Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15-22 nm) Nanowire FETs with Various Channel Diameters

• Published in: Nanomaterials (Basel, Switzerland) Switzerland), 2022-05, Vol.12 (10), p.1721
• Main Authors: Lee, Seunghwan, Yoon, Jun-Sik, Lee, Junjong, Jeong, Jinsu, Yun, Hyeok, Lim, Jaewan, Lee, Sanguk, Baek, Rock-Hyun
• Format: Article
• Language: English
• Subjects: Diameters; Field effect transistors; Grain boundaries; Grain size; Metal concentrations; Modelling; Nanotechnology; nanowire diameter; Nanowires; Pelgrom’s law; Propagation; Semiconductor devices; Silicon; Simulation; SNWFET; Standard deviation; Threshold voltage; Transistors; ultrashort gate-length; Variability; variability modeling; Variation; Voltage; Work functions
• ISSN: 2079-4991; 2079-4991
• DOI: 10.3390/nano12101721

In this study, threshold voltage ( ) variability was investigated in silicon nanowire field-effect transistors (SNWFETs) with short gate-lengths of 15-22 nm and various channel diameters ( ) of 7, 9, and 12 nm. Linear slope and nonzero y-intercept were observed in a Pelgrom plot of the standard deviation of (σ ), which originated from random and process variations. Interestingly, the slope and y-intercept differed for each , and σ was the smallest at a median of 9 nm. To analyze the observed tendency of σ , a novel modeling approach based on the error propagation law was proposed. The contribution of gate-metal work function, channel dopant concentration ( ), and variations (WFV, ∆ , and ∆ ) to σ were evaluated by directly fitting the developed model to measured σ . As a result, WFV induced by metal gate granularity increased as channel area increases, and the slope of WFV in Pelgrom plot is similar to that of σ . As decreased, SNWFETs became robust to ∆ but vulnerable to ∆ . Consequently, the contribution of ∆ , WFV, and ∆ is dominant at of 7 nm, 9 nm, and 12, respectively. The proposed model enables the quantifying of the contribution of various variation sources of variation, and it is applicable to all SNWFETs with various and .