Scattering theory of defects in crystals

Rennie, R.

doi:10.1080/00018737700101393

Cited by 8 publications

(5 citation statements)

References 171 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The pictorial representation of tunnelling spin exchange due to Kouwenhoven and Glazman (2001) is useful here, illustrated in figure 23. A description in terms of scattering is given by Rennie (1977) and a comprehensive account is to be found in the book by Hewson (1993). The expectations for magnetic properties are illustrated in figure 24.…”

Section: Knight Shifts Korringa Relaxation and Kondo Impuritiesmentioning

confidence: 99%

“…It is another example of the perennial question as to when a strongly perturbing point defect that destroys periodicity can usefully be described within a band structure framework. The discussions of screening in terms of electron scattering by Rennie (1977), Stoneham (1975) and Alducin et al (2003) are also valuable here: whereas effective mass theory is good for long range or gradual potentials, scattering theory is better for fierce short range potentials. Rennie notes that the Yukawa potential neglects some longer range terms but has the virtue of being soluble.…”

Section: The Question Of Screening Versus Bindingmentioning

confidence: 99%

See 1 more Smart Citation

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

2009

View full text Add to dashboard Cite

Although the interstitial hydrogen atom would seem to be one of the simplest defect centres in any lattice, its solid state chemistry is in fact unknown in many materials, not least amongst the elements. In semiconductors, the realization that hydrogen can profoundly influence electronic properties even as a trace impurity has prompted its study by all available means-but still only in the functionally important or potentially important materials-for the elements, Si, Ge and diamond. Even here, it was not studies of hydrogen itself but of its pseudo-isotope, muonium, that first provided the much needed microscopic pictures of crystallographic site and local electronic structure-now comprehensively confirmed by ab initio computation and such data as exists for monatomic, interstitial hydrogen centres in Si. Muonium can be formed in a variety of neutral paramagnetic states when positive muons are implanted into non-metals. The simple trapped atom is commonly only metastable. It coexists with or reacts to give defect centres with the unpaired electron in somewhat more extended orbitals. Indications of complete delocalization into effective mass states are discussed for B, α-Sn, Bi and even Ge, but otherwise all the muonium centres seen in the elemental semiconductors are deep and relatively compact. These are revealed, distinguished and characterized by µSR spectroscopy-muon spin rotation and resonance informing on sites and spin-density distributions, muon spin relaxation on motional dynamics and charge-state transitions.This Report documents the progress of µSR studies for all the semiconductors and semimetals of the p-block elements, Groups III-VI of the Periodic Table . The striking spectra and originally unanticipated results for Group IV are for the most part well known but deserve summarizing and updating; the sheer diversity of muonium states found is still remarkable, especially in carbon allotropes. The interplay of crystallographic site and charge state in Si and Ge at high temperatures, or under illumination, reflects the capture and loss of charge carriers that should model the electrical activity of monatomic hydrogen but still challenges theoretical descriptions. Spin-flip scattering of conduction electrons by the paramagnetic centres is revealed in heavily doped n-type material, as well as some modification of the local electronic structures. The corresponding spectroscopy for the solid elements of Groups III, V and VI is rather less well known and is reviewed here for the first time; a good deal of previously unpublished data is also included. Theoretical expectations and computational modelling are sparse, here. Recent results for B suggest a relatively shallow centre with molecular character; P and As show deeper quasi-atomic states, but still with substantial overlap of spin density onto surrounding host atoms. Particular attention is paid to the chalcogens. Muonium centres in Te show charge-state transitions already around room temperature; the identification of those in S and Se has been compli...

show abstract

Section: Knight Shifts Korringa Relaxation and Kondo Impuritiesmentioning

confidence: 99%

Section: The Question Of Screening Versus Bindingmentioning

confidence: 99%

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

2009

View full text Add to dashboard Cite

show abstract

“…are not taken into consider ation. A detailed review of the state of the theory and experimental data on the electronic structure of indi vidual defects in solids can be found elsewhere [1,5,[14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: The Limit Of Low Impurity Concentrationsmentioning

confidence: 99%

“…Thus, calculation of the averaged Green's function is reduced to the calculation of averages of the type (23) and to summation of the series on the right hand side of formula (22). Determination of averages of the type of (23) assumes that the characteristics of the random field U are known, and it is just these characteristics that define the model of a disordered system.…”

Section: The Localization Threshold Of Electronic States In the Lifshmentioning

confidence: 99%

Theory of the electronic structure of substitutional semiconductor alloys: Analytical approaches

Zakharov

2015

Semiconductors

View full text Add to dashboard Cite

Methods of predicting the electronic structure of disordered semiconductor alloys involving mainly isoelectronic substitution are reviewed. Special emphasis is placed on analytical methods of studying currently available models of alloys. An approximate equation for the localization threshold of electronic states in the Lifshitz model is considered, and the inaccuracy of this equation is estimated. The contributions of the perturbation potential of an individual impurity and of crystal lattice distortions in the vicinity of the impurity center are analyzed on the basis of the Faddeev equations. The contributions of intrinsic impurity potentials and volume effects to the formation of the electronic structure of semiconductor alloys are esti mated. Methods of calculating matrix elements of the perturbation potentials of isoelectronic impurities in alloys with consideration for deformation effects are considered. The procedure of calculating the composi tional dependence of the band gap of multicomponent alloys is described. A comparative analysis of various methods for predicting the formation of electronic states bound at individual isoelectronic impurities in semi conductors is conducted. The theory of the energy spectrum of charged impurities in isoelectronic alloys is presented.

show abstract

“…The condition for the p_resence of bound states in the potential 7 is detll"K-'ll = 0. Because the matrix II"K-'II from (27) is diagonal, the presence of bound state with the given 1 is equivalent to (29) Assuming that both matrices (21) and (22) are considered in the energy region close to some eigenvalue of the Hamiltonian H,, excluding the eigenvalue itself. it may be concluded that the condition (29) is approximately satisfied.…”

Section: mentioning

confidence: 99%

“Non‐muffin tin” corrections of the SCF X_α‐SW Method. I

Rubin¹,

Lobatch²,

Шульгин³

1987

Int J of Quantum Chemistry

View full text Add to dashboard Cite

The recently developed crystalline cluster method within the framework of the Johnson multiple scattering technique was successfully used in calculations of ionic cubic crystals and the defects with a cubic symmetry. In this paper a simple way of extension of the method to noncubic systems by a partial elimination of "muffin-tin" approximation (MTA) is proposed.The procedure suggested does reduce the intermediate integrals to the one-dimensional ones, and they are calculated analytically. It is supposed that an approach of taking into account the nonspherical shape of the potential inside the "muffin-tin" (MT) spheres will be effective in crystals with an ionic type of chemical bond.

show abstract

Scattering theory of defects in crystals

Cited by 8 publications

References 171 publications

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

Theory of the electronic structure of substitutional semiconductor alloys: Analytical approaches

“Non‐muffin tin” corrections of the SCF X_α‐SW Method. I

Contact Info

Product

Resources

About

Scattering theory of defects in crystals

Cited by 8 publications

References 171 publications

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

Theory of the electronic structure of substitutional semiconductor alloys: Analytical approaches

“Non‐muffin tin” corrections of the SCF Xα‐SW Method. I

Contact Info

Product

Resources

About

“Non‐muffin tin” corrections of the SCF X_α‐SW Method. I