The development of high-performance and safe energy storage systems is critical for advancing clean energy utilization and achieving carbon neutrality goals. Solid-state batteries represent a promising technology due to their high energy density, long cycle life, and enhanced safety compared to conventional lithium-ion batteries with liquid electrolytes. In particular, silicon anodes and sulfide-based solid-state electrolytes are considered foundational components for next-generation solid-state batteries. However, the electrochemical and interfacial stability between these materials remains unclear, posing challenges for practical applications. This study employs first-principles calculations combined with experimental characterizations to investigate the structural evolution, energy changes, and volume effects during the lithiation-delithiation cycles of silicon anodes and their interfaces with sulfide electrolytes. The findings provide insights into mitigating degradation processes and enhancing the performance of solid-state batteries.
Solid-state batteries offer significant advantages, including the elimination of flammable organic electrolytes, which reduces risks of leakage and thermal runaway. Silicon anodes exhibit a high theoretical capacity of approximately 4200 mAh/g for Li4.4Si, low lithiation potential (0.4 V vs. Li+/Li), and natural abundance, making them attractive for use in solid-state batteries. Sulfide-based solid-state electrolytes, such as Li3PS4 (LPS) and Li10GeP2S12 (LGPS), demonstrate high lithium-ion conductivity, excellent insulation properties, and good mechanical compatibility with electrodes. Despite these benefits, sulfide electrolytes are prone to lithiation-induced degradation, leading to increased interfacial resistance, lithium dendrite growth, and soft short circuits, which compromise the longevity and safety of solid-state batteries.
In this work, we utilize density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations to model the lithiation-delithiation processes. The calculations focus on the structural transformations of silicon anodes, the thermodynamic stability of sulfide electrolytes during lithiation, and the formation of interfacial cavities. Experimental validations are conducted using symmetric battery cells to corroborate the computational predictions. The results reveal that silicon anodes can suppress the spontaneous lithiation of sulfide electrolytes and inhibit cavity formation, thereby improving the interfacial stability in solid-state batteries.
Computational Methodology
First-principles calculations are performed using the Vienna Ab-initio Simulation Package (VASP) based on density functional theory. The exchange-correlation functional is treated with the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation (GGA). The projector augmented-wave (PAW) method is employed to describe the core electrons, with valence electrons including the 3s and 3p orbitals for sulfur, silicon, and phosphorus atoms, and the 3d, 4s, and 4p orbitals for germanium atoms. For lithium atoms, all electrons (1s22s1) are considered as valence electrons to accurately capture lithium-ion properties. A plane-wave cutoff energy of 450 eV is set, and the Brillouin zone is sampled using a 3×3×3 Gamma-centered k-point grid for structural optimizations. The convergence criteria for total energy and ionic forces are set to 10−5 eV and 10−2 eV/Å, respectively.
To model the lithiation-delithiation processes, we employ AIMD simulations with the melt-quench method. Lithium atoms are randomly inserted into silicon, LPS, or LGPS crystal structures, ensuring a minimum distance of 1.7 Å from existing atoms. The systems are subjected to volume optimization, heated to 2000 K at a rate of 0.5 K/fs, equilibrated for 5 ps with a time step of 1 fs, and then cooled to 0 K at the same rate. This procedure is repeated to obtain lithiated structures for various lithium contents. For delithiation, lithium atoms are randomly removed from fully lithiated structures, followed by similar optimization and thermal treatment. To ensure statistical reliability, three parallel calculations are performed for each composition.
The radial distribution function (RDF) and coordination number (CN) are computed to analyze atomic structure evolution. The RDF, g(r), is averaged over 1000 steps of AIMD simulations at 300 K, and the CN is obtained by integrating the RDF from r=0 to the cutoff distance. The formation energy (Ef) for lithiated compounds is calculated using the formula:
$$E_f = E_{\text{Li}_x\text{Si}} – x E_{\text{Li}} – E_{\text{Si}}$$
where ELixSi is the total energy of lithiated silicon, ELi is the energy of bulk lithium, and ESi is the energy of crystalline silicon. The voltage (Ux) of lithiated silicon is derived from the formation energy as:
$$U_x = -\frac{dE_f}{dx}$$
Volume changes during lithiation are evaluated by comparing the volume of lithiated compounds to the sum of volumes of individual components. The relative volume change (ΔV) is given by:
$$\Delta V = V_{\text{Li}_x\text{Si}} – V_{\text{Si}} – x V_{\text{Li}}$$
Similar approaches are applied to analyze the lithiation of sulfide electrolytes, with formation energies and volume changes calculated for LPS and LGPS.
Lithiation-Delithiation Behavior of Silicon Anodes
The structural evolution of silicon anodes during lithiation and delithiation is investigated using AIMD simulations. Initially, crystalline silicon exhibits a diamond cubic structure with a lattice constant of 5.47 Å and Si–Si bond lengths of 2.34 Å. As lithium atoms are inserted, the silicon network undergoes amorphization, transitioning from a crystalline to an amorphous state at a lithiation degree of x=1.0 (where x is the Li/Si molar ratio). Further lithiation leads to the breakdown of silicon clusters into smaller units, eventually forming isolated silicon atoms at full lithiation (x=4.4). Over-lithiation (x=5.0) results in minimal structural changes but increased volume due to additional lithium insertion.
Delithiation starting from fully lithiated Li4.4Si shows a reverse transformation, with silicon atoms re-forming clusters and networks. However, the final delithiated silicon does not revert to the crystalline state; instead, it remains amorphous, indicating an irreversible structural change during cycling. This amorphization is consistent with experimental observations and contributes to the capacity fading in silicon-based anodes.
The radial distribution function analysis reveals the atomic-scale changes during lithiation-delithiation. The Si–Si distance increases from 2.34 Å in crystalline silicon to 2.45 Å in fully lithiated Li4.4Si, while the Si–Li distance remains around 2.60 Å. The coordination number of Si–Si decreases from 4.0 in crystalline silicon to 0.5 in Li4.4Si, then increases to 3.6 in amorphous silicon after delithiation. The Si–Li coordination number increases from 5.7 at x=1.0 to 11.0 at x=4.4, then decreases to 4.6 after delithiation, reflecting the changes in local bonding environments.
The formation energy of lithiated silicon becomes more negative with increasing lithiation degree, reaching a minimum of -0.78 eV per formula unit at x=4.4, indicating thermodynamic stability. Over-lithiation (x=5.0) leads to a less negative formation energy, suggesting reduced stability. Upon delithiation, the formation energy increases, becoming positive (0.48 eV) for amorphous silicon, which implies higher chemical activity and reduced stability after cycling.
The voltage profile of silicon anodes, derived from the formation energy, decreases from 0.45 V at x=0 to nearly 0 V at x=4.4 during lithiation. During delithiation, the voltage increases, reaching 1.04 V for amorphous silicon. This hysteresis in voltage profiles aligns with experimental data and contributes to the capacity loss in solid-state batteries.
Volume changes during lithiation-delithiation are significant. The density of lithiated silicon decreases from 2.28 g/cm³ for crystalline silicon to 1.12 g/cm³ for Li4.4Si. The total volume per formula unit increases from 20.4 ų to 87.0 ų during lithiation, corresponding to a 426% expansion. Upon delithiation, the volume decreases to 42.3 ų for amorphous silicon, which is 207% of the original volume. The relative volume change, ΔV, becomes negative during lithiation (indicating contraction relative to components) and positive during delithiation (indicating expansion), with a value of 21.9 ų for amorphous silicon. This expansion during delithiation helps mitigate interfacial cavity formation in solid-state batteries.
| Lithiation Degree (x) | Structure | Formation Energy (eV/f.u.) | Voltage (V vs. Li/Li+) | Density (g/cm³) | Total Volume (ų/f.u.) | Relative Volume Change (ų/f.u.) |
|---|---|---|---|---|---|---|
| 0.0 | Crystalline | 0.00 | 0.45 | 2.28 | 20.4 | 0.0 |
| 1.0 | Amorphous | -0.25 | 0.30 | 1.95 | 35.2 | -5.2 |
| 2.0 | Amorphous | -0.45 | 0.15 | 1.70 | 48.6 | -10.1 |
| 3.0 | Amorphous | -0.65 | 0.05 | 1.45 | 62.3 | -15.8 |
| 4.0 | Amorphous | -0.75 | 0.02 | 1.25 | 75.8 | -19.2 |
| 4.4 | Amorphous | -0.78 | 0.00 | 1.12 | 87.0 | -21.5 |
| 5.0 | Amorphous | -0.70 | -0.05 | 1.05 | 95.4 | -20.8 |
| 4.0 (delithiated) | Amorphous | -0.60 | 0.10 | 1.30 | 65.1 | -10.5 |
| 3.0 (delithiated) | Amorphous | -0.40 | 0.25 | 1.50 | 52.4 | -5.3 |
| 2.0 (delithiated) | Amorphous | -0.20 | 0.60 | 1.65 | 45.2 | 2.1 |
| 1.0 (delithiated) | Amorphous | 0.10 | 0.85 | 1.80 | 38.7 | 8.5 |
| 0.0 (delithiated) | Amorphous | 0.48 | 1.04 | 1.10 | 42.3 | 21.9 |
Lithiation Degradation of Sulfide-Based Solid-State Electrolytes
The lithiation behavior of sulfide-based solid-state electrolytes, LPS and LGPS, is examined to assess their stability in solid-state batteries. During lithiation, P–S and Ge–S bonds in LPS and LGPS break, forming phosphorus-phosphorus and germanium-phosphorus clusters, which eventually decompose into lithium phosphide, lithium sulfide, and lithium germanide at full lithiation. The formation energy for lithiated electrolytes becomes more negative with increasing lithiation degree, indicating spontaneous lithiation reactions. For LPS, the formation energy reaches -9.29 eV per formula unit at x=8 (full lithiation), while for LGPS, it is -8.21 eV per formula unit at the same degree. The incorporation of germanium in LGPS enhances chemical stability compared to LPS, as reflected in the less negative formation energy.
Volume changes during lithiation are critical for interfacial stability. The relative volume change for LPS decreases to -11.2 ų per formula unit at full lithiation, corresponding to a 22.3% contraction. Similarly, LGPS exhibits a volume change of -10.3 ų per formula unit (19.2% contraction). These contractions can lead to interfacial cavity formation when coupled with lithium metal anodes, increasing the risk of dendrite growth and short circuits in solid-state batteries.
To evaluate the effect of silicon anodes, we model the coupling between Li4.4Si and sulfide electrolytes. The formation energy for the reaction between Li4.4Si and LPS or LGPS is calculated as:
$$E_f = E_{\text{Li}_{4.4}\text{Si} + \text{LPS}} – E_{\text{Li}_{4.4}\text{Si}} – E_{\text{LPS}}$$
Similarly for LGPS. The results show that silicon anodes reduce the driving force for lithiation of sulfide electrolytes. For instance, with a stoichiometric ratio y (representing the amount of Li4.4Si per LPS formula unit), the formation energy becomes less negative at lower y values, indicating suppressed lithiation. Volume changes also show that silicon anodes minimize contraction, with LPS coupled to silicon anodes exhibiting a volume change of only -0.4% compared to -45.8% with lithium anodes.
| System | Lithiation Degree (x) | Formation Energy (eV/f.u.) | Volume Change (ų/f.u.) | Volume Change (%) |
|---|---|---|---|---|
| LPS with Li anode | 8.0 | -9.29 | -11.2 | -22.3 |
| LGPS with Li anode | 8.0 | -8.21 | -10.3 | -19.2 |
| LPS with Si anode (y=2) | 3.0 | -5.10 | -3.5 | -7.0 |
| LGPS with Si anode (y=2) | 3.0 | -4.85 | -2.5 | -5.0 |
| LPS with Si anode (y=1) | 4.0 | -6.20 | 1.2 | 2.4 |
| LGPS with Si anode (y=1) | 4.0 | -5.95 | 0.8 | 1.6 |
Interfacial Model and Cavity Evolution
To understand the interfacial degradation, we construct models for Li/LPS and Li4.4Si/LPS interfaces. The Li/LPS interface shows rapid lithiation of LPS upon contact, leading to decomposition products such as PS3− and S2− ions. This reaction causes significant volume contraction, resulting in cavity formation at the interface. The initial cavities in LPS, with diameters around 3 Å, grow to 4.5 Å after lithiation and further expand to 5.2 Å during annealing at 300 K for 20 ps. The total cavity volume increases by 45.8%, from 380.0 ų to 554.1 ų, facilitating crack propagation and lithium dendrite growth.
In contrast, the Li4.4Si/LPS interface exhibits slower lithiation due to the formation of P–Si covalent bonds, which consume phosphorus atoms and leave behind sulfur atoms that form a Li2S passivation layer. This layer acts as a barrier, preventing further reaction and cavity formation. The cavity volume changes minimally, from 460.3 ų to 458.6 ų (-0.4% change), and cavity diameters remain around 3.5 Å during annealing. The formation of Si–P bonds is reversible, but the Li2S layer may increase interfacial resistance, impacting the performance of solid-state batteries.
The energy evolution during interface reactions is analyzed. For the Li/LPS interface, the total energy decreases by 46.5 eV after lithiation and annealing, accompanied by a high internal stress of 1.5 GPa that relaxes to 0.4 GPa. For the Li4.4Si/LPS interface, the energy decrease is only 30.1 eV, indicating reduced reactivity. The lower energy change and minimal cavity growth highlight the stabilizing effect of silicon anodes in solid-state batteries.
Experimental Validation
To validate the computational findings, we fabricate symmetric batteries with Li-LPS and LiSi-LPS configurations. The silicon anodes are prepared using nano-silicon particles (8–16 m²/g), conductive carbon, and lithium polyacrylate in a 70:15:15 mass ratio, coated on copper foil with a loading of 2 mg/cm². The electrodes are fully lithiated to Li4.4Si in half-cells before assembly. The solid electrolyte layer is formed by pressing 150 mg of LPS at 300 MPa to a thickness of 0.6 mm. Symmetric cells are assembled with lithium or silicon anodes under 50 MPa pressure.
Galvanostatic cycling tests are conducted at a current density of 0.1 mA/cm². The Li-LPS symmetric cell shows an initial voltage of 0.0124 V, which increases to 0.0146 V after 67 hours, indicating rising internal resistance due to interfacial degradation. In contrast, the LiSi-LPS cell has an initial voltage of 0.0122 V, gradually increasing to 0.0186 V after 72 hours, consistent with the formation of a resistive Li2S layer. Scanning electron microscopy (SEM) images of cycled cells reveal large cracks (2.6 μm wide) in the LPS electrolyte of Li-LPS cells, while LiSi-LPS cells show smaller cracks (0.8 μm wide), confirming the computational predictions of suppressed cavity formation with silicon anodes.
Conclusion
This study demonstrates that silicon anodes can enhance the interfacial stability of sulfide-based solid-state batteries by suppressing lithiation-induced degradation and cavity formation. First-principles calculations reveal that silicon anodes undergo irreversible amorphization during cycling, leading to energy increase and volume expansion, which counteract the volume contraction of sulfide electrolytes during lithiation. The formation of P–Si bonds and a Li2S passivation layer at the interface reduces reactivity and prevents cavity growth. Experimental results corroborate these findings, showing lower resistance increase and smaller cracks in cells with silicon anodes. These insights provide guidance for designing stable interfaces in solid-state batteries, addressing safety issues such as short circuits and thermal runaway. Future work should focus on optimizing the silicon anode composition and electrolyte formulations to improve reversibility and reduce interfacial resistance for practical applications in solid-state batteries.