Time-dependency of the threshold voltage in memristive devices

We describe a generic exponential model with four parameters for thin-film memristive devices. This model is used to analyze the time dependency of the threshold voltage which defines the transition between non-programming and programming phases of the device. A relationship between timescale of operation and threshold voltage is derived. Furthermore, self-terminating programming is considered using the results of this analysis. Finally, the effect of parameter variations on the threshold voltage is analyzed.