Mechanically-Guided Deterministic Assembly of 3D Mesostructures Assisted by Residual Stresses

Abstract

Formation of 3D mesostructures in advanced functional materials is of growing interest due to the widespread envisioned applications of devices that exploit 3D architectures. Mechanically guided assembly based on compressive buckling of 2D precursors represents a promising method, with applicability to a diverse set of geometries and materials, including inorganic semiconductors, metals, polymers, and their heterogeneous combinations. This paper introduces ideas that extend the levels of control and the range of 3D layouts that are achievable in this manner. Here, thin, patterned layers with well-defined residual stresses influence the process of 2D to 3D geometric transformation. Systematic studies through combined analytical modeling, numerical simulations, and experimental observations demonstrate the effectiveness of the proposed strategy through ≈20 example cases with a broad range of complex 3D topologies. The results elucidate the ability of these stressed layers to alter the energy landscape associated with the transformation process and, specifically, the energy barriers that separate different stable modes in the final 3D configurations. A demonstration in a mechanically tunable microbalance illustrates the utility of these ideas in a simple structure designed for mass measurement.

Keywords: 3D mesostructures; compressive buckling; microbalance; mode transition; residual stress.

Figure 1

(a) Schematic illustration of steps for fabricating 3D mesostructures using controlled, compressive buckling assisted by residual stresses. (b) Results of experiment, analytical modeling and FEA predictions for the residual-stress assisted assembly from an H-shaped 2D precursor. Results of analytical modeling and FEA (middle three panels) describe the formation of the 3D mesostructure (SU8 and SiNx), along with corresponding SEM images (right most panel) of the final configuration. Scale bars, 1 mm.

Figure 2

(a) Design diagram in the space of residual stress (σ_residual) and SU8 thickness (t_SU8), for t_SiNx =100 nm. (b) SEM images and corresponding FEA predictions for 3D mesostructures with different design parameters as marked by the circles in (a). (c) Probability to achieve pop-down mode for 2D precursors with three different design parameters (corresponding to points ‘2’, ‘10’ and ‘11’ in (a)). Scale bars, 1 mm.

Figure 3

Mechanics analyses of buckling mode control for the H-shaped 2D precursor. Strain energy of 3D structures with pop-up (blue) and pop-down (green) modes versus released strain, and the corresponding magnified view, for the design parameters (t_SU8, t_SiNx, σ_residual ) = (3 μm, 100 nm, 480 MPa) (a and b) and (4 μm, 100 nm, 480 MPa) (d and e). The insets of (a) and (d) show the corresponding final 3D configurations. (c and f) Normalized strain energy versus out-of-plane displacement for (t_SU8, t_SiNx, σ_residual, ε_release ) = (3 μm, 100 nm, 480 Mpa, 7.5%), (4 μm, 100 nm, 480 Mpa, 1.6%) and (4 μm, 100 nm, 480 Mpa, 2.4%), with the insets showing the stable buckling modes at the corresponding released strains. Here, h is the out-of-plane dimension of the first-floor structure, and it varies with changing the released strain. (g) Normalized strain energy versus out-of-plane displacement for (t_SiNx, σ_residual, ε_release) = (100 nm, 480 Mpa, 10%) and three different SU8 thicknesses. (h) Strain energy barrier versus released strain for (t_SiNx, σ_residual, ε_release) = (100 nm, 480 Mpa, 10%) and three different SU8 thicknesses. (i) Design diagram in the space of residual stress (σ_residual) and SU8 thickness (t_SU8), for t_SiNx = 50 nm, 100 nm and 150 nm. The geometric dimensions of the 2D precursor are the same as that in Figure 1, and the prestrain adopted in the analyses is 80%.

Figure 4

3D mesostructures formed through the approach of compressive buckling assisted by residual stresses. (a) 2D precursors, FEA predictions and SEM images for triangular ribbon networks made of SiNx and polymer (SU8). (b) Design diagram of triangular ribbon networks in the space of residual stress (σ_residual) and SU8 thickness (t_SU8) for selection of different buckling modes. (c) 2D precursors, FEA predictions and optical images for triple-floor structures made of SiNx and bilayers of gold and polymer (SU8). (d) Design diagram of triple-floor structures in the space of residual stress (σ_residual) and SU8 thickness (t_SU8) for selection of different buckling modes. Scale bars, 500 μm.

Figure 5

A simple, mechanically tunable micro-balance device. (a) 2D precursor for the device. (b) FEA prediction and SEM images from two different viewing angles. (c) Measured and computed dependence of the mass on the vertical displacement. (d) Mass versus vertical displacement for devices assembled with four different levels of prestrain, along with their corresponding 3D configurations. (e) The range of the micro-balance as a function of the prestrain. Scale bars, 1 mm.

Figure 6

3D millimeter-scale structures formed through the use of shape memory polymers (SMP). (a) 2D precursors, FEA predictions and optical images for a complex 3D table structure made of SMP and bilayers of copper and PET. The structure here is formed in a way that compressive buckling and stress-induced bending work independently. The results in the top and bottom rows represent the 3D configuration before and after releasing the prestrain in SMP, respectively. (b) Similar results for a hierarchical 3D structure. (c,d) Similar results for two structures with multiple folds formed by coupled compressive buckling and stressed-induced bending. Scale bars, 5 mm.