On the feasibility of all-solid-state batteries with LLZO as a single electrolyte

Replacement of Li-ion liquid-state electrolytes by solid-state counterparts in a Li-ion battery (LIB) is a major research objective as well as an urgent priority for the industry, as it enables the use of a Li metal anode and provides new opportunities to realize safe, non-flammable, and temperature-resilient batteries. Among the plethora of solid-state electrolytes (SSEs) investigated, garnet-type Li-ion electrolytes based on cubic Li7La3Zr2O12 (LLZO) are considered the most appealing candidates for the development of future solid-state batteries because of their low electronic conductivity of ca. 10−8 S cm−1 (RT) and a wide electrochemical operation window of 0–6 V vs. Li+/Li. However, high LLZO density (5.1 g cm−3) and its lower level of Li-ion conductivity (up to 1 mS cm−1 at RT) compared to liquid electrolytes (1.28 g cm−3; ca. 10 mS cm−1 at RT) still raise the question as to the feasibility of using solely LLZO as an electrolyte for achieving competitive energy and power densities. In this work, we analyzed the energy densities of Li-garnet all-solid-state batteries based solely on LLZO SSE by modeling their Ragone plots using LiCoO2 as the model cathode material. This assessment allowed us to identify values of the LLZO thickness, cathode areal capacity, and LLZO content in the solid-state cathode required to match the energy density of conventional lithium-ion batteries (ca. 180 Wh kg−1 and 497 Wh L−1) at the power densities of 200 W kg−1 and 600 W L−1, corresponding to ca. 1 h of battery discharge time (1C). We then discuss key challenges in the practical deployment of LLZO SSE in the fabrication of Li-garnet all-solid-state batteries.

While broad attention to Li-garnet solid-state batteries (SSBs) is surely helpful for the progress in this area [16][17][18][19][20] , analysis of the literature appoints to the lack of clear opinion in the research community as to the configuration of future Li-garnet SSBs. On the one hand, the researchers are mostly united with the idea that LLZO SSE should face Li metal anode, enabling to mitigate the formation of the Li dendrites (when necessary pressure is applied) [21][22][23][24][25] . On the other hand, opinions on the design of the cathode layer are more divergent. Proposed are additions of LLZO [26][27][28][29][30][31][32][33][34] or other electrolytes (ionic liquids [35][36][37][38][39] , or polymers 40 ). Considering the ongoing debates on compelling Li-garnet SSB configurations, we first analyze the very first battery structure containing LLZO as the only SSE, as schematically depicted in Fig. 1. Specifically, we intend to shed light on whether this approach is feasible, given high LLZO density (5.1 g cm −3 ) and a mediocre level of its Li-ion conductivity as compared to liquid electrolytes (up to 1 mS cm −1 at RT) 1,2,8,41 . The resulting impact of both factors requires the employment of high LLZO content in the cathode for reaching high power density, which in turn leads to the need for much higher areal capacities of solid-state cathodes as compared to the conventional counterparts for achieving same energy densities 42 . These energy/power density tradeoff considerations point to severe limitations on the LLZO content used in the solid-state cathode and cast doubt on even the feasibility of a solely LLZO approach.
In this work, taking 18650 Panasonic (231 Wh kg −1 , 636 Wh L −1 ) 43 [45][46][47][48] . We then review in detail other factors hindering the commercial deployment of Li-garnet SSBs, such as volume changes of Li upon its plaiting/stripping, and the difficulties associated with the fabrication of LLZO based solid-state cathodes, giving our perspective on these problems.

Results and discussion
Energy and power densities of Li-garnet SSBs. To assess achievable energy and power density of Ligarnet SSBs, 1D-isothermal lithium-ion battery model with single-ion conducting solid electrolyte developed by COMSOL Multiphysics 49,50 was applied to simulate their electrochemical performance during discharge. All equations governing the simulation can be found in the "Methods" section. The schematic of the model is depicted in Supplementary Fig. S1. Parameters used for simulation are summarized in Supplementary Table S1. Simulations were performed varying (i) the areal capacity of the cathode layer (0.5-5 mAh cm −2 ), (ii) the thickness of LLZO dense layer separating the cathode and Li anode layers (0.1-90 µm), (iii) the temperature (30 °C and 70 °C), and (iv) the C-rate (0.5C-5C). Examples of the resulting voltage profiles simulated at different C-rates, cathode areal capacity of 4 mAh cm −2 , and LLZO thicknesses of 30 µm are shown in Fig. 2a,b (see Supplementary Figs. S2-S25, for a complete set of simulated voltage profiles). The achievable energy and power densities were calculated from simulated voltage profiles at a specific C-rate and cathode mass loadings (areal capacities), average cell voltages, and total weight or volume of all cell components assuming a combination of 40 cathode/electrolyte/anode layers (see Supplementary Fig. S26 for details). Of note, the cell volume is calculated in the fully discharged state in which Li-garnet SSBs are to be assembled in practice. All parameters contributing to the mass and volume of the cell, such as the thickness of Cu and Al foils and the thickness of pouch Al foil are summarized in Supplementary Table S2. Thickness of the Li metal anode was fixed, corresponding to 20% of the cathode areal capacity. For instance, Li anode thickness was 1, 3, and 5 µm for cathodic areal capacities of 1, 3, and 5 mAh cm −2 , accordingly. It should also be pointed out that efficient operation of Li-garnet SSBs with high areal capacities of > 1 mAh cm −2 can be practically achieved only at stack pressures that enable to mitigate the formation of voids at the LLZO/Li interface [21][22][23][24] . As a result, the cell design requires integrating additional inactive components, which severely limits its energy density. Considering the lack of data on the optimal pressure at given current densities and the practical implementation of this requirement, we excluded this parameter from the energy and power density calculations.  44 LIBs at the gravimetric and volumetric power densities of 200 W kg −1 and 600 W L −1 , accordingly. Considering 18650 Samsung battery as a reference system with the minimum necessary electrochemical performance, we identify LLZO thicknesses and areal capacities of Li-garnet SSBs required to match its energy density at 200 W kg −1 and 600 W L −1 . Such values were named break-even thickness and areal capacities, following analogy to the break-even values in economics, representing a set of parameters at which total revenue Notably, considering the employing of a 50 µm LLZO solid-electrolyte membrane, the gravimetric break-even cathode areal capacity equals 3.55, and 3.15 mAh cm −2 for the cells at 30 °C and 70 °C. Volumetric areal capacity of 1.2 mAh cm −2 was found to be the break-even value for both temperatures of 30 °C and 70 °C. Importantly, our calculations show that an increase of the Li anode excess has a moderate impact on the gravimetric energy density of Li-garnet SSBs ( Supplementary Fig. S30a,b). For instance, when Li anode thickness was enlarged by a factor of 10, the gravimetric break-even LLZO thickness at a cathode areal capacity of 1.5 mAh cm -2 shifted only from 16.8 to 14.9 μm and from 16.8 to 15.4 μm at 30 °C and 70 °C, accordingly. Correspondingly, at a fixed cathode areal capacity of 1.5 mAh cm −2 and LLZO thickness of 15 μm, the gravimetric energy density decreases from 184.4 Wh kg −1 and 185.8 Wh kg −1 to only 180.2 Wh kg −1 and 181.2 Wh kg −1 (at 30 °C and 70 °C). With respect to the volumetric energy density, the picture is the opposite. Ten times higher Li anode amount changes significantly volumetric break-even thicknesses at a cathode areal capacity of 1.5 mAh cm -2 , from 66.2 to 53.2 μm and 67.5 to 54.3 μm (at 30 °C and 70 °C, see Supplementary Fig. S30c,d). As a result, a substantial reduction of the volumetric energy density was found in the case of employing a 10-times thicker Li anode (at a fixed cathode areal capacity of 1.5 mAh cm −2 and LLZO thickness of 15 μm): from 939 Wh L −1 to 774 Wh L −1 for 30 °C and from 942 Wh L −1 to 777 Wh L −1 for 70 °C.
Subsequently, we analyzed break-even dependences of cathode areal capacity and LLZO thickness for Li/ LLZO/LCO solid-state battery on the vol. % of LLZO in LCO solid-state cathode, which are summarized in Fig. 4. Figure 4a evidences that upon an increase of LLZO content in a composite cathode, higher areal capacity and lower LLZO solid electrolyte thickness should be used to attain the same energy densities of 180 Wh kg −1 and  Practical challenges towards the fabrication of Li-garnet all-solid-state batteries. Apart from the importance of the above-discussed findings, which highlight the viability of solely garnet SSBs in respect of achievable energy and power densities, adopting the LLZO into the battery cell structure is challenging and requires new approaches in the fabrication of solid-state cathodes and cell design. The latter are primarily related to (i) the intrinsic volume changes of Li anode upon Li plating and stripping and (ii) the chemical reaction of cathode materials with LLZO, yielding non-Li ion conductance phases. These two factors were fully excluded from the simulations.
The volume change of Li is becoming a major challenge when it comes to the deposition of high areal capacities of 1-5 mAh cm −2 that correspond to 5-25 µm of Li. This means that, on the one hand, cell design should   53 , is ca. 10 MPa, allowing to achieve stable cycling at current densities exceeding 1 mA cm -2 . The external stack pressure is, however, a double-edged sword. Although it seems necessary to inhibit void formation during lithium stripping, some theoretical 22,54 , and experimental reports 55 indicated that stack pressure could lead to quicker cell failure due to increased mechanical stress. Therefore, research is ongoing on finding optimum pressure for Li stripping and the development of cell design enabling to accommodate  www.nature.com/scientificreports/ the dynamical changes in lithium thickness. It should be noted, however, that one possible solution to avoid the Li volume change issue is to use a scaffold-type LLZO, since no external pressure is needed in this case. Thus, Li metal can be plated over the entire surface of the scaffold structure and stored in the pores. As a result, there is no dynamic change in the volume of the cell upon plaiting. Upon stripping, the voids are not forming due to the high surface area of the LLZO/Li interface. Another essential advantage of LLZO scaffolds is the possibility to increase applied current density upon Li plating/stripping up to 10 mA cm −2 without the formation of Li dendrites. For instance, as indicated by Wachsmann et al. 56 the current density of 10 mA cm −2 for porous LLZO configuration corresponds to the current density of 0.25 mA cm −2 for planar configuration, considering that the porous solid-state electrolyte might have up to ~ 40 × higher surface area compared to the planar one.
As to the compatibility of LLZO with current cathode chemistries, this issue is mainly caused by the hightemperature co-sintering between LLZO and cathode active materials. For instance, upon heat-treatment of LLZO and LiCoO 2 (LCO) cathode above 700 °C, insulating decomposition reaction products were reported 50 . High-voltage spinel cathodes (Li 2 NiMn 3 O 8 , Li 2 FeMn 3 O 8 , and LiCoMnO 4 ) start to react with LLZO even at temperatures as low as 500 °C 57 . LiFePO 4 (LFP) cathodes are difficult, if not impossible, to co-sinter with LLZO, as LFP phase decomposition already occurs above 400 °C 26 . To overcome this compatibility issue, a new design was recently proposed based on wet-chemical infiltration of the cathode active material precursors into porous LLZO solid-state electrolyte, serving as an as-sintered scaffold with their subsequent annealing at lower temperatures 26 . Alternatively, as-synthesized cathode material can be infiltrated into LLZO scaffold, as was demonstrated for LiNi 0.6 Mn 0.2 Co 0.2 O 2 (NMC622) particles by Doeff et al. 58 Although both methods are interesting, they result in relatively low amounts of active materials, leading to low cathode areal capacities.

Summary and outlook
In this work, we analyzed three key contributions to the energy and power densities of Li-garnet solid-state batteries: (i) the LLZO thickness and cathode areal capacity, (ii) Li anode excess, and (iii) the content of LLZO in composite LCO cathodes. We identified the values of each variable that allow the cell to attain the energy density of conventional Li-ion batteries (180 Wh kg −1 and 497 Wh L −1 ) at the power density of 200 W kg −1 and 600 W L −1 , corresponding to ca. 1 h of a full discharge. In short, our findings indicate the viability of solely garnet SSB configuration. The detailed conclusions and recommendations are as follows.
First, we reiterate that researchers should focus on Li-garnet SSBs with a small LLZO solid electrolyte thickness of 20-50 µm rather than continue reporting on mm-thick LLZO pellets. Only when employing such thin LLZO membranes the state-of-the-art gravimetric and volumetric energy densities of conventional Li-ion batteries at 1 h of battery discharge can be attained. Also, working with such thin LLZO thicknesses will aid in identifying at early stages technical challenges in their mass-scale manufacturing. We further note that at LLZO SSE thickness of > 50 µm the employment of cathodes with high areal capacities of > 3 mAh cm −2 is imperative for reaching high gravimetric energy densities of 180 Wh kg −1 at a power density of 200 Wh kg −1 . Thus far, the laboratory LLZO-based cells utilized electrodes with very low areal capacities (on average 0.5-1 mAh cm −2 ).
Our analysis also concerns the thickness of the Li-metal anode and the content of LLZO in the composite cathodes. Briefly, our calculations show that minimization of the Li excess in Li-garnet SSBs is not very critical for its gravimetric energy density. The employment of thick commercial Li/Cu foils with the Li thickness of ca. 50 µm still appears to be a practically viable approach. The content of LLZO in LCO solid-state cathodes should be minimized at least to the level of 30-50 vol.% as higher LLZO content requires the deployment of very thin, 2-7 µm LLZO membranes, which is not feasible to achieve experimentally. Additionally, we present recommended minimal areal capacities of LLZO-LCO cathode at given LLZO thickness and vol. % of LLZO in LCO solid-state cathode.
Apart from the cathode loadings, LLZO content in the solid-state cathode, the thicknesses of LLZO SSE, and the metallic Li anode that needs to be adjusted, we highlight that also other aspects of the Li-garnet SSB fabrication should be considered. They are the intrinsic volume changes of Li anode upon its plating and stripping and challenges related to the fabrication of LLZO composed solid-state cathodes. Although it seems that the volume changes of the Li at the anode side can be mitigated either by the employment of pressure or the use of scaffold-type LLZO membranes, it is not yet certain whether it is possible to fabricate solid-state cathodes based on LLZO and Li transition metal oxides, considering their incompatibility upon co-sintering or difficulty in the infiltration of cathode particles in LLZO porous scaffold.

Methods
Simulations of LCO positive electrode. Electronic conductivity in LCO. The conduction of electrons in the LCO can be described by following generalized Ohm's Law: where i LCO is the current density(in A m −1 ), ∇∅ LCO is the potential gradient, and σ LCO,eff represents the effective electronic conductivity of LCO (in S m −1 ), which can be calculated as follows: where σ LCO is the electronic conductivity of LCO (in S m −1 ); ε 1.5 LCO is Bruggeman factor, representing volume fraction and tortuosity of LCO in positive electrode.
Li-ion diffusion in LCO (LCO particles are considered to be perfect spheres surrounded by LLZO electrolyte): where c Li + is the species concentration (in mol m −3 ), r p is the particle mean center-surface distance (in m), D Li + is the intercalation diffusivity constant (in m 2 s −1 ), ε LCO is volume fraction of LCO in the electrode, v Liθ ,m and n m are stoichiometric numbers of Li ions and electrons required for electrochemical lithiation/delithiation of LCO, F is Faraday's constant (96,485 C mol −1 ), and i v,m is the applied current (in A m −2 ). The first condition (4) elucidates the particle diffusion rate at the center of LCO particles. The condition stems from the fact that the diffusion rate should be zero at the center of the sphere.
The second condition (5) implies the diffusion rate at the outer surface of spherical LCO particles. The diffusion rate at r = r p is equalized to the reaction rate at the surface.
Li-ion transport in LLZO. The conduction of Li ions in the LLZO can be described by following generalized Ohm's Law: where i LLZO is the current density(in A/m), ∇∅ LLZO is the potential gradient, and σ LLZO,eff represents the effective Li-ion conductivity of LLZO (in S m −1 ), which can be calculated as follows: where σ LLZO is the Li-ion conductivity of LLZO (in S m −1 ); ε 1.5 LLZO is Bruggeman factor, representing volume fraction and tortuosity of LLZO in positive electrode.

Butler-Volmer kinetics in positive electrode.
where i loc,expr is the local exchange current density, α a and α c are the anodic and cathodic transfer coefficients, η is the local over potential (in V), T is the temperature (in K), and i 0 can be expressed as follows: where c Li + ,ref is reference lithium concentration of cathode at equilibrium state (in mol m −3 ), c Li + ,max are reference and maximum lithium concentrations (in mol m −3 ), i 0,ref is reference exchange current density of electrode (in A m −2 ), c Li + is the lithium concentration on the surface of the active particles (in mol m −3 ).
The initial charge of LCO electrode ( Q cell ) was calculated as follows: where c Li + ,max is maximum lithium concentration, ε LCO is solid phase concentration, soc max and soc min are maximum and minimum state of charge and L pos is the thickness of the positive electrode. Apart from them, F and A are Faraday's constant (96,485 C mol −1 ), and area of the cell (in m 2 ), respectively.
Simulations of Li negative electrode. The electronic conductivity in Li negative electrode is governed by generalized Ohm's Law as indicated above for LCO cathode.
Butler-Volmer kinetics is described as follows: where i 0 = i 0,ref .
(3) ∂c Li + ∂t = ∇. D Li + ∇c Li + , License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.