Uniformity and signal-to-noise ratio for static and dynamic parameter designs of deposition processes

Abstract

In this paper, the relationship between the uniformity measure (U) and the Taguchi signal-to-noise ratio (SNR) for parameter design (or robust design) is investigated with a focus on the deposition process. For the static parameter design, it can be easily shown that U is directly related to the Taguchi SNR, and, as such, U can be interpreted as a measure directly related to the expected loss after the mean thickness is adjusted to the target. For the dynamic parameter design in which the target of a characteristic (e.g., the target thickness for a deposition process) changes, the Taguchi SNR is conditional on the signal parameter values (e.g., the deposition times) used in the parameter design experiment. Therefore, a new performance measure is developed considering a general distribution of the target thickness, and it is shown that U is also equivalent to this new performance measure. In summary, U can be used as a valid performance measure for the dynamic as well as static parameter design of a deposition process. Based on these findings, static and dynamic parameter design procedures for a deposition process are developed considering not only U but also the deposition rate, and the proposed dynamic procedure is illustrated with an example case study.