Helical buckling behaviors of the nanowire/substrate system

When a nanowire is deposited on a compliant soft substrate or embedded in matrix, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed threedimensional coil buckling mechanism for a silicon nanowire (SiNW) on a poly-dimethylsiloxne (PDMS) substrate is discussed. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed, and the helical buckling spacing and amplitude are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. When the debonding of SiNW from the surface of the substrate is considered, the buckling profile of the nanowire can be divided into three regimes, i.e., the in-plane buckling, the disordered buckling in the out-of-plane direction, and the helical buckling, depending on the debonding density. For a nanowire embedded in matrix, the buckled profile is almost perfectly circular in the axial direction; with increasing compression, the buckling spacing decreases almost linearly, while the amplitude scales with the 1/2 power of the compressive strain; the transition strain from 2D mode to 3D helical mode decreases with the Young's modulus of the wire and approaches to 1.25% when the modulus is high enough, which is much smaller than nanowires on the surface of substrates. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nanostructures.