First-principles calculation of defect formation energy in chalcopyrite-type CuInSe2, CuGaSe2 and CuAlSe2

In order to quantitatively evaluate the formation energies of Cu, In/Ga/Al and Se vacancies in chalcopyrite-type CuInSe₂ (CIS), CuGaSe₂ (CGS) and CuAlSe₂ (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.     

Ab initio investigation of potential indium and gallium free chalcopyrite compounds for photovoltaic application

The amazing opto-electronic properties of pseudo-ternaries Cu(In,Ga)(S,Se)₂ compounds are, for a great deal, related to their defect chemistry, for which ab initio calculation have already provided new insights. As Indium and Gallium are rare and expensive elements, the search of an alternative may become an important issue. Ab initio calculation of energies and electronic structures of various chalcopyrite type structures replacing In by other elements has been performed exploring over 16 compounds with some 10 different elements of the periodic table. Among the different possibilities, the substitution of In by the isoelectronic couples such as (Zn, Sn) and other cationic couples having an average valency of III have been evaluated in details, as well as the influence of the anion (S or Se). The most important point defects and defect complexes have been explored. Low copper vacancy (V_Cu) and defect complexes (such as V_Cu+Zn_Cu) formation energies have been found in these new compounds: for instance the formation energy of V_Cu in Cu₂SnZnSe₄ is 0.49 eV as compared to 0.48 eV in CuInSe₂ (CIS). In addition to point defect characteristics, different electronic properties (such as band structure, bonding character) are compared to the one of CIS, which is considered as our reference structure. The method used is based on the density functional theory within the framework of pseudo-potentials and plane waves basis. The results are discussed in view of the existing data, models and calculations. Based on these properties as well as the ionic/covalent bonding character some trends are exposed.     

Defect properties of CuInSe2 and CuGaSe2

Using first-principles electronic structure theory, we have calculated defect formation energies and defect transition levels in CuInSe₂ and CuGaSe₂. We show that (i) it is easy to form Cu vacancies in CuInSe₂, and (ii) it is also relatively easy to form cation antisite defects (e.g. In_Cu) for this ternary compound. Consequently, defect pairs such as (2V_Cu+In_Cu) have a remarkably low formation enthalpy. As a result, the formation of a series of Cu-poor compounds (CPCs) such as CuIn₅Se₈ and CuIn₃Se₅, is explained as a repeat of (2V_Cu+In_Cu) pairs in CuInSe₂. The very efficient p-type self-doping ability of CuInSe₂ is explained by the easy formation of the shallow Cu vacancies. The electrically benign character of the natural defect in CuInSe₂ is explained in terms of an electronic passivation of the by . For CuGaSe₂, we find that (i) the native acceptor formation energies and transition energy levels are similar to that in CuInSe₂, but the donor formation energy is larger in CuGaSe₂. (ii) The Ga_Cu donor level in CuGaSe₂ is deeper than In_Cu donor level in CuInSe₂, therefore, Ga_Cu behaves as an electron trap in CuGaSe₂, even when it is passivated by V_Cu. We have also calculated the band alignment between the CPCs and CuInSe₂, showing that it could have significant effect on the solar cell performance.     

Vacancy defects in delafossite СuАlO<Subscript>2</Subscript>: First-principles calculations

Electronic properties and formation energies of vacancy defects in delafossite CuAlO₂ have been investigated by using the first-principles density functional theory. The band structures and density of states of various vacancy defects have been obtained and analyzed. The results show that the V _Cu systems with different charge states influence the type of conductivity. The introduced vacancy defects enhance the hybridization between O-2p and Cu-3d states, which is good for p-type conductivity. The calculated formation energies indicate that the Cu vacancy is relatively easy to form and it trends to have positive charge.     

Defect properties of CuCrO2: A density functional theory calculation

Using the first-principles methods,we study the formation energetics properties of intrinsic defects,and the charge doping properties of extrinsic defects in transparent conducting oxides CuCrO2.Intrinsic defects,some typical acceptortype,and donor-type extrinsic defects in their relevant charge state are considered.By systematically calculating the formation energies and transition energy,the results of calculation show that,V Cu,O i,and O Cu are the relevant intrinsic defects in CuCrO2 ;among these intrinsic defects,V Cu is the most efficient acceptor in CuCrO2.It is found that all the donor-type extrinsic defects have difficulty in inducing n-conductivity in CuCrO2 because of their deep transition energy level.For all the acceptor-type extrinsic defects,substituting Mg for Cr is the most prominent doping acceptor with relative shallow transition energy levels in CuCrO2.Our calculation results are expected to be a guide for preparing promising n-type and p-type materials in CuCrO2.     

Electronic structures and optical properties of rutile TiO2 with different point defects from DFT + U calculations

The electronic states and formation energies of four types of lattice point defects in rutile TiO₂ are studied using the first-principles calculations. The existence of oxygen vacancy leads to a deep donor defect level in the forbidden band, while the Ti interstitial forms two local states. It is predicted that oxygen vacancy prefers to combine with Ti-interstitial to form V_O–Ti_i dimer by a partial 3d electron transfer from the Ti_i to its neighboring V_O. The charge distribution between a Ti interstitial and its neighboring Ti ions partially shields the Coulomb interactions. Lastly, optical properties of these defective lattices are discussed.     

A new Morse-oscillator based Hamiltonian for H3+: Calculation of line strengths

In two recent publications [V. Špirko, P. Jensen, P. R. Bunker, and A. Čejchan, J. Mol. Spectrosc. 112, 183–202 (1985); P. Jensen, V. Špirko, and P. R. Bunker, J. Mol. Spectrosc. 115, 269–293 (1986)], we have described the development of Morse oscillator adapted rotation-vibration Hamiltonians for equilateral triangular X₃ and Y₂X molecules, and we have used these Hamiltonians to calculate the rotation-vibration energies for H₃⁺ and its X₃⁺ and Y₂X⁺ isotopes from ab initio potential energy functions. The present paper presents a method for calculating rotation-vibration line strengths of H₃⁺ and its isotopes using an ab initio dipole moment function [G. D. Carney and R. N. Porter, J. Chem. Phys. 60, 4251–4264 (1974)] together with the energies and wave-functions obtained by diagonalization of the Morse oscillator adapted Hamiltonians. We use this method for calculating the vibrational transition moments involving the lowest vibrational states of H₃⁺, D₃⁺, H₂D⁺, and D₂H⁺. Further, we calculate the line strengths of the low-J transitions in the rotational spectra of H₃⁺ in the vibrational ground state and in the ν₁ and ν₂ states. We hope that the calculations presented will facilitate the search for further rotation-vibration transitions of H₃⁺ and its isotopes.     

锐钛矿型TiO2(101)面本征点缺陷的理论研究

采用平面波超软赝势方法计算了锐钛矿型TiO₂(101)面存在本征空位和间隙点缺陷的几何结构以及缺陷形成能.首先分析了点缺陷对表面结构的影响,发现不同类型缺陷导致缺陷周围原子有不同的位移趋势：O空位的产生导致空位周围的Ti原子向空位外移动,Ti₁和Ti₂空位的产生均使O₁自发地与周围的O原子团聚,O_i原子易被周围的氧原子吸附而成键,而Ti_i2缺陷几乎 关键词： 第一性原理 2')" href="#">TiO₂ 点缺陷 表面结构     

Ionic conductivity and point defects in pure and doped MnF2 and MgF2 single crystals

Conductivity, σ, of MnF₂ and MgF₂ single crystals, pure and doped (with Li⁺, Na⁺, Y³⁺, Gd³⁺), has been measured, from room temperature to 500°C. Further, some crystals were contaminated with O^2? as an additional impurity. These tetragonal (rutile structure) crystals both behave like typical ionic conductors. Of particular interest is the existence of a large anisotropy, σ being largest when measured parallel to the c-axis. Study of the conductivity isotherms and anisotropy as functions of impurity concentration allows identification of the conduction mechanism in terms of the migration of two mobile defects: the fiuorine-ion vacancy, V_F, and interstitial, F_i. A value of 1.44 eV was obtained for the enthalpy of formation of the intrinsic anion Frenkel defect, 0.80 eV for the migration enthalpy of a V_F and 0.88 eV for an F₁ in MnF₂ parallel to the c-axis. Similar values were obtained for MgF₂. This work shows that more information about point defects can be obtained from conductivity measurements in non-cubic cyrstals than in cubic ionic crystals, because of the additional information from conductivity anisotropy.     

Nature of gallium deep centres in lead telluride based semiconductors

Doped with Ga lead telluride was taken as a model object to explain the nature of group-III deep levels in IV-VI semiconductors and to elucidate the vapour phase doping mechanism. For this goal, interaction of various gallium-containing molecules with defect-free crystal as well as with native defects in PbTe was considered. Formation energies for different point defects created in PbTe as a result of interaction the Ga₂Te molecules, Ga₂ dimers and single Ga atoms with a host crystal were calculated using density functional theory. Particularly Ga_Pb and Ga_i together with formation of accompanied self interstitials Pb_i in various charge states were examined. In addition we propose the new type of defects - the impurity complex (2Ga)_Pb which looks like <111>-oriented gallium dumbbell. Calculations suggest the double donor behaviour and DX-like properties of this defect together with extremely low formation energy values. Namely, (2Ga)_Pb centres are preferably formed under Ga₂Te doping while (Ga₂)_Pb+Pb_i ones are formed under Ga₂ or Ga doping. In all cases, formation energies are negative and resulting defect concentration is determined by reaction kinetics only. Mechanisms of the lead vacancy compensation with the vapour phase doping are considered as well.     

Defect-induced strong ferromagnetism in Cr-doped In2O3 from first-principles theory

We demonstrate by means of first-principles calculations that the high Curie temperature observed in Cr-doped In₂O₃ is mediated by intrinsic p-type defects, namely In vacancies or O interstitials. Charge transfer from Cr 3d states to the hole states formed by these defects makes Cr ions in the mixed valence state, giving rise to a strong ferromagnetic coupling. Calculated formation energies of various defects also show that doping Cr in In₂O₃ could greatly lower the formation energies of p-type intrinsic defects even in oxygen-deficient growth conditions. These results advance our understanding of the underlying physics of diluted magnetic oxides.     

Electronic structure of substitutional defects and vacancies in GaSe

We have investigated the nature of defect states associated with substitutional impurities (Cd, In, Sn) and both Ga and Se vacancies in GaSe using ab initio electronic structure methods within density functional theory. These calculations were done using supercell model allowing for internal atomic relaxation. Binding energies (BEs) of defects obtained in this model are compared with effective mass approximation results. Significant central cell corrections are present for most of the defects. This is consistent with charge densities associated with the defect states that show clearly their strongly localized nature. Because of the difficulties associated with LDA/GGA in giving the correct band gap in semiconductors, we have only compared the acceptor BEs with available experiments. Our theoretical results agree well with the experiment for Cd_Ga and V_Ga. The fundamental role played by the Ga dimers in the formation of defect states is discussed.     

The CuPL defect and the Cus1Cui3 complex

The Cu_PL defect is characterized by intense photoluminescence (PL) emission with a 1014 meV zero-phonon line and has since long been called the ‘copper-pair’ defect. However, recent PL studies in isotopically pure ²⁸Si samples show clear evidence for four Cu atoms in this defect. This defect is one of a family of complexes that contain four (sometimes five) metal impurities. No complex containing two or three metal impurities (at least one of which is a transition metal) has been reported. We have performed systematic calculations of a priori possible Cu₄ complexes, including the Cu_s1Cu_i3 complex proposed by Shirai et al. [18]. This complex has the lowest formation energy of all the Cu₄ defects. We have studied its properties using first-principle theory. In addition to the structures, binding energies, and vibrational spectra, we studied the formation pathway in an attempt to figure out why smaller (or larger) complexes do not form. We find that Cu_s1Cu_in with n=0, 1 or 2 continue to trap Cu_i⁺ if the Fermi level is midgap, and that the process stops when n=3. © 2011 Elsevier Science. All rights reserved     

FA(Ga+,In+,Tl+) tunable laser activity and interaction of halogen atoms (F,Cl,Br,I,At) at the (001) surface of KCl crystal: ab initio calculations

An attempt has been made to examine F_A(Ga⁺,In⁺,Tl⁺) tunable laser activity and adsorptivity of halogen atoms (F,Cl,Br,I,At) at the (0 0 1) surface of KCl crystal using an embedded cluster model, CIS and density functional theory calculations with effective core potentials. The ion clusters were embedded in a simulated Coulomb field that closely approximates the Madelung field at the host surface. The nearest neighbor ions to the defect site were then allowed to relax to equilibrium. Based on the calculated strength of electron–phonon coupling and Stokes-shifted optical transition bands, The F_A(Tl⁺) center was found to be the most laser active in agreement with the experimental observation that the optical emissions of F_A(In⁺) and F_A(Ga⁺) centers were strongly quenched. The disappearance of the anisotropy and np splitting observed in the absorption of F_A(Ga⁺,In⁺,Tl⁺) centers were monotonically increasing functions of the size of the impurity cation. The F_A(Ga⁺,In⁺,Tl⁺) defect formation energies followed the order F_A(Ga⁺)>F_A(In⁺)>F_A(Tl⁺). The Glasner–Tompkins empirical relationship between the principal optical absorption of F centers in solids and the fundamental absorption of the host crystal was generalized to include the positive ion species. As far as the adsorptivity of the halogen atoms is concerned, the F and F_A(In⁺,Tl⁺) centers were found to change the nature of adsorption from physical adsorption to chemical adsorption. The adsorption energies were monotonically increasing functions of the electronegativity of the halogen and the amount of charge transferred from the defect-free surface. The calculated adsorption energies were explainable in terms of the electron affinity, the effective nuclear charge and the electrostatic potentials at the surface. The spin pairing mechanism played the dominant role in the course of adsorbate–substrate interactions and the KCl defect-free surface can be made semiconducting by F or F_A(In⁺,Tl⁺) surface imperfections.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.     

Unstable equilibrium and radiation defects in solids

A new type of point defect in solids genetically related with Frenkel's pairs which appears when there exists the instability zone of pair vacancy (v) - interstitial atom (i). It is shown that, at large instability zones typical of ‘loose’ crystalline structures, equilibrium concentration of unstable pairs i-v may exceed the concentration of usual Frenkel's pairs. In the example of the semiconducting crystals In₂Te₃ and Ga₂Te₃ having loose structure it is experimentally demonstrated that equilibrium point defects cannot be preserved by specimen quenching and that irradiation by large doses of high-energy particles does not result in stable radiation defects formation.     

Effect of ionizing irradiation on the mechanism of current passage in TlInSe<Subscript>2</Subscript> single crystals

The temperature dependence of the electrical conductivity and current-voltage characteristics of γ-irradiated TlInSe₂ single crystals with an electrical resistivity of ∼10⁸ Ω cm have been investigated. It has been established that the anomalies of the conductivity observed in weak electric fields and at low dozes of irradiation are related to the decomposition of neutral complexes containing an interstitial cation atom. In strong electric fields, a thermal-field ionization of traps occurs. The main mechanism of radiation defect formation is the formation of complexes [V _In⁻In _i ⁺], [V _Se⁻Se _i ⁻], and others with the structural defects characteristic of unirradiated crystals. The activation energy, trap concentrations, and the potential well shape near the traps have been determined.     

Ab initio potential energy curves and vibrational levels for the C and D 1Πu states of the hydrogen molecule

Two lowest eigenvalues of the Hamiltonian for the hydrogen molecule corresponding to the ¹Π_u symmetry have been calculated in the Born-Oppenheimer approximation. They represent the C and D states, respectively. Different highly flexible wavefunctions were used for both states and the calculations were performed for a wide range of internuclear distances: 1 ≤ R ≤ 12 a.u. for the C state, and 1 ≤ R ≤ 25 a.u. for the D state. The calculated potential energy curves are more accurate than any previous ab initio results for the above states. The vibrational Schrödinger equation for both states has been solved for H₂, HD, and D₂ using the Numerov method. The resulting energies and rotational constants are compared with the experimental values.     

Spectroscopic studies of atmospheric interest on NO and NO

In recent years, high-resolution photoelectron spectroscopy and ab initio calculations have considerably revised and enlarged the understanding of the electronic structure of the NO and NO⁺ molecules. The experimental potential energy curves for the different electronic states of atmospheric interest molecules like NO and NO⁺ are constructed by using the Rydberg-Klein-Rees method as modified by Vanderslice et al. The ground state dissociation energies are determined by curve fitting technique using the five parameter Hulburt-Hirschfelder (H-H) function. The estimated dissociation energies are 6.381 and 10.693 eV for NO and NO⁺, respectively. These values are in good agreement with the literature values. The r-centroids and Franck-Condon factors (FC Factors) for the band system of B²Π_r-X²Π of NO and a³Σ⁺-X¹Σ⁺, A¹Π-X¹Σ⁺ of NO⁺ molecules have been calculated employing an approximate analytical methods of Jarmain and Fraser, and Nicholls and Jarmain. The absence of the bands in these systems is explained.     

Luminescence of CuInS2: I. The broad band emission and its dependence on the defect chemistry

The emission of CuInS₂ is studied as a function of the exact composition in terms of deviations from molecularity and stoichiometry. By means of temperature-dependent (4.2–220 K) and excitation-intensity-dependent measurements, the two broad emission bands usually present are correlated with donor-acceptor transitions. In In-rich material the acceptor is located at 0.10 eV above the valence band. This acceptor is ascribed to V_Cu. In Cu-rich CuInS₂ the acceptor level is located at 0.15 eV above the valence band, which is attributed to either V_In or Cu_In. Two donor levels are identified, their ionization energies being about 35 and 72 meV. These donors are present in both In and Cu-rich samples and may originate from either intrinsic defects or impurities (Fe). Also, the influence of quenching of the crystals as well as the effect of different crystal growth methods (melt-growth and vapour-growth) on the emission is studied.