Investigation of filamentation in a-Si/Ag/Cu memristors with atomic force microscope
Cation-based Ag/Cu filaments formed in an insulating $\alpha$-Si matrix are widely used as memristors in crossbar arrays for efficient in-memory computing. However, the stochastic nature of filament formation and rupture gives rise to device-to-device and cycle-to-cycle variation. Despite successful implementation of large-scale memristor arrays, systematic studies of filament parameters and their spatial distribution in the memristors are scarce. In this work, we use conductive atomic force microscopy (c-AFM) to probe the spatial distribution of conductive filaments in $\alpha$-Si memristors. The charge transport is dominated by a limited number of discrete filaments rather than by uniform conduction across the device area. The systematic analysis of the experiment gives the mean surface density of the conductive filaments $\sim$3200 per $\mu\text{m}^2$. Both volatile and non-volatile filaments can be found within one memristor. The experimental data and the nature of volatile and non-volatile filaments may be explained within the model of multiple trap assisted tunnelling. The model yields reasonable estimates for physical properties for both types of filaments.