Electrochemical strain microscopy (ESM) is a powerful tool to resolve ionic transport and electrochemical processes with a nanoscale resolution. To ascertain the underlying mechanism that governs the signal generation of ESM imaging, a fully coupled nonlinear electrochemomechanical model based on the finite element method is developed and applied to LiMn 2 O 4 particles. The frequency dependence of the ESM response, in particular the response at high frequencies used in the detection regime, is investigated in detail. The performed analysis demonstrates that the error induced by the decoupling approximation increases with decreasing bias frequency due to the relatively large variation in ion concentration. In the high frequency regime, the results reveal that the stress effect is negligible and local electroneutrality holds, providing the simplification of numerical simulation for ESM imaging. By applying an alternative current voltage, we suggest that the detectable signal observed in ESM imaging can be attributed to the Vegard effect, which was controversial in previous linear models. The local distribution of ion concentration shows that the ionic reorganization only takes place near the tip-surface junction, the spatial extent of which can be described by two relevant lengths, the contact radius and ion drift length, which determine the spatial lateral resolution and depth resolution, respectively, in ESM imaging. Through a parametric study, the electromigration is proved to be dominant at high frequencies and the relationship between ESM amplitude and some parameters may offer a strategy to measure local electrochemical reactivity. The impact of contact force is evaluated and the results indicate that the local compression reduces ion concentration and the resultant ESM signal in the detection regime . Thus attention must be paid to the contact force when a comparison between different measurements is conducted. The combination of the numerical model and experiment holds the promise of quantitative probing of local electrochemical parameters in solids.

Electrochemical strain microscopy (ESM) can provide useful information on electrochemical reactivity in solids at the nanometer scale. In ESM, a time variant electric field applied to the sharp tip induces the ionic flow and electrochemical reaction. This triggers strains as a result of Vegard effect and flexoelectric effect, and the corresponding surface displacement can be detected by the tip. As such, the process involves mechanical-electrical-chemical coupling. A series of analytical descriptions was established to analyze the image formation and spectroscopic mechanism of ESM. However, most of the existing models are limited to the partial coupling or ignore the flexoelectric effect. In this paper, based on a fully coupled theory for thermal-electrical-chemical-mechanical processes, a model which accounts for the bulk defect electrochemical reaction, direct and inverse flexoelectric effect, and steric effect is developed for the mixed ionic-electronic conductor with an ionically blocking electrode. Here, the bulk defect electrochemical reactions are especially taken into account, which are ubiquitous in some electrochemical systems but usually omitted in the previous works. As an application of this work, the dynamic response of ESM measurement is solved numerically under the excitation of sinusoidal voltage. Numerical results reveal that there is an unambiguous ferroelectric-like hysteresis of the displacement-voltage loops, and the response is dependent on the frequency of applied excitation. Besides, the bulk defect electrochemical reaction has a salient influence on the particle distributions and the contribution of flexoelectric effect to the local surface displacement is marked. This work may help us to explain the image formation of ESM and explore the electrochemical process in solids.

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In recent years, a linearization method has been extensively employed to investigate the electromechanical fields and carrier distribution in flexoelectric semiconductors, where the assumption of a small perturbation of carrier concentration is adopted. However, this method fails to accurately describe the realistic physical process in which case the considerable variation of carrier concentration takes place. Based on the fully coupled nonlinear equations, this paper presents a finite element approach to study the electromechanical couplings and nonlinear carrier transport in flexoelectric semiconductors. This method is applied to calculate the electrostatic potential in a bent piezoelectric semiconductive nanowire (NW) going beyond simple considerations and simulate the nonlinear current-voltage (I-V) characteristics of a mechanically loaded flexoelectric p-n junction. Results indicate that the inherently nonlinear drift of carriers gives rise to the asymmetric distribution of the electric potential relative to the NW axis in the upper body. Flexoelectricity brings about a remarkable enhancement in output voltage and is responsible for the linear variation of electric potential along the length direction of the NW unless close to two ends. Furthermore, the barrier height and I-V relations of a flexoelectric p-n junction can be effectively tuned by mechanical forces due to the flexoelectric effect, the effect of which relies on the size of p-n junction configuration. This work is a good start point to comprehend the coupling of the flexoelectricity and the nonlinear carrier transport in static and dynamic cases, and offers an effective approach to numerically deal with issues involved in the flexoelectronics and piezoelectronics at the nanoscale.

Electrochemical processes in solids are affected by the properties of various interfaces, where the flexoelectric effect manifests itself considerably due to the inevitable strong gradient fields. Thus, it is crucial to study the coupling between the electrochemical process and the flexoelectric effect. Based on the continuum theory, we conduct the finite element implementation for the flexochemical effect, being the coupling between flexoelectricity, Vegard effect and chemical reactions. Then the developed method is employed to investigate the flexochemical effect arising in scanning probe microscopy (SPM), including evaluating the contributions from the flexoelectric effect and Vegard effect to the electromechanical response on material SrTiO3 (STO) in piezoresponse force microscopy (PFM) as well as to mechanical redistribution of oxygen vacancy in STO. It is found that at room temperature the nanoscale electromechanical response of the undoped STO in PFM imaging is mainly induced by the converse flexoelectricity while the contribution of direct Vegard effect is negligible. Furthermore, the contact force exerted by SPM tip in manipulating the redistribution of oxygen vacancies is multifunctional, including diminishing vacancies underneath the contact area and enriching the regions around the tip-surface contact edge and inside the sample below the tip, resulting from the synergy of the converse Vegard effect and the direct flexoelectricity. These analyses explain some experimental observations well. This paper provides a continuum framework for the analysis of electrochemomechanical systems with the flexoelectric effect.