Multiple Linear Regression Modeling of Nanosphere Self-Assembly via Spin Coating

Nanosphere lithography employs single- or multilayer self-assembled nanospheres as a template for bottom-up nanoscale patterning. The ability to produce self-assembled nanospheres with minimal packing defects over large areas is critical to advancing applications of nanosphere lithography. Spin coating is a simple-to-execute, high-throughput method of nanosphere self-assembly. The wide range of possible process parameters for nanosphere spin coating, however-and the sensitivity of nanosphere self-assembly to these parameters-can lead to highly variable outcomes in nanosphere configuration by this method. Finding the optimum process parameters for nanosphere spin coating remains challenging. This work adopts a design-of-experiments approach to investigate the effects of seven factors-nanosphere wt%, methanol/water ratio, solution volume, wetting time, spin time, maximum revolutions per minute, and ramp rate-on two response variables-percentage hexagonal close packing and macroscale coverage of nanospheres. Single-response and multiple-response linear regression models identify main and two-way interaction effects of statistical significance to the outcomes of both response variables and enable prediction of optimized settings. The results indicate a tradeoff between the high ramp rates required for large macroscale coverage and the need to minimize high shear forces and evaporation rates to ensure that nanospheres properly self-assemble into hexagonally packed arrays.