An approach to characterize and clarify hysteresis phenomena of lithium-silicon electrodes

We clarify the hysteretic behavior observed in lithiated silicon electrodes through the development and implementation of a model that describes the main features of the observed voltage hysteresis. Specifically, slow-scan voltammetry at 0.01 mV/s is used to study hysteresis in lithiated silicon thin-film electrodes. At higher scan rates, the curves U(x), where U is voltage and x is state of charge, depend on the scan rate, but no difference is seen in the curves when scanning at slow enough rates. For example, no difference is seen at 0.01 mV/s or at 0.005 mV/s, even though the same hysteretic behavior is observed for both scan rates, i.e., the lithiation curve differs significantly from the delithiation curve. The rate of 0.005 mV/s is the slowest that could be measured with state-of-the-art equipment. However, when a lithiating scan at 0.01 mV/s is suddenly set to open circuit conditions, the voltage slowly decays upwards, whereas the voltage decays downwards when delithiation is interrupted. From this, it is inferred that the rate invariance seen at 0.005 and 0.01 mV/s would have to break down at some lower scan rate, if it could be measured. A semi-empirical model is used to describe many aspects of this behavior based on the assumption of a region of rate invariance, which breaks down at higher scan rates due to transport and kinetic losses, but which also breaks down at slower scan rates due to transients that are observable but remain unexplained.