Atomic Chemical Potentials Research Articles

Chemical trends of defect formation in Si quantum dots: The case of group-III and group-V dopants

Using first-principles methods, we have systematically calculated the defect formation energies and transition energy levels of group-III and group-V impurities doped in H passivated Si quantum dots (QDs) as functions of the QD size. The general chemical trends found in the QDs are similar to that found in bulk Si. We show that defect formation energy and transition energy level increase when the size of the QD decreases; thus, doping in small Si QDs becomes more difficult. ${\mathrm{B}}_{\mathrm{Si}}$ has the lowest acceptor transition energy level, and it is more stable near the surface than at the center of the H passivated Si QD. On the other hand, ${\mathrm{P}}_{\mathrm{Si}}$ has the smallest donor ionization energy, and it prefers to stay at the interior of the H passivated Si QD. We explained the general chemical trends and the dependence on the QD size in terms of the atomic chemical potentials and quantum confinement effects.

Band-structure anomalies of the chalcopyrite semiconductorsCuGaX2versusAgGaX2(X=Sand Se) and their alloys

We have performed systematic first-principles calculations for the structural and electronic properties of chalcopyrite semiconductors ${\mathrm{AgGaS}}_{2}$, ${\mathrm{AgGaSe}}_{2}$, ${\mathrm{CuGaS}}_{2}$, ${\mathrm{CuGaSe}}_{2}$, and their alloys. We show that, in contrast to conventional semiconductors, the band structures of these compounds exhibit several anomalous behaviors: (i) The band gaps of $\mathrm{AgGa}{X}_{2}$ are larger than the corresponding $\mathrm{CuGa}{X}_{2}$ ($X=\mathrm{S}$ and Se) compounds, despite the lattice constants of $\mathrm{AgGa}{X}_{2}$ being much larger than for $\mathrm{CuGa}{X}_{2}$. (ii) The valence band offsets between common-anion pairs $\mathrm{CuGa}{X}_{2}∕\mathrm{AgGa}{X}_{2}$ are large and negative (i.e., $\mathrm{CuGa}{X}_{2}$ has higher valence band maximum than $\mathrm{AgGa}{X}_{2}$), opposite to their II-VI analogs. (iii) The valence band offsets between ${M}^{I}{\mathrm{GaS}}_{2}∕{M}^{I}{\mathrm{GaSe}}_{2}$ (${M}^{I}=\mathrm{Cu}$, Ag) are significantly smaller than their II-VI analogs. (iv) The band gap bowing parameters for the common-anion alloys are larger than the common-cation alloys, following the same trend as the valence band offsets. Moreover, we find that the wave function localization of the conduction band minimum states at the group III site plays an important role on the band gap reduction of the chalcopyrites relative to their binary analogs. The origin of the band structure anomalies observed in this system is explained in terms of the atomic sizes and chemical potentials and the increased structural and chemical freedom of these ternary compounds.

Structure and thermodynamic stability of hydrogen interstitials in BaZrO3perovskite oxide from density functional calculations

Density functional calculations have been used to study the electronic structure, preferred sites in the lattice, formation energies and vibrational frequencies for hydrogen interstitials in different charge states in the cubic phase of perovskite-structured BaZrO3. By combining ab initio results with thermodynamic modeling, defect formation at finite temperature and pressure has been investigated. We demonstrate how the site selectivity and spatial distribution of dopant atoms in the lattice can be affected by changes in the environmental conditions (atomic chemical potentials, oxygen partial pressure and temperature) used during processing of the material. In addition, we have calculated the thermodynamic parameters of the water uptake reaction for an acceptor-doped BaZrO3 crystal in equilibrium with a humid atmosphere. The interaction energies between a protonic defect and the investigated Ga, Gd, In, Nd, Sc, and Y dopants were found to be attractive, and we show that a simple model of defect association may reproduce an experimentally observed trend in the hydration enthalpy.

First-principles study of the intrinsic defects inPbFCl

First-principles pseudopotential calculations have been performed to investigate intrinsic defects including vacancies, interstitials, antisite defects, as well as Schottky and Frenkel defects in $\mathrm{PbFCl}$ crystals. For the isolated vacancies and interstitials, their formation energies are critically dependent on the atomic chemical potentials and electron Fermi energy. The charged defects for vacancies and interstitials are stable in a wide range of Fermi level, suggesting a strong ionization tendency. The present calculations also reveal that the formation energies of Schottky defects are much lower than those of Frenkel defects. Therefore it can be concluded that the Schottky defects are dominant in $\mathrm{PbFCl}$ crystals. Furthermore, Schottky defects $({V}_{\mathrm{Pb}}+{V}_{\mathrm{F}}+{V}_{\mathrm{Cl}})$ exhibit the lowest formation energy of $2.21\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Defect transition energy levels can occur between different charged states. The anion interstitials and the cation vacancies form acceptorlike defects with transition energies of 1.05, 0.57, and $(0.47,0.9)\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${\mathrm{F}}_{i}$, ${\mathrm{Cl}}_{i}$ and ${V}_{\mathrm{Pb}}$, respectively, while ${V}_{\mathrm{F}}$, ${V}_{\mathrm{Cl}}$, and ${\mathrm{Pb}}_{i}$ have high transition energies of more than $3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. In addition, the calculated profiles of densities of states for the defective supercells show that some extra states may appear in the band gap.

First-principles calculation of defect formation energy in chalcopyrite-type CuInSe 2, CuGaSe 2 and CuAlSe 2

In order to quantitatively evaluate the formation energies of Cu, In/Ga/Al and Se vacancies in chalcopyrite-type CuInSe 2 (CIS), CuGaSe 2 (CGS) and CuAlSe 2 (CAS), first-principles pseudopotential calculations using plane-wave basis functions were performed. All calculations were performed using a supercell with 64 atoms, which was eight times greater than the number of atoms in a primitive cell with eight atoms. The formation energies of point defects were calculated as a function of the atomic chemical potentials of constituent elements. Atomic arrangements around the vacancy were optimized allowing relaxation of the first- and second-nearest-neighbor atoms of the vacancy. The obtained results were as follows: (1) the formation energy of Cu vacancy was smaller than those of the other vacancies in CIS, CGS and CAS. Under the Cu-poor condition, the formation energy of Cu vacancy in CIS was lowest among those in them; (2) the formation energy of Se vacancy in CIS was relatively lower than those in CGS and CAS; (3) the formation energy of (2V Cu+In Cu) pair in CIS was greatly dependent on the chemical potential of the constituent elements, i.e. Cu, In and Se. On the other hand, the formation energies of (2V Cu+Ga Cu) in CGS and (2V Cu+Al Cu) in CAS were not largely dependent on the chemical potential of the constituent elements. Under the Cu-poor condition, the formation energy of (2V Cu+In Cu) pair in CIS was much lower than those of (2V Cu+Ga Cu) in CGS and (2V Cu+Al Cu) in CAS.

Evaluations of Phases and Vacancy Formation Energies in KNbO3 by First-Principles Calculation

In order to clarify thermodynamic relationships of the various phases of KNbO3, enthalpies of formation for cubic (Pm3m), tetragonal (P4mm), orthorhombic (Bmm2) and rhombohedral (R3m) phases of KNbO3 were calculated using a plane-wave pseudopotential method within a density functional formalism. The KNbO3 phase with the lowest symmetry was found to have the lowest enthalpy of formation. Moreover, we quantitatively evaluated the formation energies of neutral vacancies in KNbO3 as functions of the atomic chemical potentials of the constituent elements by the use of the same procedure. Relaxation of the first- and the second-neighbor atoms around the vacancy was considered in a 40-atom supercell. The formation energy of a K vacancy was found to be the lowest under an oxidizing atmosphere and that of an O vacancy was found to be the lowest under a reducing atmosphere. The formation energy of a Nb vacancy was the highest under both oxygen-rich and -poor conditions. These results are in agreement with the empirical rule that B site defects in perovskite-type oxide do not exist. These results are discussed on the basis of the band structure of KNbO3.

Investigation of vacancy in C54 TiSi 2 using ab initio method

Investigated by ab initio plane-wave ultrasoft pseudopotential method based on generalized gradient approximation (GGA), it has been found that the formation energies of the vacancies in C54 TiSi 2 largely depend on the atomic chemical potentials of Ti and Si. In Si-rich limit, the formation energies of the Si and Ti vacancy are 2.39 eV and 2.40 eV while they are 1.53 eV and 4.07 eV in Ti-rich limit, respectively. The introduction of Si or Ti vacancy only slightly changes total density of states (DOS) and it also causes no considerable charge transfer.

Ab Initio Calculation of Vacancies and Interstitials inNiSi2

An ab initio plane-wave ultrasoft pseudopotential method based on thegeneralized gradient approximations has been utilized to investigatethe electronic structure, atomic geometry, formation energy to providea better understanding of properties of Ni disilicide. The vacancy andinterstitial formation energies largely depend on the atomic chemicalpotentials. The formation energies of vacancies VSi andVNi are in the range of 0.04–0.56 eV and 1.25–2.3 eV,respectively and the formation energies of Si and Ni interstitials are3.89–4.42 eV and 0.67–1.71 eV, respectively. The smaller Niinterstitial formation energy is in agreement with the experimentalresult that Ni interstitial atom is dominant diffusion species inNiSi2.

VACANCY FORMATION IN CoSi2 AND NiSi2 FROM AB INITIO CALCULATION

The lattice structure and electronic properties of perfect and defective CoSi 2 and NiSi 2 have been calculated using an ab initio plane-wave ultrasoft pseudopotential method based on the generalized gradient approximations (GGA). Special attention is paid to the formation energies of the vacancies, which largely depend on the atomic chemical potentials of Si and metal atom: in Si -rich limit, the formation energies of Si and Co vacancies are 2.39 eV and 0.56 eV whilst those are 1.53 eV and 2.29 eV in Co -rich limit in CoSi 2, respectively. For NiSi 2, the formation energies of Si and Ni vacancies are 0.56 eV and 1.25 eV in Si -rich limit and those are 0.04 eV and 2.3 eV in Ni -rich limit.

Enthalpy of Formation of Various Phases and Formation Energy of Point Defects in Perovskite-Type NaNbO3 by First-Principles Calculation

In order to clarify the thermodynamic relations of various phases in NaNbO3, the enthalpies of formation for the cubic (Pm3m), tetragonal (P4/mbm), orthorhombic (Ccmm, Pnmm, Pbma) and rhombohedral (R3c) phases in NaNbO3 were calculated using a plane-wave pseudopotential method. The NaNbO3 phase with a lower symmetry has a smaller enthalpy of formation. The enthalpy of formation for the rhombohedral (R3c) phase is the smallest. Moreover, in order to quantitatively evaluate the formation energies of point defects in NaNbO3, first-principles pseudopotential calculations using plane-wave basis functions were performed. Relaxation of first- and second-neighbor atoms around a vacancy was considered in a 40-atom supercell. The formation energies of point defects were calculated as a function of the atomic chemical potentials of constituent elements. The formation energy of Na vacancy was the lowest under the oxidation limit of NaNbO3 and that of O vacancy was the lowest under the reduction atmosphere. The formation energy of Nb vacancy was the highest under both oxygen-rich and -poor conditions. This result agrees with the empirical rule that the B site defect in the perovskite-type oxide does not exist.

First‐principles calculation of formation energy of neutral point defects in perovskite‐type BaTiO3

AbstractQuantitative analysis of the formation energy of neutral point defects in perovskite‐type BaTiO3 was carried out by first‐principles calculation. A 40‐atom supercell was employed and relaxation of atoms within the second‐nearest‐neighbor shell of the vacancy was taken into account. The formation energy was calculated as a function of the atomic chemical potential of the constituent atoms. The theoretical formation energy of the O vacancy in BaTiO3 shows negative values in the case of the reduction limit of BaTiO3, which is in good agreement with experimental results showing an abundance of O vacancies when annealed in reducing atmosphere and n‐type electrical conduction. On the other hand, the formation energies of the Ba vacancy and Ti vacancy in BaTiO3 even under the oxidizing condition are as large as 2.21 and 5.65 eV, respectively. This also well corresponds to the experimental fact that the Ba and Ti vacancies are not formed alone in BaTiO3. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

First-principles study of defect energetics in titanium-doped alumina

First-principles plane-wave pseudopotential calculations were performed to study electronic structures, structural relaxation, and energetics of point defects in Ti-doped ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}.$ Substitutional and interstitial Ti ions with charge compensating intrinsic defects were considered, and their formation energies were evaluated under various atomic chemical potentials. It was found that substitutional ${\mathrm{Ti}}^{4+}$ ions with charge compensating Al vacancies were most stable in the oxidized condition. In contrast, as oxygen chemical potentials decreased, the formation energy of substitutional ${\mathrm{Ti}}^{3+}$ decreased to have the smallest value in the relatively reduced conditions. However, in the intermediate range of oxygen potentials, substitutional ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ exhibited similar formation energies, indicating that these Ti defects can coexist in a particular reduction environment.

First-principles study on structures and energetics of intrinsic vacancies inSrTiO3

We have performed first-principles plane-wave pseudopotential calculations to study the electronic structures, structural optimization, and formation energies of intrinsic vacancies in bulk ${\mathrm{SrTiO}}_{3}.$ The anion and cation vacancy-induced levels appeared near the valence- and conduction-band edges in the band gap. The formation energies of isolated vacancies with different charge states were obtained, and the defect reaction energies, such as Sr partial Schottky ${(V}_{\mathrm{Sr}}^{2\ensuremath{-}}{+V}_{\mathrm{O}}^{2+}),$ Ti partial Schottky ${(V}_{\mathrm{Ti}}^{4\ensuremath{-}}{+2V}_{\mathrm{O}}^{2+}),$ and full Schottky ${(V}_{\mathrm{Sr}}^{2\ensuremath{-}}{+V}_{\mathrm{Ti}}^{4\ensuremath{-}}{+3V}_{\mathrm{O}}^{2+})$ were also evaluated. It was found that depending on the atomic chemical potentials, the relative stability of the defect species or reactions is different. The overall trend of the stable defect structures can explain the electrical conductivity of ${\mathrm{SrTiO}}_{3}$ for different chemical environments experimentally observed.

First-principle study of native point defects in β-FeSi 2

The electronic structure, atomic geometry, and formation energy of native point defects of Si or Fe in β-FeSi 2 were investigated using first principle pseudopotential calculations based on the generalized gradient approximation density function theory. The formation energies of the native point defects depend largely on the atomic chemical potentials of Fe and Si. Mulliken population analysis revealed that electron transfer occurs from Si to Fe by introducing defects of Si or Fe. The density of states calculation predicts that the crystal with Si vacancies indicates p-type and that with Fe vacancies indicates n-type, which is in good agreement with previously reported experimental results.

First principles calculations of the formation energy of Cr/Al vacancies in spinel‐type MgCr2O4 and MgAl2O4

AbstractQuantitative analysis of the formation energy of Cr vacancy in MgCr2O4 was made by first principles calculation. A 56‐atom supercell was employed and relaxation of atoms within the second‐nearest‐neighbor shell of the vacancy was taken into account. The formation energy was calculated as a function of the atomic chemical potential of Cr. Theoretical formation energy of Cr vacancy in MgCr2O4 shows negative values in the case of the oxidation limit of MgCr2O4, in good agreement with experimental results showing abundance of Cr vacancies when annealed in air. On the other hand, the formation energy of the Al vacancy in MgAl2O4 under the same condition is as large as 4.76 eV. This also corresponds well to the experimental fact that Al vacancy does not form alone in MgAl2O4 in air. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Formation energy of Cr/Al vacancies in spinelMgCr2O4andMgAl2O4by first-principles calculations

First-principles pseudopotential calculations using plane-wave basis functions have been made to quantitatively evaluate the formation energy of Cr/Al vacancies in ${\mathrm{MgCr}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}.$ Relaxation of atoms within the second nearest neighbor shell of the vacancy was taken into account in a 56-atom supercell. The formation energy was calculated as a function of the atomic chemical potential of Cr/Al. It shows negative values in the case of the oxidation limit of ${\mathrm{MgCr}}_{2}{\mathrm{O}}_{4},$ which is in good agreement with experimental results showing abundance of Cr vacancies when annealed in air. On the other hand, the formation energy of the Al vacancy in ${\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}$ under the same condition is as large as 4.76 eV. This also well corresponds to the experimental fact that ${\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}$ does not form the Al vacancy alone in air.

Self-doping of cadmium stannate in the inverse spinel structure

Using first-principles total energy calculations, we have studied self-doping in the ternary transparent conducting oxide, Cd2SnO4. Formation of the CdO and SnO2 binaries limits the inverse spinel Cd2SnO4 phase into a narrow region in the atomic chemical potential (μ) space. This suggests that μSn is not independent of μCd, so a Cd-rich growth or annealing condition also implies Sn-rich, and vice versa. We found that the widely accepted intrinsic donors such as oxygen vacancy and cadmium interstitial are not responsible for the observed conductivity in Cd2SnO4: both require too much energy to form. In addition, the oxygen vacancy is rather deep. We show instead that the Sn-on-Cd antisite defect is the most probable donor responsible for the n typeness under Cd-rich conditions.

Reconstruction and energetics of the polar (112) and(1¯1¯2¯)versus the nonpolar (220) surfaces ofCuInSe2

First-principles total-energy calculation reveals a number of (112) and $(1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}2\ifmmode\bar\else\textasciimacron\fi{})$ surface structures stable at different atomic chemical potentials. All of the stable structures are charge compensated, thus semiconducting, either by cation-on-cation antisites, cation vacancies, Se adatoms, or by Se addimers. This structural richness raises the possibility for engineering ${\mathrm{CuInSe}}_{2}/\mathrm{Cu}({\mathrm{In}}_{1\ensuremath{-}x}{\mathrm{Ga}}_{x}){\mathrm{Se}}_{2}$ material properties by surface control during the growth. The experimentally observed puzzling spontaneous decomposition of the (220)/(204) surfaces into (112) and $(1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}2\ifmmode\bar\else\textasciimacron\fi{})$ is also confirmed by calculating individual surface energies.

Nitrogen solubility and N-induced defect complexes in epitaxial GaAs : N

Previous calculations suggested low-equilibrium N solubility in bulk GaAs. In epitaxial growth, however, N solubility can be significantly enhanced to as much as a few %. First-principles total-energy calculations show that this large difference is due to the lack of low-energy nucleation sites of GaN during epitaxy. As a result, the atomic chemical potential of N can be significantly larger. This gives rise to new defect physics distinctly different from those in GaAs.

Chemical Potential Equalization Principle: Direct Approach from Density Functional Theory

In the framework of the density functional theory (DFT) we develop an approximation in which the energy of a molecule is expressed as a functional of perturbations of the atomic electron densities. The result depends on atomic densities, atomic chemical potentials, and hardness kernels that can be found from the solutions of the appropriate atomic DFT problem. A generalized formulation of the chemical potential (electronegativity) equalization principle is suggested. We show how the energy functional can be transformed into a function of the net charges on atoms and discuss the relationship between our approach and the earlier introduced chemical potential (electronegativity) equalization schemes. We present examples where by approximating density perturbations with the squares of Slater orbitals, we obtain values for the net charges that are in reasonable agreement with experiment. This approach can be used for predictions of the transferred charges in the molecules of any size, and its accuracy can be continuously improved by the use of more accurate approximations to the density perturbations.