Unified bandgap engineering of graphene nanoribbons

Abstract

Unified bandgap engineering, valid both for the armchair and zigzag graphene nanoribbons (GNRs), is enunciated. Using the boundary condition appropriate for K-K 0 points of the Dirac cones, GNRs are shown to exhibit three distinct semiconducting states SC0, SC1, and SC2 with complete absence of metallic state. The experimental bandgap for 7-AGNR and 13-AGNR armchair (A) is found to be in excellent agreement with SC1 state. Similar associations are pointed out for other configurations. Both the experimental data and theoretical results show bandgap and effective mass inversely proportional to the GNR width. The effective mass is directly proportional to the bandgap. The indexing scheme connects chiral index of carbon nanotubes (CNTs) to that used for GNR by making edge corrections for the dangling bonds.

Bottom-Up Fabrication of Atomically Precise Graphene Nanoribbons

“…Interestingly, there have been different works proposing analytical relations between the effective mass and other GNR parameters. For example, Arora et al proposed the effective mass to be linearly dependent on the GNR band gap in a similar way as that claimed for carbon nanotubes: m* = (E g / 11.37) m e , with E g given in eV [83]. In turn, Raza et al related it to the aGNR width W through m* = (0.091 / W) m e for the 3p family, m* = (0.160 / W) m e for the 3p+1 family and m* = (0.005 / W) m e for the 3p-1 family (W being the distance, in nanometers, between the C atoms on either edge of the ribbon, based on a C-C bond length of 1.44 Å) [78].…”

Photoluminescence of Ultraviolet Initiated Green Emission from Electrochemically Deposited Germanium Films on (100) Silicon

“…In understanding the role of carbon-based devices, Arora and coworkers [39][40][41][42][43] discovered a curious fact that the missing bandgap in graphene perhaps can be created by quantum effects in bringing to focus the role of Dirac fermions. In particular, the conduction or valence band E g /2 = m * v 2 F is created similar to the Einstein's E = mc 2 .…”

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“…The electron transport efficiency is an important quantity which is introduced as conductance. The Landauer formula relates G (conductance) with T (probability of carrier transmission between electrodes) in graphene, 19 and h is the Planck constant: 20…”