Vacancies and interstitials in semiconductors play a fundamental role in both high temperature diffusion and low temperature radiation and implantation damage. In Ge, a serious contender material for high-speed electronics applications, vacancies have historically been believed to dominate most diffusion related phenomena such as self-diffusivity or impurity migration. This is to be contrasted with silicon, where self-interstitials also play decisive roles, despite the similarities in the chemical nature of both materials. We report on density functional calculations of the formation and properties of vacancy-donor complexes in germanium. We predict that most vacancy-donor aggregates are deep acceptors, and together with their high solubilities, we conclude that they strongly contribute for inhibiting donor activation levels in germanium.

Ab initio density-functional calculations using Gaussian orbitals are carried out on large Si and Ge supercells containing oxygen defects. The formation energies, local vibrational modes, and diffusion or reorientation energies of Oi, O2i, VO, VOH, and VO2 are investigated. The piezospectroscopic tensors for Oi, VO, and VO2 are also evaluated. The vibrational modes of Oi in Si are consistent with the view that the defect has effective D3d symmetry at low hydrostatic pressures but adopts a buckled structure for large pressures. The anomalous temperature dependence of the modes of O2i is attributed to an increased buckling of Si-O-Si when the lattice contracts. The diffusion energy of the dimer is around 0.8 eV lower than that of Oi in Si and 0.6 eV in Ge. The dimer is stable against VO or VO2 formation and the latter defect has modes close to the reported 894-cm-1 band. The reorientation energies for O and H in VO and VOH defects are found to be a few tenths of an eV and are greater when the defect has trapped an electron.

The interstitial carbon-oxygen defect is a prominent defect formed in e-irradiated Cz-Si containing carbon. Previous stress alignment investigations have shown that the oxygen atom weakly perturb the carbon interstitial but the lack of a high-frequency oxygen mode has been taken to imply that the oxygen atom is severely affected and becomes overcoordinated. Local vibrational mode spectroscopy and ab initio modeling are used to investigate the defect. We find new modes whose oxygen isotopic shifts give further evidence for oxygen overcoordination. Moreover, we find that the calculated stress-energy tensor and energy levels are in good agreement with experimental values. The complexes formed by adding both single (CiOiH) and a pair of H atoms (CiOiH2), as well as the addition of a second oxygen atom, are considered theoretically. It is shown that the first is bistable with a shallow donor and deep acceptor level, while the second is passive. The properties of CiOiH and CiO2iH are strikingly similar to the first two members of a family of shallow thermal donors that contain hydrogen.

The interstitial carbon-oxygen complex is one of the most prominent defects formed in e-irradiated Cz-Si containing carbon. Stress alignment investigations have shown that the oxygen atom only perturbs the carbon interstitial but the lack of a high frequency oxygen mode has been taken to imply that the oxygen atom is over-coordinated. Local vibrational mode spectroscopy and ab initio modeling are used to investigate the defect. We find new modes whose oxygen isotopic shifts, along with the piezoscopic stress-energy tensor support the trivalent model, thus providing evidence for oxygen over-coordination.

Combined local mode spectroscopy and ab initio modeling are used to demonstrate for the first time that oxygen atoms in thermal double donors (TDD) in Si are in close proximity. The observed vibrational modes in 16O, 18O, and mixed isotopic samples are consistent with a model involving [110] aligned oxygen chains made up of an insulating core lying between electrically active ends. The model also explains the minute spin density observed on oxygen in TDD+ as well as the piezospectroscopic tensors of the donors. The analogy between the thermal donors and quantum dots is emphasized.

Density functional modeling of Er and Er-O complexes in GaAs show that Er impurities at the Ga site are not efficient channels for exciton recombination, but decorative O atoms play crucial roles in inhibiting Er precipitation and in creating the necessary conditions for electron-hole capture. Among the defects studied, the ErGaOAs and ErGa(OAs)2 models have the symmetry and carrier trap location close to the defect responsible for the strong 1.54 µm photoluminescence band in Er, O codoped GaAs.

Density functional modelling studies of the single vacancy in large Ge clusters are presented. We take a careful look at the origin of Jahn-Teller instabilities as a function of the vacancy net charge, resulting in a variety of structural relaxations. By comparing electron affinities of the vacancy with those from defects with well established gap states, we were able to estimate three acceptor states for the vacancy at E(-/0) ≤ Ev+0.2 eV, E(≤/-) ≤ Ec-0.5 eV and eV. As opposed to the Si vacancy, the defect in Ge is not a donor. We also show that these dissimilarities have fundamental consequences for the electronic/atomic picture of other centres, such as transition metals in germanium crystals.

Density functional calculations are carried out on divacancy-oxygen (V2O and V2O2) complexes in silicon, paying particular attention to their formation and dissociation mechanisms as well as their electrical activity. The formation of V2O around 220°C is controlled by the diffusion of V2 to immobile oxygen traps, while it dissociates around 300°C into VO and V. V2O and V2O2 are found to possess deep single and double acceptor levels as well as deep donor levels similar to those of V2.

Most density-functional studies of defects in semiconductors invariably use (i) a supercell that imitates the host crystal, as well as (ii) a local treatment of the exchange-correlation potential. The first approximation has had an enormous success in many materials, provided that the size of cell is large enough to minimize long-range interactions between the infinite lattice of defects. For instance, these may arise from strain fields or from the overlap between shallow defect states. The second approximation, when combined with the periodic boundary conditions, leads to an essentially metallic density of states in Ge, which can compromise any investigation of electronic transitions involving gap levels. Here, we report on two approaches to surmount these difficulties, namely (i) to open the gap by reducing the host to a Ge cluster of atoms whose states are confined by a surface potential and (ii) to use supercells, but choosing carefully the Brillouin zone sampling scheme, taking k-points that minimize the admixture between defect-related gap states and the host density of states. These methods are utilized in the calculation of the electronic structure of the vacancy, divacancy, and vacancy-donor pairs in Ge

We present an ab initio density functional study on the electronic structure and electrical properties of divacancies in Ge. Although suffering essentially different Jahn-Teller distortions when compared to the analogous defect in Si, the relative location of the electrical levels in the gap does not differ radically in both materials. We propose a V2 model that is responsible for a donor level at Ev+0.03 eV, a first acceptor state at Ev+0.3 eV, and a second acceptor level at Ec-0.4 eV. The latter is only 0.1 eV deeper than an electron trap that has been recently linked to a divacancy in proton implanted material.

Divacancy-hydrogen complexes (V2H and V2H2) in Si are studied by ab initio modelling using large supercells. Here we pay special attention to their electronic structure, showing that these defects produce deep carrier traps. Calculated electrical gap levels indicate that V2H2 is an acceptor, whereas V2H is amphoteric, with levels close to those of the well known divacancy. Finally our results are compared with the available data from deep level transient spectroscopy and electron paramagnetic resonance experiments.

Atomic hydrogen is a concomitant impurity in semiconductors. Its presence in Si, Ge and SiGe alloys has been established by means of paramagnetic resonance, optical, electrical and theoretical modeling studies. Hydrogen self-trapping is known to occur in Si and Ge, resulting in the formation of molecular hydrogen and H2* interstitial dimers. Here we report on the properties of H22* complexes in dilute SiGe alloys, by using an ab initio density functional method. It is found that these complexes form preferentially within Si-rich regions. H2* dimers in Si-rich alloys show vibrational properties similar to those in pure Si. On the other hand, in Ge-rich material the minority Si atoms act as nucleation sites, with the consequent formation of at least one preferential H2*- Si defect variant, showing a distinct vibrational activity.

We present a comprehensive spin-density functional modeling study of the structural and electronic properties of donor-vacancy complexes (PV, AsV, SbV, and BiV) in Ge crystals. Special attention is paid to spurious results which are related to the choice of the boundary conditions (supercell-cluster approach), the resulting band-gap width, and the choice of the points to sample the Brillouin zone. The underestimated energy gap, resulting from the periodic conditions together with the local-density approximation to the exchange-correlation energy, leads to defect-related gap states that are strongly coupled to crystalline states within the center of the zone. This is shown to produce a strong effect even on relative energies. Our results indicate that in all E centers the donor atom occupies a nearly substitutional site, as opposed to the split-vacancy form adopted by the SnV complex in Si. The E centers can occur in four charge states, from positive to double negative, and produce occupancy levels at E(0/+)=Ev+0.1 eV, E(-/0)=Ev+0.3 eV, and E(=/-)=Ec-0.3 eV.

The trivacancy (V3) in silicon has been recently shown to be a bistable center in the neutral charge state, with a fourfold-coordinated configuration, V3[FFC], lower in energy than the (110) planar one [ V. P. Markevich et al. Phys. Rev. B 80 235207 (2009)]. Transformations of the V3 defect between different configurations, its diffusion, and disappearance upon isochronal and isothermal annealing of electron-irradiated Si:O crystals are reported from joint deep level transient spectroscopy measurements and first-principles density-functional calculations. Activation energies and respective mechanisms for V3 transformation from the (110) planar configuration to the fourfold-coordinated structure have been determined. The annealing studies demonstrate that V3 is mobile in Si at T>200 ∘C and in oxygen-rich material can be trapped by interstitial oxygen atoms so resulting in the appearance of V3O complexes. The calculations suggest that V3 motion takes place via consecutive FFC/planar transformation steps. The activation energy for the long-range diffusion of the V3 center has been derived and agrees with atomic motion barrier from the calculations

There is considerable experimental evidence that vacancies in Ge dominate several solid state reactions that range from self-diffusivity to metal and dopant transport. It is therefore vital that we fully understand how vacancies interact with other point defects in Ge. Here we have a look at the properties of small donor-vacancy (Sb n V m with m,n ≤ 2) complexes in Ge by ab-initio density functional modeling. Particular attention has been payed to binding energies and to the electronic activity of the complexes. We found that all aggregates may contribute to the n→ p type conversion that is typically observed under prolonged MeV irradiation conditions. In general, Sb n V m defects are double acceptors. It is also suggested that spontaneous formation of Sb3V complexes may limit the activation level of donors introduced by ion implantation.

Composition operators Cτ between Orlicz spaces L (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.

In this paper, the authors prove a new generalization and unification of some recent generalizations of Simpson, trapezoid and Ostrowski type inequalities for convex functions. Both the case with the usual canonical partition and the case with the generalized partition are considered

Some new results concerning Simpson type numerical integration are proved, discussed and compared with other similar results in the literature. A technique to improve the error estimates also in some other recent related results is pointed out

Let $w$ be a non-negative measurable function on $(0,\infty)$, non-identically zero, such that $W(t)=\int_0^tw(s)ds<\infty$ for all $t>0$. The authors study conditions on $w$ for the Lorentz spaces $\Lambda^p(w)$ and $\Lambda^{p,\infty}(w)$, defined by the conditions $\int_0^\infty (f^*(t))^pw(t)dt<\infty$ and $\sup_{00,$$ it is shown that, if $\varphi$ satisfies the $\Delta_2$-condition and $w>0$, then $\Lambda_{\varphi,w}$ is a linear space if and only if $W$ satisfies the $\Delta_2$-condition.

This article is a systematic overview of compression, smoothing and denoising techniques based on shrinkage of wavelet coefficients, and proposes (in Sections 5 and 6) an advanced technique for generating enhanced composite wavelet shrinkage strategies.

In this communication we study in detail the relations between the smoothness of f and √f in the case when the smoothness of the univariate non-negative functions f is measured via Besov and Triebel-Lizorkin space scales. The results obtained can be considered also as embedding theorems for usual Besov and Triebel-Lizorkin spaces and their analogues in Hellinger metric. These results can be used in constrained approximation using wavelets, with applications to probability density estimation in speech recognition, non-negative non-parametric regression-function estimation in positron-emission tomography (PET) imaging, shape/order-preserving and/or one-sided approximation and many others.

In this study we initiate the investigation of a new advanced technique, proposed in Section 6 of [3], for generating adaptive Besov-Lorentz composite wavelet shrinkage strategies. We discuss some advantages of the Besov-Lorentz approach compared to firm thresholding.

The current trend in modern production is directed towards shorter and shorter production runs. The two major reasons causing this trend are the rapid spread of the just in time (JIT) philosophy and the constantly increasing multiplicity of customer demands. The short runs of modern production not only constitute a challenge for production management, but they also cause some problems when applying traditional statistical methods, designed to be used for large sets of data. One of these methods is process capability studies. Since theories on how to use process capability studies in short production environments are incomplete, the aim of this paper is to present some ideas which will partly fill this gap. The theories of process capability studies for short runs presented are based on ideas of focusing on the process, not on the products, and on using data transformation. By using the transformation presented, it is possible to conduct process capability studies in a traditional straightforward manner. A simulation study shows that the suggested transformation technique works satisfactorily in real situations. Finally, the ....-plot is introduced as a method of interpreting and analyzing the capability of a short run production process. By using the .... -plot, additional information is obtained concerning the capability of a process, compared to using traditional process capability indices only.

Models of the nitrogen-hydrogen defect in GaP, which contain one and two H atoms, are investigated using ab initio density functional cluster theory. We find that a single H atom binding to N possesses two infrared absorption frequencies close to those attributed to an NH2 defect. The modes shift with its charge state consistent with the photo-sensitivity found for the defect. A third mode observed for this centre is assumed to be an overtone of the bend mode. The isotope shifts of the calculated modes are in excellent agreement with experiment in contrast with the model which contains two H atoms

Damage assessment of structures includes estimation of location and severity of damage. Quite often it is done by using changes of dynamic properties, such as natural frequencies, mode shapes and damping ratios, determined on undamaged and damaged structures. The basic principle is to use dynamic properties of a structure as indicators of any change of its stiffness and/or mass. In this paper, two new methods for damage detection are presented and compared. The first method is based on comparison of normalised modal shape vectors determined before and after damage. The second method uses so-called 𝑙1-norm regularized finite element model updating. Some important properties of these methods are demonstrated using simulations on a Kirchhoff plate. The pros and cons of the two methods are discussed. Unique aspects of the methods are highlighted.

SiC bipolar devices show a degradation under forward-biased operation which has been linked with a current induced motion of one of the two glide dislocations having either Si or C core atoms. We have carried out calculations of the core structures and dynamics of partial dislocations in 3C and 2H-SiC. In this work we present results on the effect of charge on the dislocation kinks. The calculations show that silicon kinks have a deep filled band above the valence band and the trapping of holes into this band permits motion at room temperature.

First-principles density functional calculations are used to investigate antisite pairs in 4H-SiC. We show that they are likely to be formed in close proximity under ionizing conditions, and they possess a donor level and thermal stability consistent with the series of 40 photoluminescent lines called the alphabet lines. Moreover, the gap vibrational mode of the silicon antisite defect is close to a phonon replica of the b1 line and possesses a weak isotopic shift with 13C in agreement with observation.

SiC bipolar devices show a degradation under forward-biased operation due to the formation and rapid propagation of stacking faults in the active region of the device. It is believed that the observed rapid stacking fault growth is due to a recombination-enhanced dislocation glide (REDG) mechanism at the bordering partial dislocations having either Si or C core atoms. We investigated the effect of charge on the dislocation kinks and found that only silicon kinks have a deep filled band above the valence band. Trapping of holes into this band permits dislocation glide at room temperature. This mechanism is distinct from REDG as it requires only holes to be trapped at a Si partial and not in addition electrons in stacking fault states. We furthermore looked at the pinning of dislocations by nitrogen and boron and found a strong pinning of the C core by N and of the Si core by B.

SiC is a material that seems ideal for high-power, high frequency and high temperature electronic devices. It does not suffer from large reverse recovery inefficiencies typical for silicon when switching. In contrast to silicon. SiC is however difficult to dope by diffusion, and instead ion-implantation is used to achieve selective area doping. The drawback of this technique is that irradiating the crystal with dopant atoms creates a great, deal of lattice damage including vacancies, interstitials, antisites and impurity-radiation defect complexes. Although many of the point defects can be eliminated through thermal annealing, some however, e.g. the photoluminescence (PL) D1 and DLTS Z1/Z2 centers in 4H-SiC, are stable to high temperatures. In this polytype, D1 and the related alphabet lines are the most prominent PL signals. The latter can be seen directly after low energy irradiation while D1 usually dominates the PL spectrum of implanted and irradiated SiC after annealing. Not only implantation but also rapid growth of SiC by CVD methods leads to a deterioration in quality with an increase in electrically active grown in defects. Among these, the Z1/Z2 defects are dominant in n-type 4H-SiC. as well as material that has been exposed to radiation. We use first principles density functional calculations to investigate defect models for the above mentioned defects in 4H-SiC and relate their electrical and optical activity to experiments

The DI center is a prominent defect which is detected in as-grown or irradiated SiC. It is unusual in that its intensity grows with heat treatments and survives anneals of 1700 °C. It has been assigned recently to either a close-by antisite pair or to the close-by antisite pair adjacent to a carbon antisite. We show here using local density functional calculations that these defects are not stable enough to account for DI. Instead, we assign DI to an isolated Si antisite and the four forms of the close-by antisite pair in 4H-SiC to the a, b, c, and d members of the alphabet series. The assignments allow us to understand the concentration of DI following growth, the recombination enhanced destruction of these alphabet defects and the annealing behavior of the remaining members of the series.

Recent high resolution photoluminescence studies of high quality Mg doped GaN show the presence of two acceptors. One is due to Mg and the other labeled A1 has a shallower acceptor defect. The authors investigate likely candidates for this shallow acceptor and conclude that CN is the most likely possibility. The authors also show that the CN is passivated by H and the passivated complex is more stable than MgGa-H

Although there have been made many calculations for structures of the self-interstitial in Si and small aggregates of interstitials, In, there have been relatively few attempts to relate these defects with experimental data. Here, we discuss the assignments of the self-interstitial to the AA12 EPR centre and the di-interstitial to the P6 EPR centre.

Although there is good software for sparse QR factorization, there is little support for updating and downdating, something that is absolutely essential in some linear programming algorithms, for example. This article describes an implementation of sparse LQ factorization, including block triangularization, approximate minimum degree ordering, symbolic factorization, multifrontal factorization, and updating and downdating. The factor Q is not retained. The updating algorithm expands the nonzero pattern of the factor L, which is reflected in the dynamic representation of L. The block triangularization is used as an `ordering for sparsity' rather than as a prerequisite for block backward substitution. In symbolic factorization, something called `element counters' is introduced to reduce the overestimation of the number of nonzeros that the commonly used methods do. Both the approximate minimum degree ordering and the symbolic factorization are done without explicitly forming the nonzero pattern of the symmetric matrix in the corresponding normal equations. Tests show that the average time used for a single update or downdate is essentially the same as the time used for a single forward or backward substitution. Other parts of the implementation show the same range of performance as existing code, but cannot be replaced because of the special character of the systems that are solved.

This paper describes how to use the Matlab software package CMregr, and also gives some limited information on the CM-estimation problem itself. For detailed information on the algorithms used in CMregr as well as extensive testings, please refer to Arslan, Edlund & Ekblom (2002) and Edlund & Ekblom (2004).

A subproblem in the trust region algorithm for non-linear M-estimation by Ekblom and Madsen is to find the restricted step. It is found by calculating the M-estimator of the linearized model, subject to anL 2-norm bound on the variables. In this paper it is shown that this subproblem can be solved by applying Hebden-iterations to the minimizer of the Lagrangian function. The new method is compared with an Augmented Lagrange implementation.