Realistic dimension-independent approach for charged-defect calculations in semiconductors

Abstract

First-principles calculations of charged defects have become a cornerstone of research in semiconductors and insulators by providing insights into their fundamental physical properties.But current standard approach using the so-called "jellium model" has encountered both conceptual ambiguity and computational difficulty, especially for low-dimensional semiconducting materials. In this Communication, we propose a physical, straightforward, and dimension-independent universal model to calculate the formation energies of charged defects in both three-dimensional (3D) bulk and low-dimensional semiconductors. Within this model, the ionized electrons or holes are placed on the realistic host band-edge states instead of the virtual jellium state, therefore, rendering it not only naturally keeps the supercell charge neutral, but also has clear physical meaning. This realistic model reproduces the same accuracy as the traditional jellium model for most of the 3D semiconducting materials, and 2 remarkably, for the low-dimensional structures, it is able to cure the divergence caused by the artificial long-range electrostatic energy introduced in the jellium model, and hence gives meaningful formation energies of defects in charged state and transition energy levels of the corresponding defects. Our realistic method, therefore, will have significant impact for the study of defect physics in all low-dimensional systems including quantum dots, nanowires, surfaces, interfaces, and 2D materials.

Understanding Doping of Quantum Materials

“…Experience and insights gained by the semiconductor community in the past years in DFT studies of doping conventional semiconductors [172][173][174][175][176][177][178][179][180][181] can be leveraged, extended, and deepened in studying carriers in "Quantum Materials" such as delectron oxides 87,182 or the nitrogen-vacancy center in diamond [169][170][171] , once they are described by symmetry-broken DFT (Sec. 3).…”

“…It is important to note that the culture in the computational field of doping 3d oxides and generally "correlated materials" has diverged significantly from the modern doping theory [172][173][174][175][176][177][178][179][180][181] based on the principles (1)-( 6) above in that the critical dependences of the doping process on the factors discussed in subsections 4.1-4.6 below were generally not considered in the correlated literature. [183][184][185][186] 4.1 Formation energy of dopant D ∆𝐻(𝐷, 𝑞, 𝜇 𝛼 , 𝐸 𝐹 ) in a charge state q in equilibrium with a reservoir of elemental chemical potentials {𝜇 𝛼 } and the Fermi sea with parametric energy EF (Fig.…”

“…187,188 Such differences call for corrections 𝛿𝐻 corr applied to DFT to account for supercell finite-size effects and systematic DFT errors in the band gap. [172][173][174][175][176][177][178][179] Furthermore, certain doped systems such as the nitrogen-vacancy center in diamond 170,171 or transition metal impurities in insulators 165,167 manifest atomic-like states in the gap that (just like free atoms) require many-body multiplet corrections, which can be accomplished by using DFT impurity wave functions in multiplet theory.…”

Self-Consistent Potential Correction for Charged Periodic Systems

“…Actually, correction of the electrostatic potential is required and a self-consistent potential correction scheme has been proposed for cubic bulk systems [21]. Selfconsistent potential correction for low-dimensional periodic systems is difficult because of the variation in the dielectric profile at the interface, and the methods suggested so far are restricted to special cases [22][23][24].…”

“…In low-dimensional charged periodic systems another problem arises. Except for the virtual crystal approach, where the charge of the nuclei is artificially modified [25,26], and a recently published work [24], which avoids the use of a jellium by calculating an excited state, the counter charge is distributed evenly in the model. Therefore, a substantial part of the countercharge is in the vacuum region.…”