Electrostatics of lateral p-n junctions in atomically thin materials

Abstract

The lack of analytical expressions for the electrostatics of asymmetrically doped 2D lateral junctions complicates the design and analysis of devices based on atomically thin materials. In this work, we provide analytical expressions for the electric field, electrostatic potential, and depletion width across 2D lateral p-n junctions with arbitrary, but spatially uniform doping configurations. We also extend these expressions for use in lateral 3D metal-2D semiconductor junctions and lateral 2D heterojunctions. The results show a significantly larger depletion width (∼2 to 20×) for our 2D method compared to a conventional 3D approach due to the presence of a large out-of-plane electric field. For asymmetrically doped p-n junctions, the 2D depletion width shows a logarithmic dependence on the doping density of the highly doped side, in sharp contrast with conventional electrostatics for 3D junctions. Further, we show that 2D lateral depletion widths can be significantly modulated by changing the surrounding dielectric environment and, hence, can be tuned to realize optimum device structures. Finally, we show that even though the long depletion tails in 2D lateral p-n junctions carry a significant amount of total net charge, they do not significantly affect the electric field and electrostatic potential profiles, supporting the validity of the depletion approximation in analytical modeling of 2D lateral p-n junctions.