Defect modes due to substitutional impurities in FCC lattice: Green's function approach

Lattice dynamical study of monoatomic fcc crystals containing substitutional impurities has been made by the Green's function technique, using group theory. The impurity and its 12 nearest neighbors constitute an XY₁₂ impurity space having O_h symmetry. The phonon Green function matrix is analyzed according to the irreducible representations of the point group pertaining to the substitutional impurity in the fcc lattice. The effects due to change in mass at the impurity site and the change in nearest neighbor force constants for the impurity-host atom interactions are taken into account. Analytical expressions for the various modes of vibrations pertaining to the defect space have been obtained. Local mode frequencies due to various substitutional impurities, corresponding to F_1u mode (defect atom moving) have been computed. A special model is chosen for the defecthost force and it is assumed that there are no distortions of the lattice structure due to the defect. A Kihara hardcore potential with parameters fitted to neutron data has been used to compute lattice dynamics and Green functions of the host lattices. Our theoretical results have been compared with available experimental and theoretical results. Our results show reasonably good agreement with experimental results.     

Si related defects in GaAs

High-resolution localized vibrational mode (LVM) spectroscopy of light impurities proved to be a powerful tool providing identification of the impurity, information on its lattice location and estimate of its concentration. Spitzer et al.(¹) and Newman et al.(²) studied for years especially Si in GaAs, not only for its technological importance, but also for its amphoteric behaviour. In theirs as well as in the other authors' studies the problem remains how to determine the concentrations of Si-related defects from the intensities of different LVM peaks.     

Electronic theory for impurity segregation at lattice defects in metals

A tight-binding type electronic theory is used to study the impurity segregation at lattice defects in metals. It is shown that the heat of segregation E_segr results from a simple physical origin: It is roughly proportional to the difference in the diagonal matrix elements (V_i-V₀) of impurity potentials, where V_i (V₀) is determined for atomic sites in the vicinity of lattice defects (for a perfect lattice site). Applications to impurity segregation at cleaved surfaces, screw dislocations and tilt grain boundaries are discussed.     

Effect of charged impurity correlations on transport in monolayer and bilayer graphene

We study both monolayer and bilayer graphene transport properties taking into account the presence of correlations in the spatial distribution of charged impurities. In particular we find that the experimentally observed sublinear scaling of the graphene conductivity can be naturally explained as arising from impurity correlation effects in the Coulomb disorder, with no need to assume the presence of short-range scattering centers in addition to charged impurities. We find that also in bilayer graphene, correlations among impurities induce a crossover of the scaling of the conductivity at higher carrier densities. We show that in the presence of correlation among charged impurities the conductivity depends nonlinearly on the impurity density n_i and can increase with n_i.     

Lattice dynamics of impurity clusters. Application to pairs

A general solution is obtained for the lattice dynamics of a cluster ofn-impurity atoms using the double-time Green’s function formalism. The cluster is characterized byn-mass defect andm-force constant change parameters. It is shown that this general solution for the Green’s function for then-impurity cluster can also be expressed in terms of the Green’s function for the (n−1)-impurity cluster. As an application, the cluster impurity modes for a pair are calculated using the Debye model for the host lattice dynamics. The splitting of the high frequency local modes and nearly zero frequency resonant modes due to pairs show an oscillatory behaviour on varying the distance of separation between the two impurity atoms. These oscillations are most prominent for two similar impurities and get damped for two dissimilar impurities or if one of the impurities produces a force constant change. The predictions of the calculation provide qualitative explanation of the data obtained from the infrared measurements of the resonant modes in mixed crystal system of KBr_1−c Cl _c : Li⁺ and KBr_1−c I _c : Li⁺.     

Role of defects on the electronic and magnetic properties of CrAs, CrSe and CrSb zinc-blende compounds

We present an extended study of single impurity atoms and atomic swaps in half-metallic CrAs, CrSb and CrSe zinc-blende compounds. Although the perfect alloys present a rather large gap in the minority-spin band, all defects under study, with the exception of void impurities at Cr and sp sites and Cr impurities at sp sites (as long as no swap occurs), induce new states within the gap. The Fermi level can be pinned within these new minority states depending on the lattice constant used for the calculations and the electronegativity of the sp atoms. Although these impurity states are localized in space around the impurity atoms and very fast we regain the bulk behavior, their interaction can lead to wide bands within the gap and thus loss of the half-metallic character.     

Effects of transition-metal substitution in the iron-based superconductor LaFeAsO: Momentum- and real-space analysis from first principles

We study how transition-metal substitution changes the electronic structure of the iron-based superconductor LaFeAsO in real and momentum space. We first perform ab initio density functional calculation for various sizes of supercells with one transition-metal impurity. For various substitutes (Mn, Co, Ni, Zn, and Ru), we derive effective tight-binding models by constructing the maximally localized Wannier functions from the d bands around the Fermi level. The local electronic structure around the impurity site is quantitatively characterized by their onsite potential and transfer hoppings to neighboring sites. We find that the impurities are classified into three groups according to the derived parameters. For Mn, Co, and Ni, their impurity 3d levels measured from the Fe 3d level are ～0.3, ?0.3, and ?0.8 eV, respectively, while, for the Zn case, its d level is extremely deep as ～8 eV. For the Ru case, although the onsite-level difference is much smaller (～O(0.1) eV), the transfer integrals around the impurity ion are larger than those of the pure system by 20% ～ 30%, due to the large spatial spread of the Ru 4d orbitals. We also show that the charge distribution of the extra d electrons is confined around the impurity ion. We then unfold the first Brillouin zone (BZ) for the supercell to calculate the spectral function in the BZ for the normal cell for the case of Co and Ni doping. While the charge distribution seems to suggest that Co and Ni impurities do not change the amount of mobile carriers in the system, the momentum-space analysis clearly shows that the Fermi-surface volume indeed expands by Co and Ni substitutions, which can be well described by the rigid-band shift approximation.     

Local environment and oxidation state of a Mn impurity in SrTiO3 determined from XAFS data

The local environment and oxidation state of a Mn impurity in strontium titanate doped with 3% Mn were studied by X-ray absorption fine structure spectroscopy. The effect of the synthesis conditions on the incorporation of the impurity into A and B sites was studied. It was established that Mn ions substituting for Ti are in the Mn⁴⁺ oxidation state and are on-center. Mn ions substituting for Sr are in the Mn²⁺ oxidation state and off-center, and are displaced from the lattice site by 0.32 Å absorption near the edge structure can be used to determine the ratio of Mn atoms incorporated into A and B sites in the lattice.     

Percolation mechanism of the diffusion of impurity atoms in dense surface layers

The molecular dynamics method is used to study the migration of an impurity atom on an unfilled square lattice. The calculations are performed on a lattice containing 2¹² × 2¹⁴ sites at various values of the ratio p of the frequencies of jumps impurity and lattice atoms and various relative concentrations of vacancies ? _V . In the limit of vanishingly small concentrations of vacancies, ? _V ? 1, the present simulation results are in agreement with our previous analytical results. With increasing ? _V , the diffusion coefficient of impurity atoms predicted by the simulations exceeds the result of the analytical theory, a behavior that can be explained by the growing influence of vacancy clusters, voids on the surface, in which the impurity atom can travel long distances. This is most clearly seen in the case of highly mobile impurity atoms (p ? 1), where within the characteristic time of displacement of impurity atoms, lattice atoms remain practically immobile, and the problem appears to be closely related to the percolation problem. In this case, up to ? _V ≈ 0.3, the diffusion coefficient is independent of p; then, such a dependence appears, and the diffusion coefficient increases sharply with ? _V .     

Über den Einbau von Fremdstoffen in Kristalle

Firstly, the site distribution of impurity phase, the grade of its dispersion and its chemism are mentioned, further, the various types of site distribution of impurities, first of all in the case of the isomorphism, are discussed in detail. The attention is paid to the anomalous site distribution if the valence electron states or the lattice energies of single partners are different, as well as to the site distribution with formation of vacancies or with additional occupation of vacancies. Finally, the cases of lattice sites occupation by ions of different valency, of partially isomorphous and multiply anomalous built-in of impurities are discussed.     

Local magnetic ordering of Fe impurities in Pd2MnSn

Mössbauer effect of Fe⁵⁷ embedded as very dilute substitutional impurities in Pd₂MnSn was studied. The impurities are seen to replace the three elements in the alloy. Although the Curie temperature of the alloy is 189K, well below the room temperature, the Mössbauer spectrum recorded at room temperature consisted of two distinct 6-finger magnetic hyperfine spectra and a single unsplit line. One of the 6-finger patterns which corresponds to an internal magnetic field ofH _int=?375 kOe is inferred to arise due to local magnetic coupling of the localized magnetic moments of Fe impurities at the Pd sites with those of the 4 Mn first nearest neighbours of the Fe impurities. The other 6-finger pattern which corresponds to an internal magnetic field ofH _int=?335 kOe is inferred to arise due to the local magnetic coupling of the localized magnetic moments of the Fe impurities at the Sn sites with those of the 6 Mn second nearest neighboours of the Fe impurities. The difference in the internal magnetic fields observed at the Pd and Sn sites in the alloy could be understood qualitatively, on the basis of RKKY theory, as arising due to the different conduction electron polarization contributions to the net internal magnetic field at the Fe impurity sites. The results of the measurements suggest that the localized magnetic moments of Fe⁵⁷ impurities at Pd and Sn sites are antiferromagnetically coupled with the moments of their neighbouring Mn atoms.     

Dynamics of oxygen atoms in the Ta-O interstitial system

The dynamics of oxygen atoms in a Ta-O solid solution is studied. The vibrational energies of interstitial O impurities are determined, and the metal-impurity interaction constants are calculated. The experimental data obtained suggest that an oxygen atom is displaced from the center of the octahedral interstice of the crystal lattice. The oxygen vibrational energy in tantalum is shown to satisfy the relation between the localmode energy and the transition metal-interstitial impurity distance that is common for all M-O systems.     

Contribution electronique au gradient de champ electrique sur une impurete de transition dans un environnement metallique anisotrope

The experimental data related to the electric field gradient at transition impurities either in hexagonal metals, or in cubic metals where the isotropy is perturbed by a next impurity, can be explained neither by the lattice contribution nor by the electronic contribution from the conduction band. A model is proposed here to investigate the electronic contribution arising from virtual bound 3d states on the impurity, by studying the local crystal field influence in a Friedel-Anderson model. It appears that at the 0°K limit, the localized electronic contribution to the EFG can be linearly related to the density n_d(?_F) of 3d states at the Fermi level. As a first approximation, this law is valid even at temperature different from 0°K so establishing a linear correlation between the EFG, the impurity resistivity and the amplitude of the charge perturbation around the impurity.     

Intrinsic defects, impurities and doping in ZnO nanorods grown at low temperature

We report on the defect properties of single-crystalline ZnO nanorods grown from solutions at temperatures below 90 °C. The nanorods can easily be doped by providing impurity precursors during growth. In the as-grown state the nanorods exhibit considerable lattice strain and distortions which compromise their electrical and optical properties. Upon annealing at moderate temperatures of <400 °C the lattice strain is converted into dislocation-type defects, and the dopant impurities become optically active. In the annealed state the near-bandgap photoluminescence quantum efficiency is improved more than 5 times and reaches ～16 % at room temperature. Thus with moderate annealing, interesting device applications become feasible for nanorods grown at T<90 ^°C.     

Quantum interference effects induced by multiple magnetic impurities on a triangular lattice f-wave superconductor

The effects of multi-impurity quantum interference on triangular lattice f-wave superconductors are studied by self-consistently solving Bogoliubov-de Gennes equations within the t?t′?J?V model. An overall phase diagram is presented, which shows that f-wave superconductivity dominates near 0.3 doping. Rich phenomena are induced by quantum interference effects, such as periodic modulations in charge orders, pyramid frustum structures, and a magnetic moment reverse transition, which are qualitatively different from the single-impurity case. We also examine the local density of states to show how localized quasiparticle states are created at or near the impurity sites, which can be directly measured by scanning tunneling microscopy experiments.     

Electron spin-lattice relaxation anomaly and the local pseudo freeze-out of impurity dynamics in H-bonded ferroelectrics

The strong decrease in the electron spin-lattice relaxation rate at the ferroelectric transition temperature T_c and the simultaneous increase in the transverse spin-spin relaxation rate can be both understood in terms of the local “spontaneous freeze-out” model of impurity dynamics recently proposed to explain the spontaneous dynamic symmetry breaking observed far above T_c in the EPR spectra of H-bonded ferroelectrics doped with paramagnetic impurities.     

A lattice model of nearest-neighbor hopping conduction and its application to neutron-doped Ge: Ga

A model of hopping conduction between nearest neighbors is developed in which the majority and compensating dopant atoms are assumed to form a unified simple cubic lattice in a crystalline matrix. The hopping of carriers occurs when thermally activated “equalization” of majority impurity levels takes place, while the compensating impurities block the corresponding sites. The range of relatively high temperatures is considered in which the interactions giving rise to a Coulomb gap can be neglected and the density of states of the majority impurity band is Gaussian. The concentration dependences of the activation energy for hopping conductivity ? ₃ (nonmonotonic and having a maximum) and the preexponential factor σ₃ are found. The results are compared with experimental data obtained by different authors for neutron-doped Ge: Ga.     

Conductance of metallic nanoribbons with defects

The conductances of two typical metallic graphene nanoribbons with one and two defects are studied using the tight binding model with the surface Green’s function method. The weak scattering impurities, U ～ 1 eV, induce a dip in the conductance near the Fermi energy for the narrow zigzag graphene nanoribbons. As the impurity scattering strength increases, the conductance behavior at the Fermi energy becomes more complicated and depends on the impurity location, the AA and AB sites. The impurity effect then becomes weak and vanishes with the increase in the width of the zigzag graphene nanoribbons (150 nm). For the narrow armchair graphene nanoribbons, the conductance at the Fermi energy is suppressed by the impurities and becomes zero with the increase in impurity scattering strength, U > 100 eV, for two impurities at the AA sites, but becomes constant for the two impurities at the AB sites. As the width of the graphene nanoribbons increases, the impurity effect on the conductance at the Fermi energy depends sensitively on the vacancy location at the AA or AB sites.     

Ultraviolet-visible spectroscopic characterization of lanthanum beryllate crystals doped with Er,Nd, or Pr ions

Spectroscopic characterization of lanthanum beryllate La₂Be₂O₅ (BLO) single crystals doped with trivalent ions of Eu, Nd or Pr, was carried out in the ultraviolet-visible spectral range using synchrotron radiation spectroscopy in combination with conventional optical absorption and luminescence spectroscopy techniques. On the basis of the obtained data, the energy level diagram for these trivalent impurity ions in BLO host lattice was developed; the optical and electronic properties of the crystals were determined; the possibility of the 4f-4f, 4f-5d and charge transfer transitions was analyzed; spectroscopic properties of the lattice defects formed during the introduction of trivalent impurity ions in the BLO host lattice, were investigated. We found that the lattice defects are responsible for a wide-band photoluminescence (PL) in the energy region of 400–600 nm. The most efficient excitation of the defect photoluminescence in the energy gap of BLO occurs in broad PL excitation-bands at 270 and 240 nm. The PL intensity of defects depends on the type of impurity ion and increases in the sequence: Pr-Nd-Er.     

Local impurity phase pinning and pinning force in charge density waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter h. Specifically the pinning force exhibits a threshold at h=1 with exponent . Our model exemplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made. Received 8 July 1998