Effects of random number and location of the nanosized metal grains on the threshold voltage variability of silicon gate
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Effects of random number and location of the nanosized metal grains on the threshold voltage variability of silicon gate‑all‑around nanowire n‑type metal‑oxide‑semiconductor field‑effect transistors Wen‑Li Sung1,2 · Yiming Li1,2,3,4 Received: 1 May 2019 / Accepted: 5 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this study, the effect of the metal grain number (MGN) and metal grain location (MGL) with a low/high work function (WK) on the variability of the threshold voltage (σVth) of silicon gate-all-around nanowire n-type metal-oxide-semiconductor field-effect transistors was examined by using an experimentally validated cuboid grain method. For the effect of the MGN, σVth induced by WK fluctuations strongly depended on the MGN for the same metal-gate area. For the effect of the MGL, metal grains with a low WK near the source (S) side are crucial for the magnitude of σVth. Therefore, for the weighted superposition of the WK with each metal grain, the number of metal grains with a low WK near the S side may alter the distribution of Vth and dominate the magnitude of σVth. Keywords Work function fluctuation · Random number · Random position · Gate-all-around · Nanowire MOSFETs · Threshold voltage · Variability · Metal grain
1 Introduction Silicon (Si) gate-all-around (GAA) nanowire (NW) metaloxide semiconductor field-effect transistors (MOSFETs) with high-κ/metal-gate technologies are considered one of the alternatives for emerging technological nodes because of their excellent electrical characteristics [1–6]. When a device is scaled down, the variability of the threshold voltage (σVth) of Si fin-type FETs (FinFETs) with a titanium nitride (TiN) metal gate induced by the work function fluctuation (WKF) can have a large impact at nodes below 10 nm [7]. Moreover, the random number and position of nanosized metal grains are crucial factors that are influenced by the WKF [8]. * Yiming Li [email protected] 1
Parallel and Scientific Computing Laboratory, National Chiao Tung University, Hsinchu 300, Taiwan
2
Institute of Communications Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
3
Department of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
4
Center for mmWave Smart Radar System and Technologies, National Chiao Tung University, Hsinchu 300, Taiwan
Therefore, exploring the effect of the metal grain number (MGN; MGN = (LG/G) × (Weff/G) [9], where LG is the gate length, G is the grain size, and Weff is the effective width of TiN metal gate) and the metal grain location (MGL) with a low/high work function (WK) on the σVth of Si GAA NW MOSFETs is necessary. Previously, the effect of the grain size of the metal gate induced by the WKF has been studied using various methods, such as an analytical model method [9–11], averaged WKF method [12], cuboid grain method [13, 14], and Voronoi method [15–17]. Among these methods, a Voronoi method can provide a more realistic distribution of metalgate gr
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