Design Rule for Constructing Buckling-Free Polymeric Stencil with Microdot Apertures

A polymeric stencil with microdot apertures made by using polydimethylsiloxane (PDMS) molds with pillar patterns has many advantages, including conformal contact, easy processability, flexibility, and low cost compared to conventional silicon-based membranes. However, due to the inherent deformability of PDMS materials in response to external pressure, it is challenging to construct structurally stable stencils with high structural fidelity. Here, we propose a design rule on the buckling pressure for constructing polymeric stencils without process failure. To investigate the critical buckling pressure (P-cr), stencils are fabricated by using different PDMS molds with aspect ratio variations (AR: 1.6, 2.0, 4.0, and 5.3). By observing the buckled morphology of apertures, the structures can be classified into two groups: low (AR 1.6 and 2.0) and high (AR 4.0 and 5.3) AR groups, and P-cr decreases as AR increases in each group. To investigate the results theoretically, the analysis based on Euler's buckling theory and slenderness ratio is conducted, indicating that the theory is only valid for the high-AR group herein. Besides, considering the correction factor, P-cr agrees well with the experimental results.