Quantum transport simulation of graphene-nanoribbon field-effect transistors with defects
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S.I.: T WO-DIMENSIONAL MATERIALS
Quantum transport simulation of graphene‑nanoribbon field‑effect transistors with defects Shanmeng Chen1 · Maarten L. Van de Put1 · Massimo V. Fischetti1 Received: 25 June 2020 / Accepted: 8 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present a theoretical study of the effect of defects on the charge-transport properties of gate-all-around graphene nanoribbons field-effect transistors. Electronic transport is treated atomistically using an efficient method we have recently proposed that makes use of a Bloch-wave basis obtained from empirical pseudopotentials and solves the Schrödinger equation with open boundary conditions using the quantum transmitting boundary method. The defects considered here consist in single vacancies at different locations in the ribbon (center and edge of the ribbon; in the source or drain regions or along the channel). We have found that vacancies located at different locations along the ribbon width alter differently the Kekulé patterns: Defects at the edge reduce the Ion ∕Ioff more than defects located near the center of the ribbon, and the effect is stronger in narrow ribbons. These results show that any proposed technology based on graphene nanoribbons must be able to control the quality of the material down to a single atom. Keywords Quantum transport · Graphene nanoribbon · Defects
1 Introduction Since the isolation of graphene in 2004 [1], graphene-based field-effect transistors (FETs) have attracted a growing attention as possible candidates for post-silicon electronics for both logic and high-frequency applications [2, 3]. However, the absence of a bandgap makes graphene unsuitable for complementary-logic applications, and the patterning (or growth/deposition) of graphene into nanoribbons (GNRs) is viewed as the most promising way to circumvent this issue and open a gap. Previous theoretical studies [4, 5] have shown that GNRs with zigzag edges (zGNRs) exhibit no bandgap, whereas GNRs with arm-chair edges (aGNRs) open a bandgap induced by quantum confinement. Therefore, most studies of graphene-based transistors focused on aGNRs. As expected, the bandgap of aGNRs is very sensitive to the width of the ribbon. However, the topology of the resonant bonds in the atomic hexagons (sextets) that form the * Shanmeng Chen [email protected] 1
Department of Materials Science and Engineering, The University of Texas at Dallas, 800 W. Campbell Rd., RL 10, Richardson, TX 75080, USA
crystallographic pattern of the ribbons changes strongly and discontinuously as the width of the ribbon changes. This effect is often called ‘claromaticity’ [6] from Clar’s aromatic sextet rule [7, 8] and leads to the classification of aGNRs into three ‘families’ based on their width measured by the number N of atomic lines along the width direction. In each claromatic family the bandgap decreases with increasing ribbon width because of quantum confinement. Because of their different claromaticity, aGNRs of the 3
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