Fig. 2: Surface undulation patterns and their modelling via finite element simulations.

a, Schematic showing the growth of an SCL region (in green) from a nucleation site within the TPD interlayer towards the top and bottom TCTA layers (growth direction marked with green arrows). This results in the development of the first surface undulation triggered under the applied thermal stresses (marked with black arrows). Notice the periodic onset of further secondary undulations as the cylindrical-shaped SCL region extends radially and mechanical instabilities develop. b, Simulated normalized out-of-plane displacement (top) isotropic view of the whole simulated structure, (bottom, left) isotropic view of a zoomed region containing the first surface undulation of diameter θ ≅ 250 nm within the TPD interlayer and (bottom, right) a cross-sectional view of the surface undulation region. The neo-Hookean model with material parameters C = 3.71 × 10⁶ Pa and d = 5.58 × 10⁻⁸ Pa⁻¹ is assumed in the simulations. c, Comparison between the simulation results from finite element modelling (FEM) and the experimental AFM measurements concerning the shape of the first undulation during the early propagation stages of the liquified front. AFM data is for an emerging liquid nucleus, with no associated uncertainty values. d, Comparison between a simulated wrinkled pattern of θ ≅ 1,000 nm under the assumption of the neo-Hookean model with material parameters C = 3.71 × 10⁶ Pa and d = 5.58 × 10⁻⁸ Pa⁻¹, and the AFM image of a typical pattern in 13/63/13 nm trilayers. Scale bars, 1.2 μm.