Fully Transient Simulation of Filament-Type Switching Operations in Unipolar and Bipolar Memristors by Combining Electrothermal and Phase-Field Models

Transient simulation of memristors where conductive filaments (CFs) dynamically evolve according to an electric field and temperature is a challenging subject. In the case of the valence change mechanism (VCM), the matrix and CFs can be regarded as two distinct phases, the high and low resistance phases (HRP and LRP), respectively. The HRP is stable. On the other hand, the LRP with a uniform concentration of defects is metastable. Therefore, the LRP spontaneously goes back to the HRP after some time, which explains the data retention. In many simulations of the memristor device, the defect migration was described by drift and diffusion (DD). In this case, a CF with a high defect concentration should start to dissolve immediately after forming or set because there is no electromigration at zero electric field and only diffusion by concentration gradient exists. Also, the closer to the outer part of the CF, the lower the defect concentration. In other words, the DD equation alone cannot explain the existence of the LRP with a uniform defect concentration.<br/>Phase-field model (PFM) is the most efficient to deal with a system where two distinct phases, LRP and HRP, are spatially mixed. We coupled the PFM with the electrothermal model along with defect generation and annihilation dynamics and successfully established a fully transient simulation of the forming, reset, and set operations of the VCM-based memristor. Using our model, both unipolar and bipolar switching can be simulated for the same active material by just changing boundary conditions that are bias conditions and interface properties with an electrode. It was shown that in the case of unipolar switching a CF evolves mainly by the generation and annihilation of defects whereas in the case of bipolar switching a CF evolves mainly by the electromigration of defects.<br/>In our I-V curve simulation, the higher compliance current, the thicker CF as experimentally observed. Note that our simulation does not define any specific filament region in the model geometry. Only initial defects are randomly assigned. Also, the successive pulse operations were simulated for synapse applications. Most interestingly, the effects of the interval length between pulses could be observed. The CFs can evolve for the time when no pulse is applied, which is to reduce the interface energy for total energy minimization. As a result, a longer pulse interval resulted in better linearity in the long-term depression curve. More details and the results of our simulation will be shown in the actual presentation.