Depth profile measurements of copper in silicon by ion-induced x-ray emission

Abstract

Distributions of axially channeled electrons are calculated at large depths as a function of angular momentum and transverse energy. Due to the influence of multiple scattering the electron distributions become independent of the angular momentum at a depth, where the statistical equilibrium is reached. Furthermore, the flux-peaking effect for negative particles is discussed.     

Proton channeling studies in thin crystals with a supercollimated beam

Abstract

A supercollimated beam of 4 MeV H^? ions with an angular spread of 1.5 × 10^?3 degrees, a diameter of 25 μ and a current of 10 picoamps was used to study the axial and planar channeling characteristics of single crystal silicon samples ranging in thickness from 0.5 to 1.0 μ. Since the angular spread of the beam is much smaller than most of the gross angular phenomena associated with channeling, it is possible to study the detailed characteristics of both planar and axial channeling with greater precision than before. Preliminary results indicate that this technique will allow a direct study of interatomic or continuum potential distributions and will also be useful for studying nuclear multiple scattering as a function of the tranverse energy of channeled particles relative to atomic rows and planar directions.     

The effect of channeling on MeV ion-induced auger electron production in silicon

We have measured Auger electron emission from single crystal targets of Si(111) bombarded with H⁺ and ⁴He⁺ beams in the 0.5 to 1.8 MeV range under channeled and random directions of incidence. Under channeling conditions (monitored by simultaneous measurement of the Rutherford backscattering yield), a significant reduction is observed in the intensity and also in the energy width of the KLL Auger line. These two characteristics of the Auger signal are influenced by channeling of the incident beam as evidenced by their angular dependence. The measured ratio of the channeled to random Auger signals correlates well with a simple model based on the shadow cone radius for the channeled ion, the lattice vibrational amplitude, the adiabatic K-shell excitation distance, and the electron inelastic mean free path, λ, for the 1620 eV Auger line. We derive a value for the latter quantity of 34 Å.     

Spatial and angular distribution of the heavy ion charge under channeling in crystals

A kinetic theory of passage of multiply charged heavy ions through crystals is developed that allows for diffusion in the transverse momentum space and ion-crystal charge exchange. The theory provides an adequate explanation for the observed angular distributions of heavy ions passing through oriented crystals, makes it possible to calculate the partial angular distributions of different charge states, and treats the discovered effects of “cooling” and “heating” of channeled ion beams in physical terms. The angular and spatial distribution of channeled ions with different energies is calculated. Whether a channeled beam of multiply charged heavy ions will be cooled or heated is related to the dependence of the electron capture and loss probabilities on the impact parameter when the ions interact with atomic chains. This interaction governs the run of the angular and spatial distribution of the channeled ion charge.     

Resonant coherent excitation of 94 MeV/u Ar17+ ions in the $$(2\bar 20)$$ planar channel of a silicon crystal

The charge exchange and characteristic x-radiation of channeled ions under resonant coherent excitation are simultaneously described in terms of the density matrix formalism. The survival fraction of 94 MeV/u Ar¹⁷⁺ ions in the \((2\bar 20)\) planar channel of a silicon crystal is calculated, and the angular distribution of x-ray emission of these ions is analyzed.     

Photon emission from channeled heavy ions excited Resonant-coherently

Abstract

The possibility of the radiative deexcitation from channeled heavy ions excited by the Okorokov Effect (Resonant coherent excitation) is discussed and the experiments on the photon emission due to the deexcitation from hydrogen-like Ne⁹⁺ and Fe⁸⁺ ions are reported.     

Radiation of channelled particles in crystals: A review

Abstract

The present paper is a review of basic works dedicated to the radiation emitted by channeled particles in crystals in a low (～100 MeV), intermediate (0.1 ? E ? 30 GeV), and high (E ? 100 GeV) energy ranges.     

On the orientation effect of the neutron yield increase in <Emphasis Type="Italic">d</Emphasis>(<Emphasis Type="Italic">d,n</Emphasis>)<Superscript>3</Superscript>Hе reactions at an energy of 7–12 keV in TiD<Subscript>2</Subscript> crystals

The orientation dependence of the d(d, n)³He reaction probability in a TiD₂ crystal at a deuteron energy of 7–12 keV is investigated. The BCM-1.0 code developed for calculating the trajectories of channeled particles within classical mechanics is used to simulate deuteron trajectories at (200)-planar channeling in a 0.15-μm-thick Ti crystal with the angular divergence of the beam taken into account. The enhancement of the reaction probability in the computer experiments is 2.1 in the case of a parallel deuteron beam and near-zero crystal entry angles relative to the (200) planes. In the case of a deuteron beam with its angular divergence equal to 1/5 of the critical channeling angle, the maximum reaction-probability enhancement is 1.5. The results of calculations agree qualitatively with recent experiments performed at Tomsk Polytechnic University.     

Linear polarization of channeling radiation from axially channeled electrons

Abstract

The degree of polarization of channeling radiation emitted by axially channeled electrons has been calculated using the many-beam method. The polarization was found to be substantial, and to increase monotonically with the channeling angle. The many-beam results are compared with those obtained from the single-string approximation and are found to be significantly different.     

The use of channeling-effect techniques to locate interstitial foreign atoms in silicon

When the channeling-effect technique is used to determine the lattice location of an impurity which is not completely substitutional, quantitative interpretation of the results requires knowledge of the interaction yield between a channeled beam and an interstitial atom. We have investigated this problem for Yb implanted into silicon. Along the <110> direction, a peak of almost a factor of two is observed in backscattering yield from the Yb atoms, using a 1-MeV He beam. The height and angular width of the peak is satisfactorily interpreted in terms of flux-peaking of the channeled beam in the central region of the <110> channels.

The existence of such a large flux-peaking effect seriously complicates quantitative determination of the location of non-substitutional impurities. However, it is still possible to establish rather accurately the lattice position of the impurity, provided the measured minimum yields and angular widths of the <111> and <100> dips are taken into account.     

Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions [kcirc] and [kcirc]′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis : along [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.     

Effect of atomic arrangement on penetration of charged particles into crystals

The angular and spectral distributions of protons having initial energies of 4–7 MeV have been studied in simple cubic ionic crystals and in germanium and silicon crystals with and without the channeling effect. The average energy losses of the channeled and unchanneled protons in the crystals were measured. The concentration of structural defects in the crystals is shown to affect the proton energy spectra measured when channeling occurs. A procedure involving photographic plates was used to study the angular distributions of the channeled protons. The possible use of proton diffraction to study the structure and other characteristics of crystals is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 8, pp. 86–91, August, 1969.     

Peculiarities of heavy ion channeling

Abstract

Depth distributions of implanted Mg⁺- and Ca⁺-ions and the corresponding radiation damage were studied for different channeling orientations of silicon crystals. The shape of the implantation profiles is discussed by using simple models for dechanneling and energy loss processes. A correlation between dechanneling, damage production and depth distributions of the channeled ions could be observed. This correlation is seen by the maxima shifts in damage and implanted ion distributions between channel and random incidence.     

Simple numerical method of computing the probabilities of angular momentum Jν occurring among possible vectors J Resulting from n angular momentum jμ summation (μ=1?n)

Arelatively simple numerical method of summing angular momentum vectors with maintaining space quantization rules of each summed angular momentum has been presented. The method enables the calculation of the values of probability (p j _μ) of finding a definite angular momentum J _μ among all vectors J being the results of quantum summation of n angular momentum vectors j _μ(μ=1-n. It may be used, e.g., in the calculations of angular momentum of many-particle states. The significance of the paper is connected with the possibility of taking into account, in a simple way, the angular momentum conservation principle for a system which consists of an arbitrary number of excitons. From Yadernaya Fizika, Vol. 67, No. 11, 2004, pp. 2123–2128. Original English Text Copyright ? 2004 by Kaczmarczyk. This article was submitted by the author in English.     

Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions [kcirc] and [kcirc]′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis: along [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.     

Measurement of average electron densities in Si and Ge using MeV δ-rays produced by channelled high-energy projectiles

For the first time, average electron densities in silicon and germanium were measured using the channeling effect for 5 and 12 GeV/c protons, π⁺ and π^?. In the investigation, the yield of MeV electrons emitted through the back of the target was measured. Such gd-ray yields are proportional to the local electron density averaged along the path of the projectile in the target. For well-aligned, positive particles, the electron yield is reduced to around 15% of normal yield for germanium and 25% for silicon, whereas negatively charged, channeled projectiles give an increase in yield by a a factor of three compared to normal yield. The experimental results have been compared to yield curves calculated using the Lindhard channeling model in connection with special potential models, and very good agreement is obtained for positive particles when the electron density in the middle of the channels is obtained by summing the contributions from many neighbouring strings. For positive projectiles, this channeling method is most sensitive far away from the strings, where other techniques are weak. The results for negative, channeled particles agree fairly well with simplified theoretical calculations, neglecting dechanneling and the lack of equilibrium in angular momenta in the transverse plane.     

Effectiveness of volume trapping into channeling in curved crystals

An analytical formula is obtained for the efficiency of scattering-induced particle transitions from above-barrier into channeled states in the volume of curved crystals (volume trapping). The predictions of the theory are in good agreement with experiments and computer simulation. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 698–701 (10 May 1996)     

The Tensors of the Averaged Relative Energy–Momentum and Angular Momentum in General Relativity and Some of Their Applications

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper.      

A study of small impact parameter ion channeling effects in thin crystals

We have recorded channeling patterns produced by 1–2 MeV protons aligned with ?1 1 1? axes in 55 nm thick silicon crystals which exhibit characteristic angular structure for deflection angles up to and beyond the axial critical angle, ψ _a . Such large angular deflections are produced by ions incident on atomic strings with small impact parameters, resulting in trajectories which pass through several radial rings of atomic strings before exiting the thin crystal. Each ring may focus, steer or scatter the channeled ions in the transverse direction and the resulting characteristic angular structure beyond 0.6ψ _a at different depths can be related to peaks and troughs in the nuclear encounter probability. Such “radial focusing” underlies other axial channeling phenomena in thin crystals including planar channeling of small impact parameter trajectories, peaks around the azimuthal distribution at small tilts and large shoulders in the nuclear encounter probability at tilts beyond ψ _a .     

Resonant influence of hypersound on the radiation of an axially channeled electron

Abstract

The spectral intensity of the radiation emitted by an axially channeled electron in a single crystal excited by a longitudinal hypersonic wave propagating along the channeling direction has been calculated for the energy range 10MeV ≤ E ≤ 100 MeV. It has been shown that under the influence of acoustic vibrations excited in the single crystal a resonant intensification of the electron channeling radiation, a variation of its spectral distribution as well as inverse radiative transitions are possible.