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A physics-based compact device model is developed for the conducting-bridge random-access memory (CBRAM). By considering the dependence of ion migration velocity on the electric field, the vertical and lateral growth/dissolution dynamics for the metallic filament are investigated. Both time-dependent transient and “quasi-static” switching characteristics of the CBRAM are captured. Moreover, the I-V characteristics of the CBRAM can be reproduced. By further considering the compliance effect on the size of the metallic filament, the on-state resistance modulation is fitted, and the multilevel capability is included in the model. This model is verified by the experiments data from the Ag/Ge0.3Se0.7-based CBRAM cells. This model reveals that experimentally measured switching parameters such as the threshold voltage and the cell resistance are dynamic quantities that depend on the programming duration time. The time-dependent switching process of the CBRAM is quantified, thus paving the way for a compact SPICE model for circuit simulation.