Work Function Modulation\nin 2D Carbon Allotropes via\nDefect Engineering for Field Emission Applications: A DFT Analysis

Two-dimensional (2D) materials from the carbon family,\nincluding\nγ-graphyne, holey graphyne, and biphenylene, are expected to\nexhibit remarkable properties such as adjustable band gaps, high surface-to-volume\nratio, rapid carrier mobility, excellent thermal conductivity, and\nstability. The electronic properties of these materials exhibit distinct\nbehavior in the presence of structural imperfections, such as vacancy\ndefects. In this work, we explore the changes in the electronic properties\nof γ-graphyne, holey graphyne, and biphenylene monolayers after\nthe introduction of periodic vacancy utilizing first-principles density\nfunctional theory. The work function of the defective structure is\nfound to depend on the hybridization of the removed carbon atom. Double-vacancy\ndefects in γ-graphyne lowered the work function from 5.39 to\n5.17 eV. Removing an sp-hybridized carbon atom in holey graphyne reduced\nthe work function from 5.56 to 5.29 eV, while removing an sp<sup>2</sup> carbon atom increased the work function to 5.72 eV, indicating a\nstrong correlation between carbon hybridization and work function.\nThe band structure of defective structures shows interesting features\nlike a flat bands. This investigation could offer valuable insights\ninto how defect engineering in 2D materials can tailor electronic\nproperties to achieve the desired characteristics, facilitating the\ndesign of field emission materials with reduced work functions.