A Strategy to Characterize Nanofabrication Processes With Large RPM (Experimental Run, Physics, and Measurement) Uncertainties

Abstract

The bottom-up fabrication of nanostructures can simultaneously face large uncertainties from experimental runs (R), physical understanding (P), and measurement (M). No systematic strategy has been reported to manage these three types of uncertainties, abbreviated as RPM, concurrently to achieve better understanding of nano fabrication processes. Previously, we developed cross-domain model building and validation (CDMV) approach to handle large physical and measurement (PM) uncertainties in nano fabrication process modeling. In this paper, we propose to prioritize RPM uncertainties and to incorporate the analysis of run variations into process modeling. Under a Bayesian hierarchical framework, this new strategy will first handle PM uncertainties at the basic level to identify a model structure using CDMV approach. The rationale is that the uncertainty due to experimental runs should not fundamentally change the process physics or the model structure, but impacts on the model parameters. At a lower hierarchy, process model parameters varying or invariant to runs are treated as random effects or fixed effects to be identified respectively. Demonstrated in a nanowire growth process example, the new strategy not only assists to establish an improved process model, but also to uncover the variation sources contributing to large run variations. The obtained physical insights can guide further process investigation. Note to practitioners: experimental investigation of nanofabrication processes often encounters large uncertainties due to a lack of conclusive understanding of process physics, measurement noise, and variability among experimental runs. Trial-and-error strategy is commonly adopted under this scenario to explore the process physics with little guidance, resulting in increased cost of experimentation or fabrication. This paper presents an alternative strategy to make more efficient use of data to manage large RPM uncertainties and achieve better process understandings for process improvement.