Impurity Formation Energy Research Articles

First-principles study on transition metal-doped anatase TiO2

The electronic structures, formation energies, and band edge positions of anatase TiO2 doped with transition metals have been analyzed by ab initio band calculations based on the density functional theory with the planewave ultrasoft pseudopotential method. The model structures of transition metal-doped TiO2 were constructed by using the 24-atom 2 × 1 × 1 supercell of anatase TiO2 with one Ti atom replaced by a transition metal atom. The results indicate that most transition metal doping can narrow the band gap of TiO2, lead to the improvement in the photoreactivity of TiO2, and simultaneously maintain strong redox potential. Under O-rich growth condition, the preparation of Co-, Cr-, and Ni-doped TiO2 becomes relatively easy in the experiment due to their negative impurity formation energies, which suggests that these doping systems are easy to obtain and with good stability. The theoretical calculations could provide meaningful guides to develop more active photocatalysts with visible light response.

First-principles characterization of lanthanum occupying tendency in -Fe and effect on grain boundaries

The -Fe 3[110] (112) symmetrical tilt grain boundary model is established by the coincidence site lattice theory. First-principles plane wave ultrasoft pseudopotential method based on the density functional theory is used to calculate the La occupying tendency in -Fe. The results show that La elements tend to be located at grain boundary in the -Fe since the impurity formation energy keeps lowest. On this basis, the electronic structure of La doped in -Fe grain boundary is also calculated. The results indicate that the charges in the system are redistributed to provide more electrons for the grain boundary bonding when the La occupies -Fe grain boundary. Meanwhile, Fe atoms obtain more electrons, and the La doped region combination has the ion-tendency toward strengthening the interaction between La atom and Fe atoms in the adjacent boundary region, and the Fe atom bonds in the grain boundaries and on both sides of the grain boundary also strengthen, which is the reason why the mechanical properties change from the energy point of view. Moreover, La addition also makes the atomic density of states on the grain boundary move to the left, reduce the total energy of the system, and make the grain boundary more stable.

First-prinicples study of Mn-N co-doped p-type ZnO

Based on first-principles plane-wave ultrasoft pseudopotential density functional theory method,the lattice structure, formation energy, density of states and charge density of the ZnO:(Mn,N) system are calculated and studied theoretically. Results show that Mn and N co-doped ZnO system is more suitable for doping into a p-type system, for it has a lower impurity formation energy and higher chemical stability; Mn and N in a proportion of 1:2 doping system can effectively reduce the formation energy of the system and so it is more stable; when the system forms a double acceptor level defects, the p-type characteristic of the system is more obvious, for the solubility of impurities and the number of carriers in the system are increased. In addition, it is found that more impurities can go through the Fermi level density of states in the Mn-N co-doped system, while the 2p state density of N is widened and effective mass of holes is smaller and more delocalized.Moreover,compared with the Mn-N-doped system, the density of states of Mn-2N co-doped system is more dispersed near the Fermi level, and the non-localized characteristics are distinctive, thus it is expected to be a more effective means of p-type doping.

Electronic structures of halogen-doped Cu2O based on DFT calculations

In order to construct p—n homojunction of Cu2O-based thin film solar cells that may increase its conversion efficiency, to synthesize n-type Cu2O with high conductivity is extremely crucial, and considered as a challenge in the near future. The doping effects of halogen on electronic structure of Cu2O have been investigated by density function theory calculations in the present work. Halogen dopants form donor levels below the bottom of conduction band through gaining or losing electrons, suggesting that halogen doping could make Cu2O have n-type conductivity. The lattice distortion, the impurity formation energy, the position, and the band width of donor level of Cu2O1−xHx (H = F, Cl, Br, I) increase with the halogen atomic number. Based on the calculated results, chlorine doping is an effective n-type dopant for Cu2O, owing to the lower impurity formation energy and suitable donor level.

The relationship between depth-resolved composition and strain relaxation in InAlN and InGaN films grown by molecular beam epitaxy

A study of the relationship between strain and the incorporation of group III elements in ternary InGaN and InAlN grown by molecular beam epitaxy is reported. Using X-ray Photoelectron Spectroscopy compositional depth profiles with x-ray diffraction, we are able to find a clear relationship between strain and In incorporation including tensile-strained InAlN which has, to date, not been studied. The results show that fully strained films contain homogeneous indium composition while partially relaxed films have a non-homogeneous indium composition with depth. These results can be interpreted by considering the impurity formation energies of indium in host lattices.

Influence of H, C, N and O impurities on the stability of Mg and Al from first-principles calculations

The influence of H, C, N and O impurities on the energetic and mechanical stabilities of Mg and Al were studied by first-principles total energy calculations. The occupation preference and formation energy of impurities in Mg and Al were estimated. H and C decrease the energetic stability of Mg and Al, while N and O significantly increase it. In Mg, H and O prefer to occupy the tetrahedral site, while C and N tend to occupy the octahedral site. In Al, only C prefers the octahedral site, while other elements will occupy the tetrahedral site. Electronic structures were analyzed to clarify the bonding properties and stability mechanisms of H, C, N and O in Mg and Al. The bonding characteristics around the Fermi energy level respond to the influence of impurities on the stability of Mg and Al. This work shows that all the impurities form strong bonds with the host atoms, but H and C weaken the interactions between host atoms, while N and O rarely affect these kinds of interactions. It seems that these bonding characteristics are independent of the crystal structures of matrices and the valence electron configurations of the host atoms. Elastic constants of impurity-containing systems were estimated from curves of energy against strain to evaluate the mechanical stability and elastic properties of the systems considered. All the impurity-containing systems satisfy the mechanical stability criteria. The influence of impurities on the elastic properties of Mg and Al was also studied.

As vacancies, Ga antisites, and Au impurities in zinc blende and wurtzite GaAs nanowire segments from first principles

In this paper some specific issues related to point defects in GaAs nanowires are addressed with the help of density functional theory calculations. These issues mainly arise from the growth of nanowires under conditions different from those used for thin film or bulk GaAs, such as the coexistence of zinc blende and wurtzite polytypes, the use of gold particles as catalyst, and the arsenic-limited growth regime. Hence, we carry out density functional calculations for As vacancies, Ga${}_{\mathrm{As}}$ antisites, and Au impurities in zinc blende (ZB) and wurtzite (WZ) GaAs crystals. Our results show that As vacancies can diffuse within a ZB GaAs crystal with migration barriers of $\ensuremath{\sim}$1.9 eV. Within WZ GaAs, As vacancy diffusion is found to be anisotropic, with low barriers of 1.60 up to 1.79 eV (depending on doping conditions) in the $ab$ plane, while there are higher barriers of 2.07 to 2.44 eV to diffuse along the $c$ axis. The formation energy of Au impurities is found to be generally much lower than those of arsenic vacancies or Ga${}_{\mathrm{As}}$ antisites. Thus, Au impurities will be the dominant defects formed in Au-catalyzed nanowire growth. Moreover, we find that it is energetically more favorable by 1 to 2 eV for a Au impurity to replace a lattice Ga atom than a lattice As atom in GaAs. A Au substitutional defect for a lattice Ga atom in ZB GaAs is found to create a charge transfer level in the lower half of the band gap. While our calculations locate this level at ${E}_{v}+0.22$ eV, taking into account the inaccuracy of the density functional that ought to be corrected by a downshift of ${E}_{v}$ by about 0.2 eV, results in good agreement with the experimental result of ${E}_{v}+0.4$ eV.

Effects of alloying elements on structural, electronic and mechanical properties of AlSc2 by first-principles calculations

The structural, electronic and mechanical properties of AlSc2 intermetallic compound doped with Ti, V, Cr, Y, Zr, Nb, Mo and La elements have been calculated by using first-principle calculations based on density functional theory within GGA. It is found that microalloying with different elements has significant effect on AlSc2. From the calculated impurity formation energy, only doping with rare earth elements Y and La lessens the stability of AlSc2, so we no longer consider them. Doping of these transitional metal elements decreases the lattice parameters to a different extent. The band structure suggests that the doped AlSc2 also exhibits metallic properties, and the density of states and the charge density are also analyzed. The isotropic bulk modulus B, shear modulus G, Young’s modulus E of each system are obtained using the Voigt–Reuss–Hill averaging scheme. The B/G ratio and microhardness are calculated to determine the brittle and ductile behaviors and stiffness, respectively. Three shear factors i.e. A1, A2 and A3 for hexagonal crystal and the percentage anisotropy in compression and shear, are used to estimate elastic anisotropy.

Mechanisms of Visible Light Photocatalysis in N-Doped Anatase TiO2with Oxygen Vacancies from GGA+U Calculations

We have systematically studied the photocatalytic mechanisms of nitrogen doping in anatase TiO2using first-principles calculations based on density functional theory, employing HubbardU(8.47 eV) on-site correction. The impurity formation energy, charge density, and electronic structure properties of TiO2supercells containing substitutional nitrogen, interstitial nitrogen, or oxygen vacancies were evaluated to clarify the mechanisms under visible light. According to the formation energy, a substitutional N atom is better formed than an interstitial N atom, and the formation of an oxygen vacancy in N-doped TiO2is easier than that in pure TiO2. The calculated results have shown that a significant band gap narrowing may only occur in heavy nitrogen doping. With light nitrogen doping, the photocatalysis under visible light relies on N-isolated impurity states. Oxygen vacancies existence in N-doped TiO2can improve the photocatalysis in visible light because of a band gap narrowing and n-type donor states. These findings provide a reasonable explanation of the mechanisms of visible light photocatalysis in N-doped TiO2.

First-Principles Calculations on Electronic Structures of N/V-Doped and N-V-Dodoped Anatase TiO2(101) Surfaces

The energetic and electronic properties of N/V-doped and N-V-codoped anatase TiO(2) (101) surfaces are investigated by first-principles calculations, with the aim to elucidate the relationship between the electronic structure and the photocatalytic performance of N-V-codoped TiO(2). Several substitutional and interstitial configurations for the N and/or V impurities in the bulk phase and on the surface are studied, and the relative stability of different doping configurations is compared by the impurity formation energy. Systematic calculations reveal that N and V impurities can be encapsulated by TiO(2) to form stable structures as a result of strong N-V interactions both in the bulk and the surface model. Through analyzing and comparing the electronic structures of different doping systems, the synergistic doping effects are discussed in detail. Based on these discussions, we suggest that N(O)V(Ti) codoping cannot only narrow the band gap of anatase TiO(2), but also forms impurity states, which are propitious for the separation of photoexcited electron-hole pairs. In the case of N(O)V(Ti) -codoped TiO(2) (101) surfaces, this phenomenon is especially prominent. Finally, a feasible synthesis route for N(O)V(Ti) codoping into anatase TiO(2) is proposed.

Atomic scale interfacial and compositional characteristics of the σ and γ phases of Ni-based single-crystal superalloys

High-resolution transmission electron microscopy and high-angle annular dark-field imaging were used to study differences in the interfacial and compositional characteristics between the plate-shaped σ and γ phases in a Ni-based single-crystal superalloy. An atomic structural model of the interface between the σ and γ phases that includes a step was proposed. The σ phase exhibits the following relationship with the matrix: [001]γ//[112¯]σ, (2¯20)γ//(1¯10)σ, (2¯2¯0)γ//(111)σ, [011]γ//[110]σ, (11¯1)γ//(001¯)σ. The compositional characteristics of the σ phase indicate that it is rich in high-Z elements (Z is the atomic number), especially the alloying element rhenium (Re). The impurity formation energies for the σ and γ phases doped with Re in different sublattices were investigated using the first-principles method based on the density functional theory. The bonding characteristics of the undoped and doped σ and γ phases were analyzed with the valence charge densities and the density of states. The results indicate that the alloying element Re, with a large atomic size, substitutes the W atom preferentially, owing to the nature of the bonding and the interstitial spaces in the crystal structure.

Theoretical Study of the Electronic Structures of Li-Doped ZnO

The first-principles with pseudopotentials method based on the density functional theory was applied to calculate the geometric structure, the formation energy of impurities and the electronic structure of Li-doped ZnO. In the system of Li-doped ZnO, LiZn can not result in lattice distortion. In contrast with that case, LiO and Lii result in lattice distortion after Li doping in ZnO. In Li-doped ZnO, LiO is the most unstable than the other cases. Simultaneously, Lii is more stable than LiZn according to that Lii has smaller formation energy. Furthermore, the electronic structure of Li-doped ZnO indicates that that LiZn behaves as acceptor, while Lii behaves as donor. In conclusion, in Li-doped ZnO, Lii is always in the system to compensate the acceptor. Singly doping Li in ZnO is difficult to gain p-ZnO for the self-compensation. The results are in good agreement with other calculated and experimental results.

Impurity doping into Mg2Sn: A first-principles study

We studied the formation energy and atomic structure of impurities in Mg2Sn using first-principles plane-wave total energy calculations. Twenty elements, namely H, Li, Na, K, Rb, Sc, Y, La, Cu, Ag, Au, B, Al, Ga, In, N, P, As, Sb, and Bi, were selected as the impurity species. We considered structural relaxation of the atoms within the second nearest neighbors of the impurity atom in the 48-atom supercell. The results of the formation energy calculations suggested that Sc, Y, La, P, As, Sb, and Bi are good n-type dopants whereas Li and Na are good p-type dopants. The electrical properties of Li-, Na-, and Ga-doped Mg2Sn and La-doped Mg2(Si, Sn) composites reported previously can be explained by the low formation energies of Li, Na, Ga, and La in Mg2Sn.

Effects of nitrogen concentration on N-doped anatase TiO2: Density functional theory and Hubbard U analysis

To fully comprehend the photocatalytic mechanisms of anatase TiO2−xNx of various nitrogen concentrations, this study performed first principles calculations based on density functional theory, employing Hubbard U on-site correction, to evaluate the crystal structure, impurity formation energy, and electronic structure. An effective Hubbard U of 8.47eV was adopted to correctly determine the band gap of pure anatase TiO2. The calculations show that increasing the concentration of nitrogen requires greater formation energy during the synthesis of N-doped TiO2. Under light nitrogen doping (≤6.25at.%), N isolated impurity states form above the top of valence band meanwhile the band gap does not change noticeably. Under heavy nitrogen doping (≥8.33at.%), a narrowing of the band gap and broadening of the valence band occur, which might explain the red shift at the edge of the optical absorption range observed in some experimental studies. These findings provide a reasonable explanation of recent experimental results.

Theory of nitrogen doping of carbon nanoribbons: Edge effects

Nitrogen doping of a carbon nanoribbon is profoundly affected by its one-dimensional character, symmetry, and interaction with edge states. Using state-of-the-art ab initio calculations, including hybrid exact-exchange density functional theory, we find that, for N-doped zigzag ribbons, the electronic properties are strongly dependent upon sublattice effects due to the non-equivalence of the two sublattices. For armchair ribbons, N-doping effects are different depending upon the ribbon family: for families 2 and 0, the N-induced levels are in the conduction band, while for family 1 the N levels are in the gap. In zigzag nanoribbons, nitrogen close to the edge is a deep center, while in armchair nanoribbons its behavior is close to an effective-mass-like donor with the ionization energy dependent on the value of the band gap. In chiral nanoribbons, we find strong dependence of the impurity level and formation energy upon the edge position of the dopant, while such site-specificity is not manifested in the magnitude of the magnetization.

Effect of Fe Concentration on Fe-Doped Anatase TiO2from GGA +UCalculations

To comprehend the photocatalytic mechanisms of anatase <svg style="vertical-align:-3.21404pt;width:55.6875px;" id="M1" height="14.8" version="1.1" viewBox="0 0 55.6875 14.8" width="55.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8)"> <g transform="translate(72,-60.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0">T</tspan> <tspan style="font-size: 12.50px; " x="7.5268059" y="0">i</tspan> </text> <text transform="matrix(1,0,0,-1,-60.95,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0">1</tspan> </text> <text transform="matrix(1,0,0,-1,-56.57,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0">−</tspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0">𝑥</tspan> </text> <text transform="matrix(1,0,0,-1,-45.26,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0">F</tspan> <tspan style="font-size: 12.50px; " x="6.9016562" y="0">e</tspan> </text> <text transform="matrix(1,0,0,-1,-32.81,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0">𝑥</tspan> </text> </g> </g> </svg>O<sub >2</sub> with various concentrations of Fe, this study performed first principles calculations based on density functional theory with Hubbard U on-site correction to evaluate the crystal structure, impurity formation energy, and electronic structure. We adopted the effective Hubbard U values of 8.47&#x2009;eV for Ti 3d and 6.4&#x2009;eV for Fe 3d. The calculations show that higher concentrations of Fe are easily formed in anatase TiO<sub >2</sub> due to a reduction in the formation energy. The band gap of Fe-doped TiO<sub >2</sub> decreases Fe doping level increases as a result of the overlap among the Fe 3d, Ti 3d, and O 2p states, which enhances photocatalytic activity in the visible light region. Additionally, a broadening of the valence band and Fe impurity states within the band gap might also contribute to the photocatalytic activity.

First-principles investigation of electronic structure and optical properties in N-F codoped ZnO with wurtzite structure

The electronic structures and optical properties of pure, N-doped and N-F codoped ZnO are investigated based on the density-functional theory. The calculations of the impurity formation energies and ionization energies for these systems indicate that incorporating the reactive donor F into N doped ZnO systems, not only enhances the N acceptor solubility, but also leads to a shallower N acceptor energy level in the band gap in p-type codoped ZnO. In addition, we analyze the imaginary part of the dielectric functions, and reflectivities for pure and N-F codoped ZnO. Compared with the pure ZnO, the remarkable feature in the dielectric function for N-F codoped ZnO is that there is a sharp peak in the low-energy region.

Strain-Enhanced Doping in Semiconductors: Effects of Dopant Size and Charge State

When a semiconductor host is doped by a foreign element, it is inevitable that a volume change will occur in the doped system. This volume change depends on both the size and charge state difference between the dopant and the host element. Unlike the "common expectation" that if the host is deformed to the same size as the dopant, then the formation energy of the dopant would reach a minimum, our first-principles calculations discovered that when an external hydrostatic strain is applied, the change of the impurity formation energy is monotonic: it decreases if the external hydrostatic strain is applied in the same direction as the volume change. This effect also exists when a biaxial strain is applied. A simple strain model is proposed to explain this unusual behavior, and we suggest that strain could be used to significantly improve the doping solubility in semiconductor systems.

Impurity doping inSiO2: Formation energies and defect levels from first-principles calculations

Substitutional doping properties of silicon dioxide are investigated systematically with ab initio calculations. The dopants include a range of elements from group-III, group-V, and group-VII. We find that ${\text{SiO}}_{2}$ has a relatively symmetric doping profile in terms of its ionization energies, i.e., relatively shallow acceptor levels and donor levels are both predicted, despite its wide experimental band gap of 9.65 eV. The best candidates for $p$-type and $n$-type doping are ${\text{Al}}_{\text{Si}}$ and ${\text{P}}_{\text{Si}}$ with calculated ionization energy of 0.86 eV and 0.74 eV, respectively, both being less than 10% of the total band gap. Larger doping asymmetry exists in terms of the impurity formation energy: under optimum (O-rich) growth conditions, the shallowest acceptor, ${\text{Al}}_{\text{Si}}$, and donor, ${\text{P}}_{\text{Si}}$, have formation energies of 1.75 eV and 3.05 eV, respectively. These results provide theoretical insights on how to make this previously considered absolute insulator work as a wide-gap semiconductor at elevated temperatures.

First-Principle Studies on Conductive Behaviors of P-Type ZnO Codoped by N and B

Using a first-principle method, the electronic structures and the impurity formation energy of ZnO, ZnO (N), ZnO (N+B), and ZnO (2N+B) have been calculated, based on which the feasibility to obtain p-type ZnO is discussed. According to the results, when ZnO is single doped by N, the acceptor level is deep, and the formation energy is negative, so the ideal p-type ZnO can not be obtained by this way. On the contrary, when 2N+B are codoped into ZnO, the acceptor level becomes much lower, and the formation energy is positive, so it is a better way to obtain p-type ZnO.