Trench Formation under the Tunable Nanogap: Its Depth Depends on Maximum Strain and Periodicity

Metallic nanogaps have been studied for many years in the context of a significant amount of field enhancements. Nanogaps of macroscopic lengths for long-wave applications have attracted much interest, and recently one dimensional tunable nanogaps have been demonstrated using flexible PET substrates. For nanogaps on flexible substrates with applied tensile strain, large stress is expected in the vicinity of the gap, and it has been confirmed that several hundred nanometer-deep trenches form beneath the position of the nanogap because of this stress singularity. Here, we studied trench formation under nanogap structures using COMSOL Multiphysics 6.1. We constructed a 2D nanogap unit cell, consisting of gold film with a crack on a PDMS substrate containing a trench beneath the crack. Then, we calculated the von Mises stress at the bottom of the trench for various depths and spatial periods. Based on it, we derived the dependence of the trench depth on the strain and periodicity for various yield strengths. It was revealed that as the maximum tensile strain increases, the trench deepens and then diverges. Moreover, longer periods lead to larger depths for the given maximum strain and larger gap widths. These results could be applied to roughly estimate achievable gap widths and trench depths for stretchable zerogap devices.