Theory of impurity scattering: Interstitial impurities

A framework for studying impurity scattering in dilute, non-magnetic, metal alloys can be developed from a knowledge of the exact electronic eigenstates of a single impurity in an otherwise perfect lattice of muffin tin potentials. Such an approach has been developed for systems in which the impurity occupies a substitutional site of the lattice, as will be discussed by Coleridge, Lee, Harris, and other speakers of this conference. In this paper, motivated by recent experimental studies of Dingle temperature anisotropies induced by hydrogen impurities in copper, we will discuss the analogous treatment of scattering by interstitial impurities. In contrast to a substitutional impurity, an interstitial impurity introduces an additional scattering site into the lattice. Whereas the substitutional impurity wavefunctions can be described in terms of the same structure factors as can the Bloch wavefunctions for the pure host lattice, the interstitial impurity wavefunctions depend upon additional structure factors appropriate to the new scattering geometry. These additional structure factors appear in the transition matrix for impurity-induced scattering between Bloch states of the host lattice, and consequently in the weight factors involved in a partial wave analysis of the Dingle temperature anisotropies.     

Impurity scattering on the Fermi surface of aluminum

A calculation is described for the anisotropic relaxation time due to impurity scattering on the Fermi surface of aluminum. The Bloch states and the Fermi surface are obtained from Ashcroft's 4-OPW model, while the scattering potentials are obtained from locally re-screened form factors. Numerical results reveal that strong anisotropicsin the electronic lifetime arise for s-like impurities such as Si and Ge. A phase shift model is introduced to explain these anisotropies. The predicted anisotropies appear to be in reasonable agreement with experimental values for the Dingle temperature. The relaxation time for d.c. conductivity is obtained from iterative solution of the Boltzmann equation.     

Model calculations of anisotropic electron lifetimes due to dilute substitutional impurities in molybdenum

The de Haas-van Alphen technique forms a sensitive probe of the electronic structure of dilute alloys because of its dependence on the seattering rate in the forward direction. We report the results of a first principle model calculation of the scattering rate of dilute impurities in molybdenum which focuses on the anisotropy of the host wave function on the Fermi surface. This simplified model treats the impurity potential as an atomic potential screened by a Thomas-Fermi function. Substitutional impurities in bcc molybdenum have been studied using the Greens function (KKR) wave functions. The band structure calculated via the KKR method was fitted to a Fourier series representation in order to accurately determine a sufficiently large number of states on the Fermi surface. The KKR wavefunctions were used to calculate scattering rates for the substitutional impurity since the impurity potential can be best described in an angular momentum representation which is inherent to the Greens function method. Our detailed results, to be presented, suggest additional experiment to be done.     

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.     

Electronic structure of H and He in metal vacancies

The electronic structure of H and He impurities in metals is calculated using the Gunnarsson-Hjelmberg method of solving the Kohn-Sham equation. The jellium model is used for the metal. The differences between interstitial and substitutional impurity sites are emphasized. For normal metallic densities it is found that both impurities favour sites of lower than average conduction electron density because here the impurity electrons can relax to a situation of lower kinetic energy.     

Electronic structure of non-magnetic impurities in dilute alloys of Al

The electronic structure of substitutional non-magnetic impurities Cu, Ag, Cd, Mg, Zn, Ga, In, Ge, Si and Sn in Al is studied using density functional theory. A simple physical model is proposed to calculate the effective charges on impurities in trivalent metal Al. A linear relation is found between the effective charges on impurities and impurity vacancy capture radii. The spherical solid model (SSM) is used to account for discrete nature of the host. The impurity-induced change in charge density, scattering phase shifts, host-impurity potential, residual resistivity and impurity self-energy are calculated. Higher order scattering phase shifts are found significant and the host-impurity potential is found proportional to effective charge on impurity in its vicinity. The self-consistently calculated potential is used to calculate the electric field gradients (EFGs) at the first and second nearest neighbours (1NNs, 2NNs) of impurity. The calculated values are in agreement with the experimental results.     

Electronic structure calculations of substitutional and interstitial hydrogen in Nb

We report the results of a theoretical study on the effects of substitutional and interstitial hydrogen atoms in niobium. We confirm that any contaminated hydrogen will occupy the interstitial site over the substitutional site in niobium. For interstitial hydrogens, the lattice deformation increases with the percentage content of hydrogen, though it is negligible at low concentrations. Substitutional hydrogens are found to prefer off-center sites in the host lattice.     

Magnetic hyperfine fields of 5sp impurities in vacancy complexes in ferromagnetic metals

A survey is given of recent experimental results for the hyperfine interactions of 5sp impurities in vacancy complexes in ferromagnetic 3d host metals. Emphasis is put on changes of the impurity magnetic hyperfine fields in such complexes as compared to substitutional lattice sites. Systematic trends are presented, which are beginning to emerge from studies of Cd and Sn impurities in particular.     

硅中的过渡元素杂质能级

本文提出了半导体中过渡元素杂质的一个简单模型,用格林函数方法计算了硅中替代和间隙原子产生的杂质能级和波函数。发现两者的性质有很大的差别。替代原子只有当d原子能级V_d低于价带顶时才能产生杂质能级。它的波函数主要是悬键态,当能级靠近导带边时变成正键态。间隙原子只有当V_d高于价带顶时才能产生杂质能级。它的波函数主要是中心原子d态,当能级靠近导带边时变成弱反键态。最后定性地说明了过渡元素杂质能级的化学趋势和一些实验事实。 关键词：     

Theoretical aspects of hydrogen in crystalline semiconductors

Hydrogen in semiconductors displays behavior quite different from any other impurity, causing effects which can be either beneficial or detrimental to the electronic properties. Theoretical calculations have been able to elucidate many puzzling aspects of this behavior, by providing a microscopic picture of the interactions of hydrogen with the host lattice and with other impurities. I will critically review the available theoretical techniques, and address the following topics: microscopic structure of isolated interstitial hydrogen, as well as various hydrogen-impurity complexes; electronic structure, including the relative stability of different charge states; diffusion; and H motion around impurities.     

Self-consistent calculation of hyperfine fields and adiabatic potential of impurities in iron

Hyperfine fields of impurities of the atomic number Z=1–56 at the substitutional site and those of light impurities of Z=1–9 at the interstitial sites in ferromagnetic iron are calculated by the KKR method adapted to the system containing a single impurity atom. The potential of the impurity atom is determined self-consistently by use of the local spin density functional formalism. The results for nonmagnetic sp valence impurities agree with those of the previous nonself-consistent calculation by Katayama-Yoshida, Terakura and Kanamori except for a few cases, confirming their theory of the systematic variation of hyperfine fields. The calculation for magnetic impurities of transition elements is presented for the first time in this paper. The calculations mentioned so far assume that impurities are situated at the center of each site. For the purpose of discussing the stability of the impurity positions, the change of the adiabatic potential due to displacements from the center is calculated by carrying out similar self-consistent calculations for off-center impurity positions. It is concluded that positive muon and some light impurities including boron will be displaced from the center when trapped in a vacancy.     

Hyperfine Fields of Light Interstitial Impurities in Ni

The magnetic hyperfine interaction of light interstitial impurities in Ni have been studied by means of the Korringa–Kohn–Rostoker (KKR) band structure method. This method allows to deal with the impurity problem by solving the corresponding Dyson equation for the Green’s function. It also allows to account for lattice relaxations. For this purpose a new technique was developed that allows to handle in principle arbitrary lattice distortions. Corresponding calculations have been performed for the magnetic hyperfine fields of the light interstitial impurities H to Ne in Ni. By minimising the force on the nearest neighbour host atoms their equilibrium position was determined. The resulting hyperfine fields for the equilibrium configuration are found to be in rather good agreement with available experimental data.     

Observation of a new gettering mechanism in (Hg,Cd)Te

A new gettering mechanism is proposed for substitutional impurities which diffuse by an interstitial process. In this mechanism, an externally imposed gradient of self interstitials generates a gradient in impurity interstitials leading to the segregation of fast diffusing impurities to low interstitials, high vacancy regions. Data are presented to support this model in (Hg, Cd)Te alloys, as well as explicitly rule out gettering by dislocations, by segregation to precipitates, or by enhanced solubility arising from the interaction of the impurity with a varying Fermi level.     

Solubility of Substitutional Impurities in Interstitial Solid Solutions

The solubility coefficient of a substitutional impurity in interstitial solid solutions is calculated within a dynamic model. The presence of an interstitial component increases solubility. In solutions where the interaction between interstitial atoms is negative, a long-range order occurs at interstitial sites at temperatures lower than a certain value. This also causes changes in solubility. An increase in solubility of substitutional impurities is due to ordering at temperatures close to the transition point in the case where the concentration of the interstitial component exceeds 11 at. %. Conversely, solubility decreases due to ordering at lower concentrations. It is shown that an isotopic effect must be observed in solubility of substitutional atoms.     

Ab initio theory of transport in FeRh-based natural magnetic multilayers

The electronic structure and the residual resistivity of random FeRh-based alloys in the CsCl structure are calculated for different spin configurations using the tight-binding linear muffin–tin orbital method. The effect of substitutional impurities (Pd, Rh) is described by means of the coherent potential approximation. It is shown that impurity scattering leads to giant magnetoresistance effects in qualitative agreement with experiment.     

Restwiderstand von Bleischichten nach Implantation von Manganionen

The method of ion-implantation is applied to doping thin lead films with small amounts of manganese. The incident ion intensity is integrated to determine the concentration of magnetic impurities. A marked increase in film resistivity is caused by radiation damage induced in the host lattice and by resonance scattering of conduction electrons on the magnetic impurity sites. Both effects can be observed separately.     

Dopant-assisted concentration enhancement of substitutional Mn in Si and Ge

The influence of p- and n-type electronic dopants on Mn incorporation in bulk Si and Ge is studied using first-principles calculations within density functional theory. In Si, it is found that the site preference of a single Mn atom is reversed from interstitial to substitutional in the presence of a neighboring n-type dopant. In Ge, a Mn atom is more readily incorporated into the lattice when an n-type dopant is present in its immediate neighborhood, forming a stable Mn-dopant pair with both impurities at substitutional sites. A detailed analysis of the magnetic exchange interactions between such pairs reveals a new type of magnetic anisotropy in both systems.     

Nontransition element impurities in ferromagnetic transition metals

Effects of nontransition element impurities on the ferromagnetism of transition metals are discussed in the light of our theoretical analyses of the hyperfine interaction data of implanted nuclei which have been carried out in recent years. A detailed discussion of the effective filling of the d band by impurity valence electrons is given after presenting a brief summary of our theory of the hyperfine interaction. The change of the saturation magnetization is discussed in particular. It is pointed out that an sp valence impurity at an interstitial site in iron can increase the magnetic moments of surrounding host atoms.     

Diffusion of electrons scattered by short-range impurities in a quantizing magnetic field

Formulas for transverse diffusion and conductivity in a semiconductor are obtained for electrons scattered by neutral impurities in a quantizing magnetic field. The formulas are valid for an impurity potential of arbitrary depth. Based on Kubo’s theory [1], calculations are performed using electron wavefunctions of the problem of single-impurity scattering in a magnetic field [2]. The poles of the scattering amplitude correctly determine electron eigenstates and magnetic impurity states. As a result, an exact expression is found for the dependence of transverse diffusion coefficient D _⊥ on longitudinal electron energy ? due to scattering by short-range (neutral) impurities. The behavior of D _⊥(?) is examined over an interval of magnetic field strength for several values of impurity potential depth. The experimental observability of diffusion and conductivity using IR lasers is discussed.     

Diffusion and lattice location of lithium in zinc telluride

The diffusion of Li in ZnTe has been investigated in the temperature range 400–700°C by use of nuclear analysis and chemical or ion beam etching techniques. The penetration profiles are complex and most of them were found to show three regions. The experimental results are interpreted as a superposition of different diffusion mechanisms: one where the impurity diffuses simultaneously in substitutional and interstitial forms, the interstitial form being trapped at defects, and the other which involves short-circuit paths. Activation energies and diffusion constants D_o were measured. Furthermore the channeling technique was used for lattice location. This revealed that (60–80)% of the lithium atoms occupy the zinc substitutional site following annealing at 500°C.