Core Viewpoint - Variability is a significant challenge in the semiconductor manufacturing industry, with random variability emerging as a critical issue affecting yield, reliability, and performance as device feature sizes shrink to atomic levels [1][26]. Group 1: Types of Random Effects - There are four types of random effects in semiconductor manufacturing: - Line Edge Roughness (LER) or Line Width Roughness (LWR) affects gate leakage current, wire resistance, chip power consumption, and reliability [6]. - Local Critical Dimension Uniformity (LCDU) leads to variations in critical dimensions among adjacent devices, impacting yield and chip speed [7]. - Local Edge Placement Error (EPE) can cause short circuits or open circuits, affecting yield and reliability [8]. - Random Defects such as bridging or breakage of chip features can also impact yield and reliability [11]. Group 2: Increasing Severity of Randomness - Random variability has become more severe in the latest process nodes, with local random variability now potentially accounting for over 50% of certain manufacturing errors [3][26]. - The introduction of EUV (Extreme Ultraviolet) lithography has exacerbated the issue, as the photon count for exposure is significantly lower compared to older technologies, leading to substantial differences in adjacent feature sizes [21][22]. Group 3: Measurement and Control of Randomness - Accurate measurement of random effects is crucial for optimization and control in semiconductor manufacturing, as traditional measurement tools may introduce significant errors [24]. - The industry requires specialized measurement and analysis techniques to accurately report random errors and must adopt probabilistic methods for analysis, moving away from deterministic approaches [25]. - Effective control of randomness can improve both yield and productivity, but it requires precise measurement technologies [28][29].