Density-functional Supercell Calculations Research Articles

Enhancement of the magnetic anisotropy in single semiconductor nanowires via surface doping and adatom deposition

The magnetic anisotropy of single semiconductor (ZnO and GaN) nanowires incorporating both a transition metal (Co and Mn, respectively) as a substitutional surface dopant and a heavy metal (Au, Bi, or Pt) adatom is studied by performing density-functional supercell calculations with the Hubbard U correction. It is found that a substantial enhancement in the magnetic anisotropy energy is obtained through the deposition of Bi; the deposition of Au and Pt leads to significant variation in other magnetic properties, but not in the magnetic anisotropy energy. An analysis within a band description shows that the coexistence of Bi adatom and a surface dopant with large spin moment activates a mechanism involving reorientation and readjustment of the spin moments of electrons in occupied bands in response to the change of magnetization direction, which promotes giant magnetic anisotropy. Our results for adsorption energetics indicate that the accommodation of Bi in the neighborhood of the surface dopant is more likely in GaN nanowires, because the Bi adatom does (not) tend to be closer to the Mn (Co) dopant on the surface of GaN (ZnO) nanowire. The stability of GaN nanowire with giant magnetic anisotropy owing to the incorporation of both Mn and Bi is demonstrated by performing ab initio molecular dynamics simulations at temperatures considerably higher than room temperature. These results suggest that adatom deposition and surface doping can be used complementarily to develop single nanowire-based spintronic devices.

Easy-plane magnetic anisotropy of a single dopant in a single semiconductor nanowire

The magnetic anisotropy of an isolated substitutional Co impurity in a single ZnO nanowire is studied by performing density-functional supercell calculations with the Hubbard U correction. The variation of the magnetic anisotropy energy with the location of the Co atom in different regions of the nanowire is explored. Contrary to usual expectation, it is found that single Co-doped ZnO nanowire possess an easy plane (as opposed to easy axis) of magnetization, which is neither parallel nor perpendicular to the nanowire axis; the orientation of the easy plane is determined by the local geometry around the dopant. Our results also show that the magnetic anisotropy energy is enhanced by almost an order of magnitude when the Co impurity moves to a surface site from an interior site. This enhancement is elucidated on the basis of local bonding characteristics, because a pronounced variation of the orbital moment of Co with the magnetization direction is observed only when Co is located at the nanowire surface. The complementary analysis of these findings shows that the magnetic anisotropy of a single dopant in a single nonmagnetic semiconductor nanowire can be directionally manipulated and substantially enhanced by controlling the local chemical environment of the dopant in the absence of magnetic coupling. Our findings thus imply that the directional control of magnetic anisotropy needs to be achieved for applications of magnetic ion doped semiconductor nanowires.

Schottky barrier heights of defect-free metal/ZnO, CdO, MgO, and SrO interfaces

The Schottky barrier heights (SBHs) of defect-free interfaces of ZnO, CdO, MgO, and SrO with various metals and different terminations are investigated by density functional supercell calculations. The oxide bands are corrected for their density functional bandgap error by applying a U-type term to their metal-d and O-p states where necessary. The p-type SBHs are found to decrease linearly with increasing metal work function. The pinning factor S of the non-polar and polar interfaces is similar for each oxide. S is found to be 0.26, 0.56, 0.74, and 0.96 for CdO, ZnO, MgO, and SrO, respectively, with S increasing with increasing oxide ionicity. The calculated pinning factors are generally consistent with the metal-induced gap state model in terms of variation in ionicity and dielectric constant. A significant shift of SBHs from the non-polar to the polar interfaces of 0.4, 1, and 0.5 eV for ZnO, MgO, and SrO, respectively, is found, which can be explained by an interfacial dipole. Our results are also useful to describe Co,Fe|MgO interfaces in magnetic tunnel junctions.

Tuning the high-κ oxide (HfO2, ZrO2)/4H-SiC interface properties with a SiO2 interlayer for power device applications

SiC based power devices are promising for the next generation energy-efficient power converters. But its device performance is always largely limited by the tradition thermal SiO2 gate dielectric. The high-κ dielectric gate oxides have been widely used in Si and III-V devices. However, high quality dielectric layer using high-κ oxide for SiC power device is still lacking sufficient theoretical investigation. In this paper, the properties of XO2/4H-SiC (X = Hf or Zr) interfaces with a SiO2 interlayer are systematically studied by density-functional supercell calculations. Reliable interface atomic structures without any gap states have been built according to the electron counting rule. Based on the models, the electronic structure of each interface is obtained by hybrid functional. The interfacial characteristics including the averaged potential and charge transfer analysis are calculated in detail. The calculated band edge line-ups are comparable with the experimental reports. In term of the band alignment, HfO2 and ZrO2 directly bonding to SiC are not suitable dielectric materials for SiC based power device, due to the relatively smaller conduction band offsets (CBO). While introducing the SiO2 interlayer can effectively tune the interface properties, especially the band alignment. With HfO2(ZrO2)/SiO2 stack as the dielectric layer for 4H-SiC, the interface has the large CBO (>1 eV) to efficaciously confine the channel carriers, indicating that the HfO2(ZrO2)/SiO2/4H-SiC stack is the promising strategy for SiC based power device applications.

Phase dependence of Schottky barrier heights for Ge–Sb–Te and related phase-change materials

The large difference of dielectric functions between the amorphous and crystalline phases of Ge–Sb–Te based phase-change materials (PCMs) used in memory storage devices also affects their Schottky barrier heights (SBHs) and thus their electrical device properties. Here, the SBHs of each phase of Ge2Sb2Te5, GeTe, GeSe, and SnTe are found by density functional supercell calculations. The Fermi level pinning factor S calculated for the crystalline phases (with a larger dielectric constant) is smaller than their amorphous phases, agreeing well with the empirical relationship linking SBH to a dielectric constant. The relatively large dielectric constant of crystalline PCMs arises from their resonant bonding (metavalent bonding), but their pinning factor is not always as small as empirically expected. The results are useful for optimizing the design of metal contacts for Ge–Sb–Te type phase-change memory devices.

Density Functional Theory Studies of the Metal–Insulator Transition in Vanadium Dioxide Alloys

Vanadium dioxide (VO2) is of great interest because it has a metal–insulator transition involving a change in structure and electronic structure. For certain applications, it is useful to vary the bandgap and the transition temperature. Although strain can be used, another method is to alloy VO2 with oxides such as GeO2 or MgO. Herein, density functional supercell calculations are carried out on these alloys. The bandgap of the alloys does not change because the band edges of the M1 phase consist of V 3d bands, where V is sixfold bonded. However, there is also a fivefold VO2/MgO structure with a much larger bandgap of up to 2.1 eV. For Ge alloying, the structure reverts to the rutile phase but with a bandgap, because GeO2 has a rutile phase. It is also found that hydrogen doping varies the oxide gap between 0 to 1 eV. The result is consistent with experimental observations and it gives an important view to explain the mechanism of alloying.

Spin relaxation in fluorinated single and bilayer graphene

We present a joint experiment-theory study on the role of fluorine adatoms in spin and momentum scattering of charge carriers in dilute fluorinated graphene and bilayer graphene. The experimental spin-flip and momentum scattering rates and their dependence on the density of fluorine and carrier doping are obtained through weak localization and conductivity measurements, respectively, and suggest the role of fluorine as resonant magnetic impurities. For the estimated fluorine concentration of a few 100 ppm, the observed spin lifetimes are in the range of 1-10\,ps. Theoretically, we established tight-binding electronic structures of fluorinated graphene and bilayer graphene by fitting to density functional supercell calculations and performed a comprehensive analysis of the spin-flip and momentum scattering rates within the same devices, aiming to develop a consistent description of both scattering channels. We find that resonant scattering in graphene is very sensitive to the precise position of the resonance level, as well as to the magnitude of the exchange coupling between itinerant carriers and localized spins. The experimental data point to the presence of weak spin-flip scatterers that, at the same time, relax the electron momentum strongly, nearly preserving the electron-hole symmetry. Such scatterers would exhibit resonance energies much closer to the neutrality point than what density functional theory predicts in the dilute limit. The inclusion of a magnetic moment on fluorine adatoms allowed us to qualitatively capture the carrier density dependence of the experimental rates but predicts a greater (weaker) spin (momentum) relaxation rate than the measurements. We discuss possible scenarios that may be responsible for the discrepancies. Our systematic study exposes the complexities involved in accurately capturing the behavior of adatoms on graphene.

Optical Properties of Vanadium in 4 H Silicon Carbide for Quantum Technology

We study the optical properties of tetravalent vanadium impurities in 4H silicon carbide (4H SiC). Emission from two crystalline sites is observed at wavelengths of 1.28 \mum and 1.33 \mum, with optical lifetimes of 163 ns and 43 ns. Group theory and ab initio density functional supercell calculations enable unequivocal site assignment and shed light on the spectral features of the defects. We conclude with a brief outlook on applications in quantum photonics.

Atomic structure and band alignment at Al2O3/GaN, Sc2O3/GaN and La2O3/GaN interfaces: A first-principles study

The atomic structures, chemical bonding and band alignment at trivalent oxides X2O3 (where X = Al, Sc and La) and GaN interface are studied based on the density functional supercell calculations. The insulating interfaces with small roughness and a clean bandgap are built based on the electron counting rule. The results prove that GaO bonds dominate the interfacial chemical bonding for all the interfaces, and the calculated oxide/GaN band alignment consistent with the experimental values. All the oxides are proved to have the type-I band alignment with GaN with hybrid functional calculation. For the Al2O3 interface, the calculated valence band offset is 1.17 eV, while that for the Sc2O3 and La2O3 interface are 0.81 eV and 0.95 eV, respectively. The calculated conduction band offsets are all larger than 1 eV, and as large as 1.8 eV for the Al2O3 interface. The theoretically calculated band alignments indicate that the studied trivalent oxides Al2O3, Sc2O3 and La2O3 are all suitable gate insulators for GaN-based MOSFET applications.

Modeling of surface gap state passivation and Fermi level de-pinning in solar cells

The behavior of gap states due to coordination defects (e.g., dangling bonds) and metal induced gap states (MIGS) is compared using density functional supercell calculations. While both types of gap states cause carrier recombination, they are passivated in different ways. Defects can be passivated by shifting their states out of the gap, whereas MIGS lie on normally coordinated atoms and their states cannot be shifted. Their “passivation” requires the insertion of an insulating layer to attenuate them sufficiently before they enter the semiconductor. We show that MIGS also cause Fermi level pinning, inhibiting the control of the work function by the contacts, and so they must also be attenuated to enable certain solar cell designs.

Chemical bonding and band alignment at X2O3/GaN (X = Al, Sc) interfaces

The chemical bonding and the band alignment at Al2O3/GaN and Sc2O3/GaN interfaces are studied using density functional supercell calculations. Using bonding models based on the electron counting rule, we have created the insulating interfaces with a small roughness and a clean bandgap. Ga-O bonds dominate the interfacial chemical bonding at both interfaces. The calculated band alignment agrees with the experimental values. For the Al2O3 interface, the calculated valence band offset is 1.17 eV using hybrid functionals, while that for the Sc2O3 interface is 0.81 eV. The conduction band offsets for both are larger than 1 eV, and is as large as ∼2 eV for the Al2O3 interface. The calculated band alignments indicate that Al2O3 and Sc2O3 are both suitable insulators for GaN-based MOSFET applications.

Surface doping of ZnO nanowires with Bi: Density-functional supercell calculations of defect energetics

Defect calculations using the density and hybrid functionals in combination with the supercell approach are employed to characterize the electrical properties of a number of ZnO nanowires of various thicknesses doped with Bi atoms occupying surface sites. The variation of the differences between the total energies of charged and neutral supercells with the supercell size is studied, which led the authors to devise an extrapolation procedure to obtain reliable defect energetics in the dilute defect limit. The calculated defect formation energies indicate that although the substitution of Bi into Zn or O sites can take place spontaneously under suitable thermodynamic conditions, the substitution into Zn sites is generally more likely. The defect (charge-state) transition energies are computed and parameterized as a function of the nanowire thickness. It is revealed that the substitution of Bi into O (Zn) sites on the surface of ZnO nanowires yields deep acceptor (shallow donor) levels (except for extremely thin nanowires). It is therefore concluded that the incorporation of Bi into the surface of ZnO nanowires results in $n$-type doping.

Oxygen vacancies and hydrogen in amorphous In-Ga-Zn-O and ZnO

Hydrogen is known to be present as an impurity in amorphous oxide semiconductors at the 0.1% level. The behavior of hydrogen and oxygen vacancies in amorphous In-Ga-Zn-O is studied using density functional supercell calculations. We show that the hydrogens pair up at oxygen vacancies in the amorphous network, where they form metal-H-metal bridge bonds. These bonds are shown to create filled defect gap states lying just above the valence band edge, infrared modes at about 1400 and $1520\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, and they are shown to give a consistent mechanism to explain the negative bias illumination stress instability found in oxide semiconductors such as In-Ga-Zn-O (IGZO).

Double negatively charged carbon vacancy at the h- and k-sites in 4H-SiC: Combined Laplace-DLTS and DFT study

We present results from combined Laplace-Deep Level Transient Spectroscopy (Laplace-DLTS) and density functional theory studies of the carbon vacancy (VC) in n-type 4H-SiC. Using Laplace-DLTS, we were able to distinguish two previously unresolved sub-lattice-inequivalent emissions, causing the broad Z1/2 peak at 290 K that is commonly observed by conventional DLTS in n-type 4H-SiC. This peak has two components with activation energies for electron emission of 0.58 eV and 0.65 eV. We compared these results with the acceptor levels of VC obtained by means of hybrid density functional supercell calculations. The calculations support the assignment of the Z1/2 signal to a superposition of emission peaks from double negatively charged VC defects. Taking into account the measured and calculated energy levels, the calculated relative stability of VC in hexagonal (h) and cubic (k) lattice sites, as well as the observed relative amplitude of the Laplace-DLTS peaks, we assign Z1 and Z2 to VC(h) and VC(k), respectively. We also present the preliminary results of DLTS and Laplace-DLTS measurements on deep level defects (ET1 and ET2) introduced by fast neutron irradiation and He ion implantation in 4H-SiC. The origin of ET1 and ET2 is still unclear.

Face Dependence of Schottky Barriers Heights of Silicides and Germanides on Si and Ge

Density functional supercell calculations of the Schottky barrier heights (SBH) of metal germanides and silicides on Si or Ge find that these vary with the facet, unlike those of elemental metals. In addition, silicides and germanides show a stronger dependence of their SBHs on the work function than those of elemental metals, as seen experimentally. Both effects are beyond the standard metal induced gap states model. NiSi2 is found to have a much lower SBH on n-Si(100) than on n-Si(111), as seen experimentally. It is shown how such results can be used to design lower SBH contacts for n-Ge, which are needed technologically. The SBHs of the better behaved Si/silicide interfaces can be used to benchmark the behavior of the less well behaved Ge-germanide interfaces for this purpose. The dependence of the SBH of epitaxial Pb-Si(111) on its reconstruction is also covered.

Atomistic Corrective Scheme for Supercell Density Functional Theory Calculations of Charged Defects

A new method to correct formation energies of charged defects obtained by supercell density-functional calculations is presented and applied to bulk, surface, and low-dimensional systems. The method relies on atomistic models and a polarizable force field to describe a material system and its dielectric properties. The polarizable force field is based on a minimal set of fitting parameters, it accounts for the dielectric screening arising from ions and electrons separately, and it can be easily implemented in any software for atomistic molecular dynamics simulations. This work illustrates both technical aspects and applications of the new corrective scheme. The method is tested on systems in vacuo to validate the energy scheme. It is applied to charged defects in the bulk and at the surface of realistic materials to achieve comparison with published results obtained by using available corrective schemes based on continuum electrostatics treatments. Moreover, to demonstrate its generality, the method is used to correct the formation energy obtained by DFT of a singly negatively charged S vacancy in monolayer, bilayer, trilayer and bulk MoS2.

Muonium in Sulphur: μSR's Oldest Puzzle

New level–crossing resonance data shows the muonium defect centre in solid sulphur to have axial symmetry with huge dipolar anisotropy at low cryogenic temperatures. Above 100K,the two principal values of the hyperfine tensor fall dramaticallyand pro rata, both apparently collapsingto zeroatthe melting point. Thefallis accompaniedby the onset of muon spin–lattice relaxation, visible on the microsecond timescale with low–field rates peaking around room temperature. In conjuction with old zero–field data, the low–T hyperfine parameters are determined accurately. New supercell density–functional calculations suggest their assignment to muonium at a bond–centre (BC) site in a closed–ring S8Mu BC complex. The striking decrease of time–average parameters and the appearance of fluctuations causing relaxation are attributed to a dynamic equilibrium or chemical exchange with neutral configurations having much lower hyperfine coupling, accessed by small cyclic displacements from the BC site. Time–average occupancy of this site falls with temperature and vanishes at the melting point.

Accurate prediction of defect properties in density functional supercell calculations

The theoretical description of defects and impurities in semiconductors is largely based on density functional theory (DFT) employing supercell models. The literature discussion of uncertainties that limit the predictivity of this approach has focused mostly on two issues: (1) finite-size effects, in particular for charged defects; (2) the band-gap problem in local or semi-local DFT approximations. We here describe how finite-size effects (1) in the formation energy of charged defects can be accurately corrected in a simple way, i.e. by potential alignment in conjunction with a scaling of the Madelung-like screened first order correction term. The factor involved with this scaling depends only on the dielectric constant and the shape of the supercell, and quite accurately accounts for the full third order correction according to Makov and Payne. We further discuss in some detail the background and justification for this correction method, and also address the effect of the ionic screening on the magnitude of the image charge energy. In regard to (2) the band-gap problem, we discuss the merits of non-local external potentials that are added to the DFT Hamiltonian and allow for an empirical band-gap correction without significantly increasing the computational demand over that of standard DFT calculations. In combination with LDA + U, these potentials are further instrumental for the prediction of polaronic defects with localized holes in anion-p orbitals, such as the metal-site acceptors in wide-gap oxide semiconductors.

Stability and band gaps of InGaP, BGaP, and BInGaP alloys: Density-functional supercell calculations

Energies and band gaps of (InGa)P, (BGa)P and (BInGa)P alloys, including the antisite boron substitutions, are calculated using supercells and the density-functional method. The influence of the substituent concentration and arrangement on the stability and band gaps is investigated and compared with experimental findings. Linearly corrected band-gap widths reproduce well experimental and GW data. The most stable structures of the ternary alloys are 200/211 arrangements of the substituents. The T–x phase diagram for (InGa)P provides no miscibility gap for usual growth temperatures. However, for (BGa)P alloys a large miscibility gap is obtained between about 2% and 99% boron, what confirms experimental results. In quaternary (BInGa)P, boron and indium atoms prefer the (220) but also the (110) position to each other. A 2:1 ratio is preferred for the indium to the boron content. Supercell with the most probable B1InnGa31−nP32 structure (n = 2).

Absence of superconductivity in hole-dopedBaFe2−xCrxAs2single crystals

We investigate the physical properties and electronic structure upon Cr doping in the iron arsenide layers of ${\text{BaFe}}_{2}{\text{As}}_{2}$. This form of hole doping leads to suppression of the magnetic/structural phase transition in ${\text{BaFe}}_{2\ensuremath{-}x}{\text{Cr}}_{x}{\text{As}}_{2}$ for $x>0$, but does not lead to superconductivity. For $x\ensuremath{\le}0.75$ values, temperature dependence of the resistivity, specific heat, magnetic susceptibility, Hall coefficient, and single-crystal x-ray diffraction data are presented. The resulting phase diagram is suggestive that superconductivity does not derive simply from the suppression of the structural/magnetic transitions. The materials show signatures of approaching a ferromagnetic state for $x$ as little as 0.36 by an enhanced Wilson ratio. Such results reflect renormalization due to spin fluctuations and they are supported by density-functional supercell calculations for slightly higher doping level of $x=1$. Calculations show a strong interplay between magnetic ordering and chemical ordering of Fe and Cr, with a ferromagnetic ground state.