Evaluation of Charged Defect Energy in Two‐Dimensional Semiconductors for Nanoelectronics: The WLZ Extrapolation Method

Abstract

Defects play a central role in controlling the electronic properties of two‐dimensional (2D) materials and realizing the industrialization of 2D electronics. However, the evaluation of charged defects in 2D materials within first‐principles calculation is very challenging and has triggered a recent development of the WLZ (Wang, Li, Zhang) extrapolation method. This method lays the foundation of the theoretical evaluation of energies of charged defects in 2D materials within the first‐principles framework. Herein, the vital role of defects for advancing 2D electronics is discussed, followed by an introduction of the fundamentals of the WLZ extrapolation method. The ionization energies (IEs) obtained by this method for defects in various 2D semiconductors are then reviewed and summarized. Finally, the unique defect physics in 2D dimensions including the dielectric environment effects, defect ionization process, and carrier transport mechanism captured with the WLZ extrapolation method are presented. As an efficient and reasonable evaluation of charged defects in 2D materials for nanoelectronics and other emerging applications, this work can be of benefit to the community.

Antisite defect qubits in monolayer transition metal dichalcogenides

“…1d . Charge-state corrections for the charged antisite systems were obtained by using an extrapolation method, see Methods 32 , 33 . Energy windows for the Fermi level in the gap where the neutral charge state is most stable are: 1.43 eV, 0.88 eV, 0.48 eV, 1.01 eV, 1.24 eV, 0.19 eV for W S 0 , W Se 0 , W Te 0 , Mo S 0 , Mo Se 0 , and Mo Te 0 , respectively (Supplementary Fig.…”

“…The ionized energy of donor/acceptor is defined as the energy difference of transition level ( + / 0 )/(0/ - ) and CBM/VBM. In a low-dimensional system, due to anisotropic screening, ionization energy (IE) diverges with respect to the vacuum, and we applied a charge-correction method 32 , 33 . We assume that the chemical potentials of M and X are in thermal equilibrium with MX 2 , i.e., , where is the energy of the perfect MX 2 system.…”

“…(1) A paramagnetic, long-lived triplet ground state with multiple in-gap defect levels. (2) An optical transition path between the ground and excited triplet states as well as a spin-selective (nonradiative) decay path between the different spin-multiplet states for qubit initialization. And, (3) distinguishable luminescence signatures for the two spin sublevels for qubit readout.…”

“…1 Spin-qubits based on solid-state defects have emerged as promising candidates because these qubits can be initialized, selectively controlled, and readout with high fidelity at ambient temperatures. 2,3 Solid-state defects, especially in 2D TMDs offer advantages of scalability and ease of device fabrication. Point defects as spin qubits have been demonstrated in traditional semiconductor systems, 4 including the nitrogen-vacancy (NV − ) center in diamond and the spin-1/2 defect in doped silicon, 3,5,6, 7,8, among other possibilities 4,[9][10][11] In particular, Si-vacancy complex in diamond, 11 vacancy defects in SiC, 12 and vacancy complexes in AlN 10 have been predicted as qubits.…”

Quantum point defects in 2D materials: The QPOD database

“…In a post process step, the spurious interactions between periodically repeated images is removed from the total energy using an electrostatic correction scheme that involves a Gaussian approximation to the localised charge distribution and a model for the dielectric function of the material [21]. While this approach is fairly straightforward and unambiguous for bulk materials, it becomes significantly more challenging for 2D materials due to the spatial confinement and non-local nature of the dielectric function and the dependence on detailed shape of the neutralising background charge [47,48,49,50].…”