RETRACTED: Optimization of a Carbon Dioxide-Assisted Nanoparticle Deposition Process Using Sequential Experimental Design with Adaptive Design Space (Retracted article. See vol. 59, pg. 15807, 2020)

A sequential design of experiments methodology with an adaptive design space is proposed and implemented to optimize a nanofabrication technique that possesses significant uncertainty in terms of design region and model structure along with an engineering tolerance requirement. This method is termed Layers of Experiment (LoE) with Adaptive Combined Design (ACD) and is developed specifically for advanced technology processes where there is little or no foreknowledge of the design region and/or model structure from either mechanistic understanding or empirical studies. This technique was applied to optimize an elevated pressure, elevated temperature carbon dioxide (epet-CO2) nanoparticle deposition process where silver nanoparticles were deposited directly from an organometallic precursor in the fluid phase onto a silicon wafer surface. A target mean nanoparticle size of 40 nm was chosen, with surface enhanced Raman spectroscopy (SERS) as the motivating application. Using the LoE/ACD method, it was possible to find the process optimum for the epet-CO2 process and build a reliable model using only 12 experiments conducted in two sequential layers. With temperature as the design variable, the first layer of experiments was conducted in the region [60 degrees C, 150 degrees C], while the second layer was conducted in the region [98 degrees C, 128 degrees C], indicating that the LoE/ACD algorithm reduced the size of the design region by 60 degrees C while building a reliable model for statistical inference. In the first layer, a purely space-filling design was used since the model structure was unknown; in the second layer, the ACD approach yielded a design weighted between space-filling and D-optimal, favoring the D-optimal design. The optimized temperature for fabricating 40 nm diameter silver nanoparticles in this system was 117 degrees C.