Bin Wu

Memristors based on 2D layered materials could provide biorealistic ionic interactions and potentially enable construction of energy-efficient artificial neural networks capable of faithfully emulating neuronal interconnections in human brains. To build reliable 2D-material-based memristors suitable for constructing working neural networks, the memristive switching mechanisms in such memristors need to be systematically analyzed. Here, we present a study on the switching characteristics of the few-layer MoS₂ memristors made by mechanical printing. First, two types of dc-programmed switching characteristics, termed rectification-mediated and conductance-mediated behaviors, are observed among different MoS₂ memristors, which are attributed to the modulation of MoS₂/metal Schottky barriers and redistribution of vacancies, respectively. We also found that an as-fabricated MoS₂ memristor initially exhibits an analog pulse-programmed switching behavior, but it can be converted to a quasi-binary memristor with an abrupt switching behavior through an electrical stress process. Such a transition of switching characteristics is attributed to field-induced agglomeration of vacancies at MoS₂/metal interfaces. The additional Kelvin probe force microscopy, Auger electron spectroscopy analysis, and electronic characterization results support this hypothesis. Finally, we fabricated a testing device consisting of two adjacent MoS₂ memristors and demonstrated that these two memristors can be ionically coupled to each other. This device interconnection scheme could be exploited to build neural networks for emulating ionic interactions among neurons. This work advances the device physics for understanding the memristive properties of 2D-material-based memristors and serves as a critical foundation for building biorealistic neuromorphic computing systems based on such memristors.

Mechanical degradation is one of the main causes of capacity fade in lithium-ion batteries. During lithium intercalation and de-intercalation, the active material particles of battery electrodes experience mechanical deformation, which induces stress inside particles and in-between particles. These stresses can lead to cracks and fractures of the electrode, such as cracks inside particles or in-between particles, causing isolation of active materials, disruption of the electrically conductive particle network and exposure of fresh surfaces for side reactions that result in capacity degradation. This work aims to develop a multi-scale mechanical-electrochemical model which enables fully coupled mechanics and electrochemistry at both particle and electrode levels by incorporation of particle interaction. Coupled electrochemical and mechanical modelling is essential to investigate stress generation and to evaluate its effect on battery performance. However, prior models are mostly focused on a single, isolated particle. While these models are very useful to consider stress and fracture inside a particle, they cannot be used for problems such as fracture in-between particles since particle interaction is omitted. Moreover, the electrode level model coupling of mechanics and electrochemistry is lacking. There have been several attempts to couple the mechanical model of isolated particles with the porous electrode model to analyze the distribution of intercalation stresses inside different particles across the electrode. In those attempts, however, the particles are considered isolated with no interaction between them. It should be noted that particle interaction can result in significant stress level comparable to the stress generated from the concentration gradient. Mechanical stress can change the electrochemical potential of a solid, and therefore (i) affects the diffusion in the solid, and (ii) affects the electrochemical reaction between the solid and the electrolyte. Although the first effect has been generally addressed, the second effect of mechanical stress on the electrochemical reaction rate has not been included in most models. Including the second effect is necessary when modeling particle interaction since stress gradient in the electrode leads to spatial-dependent interaction stress between particles. It is necessary to account for different intercalation/de-intercalation currents for particles under different stress states that are dependent on their interaction with neighbor particles. Fig. 1 illustrates our concept to model particle interaction and to link the particle level and the continuum electrode level. Each spatial point in the continuum level corresponds to a particle level representative volume element (RVE) consisting of many particles and porous volume occupied by the electrolyte. The shade of color in the particle represents lithium concentration. At the particle level, solid diffusion is modeled using a generalized electrochemical potential, which captures the effects of phase transition and mechanical stress. The stress in a particle is a superposition of the stress from lithium concentration gradient inside the particle (σ_ij  ^c ) and the stress from particle interaction (σ_ij  ⁱ ). The stress σ_ij  ^c  can be calculated by the lithium concentration distribution inside the particle using an analogy to thermal stress. Regarding the interaction stress, each particle can be considered to be an inclusion embedded in a matrix composed of all other particles. According the Eshelby’s inclusion theory, the stress in a spherical inclusion resulting from its interaction with the matrix is uniform. Thus, the interaction stress, σ_ij  ⁱ , is uniform inside the particle. At the electrode level, we consider coupled electrochemical reaction and stress field both in the electrode thickness direction and in an in-plane direction, which can be called pseudo-3D model in comparison to the classical pseudo-2D model. The electrode level stress (Σ_ij ) is calculated on the continuum with effective mechanical properties and the eigenstrains of the RVE. Conceptually, the electrode level stress at a spatial point in the electrode can be viewed as the mechanical loading on an RVE at that point. A relation between the electrode level stress (Σ_ij ) and the particle interaction stress (σ_ij  ⁱ ) has been developed using volume average approach. The effect of stress on the intercalation current is captured by a stress-dependent over-potential. An important finding we have obtained with this model is a new degradation mechanism, where small electrochemically inactive regions can potentially cause major degradation. We find that the tensile stress generated in the vicinity of an inactive region is large enough to easily break the binder between particles, resulting in fracture or growth of the inactive region. The result points to an approach to reduce degradation by improving the homogeneity of the electrode. Figure 1

Mechanical degradation is one of the most significant mechanisms that affect the cycle life of lithium-ion batteries. Cracks and fractures have been observed in both cathode and anode active material particles, which lead to isolation of active materials, disruption of the electrically conductive network and exposure of fresh surfaces that cause side reactions. These effects significantly reduce the battery capacity and increase the internal resistance. Modeling and simulation are essential to study the generation and effects of stress inside batteries. Treating the intercalation-induced stress analogously to thermal stress, a model has been developed to study the stress and concentration inside a particle. ¹ This model has been extended to study various problems at both particle and cell levels. Nevertheless, this model and its extensions are based on the assumption of solid particles. This assumption does not apply for active materials with an agglomerate structure, such as LiNi_0.8Co_0.15Al_0.05O₂ (NCA). ² In these materials, many nanometer-scale primary particles agglomerate to a micrometer-scale secondary particle by the adhesion of binder. The secondary particle is porous rather than a compact solid, as the electrolyte is found to be soaked into the agglomerate. ² Therefore, charge transfer reactions are expected to occur between the primary particle surface and the electrolyte inside a secondary particle. Although electrochemical models have been developed to investigate the characteristic of an agglomerate accounting for the effects of its internal structure, ³ no mechanical model has been developed to study the stress in agglomerates for lithium-ion batteries. Meanwhile, multiple experiments have reported observations of fracture of agglomerates after cycling, which is a major mechanism of capacity degradation. This calls for a fully understanding of the mechanical behaviors at the agglomerate level. This work presents a coupled mechanical and electrochemical model to predict the intercalation-induced stress in a secondary particle with an agglomerate structure, as shown in Fig. 1. In this model, the electrochemical and transport processes are accounted for at both the secondary and primary particle levels. The porous electrode theory is applied at the secondary particle level, and the solid diffusion is incorporated at the primary particle level. Simulation results from the electrochemical model revealed that a major concentration gradient exists along the radius of the secondary particle, while the concentration is fairly uniform in each primary particle. Based on this finding, the mechanical model focused on the stress generation at the secondary particle level. The secondary particle is assumed to be mechanically homogeneous with effective properties, which can be calculated from the porosity and properties of bulk materials. Because the primary particle is much smaller than the secondary particle, the secondary particle is regarded as a continuum. Each spatial point in the secondary particle is composed of many primary particles at that location. Therefore the stress at each spatial point represents the loading stress exerted on the primary particles at that location. This loading stress is important to know since it is the cause of separation of primary particles, i.e. fracture in the secondary particle. The intercalation-induced stress is calculated using the analogy to thermal stress. The developed model has been applied to investigate factors affecting the stress generation behaviors. The results are summarized as follows: 1) A strong dependence of OCP on the solid lithium concentration leads to a more uniform current density in the secondary particle, which reduces the stress level. 2) A large magnitude of over-potential at the secondary particle surface causes severely non-uniform current density, and thus larger stresses. 3) The primary particle size shows a significant effect on the current density, concentration and stress profiles. A larger primary particle size results in a smaller active surface area per volume, which reduces the impact of non-uniform current density and thus reduces the stress level in the secondary particle. However, the concentration gradient inside the primary particle becomes pronounced with the increase of the primary particle size, which may generate stress inside the primary particle. 4) The comparison between a porous secondary particle and a solid particle of the same size shows that the stress is greatly alleviated in the porous secondary particle. This is attributed to the lower Young’s modulus of the porous particle, and more importantly, to the smaller concentration gradient in the porous secondary particle. References 1. X. Zhang, W. Shyy, and A. Marie Sastry, J Electrochem Soc, 154, A910 (2007). 2. D. Abraham, D. Dees, J. Knuth, and E. Reynolds, ARGONNE National Laboratory (ANL-05/21), 196 (2005). 3. S. Lueth, U. S. Sauter, and W. G. Bessler, J Electrochem Soc, 163, A210 (2016). Figure 1

Many electrode materials for lithium-ion battery applications are composed of secondary particles. Such an active material particle is not a solid particle, but consists of many fine primary particles. This work presents a coupled mechanical and electrochemical model to predict the intercalation-induced stress in a secondary particle with an agglomerate structure. In this model the electrochemical and transport processes are accounted for at both the secondary and primary particle levels. For mechanical analysis the secondary particle is treated as a continuum with stress calculated through lithium concentration and elastic deformation. With this model we revealed several important factors that affect stresses in secondary particles. Our simulations show that a stronger dependence of the open circuit potential of the active material on lithium-ion concentration reduces the stress level. A larger magnitude of over-potential at the surface of a secondary particle causes larger stresses. A larger primary particle size helps to reduce the stresses in the secondary particle as long as the secondary particle is a continuum containing many primary particles. Finally, a comparison between a porous secondary particle and a solid particle of the same size shows that the stress level in a porous secondary particle is much smaller.