Stress dependence of the chemical potential of lithium in a silicon electrode

We report operando measurements and concurrent modeling of the stress dependence of the chemical potential of lithium in a silicon electrode. An experimental study is carried out on hydrogenated amorphous silicon thin films in which the electrode stress state is modified operando during electrochemical lithiation and delithiation by applying an external mechanical load. During galvanostatic cycling, the electrode is periodically subjected to a tensile strain, inducing stress variations that are reflected in voltage changes. The measured stress-induced voltage changes are interpreted using a well-established chemomechanical model of lithium insertion in silicon. Comparison of voltage measurements with model predictions allows us to determine the concentration-dependent Young's modulus (from 29 GPa to 26 GPa with increasing lithium content) and some of the viscoplastic parameters of lithiated silicon. The calibrated model shows good predictive capability when applied to lithiation cycles performed at a C-rate different from that of the calibration cycle. However, it shows limitations in explaining voltage changes under delithiation. These results show that thermodynamically-consistent chemomechanical models of lithiation not only adequately describe the effect of lithium insertion and deinsertion on stress, as already shown in the literature, but also capture the reverse effect of stress on lithium chemical potential in silicon. In this respect, this work opens up new perspectives for the quantitative validation and calibration of existing diffusion-deformation theories, notably by highlighting their possible limitations.