Tailoring Graphene Work Function via Size, Functionalization, Defects, and Doping: A First‑Principles Investigation

Abstract

We employ first‑principles density functional theory to systematically design and evaluate the work function (WF) of graphene for electronic device applications. By exploring pristine, hydroxyl‑modified, defective, and doped graphene structures, we reveal that WF is strongly dependent on ribbon width, surface functionalization, defect position, and dopant type. Pristine zigzag graphene exhibits a higher WF than armchair graphene, and increasing ribbon width consistently lowers WF. Hydroxyl groups raise WF, with the effect magnified by both the number of groups and their clustering. Defects generally reduce WF, with central vacancies having the most pronounced impact. Substitutional doping with B or Al (p‑type) significantly elevates WF, while N or P (n‑type) sharply decreases it; Si doping has a modest, stable effect. We also calculate formation energies to assess dopant feasibility, showing that B and N are easily incorporated, whereas Al is challenging. These insights provide a robust theoretical foundation for tailoring graphene’s electronic properties in device engineering.

Background

Graphene’s exceptional electrical, mechanical, and chemical properties have propelled it into diverse applications—sensors, field‑effect transistors (FETs), photovoltaic electrodes, Schottky diodes, vacuum tubes, and LED junctions—often outperforming conventional materials. However, device performance hinges on the graphene work function (WF), which governs charge injection, Schottky barrier height, and overall band alignment. Typical experimental WF values range from 4.2 to 4.8 eV. Numerous strategies have been reported to tune WF, including chemical doping, surface functionalization, defect engineering, strain, electrostatic gating, and laser irradiation. Yet, comparative studies across graphene chirality, size, and defect position remain limited, and the thermodynamic feasibility of dopants is frequently overlooked. This work addresses these gaps through a comprehensive first‑principles analysis.

Methods

All calculations were performed using the CASTEP code with density functional theory (DFT). We employed the generalized gradient approximation (GGA) for exchange–correlation, chosen for its superior handling of inhomogeneous electron densities. The vacuum spacing was set to 15 Å to eliminate slab interactions, and ultrasoft pseudopotentials with a 340 eV cutoff were used. A 9×9×1 Monkhorst–Pack k‑point mesh and Methfessel–Paxton smearing (0.05 eV) ensured convergence. Work functions were obtained from the difference between the vacuum level and the Fermi energy (WF = V₀ – E_f).

Results and Discussion

Effect of Ribbon Width and Chirality on WF

We modeled zigzag and armchair graphene nanoribbons (GNRs) from 1 to 7 unit cells in width. WF decreases monotonically with increasing width for both chiralities; larger ribbons approach the bulk graphene WF (~4.48 eV). Zigzag GNRs consistently display higher WF than armchair counterparts, attributable to their distinct crystal symmetries. Band gap analyses (Table 1) confirm that larger widths reduce gaps, supporting the WF trends.

Influence of Hydroxylation, Defects, and Their Positions

Hydroxyl functionalization raises WF, with a single OH raising WF to 4.50 eV and multiple OH groups reaching 5.10 eV. Symmetric, clustered OH arrangements produce the highest WF, whereas dispersed groups lower it slightly (4.66–4.83 eV). Defects, modeled as single carbon vacancies, generally lower WF. Central vacancies yield the lowest WF (4.34 eV), whereas off‑center vacancies slightly increase WF relative to pristine GNRs (4.36 eV). These results align with previous experimental observations of defect‑induced WF reduction.

Doping Effects of B, N, Al, Si, and P

Doping concentrations were varied from 2.4 % to 14.6 % (1–6 dopant atoms in a 4×4 supercell). p‑type dopants B and Al raise WF, with B achieving 5.15 eV at 14.6 % doping. n‑type dopants N and P lower WF dramatically, reaching 3.23 eV for P at the highest concentration. Si doping shows a modest, stable WF. Formation energy calculations reveal that B and N dopants are thermodynamically favorable, while Al, Si, and P exhibit high formation energies, indicating lower incorporation likelihood.

Conclusions

Our systematic first‑principles study demonstrates that graphene WF can be finely tuned through ribbon width, hydroxyl functionalization, defect engineering, and selective doping. These findings provide clear guidelines for optimizing graphene’s electronic properties in next‑generation device architectures.