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In this paper, the correlation between line-edge roughness (LER) and line-width roughness (LWR) is investigated. Based on the characterization methodology of auto-correlation functions (ACF), a new theoretical model of LWR is proposed, which indicates that the LWR ACF is composed of two parts: one involves LER information; the other involves the cross-correlation of the two edges. Additional characteristic parameters for LER/LWR are proposed to represent the missing cross-correlation information in conventional approaches of LER/LWR description, other than LER/LWR amplitude and auto-correlation length. An improved simulation method for correlated LERs is also proposed, which can provide helpful guidelines for the characterization, modeling, and the optimization of LER/LWR in nanoscale CMOS technology. The experimental results and device simulation results are discussed in detail in the part II of this paper.