Critical film thickness for fracture in thin-film electrodes on substrates in the presence of interfacial sliding

It is well known that thin-film electrodes on substrates could fracture during lithium insertion/extraction above a critical film thickness. Recent studies have revealed that lithium could facilitate sliding at the interface between lithiated Si and the underlying substrate. In this paper, we investigate fracture in thin-film electrodes and derive the critical film thickness for fracture as a function of both the fracture toughness of the film and the sliding resistance of the interface. The analysis indicates that a slippery interface due to lithiation could significantly decrease the critical thickness for fracture.