffers important structural changes due to the rupture of Si–Si bonds and the formation of Si–Li ones. Fig. 11 illustrates the Young's modulus (Y) of the studied H-SiNWs as a function of the number of Li atoms per unit cell (nLi ), or concentration (CLi ), for both surface- and interstitial-lithiation cases. Y can be calculated as Y¼
1 ∂2 E ; 2 V ∂ε ε¼0
where V is the equilibrium volume of the unit cell of the nanowire, E is its total energy, and ε ¼ ΔL=L is the axial strain; being ΔL the change in the nanowire's unit cell equilibrium length L [31,43,44]. The maximum elongations considered for all the studied nanowires were less than 3% respect their equilibrium length, in order to stay in the elastic regime. For the surface-lithiation case, Y increases when nLi augments, indicating that these nanowires can have a good mechanical resistance during the lithiation process and then, the useful life of the anode could be increased. In contrast, for the interstitial-lithiated nanowires, the Y values are close to 105 MPa for 0 nLi 8 (0% CLi 6:8%), whereas at nLi ¼ 10 (CLi ¼ 10:3%), Y suddenly drops, revealing an internal stress that leads to noticeable structural changes that hinder the Li-storage capacity of the nanowire. Those Y values are similar to those previously reported for H-SiNWs with similar diameter and grown along the [111] crystallographic direction [37], where the Young's moduli is close to 80 GPa for 12 interstitial Li atoms.
Acknowledgements
4. Summary
This work was supported by multidisciplinary projects 2016-1770, 2016-1771, 2018-1969, 2018-1937 from SIP-Instituto Politecnico Nacional, and UNAM-PAPIIT IN107717. Computations were performed at Miztli (project LANCAD-UNAM-DGTIC-180), Xiuhc oatl of LANCADCinvestav, and Abacus-I of Cinvestav-EDOMEX. J.E.G. acknowledges the postdoctoral fellowship from CONACYT-SENER.
In this work, we present a DFT study of the effects of surface and
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Fig. 11. Young's modulus (Y) of H-SiNWs grown along the [001] crystallographic direction with surface (red circles) and interstitial (black squares) Li atoms as a function of the number of Li atoms per unit cell (nLi ). The corresponding Li concentration (CLi ) is indicated in the upper horizontal axis. The Y of [111] H-SiNWs with interstitial Li atoms, taken from Ref. [37], is also included (blue triangles). The dashed gray line indicates the Y value for bulk Si along the [001] crystallographic direction. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 444
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Lithiation effects on the structural and electronic properties of Si nanowires as a potential anode material F. De Santiago a, J.E. Gonzalez a, A. Miranda a, A. Trejo a, F. Salazar a, *, L.A. Perez b, M. Cruz-Irisson a a b
Instituto Politecnico Nacional, ESIME-Culhuac an, Av. Santa Ana 1000, 04430, Mexico, Ciudad de Mexico, Mexico Instituto de Física, Universidad Nacional Autonoma de Mexico, A.P. 20-364, 01000, Mexico, Ciudad de Mexico, Mexico
A R T I C L E I N F O
A B S T R A C T
Keywords: Silicon nanowires Li batteries Electronic properties Young's modulus
The need for better energy-storage materials has attracted much attention to the development of Li-ion battery electrodes. Si nanowires have been considered as alternative electrodes, however the effects of Li on their electronic band gap and mechanical properties have been scarcely studied. In this work, a density functional study of the electronic and mechanical properties of hydrogen passivated silicon nanowires (H-SiNWs) grown along the [001] direction is presented. The Li atoms are gradually inserted at interstitial positions or replacing surface H atoms. The results show that, for surface-lithiated H-SiNWs, the semiconducting band gap decreases when the concentration of Li atoms increases; whereas the H-SiNWs become metallic even with the addition of only one interstitial Li atom. The formation energy diminishes with the concentration of Li atoms for surface-lithiated HSiNWs, whereas the contrary behavior is found in the interstitial-lithiated H-SiNWs. Furthermore, for the surfacelithiation case, the Li binding energy reveals the existence of Si–Li bonds, whereas for the interstitial-lithiation case, the Li binding energy increases when the Li grows up to a critical concentration, where some Si–Si bonds break. Finally, for the case of surface-lithiation, the Young's modulus (Y) increases with the concentration of Li, whereas for the interstitial-lithiation case, Y suffers a sudden diminution at a certain Li concentration due to the large internal mechanical stresses within the nanowire structure. These results should be considered when regarding H-SiNWs as potential electrodes in Li-ion battery anodes.
1. Introduction
current collector. The bulk Si as anodic materials has higher theoretical capacities for Li storage (4200 mAh/g) [2–4] than the graphite used in commercial batteries (372 mAh/g) [5]. The volumetric expansion during the insertion of Li atoms is around 400% for bulk Si [6,7]. As a result of the crystal structure breakdown by Li atoms, its storage capacity, Li diffusion and electron transport is reduced [6,8]. One possible alternative of anodic materials are arrays of silicon nanowires (SiNWs), grown on metallic substrates, since their great surface/volume aspect ratio allow the storage of more Li atoms than the bulk material [8]. Furthermore, the free space between the nanowires in the array diminishes the internal stress during the Li insertion. Another important issue that can modify the electronic and mechanical properties of SiNWs is the chemical passivation of the nanowire surface. The effects of hydrogen passivation have been widely studied in nanoporous and nanowire structures [9–12] and in two-dimensional systems, such as graphene [13,14]. The hydrogenated graphene or graphane has a non-planar chair-like structure and a semiconducting
Lithium ion batteries have attracted much attention of the scientific community since they offer the best performance for supplying energy to portable electronic devices, and it is expected that their capacity could increase in the next generation of batteries, allowing, for example, energy supply in applications ranging from medical devices working inside the human body, electric vehicles, to the development of great scale energy storage devices for alternative energies. However, in order to increase the scale of the Li-ion battery applications, some problems should be solved before, such as extending the battery useful life, the increment of its gravimetric capacity [1], the reduction of the charging time, the increase of the energy supply under high energy demand, and its safety. In this context, it is necessary to find new materials with low working potential respect to Li/Liþ, high energy storage capacity with high Li diffusion, capable to support internal stresses during the charge/discharge cycles, also warranting an efficient electronic transport from the electrode to the
* Corresponding author.. E-mail addresses: [email protected] (F. Salazar), lperez@fisica.unam.mx (L.A. Perez), [email protected] (M. Cruz-Irisson). https://doi.org/10.1016/j.ensm.2019.04.023 Received 11 November 2018; Received in revised form 18 April 2019; Accepted 18 April 2019 Available online 24 April 2019 2405-8297/© 2019 Elsevier B.V. All rights reserved.
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behavior after the first charge/discharge cycle, in comparison with oxide coated SiNWs [26]. Nowadays, several theoretical methods can be used to study the physical and chemical properties of anodic and cathodic materials, where the system size defines the method to be applied, allowing for a multiscale simulation approach to the development of Li ion batteries [27]. In particular, density functional theory (DFT) has been used to study the structural and electronic properties of those materials. For example, Hubbard-U-corrected DFT in the generalized gradient approximation (GGAþU) accurately predicts the structural and vibrational properties of cathodic materials such as LiMn2O4 [28] and LiFePO4 [29]. On the other hand, previous DFT studies of single Li atom insertion into SiNWs suggest that surface sites are energetically more favorable than interstitial ones [30]. In this work, we present a systematic DFT study of the electronic and mechanical properties of 2.5 nm-diameter H-SiNWs grown along the [001] crystallographic direction, with surface and interstitial Li atoms, in order to understand how the Li intercalation in H-SiNWs could allow the design of electrode materials that could improve the battery performance.
behavior that contrast with the planar structure and zero band gap of pristine graphene. Likewise, the pristine SiNWs can have either metallic or semimetallic behavior [15], while H-SiNWs are semiconductors [10, 16]. On the other hand, it is expected that the SiNWs do not suffer great mechanical stresses during the insertion/detachment of Li atoms, but this problem is still under study [17], however, recent reports indicate that the volumetric expansion in pristine SiNWs is anisotropic [18,19]. According to experimental results, the electronic and optical properties of SiNWs under elastic strain suffer important changes that could lead to new technological applications in the semiconductor industry [20]. Currently, there is no consensus about the optimal location of Li atoms in the nanowire structure and maximum Li concentration that H-SiNWs can store before overcoming their elastic limit. Experimental results reveal Li atoms inside SiNWs up to a distance of 1 nm from the surface [21], as well as an anisotropic swelling of SiNWs attributed to the interfacial processes involving large volumetric strains at the lithiation reaction front that depend on the crystallographic orientation [22]. Moreover, experimental evidence reveals that the axial tensile strength for lithiated pristine SiNWs with diameters greater than 100 nm decreases in comparison with non lithiated pristine ones [23,24]. As stated above, H-SiNWs have semiconductor behavior [10,16,25] however, the effects of the Li atoms on their electronic and mechanical properties have been barely studied. These passivated nanowires have the advantage of being crystalline with no surface dangling bonds, then we expect that the chemical reactions within the electrolyte decrease, thus increasing the useful life of the electrode. Moreover, experimental reports indicate that H passivated SiNWs exhibit superior electrochemical properties such as larger Li storage capacity, higher Coulombic efficiency, and a more stable
2. Theory and model We consider infinitely long H-SiNWs with a diameter of 24.7 Å, and grown along the [001] crystallographic direction as in Ref. [31]. Two cases were considered for the intercalation of Li atoms: the first one, referred as surface-lithiation, where some surface H atoms are replaced by Li ones, as shown in Fig. 1(a). In the second case, referred as interstitial-lithiation, some Li atoms were placed into positions
Fig. 1. Top and side views of non-relaxed unit cells of H-SiNWs. The yellow, white, and violet spheres represent the Si, H, and Li atoms, respectively. The numbers besides the Li atoms indicate the sequence by which (a) the H atoms were replaced by Li ones and (b) the Li atoms were inserted into the nanowire structure. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 439
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error of less than 0.8% [16].
equivalent to those reported as the more energetically stable for bulk silicon [32], and H-SiNWs [30], the so-called Td positions, as illustrated in Fig. 1(b). These Fig. 1(a) and (b) depict the considered non-relaxed initial morphologies for both mentioned cases. The numbers besides the Li atoms indicate the sequence by which the H atoms were replaced by Li ones, as well as the sequence by which the interstitial Li atoms were inserted into the H-SiNWs. The Li concentration for each case is obtained as CLi ¼ ðnLi 100%Þ=Nw where nLi is the number of Li atoms and Nw is the number of atoms in the unit cell of the H-SiNW. All calculations were performed using DFT within the local density approximation (LDA) with standard norm-conserving pseudopotentials [33], in their fully nonlocal form [34], as implemented in the SIESTA code [35]. We also used double-ζ s, p-basis and a single d orbital, as well as an energy cutoff of 150Ry to define the real-space grid for numerical integrations. The Brillouin zone of the H-SiNW unit cell was sampled with 1 1 24 k-points within the Monkhorst–Pack scheme for density of states calculations. All nanowires were free to relax until the Hellmann-Feynman forces were less than 2 meV/Å. The H-SiNWs periodic supercells have a lateral separation of nine times their diameter, enough to consider them as isolated. The suitability of the pseudopotential was tested by calculating the bond lengths and lattice constant for the bulk Si diamond structure; both calculated quantities are in good agreement with the corresponding experimental values [36] within an
3. Results and discussion Fig. 2 shows the relaxed geometries of the unit cell of the H-SiNWs with different number of Li atoms (nLi ) for both surface- and interstitiallithiation cases. Notice how the interstitial Li modifies the crystalline structure of the H-SiNWs, in contrast to the surface case where the Si atoms remain unaltered along the [001] growth direction. It is worth mentioning that when the number of interstitial Li atoms per unit cell is greater than 3, the H-SiNWs suffer structural changes where the Si–Si bonds around the Li atoms change their length due to the electrostatic interaction between Li atoms. This effect increases with the concentration of interstitial Li, leading to broken bonds that cannot be restored when the Li atoms are taken out from the structure, i.e., the nanowire crystalline structure is lost. In contrast, for the surface lithiation case, an even number of Li atoms preserve the nanowire symmetry and the structure only suffers small deformations at the surface, maintaining its internal structure. Fig. 3 shows the electronic band structures and densities of states of the H-SiNWs with different concentrations of surface Li atoms (a) 0%, (b) 0.9%, (c) 5.1% and (d) 10.3%, following the sequence depicted in Fig. 1(a). The band gap (ΔEg ) is direct for all studied Li concentrations,
Fig. 2. Cross views of the relaxed H-SiNWs for the surface- (left) and interstitial-lithiation (right) cases. The number of Li atoms per unit cell (nLi ) is shown at the first column. 440
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Fig. 3. Electronic band structures (left panels) of H-SiNWs with (a) 0 (0%), (b) 1 (0.9%), (c) 6 (5.1%), and (d) 12 (10.3%) surface Li atoms per unit cell, respectively. The corresponding concentrations ðCLi Þ are indicated in parenthesis. Right panels: Total (black line) and partial electronic densities of states per atomic species Si (red line), H (blue line), and Li (green line). The dashed line correspond to the Fermi energy shifted to zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
found for the surface-lithiation case. This behavior can be contrasted with [111]-H-SiNWs, where the Li states have a larger contribution to the conduction band [37]. The relative energetic stability of the lithiated H-SiNWs was obtained from the formation energy (Ef ) per number of atoms in the unit cell (M), which can be calculated as
and the addition of Li atoms leads to new bands within the band gap of the former H-SiNWs. In consequence, ΔEg diminishes when the concentration of surface Li atoms increases, as shown in Fig. 4. Observe that the semiconducting behavior remains even for 12 surface Li atoms per unit cell and the band gaps are still larger than that calculated for the bulk Si within the same theory level. It is worth to mention that all values of ΔEg are lower that for H-SiNWs grown along [111] crystallographic direction [16] whose values range from 1.75 eV to 0.87 eV for 0 and 12 surface Li atoms, respectively. Fig. 5 shows the electronic band structures and densities of states of the H-SiNWs with different concentrations of interstitial Li atoms following the sequence depicted in Fig. 1(b). In contrast to the surface lithiation case, a completely different behavior is observed when the Li atoms occupy interstitial positions (Td ) in the H-SiNW structure. The Fermi energy shifts to the conduction band even with just one interstitial Li atom, resulting in a metallic or semimetallic character. Notice that the number of bands increases with the interstitial Li atom concentration. Moreover, as expected, the main contribution to the electronic states is due to the Si atoms (red lines), whereas the Li atoms (green lines) have a slight contribution to the conduction bands, which is lower than that
Ef ¼
1 1 EðSiNW þ nLi Þ nSi EðSibulk Þ ðnH nLi Þ EðH2 Þ nLi EðLiÞ ; M 2
where EðXÞ is the calculated total energy of system X. Here, SiNW þ nLi denotes the system formed by the H-SiNW unit cell with nLi surface or interstitial Li atoms, EðSibulk Þ, EðH2 Þ, and EðLiÞ is the energy per atom of bulk Si, hydrogen molecule and one isolated Li atom, respectively, while nH and nSi denote the number of H and Si atoms per unit cell, respectively. For the interstitial lithiation case, the coefficient of the third term in the previous equation, (nH nLi ), must be replaced by nH . Fig. 6 shows the formation energy of the lithiated H-SiNWs as a function of the number of Li atoms per unit cell (nLi ), or concentration (CLi ), for both surface and interstitial lithiation cases. A lower Ef value indicates that the system is relatively more stable than another system with a higher value. Notice that the replacement of surface H atoms by Li ones, increases the relative energetic stability of the SiNWs, while the addition of interstitial Li atoms diminishes it. Comparing these results with those previously reported for [111]SiNWs with similar diameters, it is found that the [001]-SiNWs are more energetically stable that [111]-SiNWs for both surface and interstitial cases [37]. On the other hand, we also performed a Hirshfeld population analysis [38] to estimate the electronic charge distribution around each atom of the H-SiNW unit cell. Fig. 7 shows the Hirshfeld average charge (ρXav ðnLi Þ) for each species X as a function of the concentration of surface and interstitial Li atoms. ρXav is given by
ρXav ðnLi Þ ¼
nX 1 X ρX ; nX i¼1 i
where ρXi is the Hirshfeld electronic charge associated to atom i of species X and nX is the number of atoms of species X in the unit cell (X ¼ Si, H, Li). As expected, all H atoms gain electronic charge evidencing that there are Si–H bonds at the nanowire for both studied cases. This charge slightly decreases when the surface Li concentration increases, whereas for the interstitial lithiation case, it stays almost constant. The average charge of the Si atoms for the surface lithiation case decreases (it becomes more negative) when the Li concentration augments, indicating a charge transfer from the Li atoms, which is reflected on the average
Fig. 4. Energy band gap (ΔEg ) as a function of the number of surface Li atoms per unit cell (nLi ) or concentration (CLi ), following the sequence depicted in Fig. 1(a). The dashed line corresponds to the calculated bulk Si band gap. 441
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Fig. 5. Electronic band structures (left panels) of H-SiNWs with (a) 1 (0.9%), (b) 6 (5.1%), (c) 8 (6.8%), and (d) 12 (10.3%) interstitial Li atoms per unit cell, respectively. The corresponding concentrations ðCLi Þ are indicated in parenthesis. Right panels: Total (black lines) and partial electronic densities of states per atomic species, Si (red lines), H (blue lines), and Li (green lines). The dashed line correspond to the Fermi energy shifted to zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 7. Hirshfeld average atomic charge (ρXav ) for species X ¼ Si (black symbols), X ¼ H (red symbols) and X ¼ Li (blue symbols) as a function of surface (open symbols) and interstitial (solid symbols) Li atoms per unit cell (nLi ). The corresponding Li concentration (CLi ) is indicated in the upper horizontal axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 6. Formation energy per atom (Ef ) as a function of the number of Li atoms per unit cell (nLi ). The corresponding concentration (CLi ) is indicated in the upper horizontal axis. Red circles and black squares correspond to the surfaceand interstitial-lithiation cases, respectively. The blue triangles correspond to [111] H-SiNWs with interstitial Li atoms. The data was taken from Ref. [37]. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
calculated adsorption energy of the Li atom (see Eq. (1) in Ref. [39]) which has a value of 3.2 eV, indicating chemisorption [40]. For the interstitial case with one Li atom per unit cell, the δρð! rÞ analysis shows that no Si–Li bond is formed (see Fig. 9(a)), whereas for r Þ analysis shows, that the charge the H-SiNW with 8 Li atoms the δρð! density around Si atoms strongly depends on the position of the Li atoms in the relaxed structure. For example, Fig. 9(b) shows that the charge distribution along the Si–Si bonds is practically not affected by the presence of the Li atom. In contrast, Fig. 9(c) depicts another region of the same H-SiNW with 8 Li atoms, where some Si–Si bonds are broken and Si–Li bonds are formed. As discussed below, these new bonds increase the Li binding energy when the concentration of Li atoms increases. Moreover, the rupture of Si–Si bonds by interstitial Li atoms leads to a diminution of the nanowire mechanical resistance, as shown by the Young's modulus analysis below. To complete the investigation of the effects of interstitial lithiation in H-SiNWs, we also studied the case of an isolated interstitial Li atom. We
positive charge of the surface Li atoms. This indicates that there are Si–Li bonds. For the Li interstitial case, the average charge of the Si atoms decrement is lower than the surface-lithiation case for a concentration larger than four Li atoms. In order to confirm the formation of Si–Li bonds at the surface of the r Þ ¼ ρð! r Þ nanowires, we calculated the charge density difference δρð! ρatom ð! r Þ Δb ðnÞ ¼ EðH SiNWÞ , where ρð! r Þ is the valence pseur Þ is the sum of atomic valence pseudocharge density, and ρatom ð! r Þ for a Si atom docharge densities of each atom species. Fig. 8 shows δρð! in three different environments. For the fully H-passivated nanowire, notice that the four valence bonds show a spherical distribution. For the dangling-bond case, where an H atom is missing, there is a clear charge redistribution along the three valence bonds. Finally, for a Si atom close to a Li one, finite values of δρð! r Þ are observed between them indicating the formation of a chemical bond. This has been corroborated by the
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Fig. 8. Charge density difference distribution, δρð! r Þ, for (a) fully H-passivated Si nanowire, (b) Si nanowire with a dangling bond and (c) Si nanowire with a surface Li atom.
Fig. 9. Charge density difference distribution, δρð! r Þ, for (a) one interstitial Li atom in a hydrogen-passivated SiNW (H-SiNW), as well as for a H-SiNW with 8 interstitial Li atoms, where the displayed Li atoms show (b) no bond formation and (c) a Si–Li bond.
considered a single Li atom, placed at the position 1 depicted in Fig. 1(b), in an H-SiNW of diameter 24.7 Å whose supercell has 351 atoms and it is formed by 3 unit cells. Then, the distance between the periodic images of the Li atom is ~16 Å, which guarantees that there are no interactions between them. The results show that the nanowire geometry does not suffer noticeable changes and the electronic structure analysis reveals a metallic behavior. A similar behavior was obtained when the Li atom is placed at position 8 of Fig. 1(b). These results confirm that the transition from semiconducting to metallic behavior in H-SiNWs is due to the effect of the interstitial Li atoms. A further analysis reveals that one negatively charged Li atom, placed at the center of the H-SiNW (at the Td position), modifies the nanowire structure around it and introduces occupied states into the former empty conduction band and then the nanowire also becomes metallic. Moreover, our calculations indicate that the same behavior occurs when an interstitial Li anion is introduced in bulk silicon. In contrast, when one positively charged Li atom is placed at the same position, there are no noticeable structural changes in the nanowire and the electronic band structure still shows a semiconducting behavior. These results indicate that the charge state of Li atoms also plays an important role in the structural and electronic properties of H-SiNWs. The Li-atom binding energy (Δb ) quantifies how much energy is necessary to extract nLi atoms from the lithiated nanowire and it is relevant for Li storage applications. For the surface-lithiation case, Δb is given by 1 Δb ðnLi Þ ¼ EðH SiNWÞ þ nLi EðLiÞ nLi EðH2 Þ EðSiNW þ nLi Þ; 2
Fig. 10. Normalized lithium binding energy (Δb ) as a function of the number of Li atoms per unit cell (nLi ) for H-SiNWs with surface (red circles) and interstitial (black squares) Li atoms. The corresponding Li concentration (CLi ) is indicated in the upper horizontal axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
where EðH SiNWÞ is the energy of the fully H passivated SiNW. For the interstitial-lithiation case, we use the latter equation without the term concerning the hydrogen molecule energy. Fig. 10 shows the binding energy per Li atom in the unit cell as a function of the Li concentration. Observe that the binding energy of the surface Li atoms is practically independent of the number of Li atoms, remaining close to 2.2 eV. This
value is close to the binding energy found for surface Li atoms on Si layers [41]. On the other hand, the calculated binding energy of a single interstitial Li atom is in good agreement with previous theoretical studies [42]. Also observe that, in general, the binding energy of surface Li atoms 443
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interstitial Li atoms in the electronic and mechanical properties of hydrogen-passivated SiNWs grown along the [001] crystallographic direction with a diameter of 24.7 Å. The electronic band structure of the surface-lithiated H-SiNWs indicates a semiconducting behavior with direct band gap, whose size tends to diminish when the Li concentration increases. In contrast, the H-SiNWs with interstitial Li atoms become metallic, even when just one interstitial Li atom is added to the nanowire. Moreover, the relative energetic stability of the surface-lithiated HSiNWs increases when the Li concentration augments, whereas, for the interstitial-lithiation case, the opposite behavior is found. Also, for the surface-lithiated case, the binding energy and charge density difference analysis indicate that the Si–Li bond energy is almost independent of the Li concentration. On the other hand, the Young's modulus of the surfacelithiated SiNWs increases with the Li concentration, which is very convenient for their potential application as anodic material. In contrast, for the H-SiNWs with interstitial Li, the binding energy per Li atom is lower than the surface case and it grows when the Li concentration increases up to a critical concentration nLi ¼ 8 (CLi ¼ 6:8%), where the binding energy per Li atom has a similar value to the surface case. At nLi ¼ 10 (CLi ¼ 8:5%), the H-SiNW Young's modulus suffers an abrupt decay, indicating a structural instability due to the breaking of Si–Si bonds and the formation of Si–Li bonds. Furthermore, for all the studied Li concentrations, the Young's moduli of the surface lithiated SiNWs are higher than the interstitial lithiated ones. These results indicate that former could be more appropriate than the latter as electrodes in Li ion batteries. Finally, the H-SiNWs studied in this work are very small in comparison with those usually synthetized and then the results obtained cannot be directly compared with current available experimental results, however, they follow the experimental trends.
is larger than that of the interstitial ones for almost all concentrations, indicating that the surface Li atoms are bonded to Si atoms while, for the interstitial case, the Li atoms do not necessarily form bonds with the Si atoms. However, when nLi increases the H-SiNW suffers important structural changes due to the rupture of Si–Si bonds and the formation of Si–Li ones. Fig. 11 illustrates the Young's modulus (Y) of the studied H-SiNWs as a function of the number of Li atoms per unit cell (nLi ), or concentration (CLi ), for both surface- and interstitial-lithiation cases. Y can be calculated as Y¼
1 ∂2 E ; 2 V ∂ε ε¼0
where V is the equilibrium volume of the unit cell of the nanowire, E is its total energy, and ε ¼ ΔL=L is the axial strain; being ΔL the change in the nanowire's unit cell equilibrium length L [31,43,44]. The maximum elongations considered for all the studied nanowires were less than 3% respect their equilibrium length, in order to stay in the elastic regime. For the surface-lithiation case, Y increases when nLi augments, indicating that these nanowires can have a good mechanical resistance during the lithiation process and then, the useful life of the anode could be increased. In contrast, for the interstitial-lithiated nanowires, the Y values are close to 105 MPa for 0 nLi 8 (0% CLi 6:8%), whereas at nLi ¼ 10 (CLi ¼ 10:3%), Y suddenly drops, revealing an internal stress that leads to noticeable structural changes that hinder the Li-storage capacity of the nanowire. Those Y values are similar to those previously reported for H-SiNWs with similar diameter and grown along the [111] crystallographic direction [37], where the Young's moduli is close to 80 GPa for 12 interstitial Li atoms.
Acknowledgements
4. Summary
This work was supported by multidisciplinary projects 2016-1770, 2016-1771, 2018-1969, 2018-1937 from SIP-Instituto Politecnico Nacional, and UNAM-PAPIIT IN107717. Computations were performed at Miztli (project LANCAD-UNAM-DGTIC-180), Xiuhc oatl of LANCADCinvestav, and Abacus-I of Cinvestav-EDOMEX. J.E.G. acknowledges the postdoctoral fellowship from CONACYT-SENER.
In this work, we present a DFT study of the effects of surface and
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Fig. 11. Young's modulus (Y) of H-SiNWs grown along the [001] crystallographic direction with surface (red circles) and interstitial (black squares) Li atoms as a function of the number of Li atoms per unit cell (nLi ). The corresponding Li concentration (CLi ) is indicated in the upper horizontal axis. The Y of [111] H-SiNWs with interstitial Li atoms, taken from Ref. [37], is also included (blue triangles). The dashed gray line indicates the Y value for bulk Si along the [001] crystallographic direction. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 444
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