First-principles calculation of the non-equilibrium quasi-Fermi levels in defective WSe₂ p-n junctions

While the two-dimensional p-n junctions have been extensively studied for electronic and optoelectronic devices, the semiclassical approaches without considering atomistic details are still insufficient to describe its electronic structures, such as long depletion width and the role of defects. To overcome such limitations, we combine the multi-space constrained-search density functional theory (MS-DFT) formalism [1] together with the simulated doping method [2] for describing the doped p-n junction under finite-bias conditions. By calculating the lateral WSe₂ p-n junctions, we find that the charge density profile in the depletion region calculated within the first-principles approach is more diffuse than the analytical assumption, leading to a longer depletion width than the analytical expression. We then introduce Se (W) vacancy in the depletion region and show that as the forward bias voltage increases, the depletion width of the p-doped (n-doped) WSe₂ decreases faster than that of the n-doped (p-doped) WSe₂. Thanks to the MS-DFT that uniquely allows plotting quasi-Fermi level (QFL) profiles within the first-principles calculation, we also extract the QFL profiles in the defective WSe₂ p-n junction. Careful analysis of the QFL profiles shows that the asymmetrically varying depletion width in defective WSe₂ p-n junction originates from the asymmetrically penetrated QFL profiles mediated by the defect. Our findings highlight the importance of the first-principles approaches for 2D p-n junction devices in terms of the design of next-generation 2D p-n junction devices.

[1] J. Lee, H. S. Kim, and Y.-H. Kim, Adv. Sci. 7, 2001038 (2020); J. Lee, H. Yeo, Y.-H. Kim, Proc. Natl. Acad. Sci. U.S.A. 19, 10142-10148 (2020).

[2] O. Sinai and L. Kronik, Phys. Rev. B 87, 235305 (2013).