Figure 4: Improved fracture resistance of the clamped Si nanopillar on lithiation.

(a,b) SEM images of crystalline <110> Si pillar of 1-μm diameter and the walls with gap of 300 nm. The pillar is clamped by the walls and expanded along <100> direction upon lithiation. Significant crack is not found. (c,d) SEM images of crystalline <110> Si pillar of 2.2 μm diameter and the walls with gap of 300 nm. After lithiation, the cracks are found between <110> and <100> directions as indicated by red arrows. Scale bars, 1 μm. (e) Column chart of the fracture ratio of the clamped <110> Si pillars for various diameters. To compare the effect of mechanical clamping for the fracture resistance, the fracture ratio of unclamped <110> pillar is shown as red columns²⁰. (f) Finite element analysis of in-plane principal stress of unclamped (left) and clamped (right) <110> Si pillar after full lithiation. Initial diameter is 550 nm (dot circle) and lateral displacement of clamped pillar is confined to 160 nm (solid line). (g) Column chart of the population of the fracture location as an angle of the crack in the clamped <110> Si pillar upon lithiation (blue). The population of the fracture location of the unclamped <110> pillar (red) compares how mechanical clamping changes the fracture behaviour⁶.