Defect Wave Function Research Articles

Symmetry Breaking and Spin-Orbit Coupling for Individual Vacancy-Induced In-Gap States in MoS2 Monolayers.

Spins confined to point defects in atomically thin semiconductors constitute well-defined atomic-scale quantum systems that are being explored as single-photon emitters and spin qubits. Here, we investigate the in-gap electronic structure of individual sulfur vacancies in molybdenum disulfide (MoS2) monolayers using resonant tunneling scanning probe spectroscopy in the Coulomb blockade regime. Spectroscopic mapping of defect wave functions reveals an interplay of local symmetry breaking by a charge-state-dependent Jahn-Teller lattice distortion that, when combined with strong (≃100 meV) spin-orbit coupling, leads to a locking of an unpaired spin-1/2 magnetic moment to the lattice at low temperature, susceptible to lattice strain. Our results provide new insights into the spin and electronic structure of vacancy-induced in-gap states toward their application as electrically and optically addressable quantum systems.

Topological insulating phase arising in transition metal dichalcogenide alloy

Transition metal dichalcogenides have been the subject of numerous studies addressing technological applications and fundamental issues. Single-layer PtSe2 is a semiconductor with a trivial bandgap, in contrast, its counterpart with of Se atoms substituted by Hg, Pt2HgSe3 (jacutingaite, a naturally occurring mineral) is a 2D topological insulator with a large bandgap. Based on ab-initio calculations, we investigate the energetic stability, and the topological transition in Pt(Hg x Se)2 as a function of alloy concentration, and the distribution of Hg atoms embedded in the PtSe2 host. Our findings reveal the dependence of the topological phase with respect to the alloy concentration and robustness with respect to the distribution of Hg. Through a combination of our ab-initio results and a defect wave function percolation model, we estimate the random alloy concentration threshold for the topological transition to be only . Our results expand the possible search for non-trivial topological phases in random alloy systems.

N2, NO, and O2 molecules in LiGaO2 in both Ga and Li sites and their relation to the vacancies

Doping of the ultrawide bandgap semiconductor LiGaO2 (Eg=5.6 eV) with N2, NO, and O2 molecules placed in either Ga or Li vacancies is studied using first-principles calculations. These molecular dopants are considered potential acceptors for p-type doping. Their optimal placement and orientation relative to the lattice is studied as well as their transition levels and energy of formation. Unfortunately, they are found to have deep acceptor level transition states. We discuss the relation of the transition levels to the one-electron levels, their spin state, and defect wave functions. They are found to be closely related to those of the corresponding vacancies.

Defect capturing and charging dynamics and their effects on magneto-transport of electrons in quantum wells

The calculated defect corrections to the polarization and dielectric functions for Bloch electrons in quantum wells are presented. These results were employed to derive the first two moment equations from the Boltzmann transport theory and then applied to explore the role played by defects on the magneto-transport of Bloch electrons. Additionally, we have derived analytically the inverse momentum-relaxation time and mobility tensor for Bloch electrons by making use of the screened defect-corrected polarization function. Based on quantum-statistical theory, we have investigated the defect capture and charging dynamics by employing a parameterized physics-based model for defects to obtain defect wave functions. Both capture and relaxation rates, as well as the density for captured Bloch electrons, were calculated self-consistently as functions of temperature, doping density and chosen defect parameters. By applying the energy-balance equation, the number of occupied energy levels and the chemical potential of defects were determined, with which the transition rate for defect capturing was obtained. By applying these results, the defect energy-relaxation, capture and escape rates, and Bloch-electron chemical potential were calculated self-consistently for a non-canonical subsystem of Bloch electrons. At the same time, the energy- and momentum-relaxation rates of Bloch electrons, as well as the current suppression factor, were also investigated quantitatively. By combining all these results, the temperature dependence of the Hall and longitudinal mobilities was presented for Bloch electrons in either single- or multi-quantum wells.

Chemical trends of cation-vacancy-induced d0 ferromagnetism in dilute zinc chalcogenides

The realization of ferromagnetism in d0 semiconductors is important for its applications in spintronics and instructive to the understanding of the magnetic behavior in dilute magnetic semiconductors (DMSs), but its origin is still not fully uncovered, due to the limitation of the density functional used in previous studies. Here, using more sophisticated hybrid functional (HSE06), we reexamine the cation-vacancy induced ferromagnetism in a series of Zn chalcogenides, ZnX (X = O, S, Se, Te), and compare it with previous theoretical studies. The HSE06 calculations show that the spontaneous magnetization of Zn vacancy (VZn) in ZnX is possible, except for ZnTe, due to the more delocalized nature of Te 5p orbitals than O 2p, S 3p and Se 4p orbitals. The ferromagnetic (FM) ground states can then be realized in these systems because the FM coupling between individual VZn could lower energy based on the band-coupling model. Moreover, the HSE06 calculations indicate that the FM coupling gradually increases from ZnO to ZnS and to ZnSe because of the enhanced coupling between the more and more extended defect wavefunctions. The result suggests that it may be more likely to achieve the room-temperature ferromagnetism in ZnS and ZnSe than ZnO, pointing out an alternative way to develop d0 DMSs. Experimental test of the theoretical predictions is called for.

Manipulating Single‐Photon Emission from Point Defects in Diamond and Silicon Carbide

AbstractPoint defects in semiconductors are emerging as an important contender platform for quantum technology (QT) applications, showing potential for quantum computing, communication, and sensing. Indeed, point defects have been employed as nuclear spins for nanoscale sensing and memory in quantum registers, localized electron spins for quantum bits, and emitters of single photons in quantum communication and cryptography. However, to utilize point defects in semiconductors as single‐photon sources for QT, control over the influence of the surrounding environment on the emission process must be first established. Recent works have revealed strong manipulation of emission energies and intensities via coupling of point defect wavefunctions to external factors such as electric fields, strain and photonic devices. This review presents the state‐of‐the‐art on manipulation, tuning, and control of single‐photon emission from point defects focusing on two leading semiconductor materials—diamond and silicon carbide.

Chemical trend of a Cu impurity in Zn chalcogenides

Cu is usually considered as an effective dopant to introduce shallow acceptors in Zn chalcogenides because it is on the left-hand side of Zn in the Periodic Table. Here, using first-principles calculations based on the hybrid functional with spin polarization, we show that contrary to the common expectation, Cu substituting Zn ($\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$) in bulk Zn chalcogenides actually generates rather deep acceptor levels in ZnO, ZnS, and ZnSe, i.e., 2.91, 1.03, and 0.53 eV above the valence-band maximum (VBM), respectively, except in ZnTe (0.13 eV). More interestingly, the absolute Cu impurity energy level does not follow the variation of the VBM, decreasing from ZnTe to ZnSe to ZnS to ZnO, instead, it is the highest in ZnO. The abnormal behavior of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ in ZnO is attributed to the fact that, due to the very low O $2p$-orbital energy, the $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ defect wave function has dominantly localized the Cu $3d$-orbital component, whereas in other Zn chalcogenides, anion $p$ states are dominant. The localized Cu $3d$ state leads to the enhanced exchange energy that elevates the acceptor level, which explains why the Cu impurity level is abnormally deep in ZnO. This finding provides insight in designing shallow acceptor levels in II--VI semiconductors.

Oxygen vacancies on SrO-terminatedSrTiO3(001)surfaces studied by scanning tunneling spectroscopy

The electronic structure of $\mathrm{SrTi}{\mathrm{O}}_{3}(001)$ surfaces was studied using scanning tunneling spectroscopy and density-functional theory. With high dynamic range measurements, an in-gap transition level was observed on SrO-terminated surfaces, at 2.7 eV above the valence band maximum. The density of centers responsible for this level was found to increase with surface segregation of oxygen vacancies and decrease with exposure to molecular oxygen. Based on these findings, the level is attributed to surface O vacancies. A level at a similar energy is predicted theoretically on SrO-terminated surfaces. For $\mathrm{Ti}{\mathrm{O}}_{2}$-terminated surfaces, no discrete in-gap state was observed, although one is predicted theoretically. This lack of signal is believed to be due to the nature of the defect wave function involved, as well as the possible influence of transport limitations in the tunneling spectroscopy measurements.

Polymorphism of indium oxide: Materials physics of orthorhombic In2O3

Indium sesquioxide is the most widely used conductive oxide for optoelectronic applications. The isolation of a novel orthorhombic phase of In${}_{2}$O${}_{3}$ at ambient pressures opens a new avenue for tuning the materials properties. Through an explicit comparison of the stable bixbyite and metastable orthorhombic phases of In${}_{2}$O${}_{3}$, using a hybrid density functional theory approach, we assess the impact of the loss of inversion symmetry and the distortion of the oxide sublattice on the electronic and defect structure. The band structure of the orthorhombic phase retains the key features of a transparent conductive oxide, with a large separation between the fundamental and optical band gaps. The dominant point defect---the oxygen vacancy---shows similar behavior in both phases with the coexistence of a localized defect wave function in the neutral state and a resonant transition level to the positively charged state. The natural valence band alignment between the cubic and orthorhombic phases is estimated to be 0.22 eV.

Bowing of the defect formation energy in semiconductor alloys

Using the first-principles method and special quasirandom structure approach, we have studied the formation energies of two prototype defects in alloys, Ge${}_{\mathrm{As}}$ in Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As and Cu${}_{\mathrm{Cd}}$ in CdS${}_{x}$Te${}_{1\ensuremath{-}x}$. We find that giant bowing effects for the defect formation energy can exist in semiconductor alloys. The bowing effect originates from the concentrated distribution of defects at low energy sites caused by the defect wave-function localization and the size-mismatch-induced strain effect. Because the bowing effect can drastically reduce the defect formation energy---even in dilute semiconductor alloys---it can have wide applications, such as alloy-enhanced defect solubility in semiconductors.

Electron spin resonance signature of the oxygen vacancy in HfO2

The oxygen vacancy has been inferred to be the critical defect in HfO2, responsible for charge trapping, gate threshold voltage instability, and Fermi level pinning for high work function gates, but it has never been conclusively identified. Here, the electron spin resonance g tensor parameters of the oxygen vacancy are calculated, using methods that do not over-estimate the delocalization of the defect wave function, to be gxx = 1.918, gyy = 1.926, gzz = 1.944, and are consistent with an observed spectrum. The defect undergoes a symmetry lowering polaron distortion to be localized mainly on a single adjacent Hf ion.

Two-nucleon spectral function of the16O nucleus using the lowest-order constrained variational state-dependent correlation functions of the Reid and Av18interactions

In this work, the two-nucleon spectral functions (TNSFs) are defined in terms of the state- and the density-dependent correlation functions in the framework of the lowest-order constrained variational (LOCV) method to calculate the TNSF of the ${}^{16}\text{O}$ nucleus in the ${}^{16}\text{O}$$(e,{e}^{\ensuremath{'}}NN)$${}^{14}\text{C}$ reaction. The Reid soft-core (Reid68) and the ${\text{Av}}_{18}$ potentials are used as the internucleon interactions. Since, the short-range correlation effects are imposed on the wave functions for the individual channels (e.g., the ${}^{1}{S}_{0}$ and ${}^{3}{P}_{J}$ channels); therefore, the defect wave functions are obtained for various channels such that the high relative momenta ($p>4\phantom{\rule{0.28em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$) are ignored. The resulting TNSFs for the ${}^{16}\text{O}$ nucleus are compared with those of the dressed random phase approximation (DRPA) calculations of Geurts et al. and the experimental predictions, especially those of Onderwater et al., (NIKHEF group), where reasonable agreement is found. It is shown that the optimized state-dependent defect wave functions have substantial effects on the TNSF and it is not justified to use the simplified parametrized two-body correlation functions in all of the channels. In agreement with the experimental data of Onderwater et al., the knockout of a ${}^{1}{S}_{0}$ pair proton dominates the above reaction cross section. Finally, it is demonstrated that the ${0}^{+}$ and ${2}^{+}$ peaks, which are expected to be observed in the above reaction cross section, are moved to the lower momenta of out-going protons when the state-dependent correlation functions are imposed.

Understanding and correcting the spurious interactions in charged supercells

The supercell technique is widely spread for the simulation of charged point defects. Charged defects in a supercell are unfortunately subjected to spurious image interactions, which are usually handled by introducing two correcting terms: a Madelung-type correction that accounts for the electrostatic interactions of repeated charges in a compensating background and a potential alignment term that refers the charged supercell to the electron reservoir. We demonstrate that the Madelung correction already brings a large potential shift that slowly converges as $1/L$ with increasing supercell sizes. We hence define a potential alignment devoid of any double counting. We finally propose a simple evaluation for the nearest-neighbor interaction that removes the remaining spurious hybridization of the defect wave functions between images. The application of these three corrections together drastically speeds up the convergence with respect to supercell size for all defects that are not too shallow.

Evaluating the C, N, and F Pairwise Codoping Effect on the Enhanced Photoactivity of ZnWO4: The Charge Compensation Mechanism in Donor–Acceptor Pairs

We perform first-principles density function theory calculations to study the geometric and electronic structures and photoactivity of C, N, and F monodoped and pairwise codoped ZnWO4. By incorporating single C, N, or F into ZnWO4, considering substitutional as well as interstitial locations of dopants in the ZnWO4 lattice, we find that the photon transition energy decreases to varying degrees, while the partially occupied states induced by the impurity are located in the gap, which may act as recombination centers and reduce the photoinduced current density. By analyzing the defect wave function character, we propose several pairwise codoped ZnWO4 systems, such as Cs+2Fs-, Ns+Fs-, Ci+2Ns-, and Ni+Fs-codoped ZnWO4, to passivate the partially occupied states in the monodoping systems by the charge compensation effect in the donor–acceptor pairs, resulting in occupied states in the gap and reducing the formation energy compared with the monodoping systems. The Cs+2Fs and Ns+Fs codoping do not narrow the host band gap of ZnWO4, while they decrease the excitation energy from the occupied gap states to the conduction band minimum to some extent. The Ci+2Ns and Ni+Fs codoping in the ZnWO4 can red shift the transition energy of photoexcited electrons from the impurity levels to the conduction band minimum to the ideal visible-light region; therefore, the Ci+2Ns codoping can decrease the host band gap of ZnWO4 by about 0.3 eV. Our results show that the partially occupied states in the monodoping ZnWO4 can be passivated by the charge compensation effect in the donor–acceptor pairs, thus improving the photoactivity and reaching the visible-light photoactivity for ZnWO4.

Defect-Induced Magnetism in Neutron Irradiated 6H-SiC Single Crystals

Defect-induced magnetism is firstly observed in neutron irradiated SiC single crystals. We demonstrated that the intentionally created defects dominated by divacancies (V(Si)V(C)) are responsible for the observed magnetism. First-principles calculations revealed that defect states favor the formation of local moments and the extended tails of defect wave functions make long-range spin couplings possible. Our results confirm the existence of defect-induced magnetism, implying the possibility of tuning the magnetism of wide band-gap semiconductors by defect engineering.

Quantum confinement, core level shifts, and dopant segregation in P-dopedSi⟨110⟩nanowires

We examine P-doped $\text{Si}⟨110⟩$ nanowires by employing a real-space pseudopotential method. We find the defect wave function becomes more localized along the nanowire axis and the donor ionization energy increases, owing to quantum confinement. It is more difficult to dope a P atom into a $\text{Si}⟨110⟩$ nanowire than to dope Si bulk because the formation energy increases with decreasing size. By comparing the formation energy for different P positions within a nanowire, we find that if a P atom at the nanowire surface can overcome the energy barrier close to the surface, there is a tendency for the dopant to reside within the nanowire core. We calculate P core levels shift as P changes position within the nanowire and provide a means for x-ray photoelectron spectroscopy experiments to determine the location of P atoms within a Si nanowire.

Accurate defect levels obtained from the HSE06 range-separated hybrid functional

Defect levels are a problem for standard implementations of density-functional theory and the error also influences the energetics. We demonstrate that the HSE06 functional, which describes the electronic structure of all group-IV semiconductors well (including Ge), gives highly accurate charge transition levels, too, if the defect wave function is host related---independent of localization. The degree of fulfilling the generalized Koopmans' theorem shows the reliability of the results and the highest-occupied eigenvalue always seems to give the correct vertical ionization energy.

Defect Energy Levels in Density Functional Calculations: Alignment and Band Gap Problem

For materials of varying band gap, we compare energy levels of atomically localized defects calculated within a semilocal and a hybrid density-functional scheme. Since the latter scheme partially relieves the band gap problem, our study describes how calculated defect levels shift when the band gap approaches the experimental value. When suitably aligned, defect levels obtained from total-energy differences correspond closely, showing average shifts of at most 0.2 eV irrespective of band gap. Systematic deviations from ideal alignment increase with the extent of the defect wave function. A guideline for comparing calculated and experimental defect levels is provided.

Defect-Induced Intrinsic Magnetism in Wide-Gap III Nitrides

Cation-vacancy induced intrinsic magnetism in GaN and BN is investigated by employing density-functional theory based electronic structure methods. The strong localization of defect states favors spontaneous spin polarization and local moment formation. A neutral cation vacancy in GaN or BN leads to the formation of a net moment of 3 muB with a spin-polarization energy of about 0.5 eV at the low density limit. The extended tails of defect wave functions, on the other hand, mediate surprisingly long-range magnetic interactions between the defect-induced moments. This duality of defect states suggests the existence of defect-induced or mediated collective magnetism in these otherwise nonmagnetic sp systems.

Jahn–Teller Distortion of the Zinc Vacancy in ZnGeP2

A symmetry analysis and a simple dangling bond model are presented for the VZn− in ZnGeP2, identifying a possible Jahn–Teller distortion mechanism which could naturally explain the localization of the defect wavefunction on two of the nearest-neighbouring P atoms, as deduced for the electron nuclear double resonance experiments.