Impurity lattice location and recovery of structural defects in semiconductors studied by emission channeling

Doping of semiconductors by ion implantation usually requires implantation doses below 10¹³ cm^–2 to obtain typical impurity concentrations of <10¹⁸ cm^–3. The lattice location of impurities as well as the defect recovery after such low dose implantations can be studied using the emission channeling technique. In this technique, single crystals are doped with radioactive probe atoms and the channeling effects of electrons, positrons or -particles emitted from these atoms are measured. We present a quantitative analysis of electron emission channeling measurements after heavy-ion implantation into Si and III–V compound semiconductors by comparison with calculated channeling profiles based on the dynamical theory of electron diffraction. For In atoms implanted into Si, complete substitutionality was found after rapid thermal annealing to 1200 K. For lower annealing temperatures, the observed channeling effects indicate small mean displacements (of about 0.2 Å) of the In atoms from substitutional sites, caused by residual implantation defects. For GaAs, GaP and InP implanted at low temperatures with In or Cd isotopes, pronounced recovery stages around 300, 400 and 350 K, respectively, were observed and substitutional fractions close to 100% were derived after annealing above the stage.     

830 nm emission in sodium vapor

We demonstrate that the intriguing 830 nm coherent emission, which is observed when sodium vapor is pumped with a high-power pulsed laser tuned near the 3S4D two-photon transition, is due to an axially phase-matched six-wave mixing process. This conclusion is based upon the observation of emission near 584 nm, which is coupled to the 830 nm emission in the six-wave mixing process: ₁+₂=2_L–_4D4P –_4P3D . In addition, we have observed coherent emission near 1.16 m, which is due to an analogous process involving cascade through the 4S (as opposed to the 3D) state. We calculate the wavelengths of all photons involved in these processes using the standard formulas of parametric wave-mixing theory, and show that they can be predicted to within experimental uncertainties. Finally we report observations of significant blue shifts of the 830 nm and 1.16 m emissions in a mixed sodium-potassium vapor. These shifts can be readily understood by considering the effect of the potassium on the frequency-dependent refractive index of the vapor. Due to these results, other recent interpretations of the 830 nm emission as stimulated excimer emission on the Na₂ 1³ _g ⁺ 1³ _u ⁺ band must now be rejected.     

The magnetic behavior of Co atoms on the surface and in the interior of the noble metals Au,Ag and Cu

The magnetism of Co atoms in the interior and on the surface of the noble metals has been studied by means of the anomalous Hall effect. On the surface of all three noble metals Co possesses a magnetic moment even at lowest studied coverages of 0.02 atomic layers. Ferromagnetic ordering appears at Co thicknesses of about one atomic layer. Co as a bulk impurity is non-magnetic in Cu whereas it is magnetic in Ag.     

Structural state of Cu-Be-Ag alloys in the process of decomposition of solid solution

Investigation of aging Cu-1.5% Be-2% Ag and Cu-1% Be-4% Ag alloys was carried out in this study by the methods of x-ray analysis of monocrystals, and electron microscopy. In the aging process at 218, 300, and 450C, laminar zones of Guinier-Preston, enriched with beryllium and silver atoms were formed. Entry of silver into the zones widens the upper temperature interval of the zone stage to 450C. With the increase of annealing time the metastable-phase was precipitated. The crystals of -phase are precipitated with orientation in the direction (100) in consequence of interactions of the fields of elastic stresses occurring around -precipitations, and periodic structure is formed in the alloy. The stable phase-CuBe and Ag was precipitated in the Cu-1% Be-4% Ag-alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–25, August, 1972.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

Energy relaxation in aϕ 4 with long range interactions

We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of ⁴-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E _n(t)E _n > of the fluctuations of the one-particle energiesE _n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N₀(T). The temperature dependent time scale ₀ can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .     

Percolation of level sets for two-dimensional random fields with lattice symmetry

Let (x),x², be a random field, which may be viewed as the potential of an incompressible flow for which the trajectories follow the level lines of . Percolation methods are used to analyze the sizes of the connected components of level sets {x:(x)=h} and sets {x:(x)h} in several classes of random fields with lattice symmetry. In typical cases there is a sharp transition at a critical value ofh from exponential boundedness for such components to the existence of an unbounded component. In some examples, however, there is a nondegenerate interval of values ofh where components are bounded but not exponentially so, and in other cases each level set may be a single infinite line which visits every region of the lattice.     

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

Temperature dependence of anomalous Rutherford scattering of fast electrons in crystals

In contrast to the channeling of positively charged particles, the effect of the crystal temperature on orientational scattering of fast electrons has not been investigated up to now. Only in [1] did they observe a decrease in the efficiency of the inverse scattering of ^–-particles upon the heating of <100> KCl and KBr crystals, which they explained by a decrease in the efficiency of focusing of the electrons on chains of atoms. In this article the effect of thermal vibrations of atoms on the interaction of electrons with single crystals is discussed within the framework of the model of bound states of fast electrons with atomic arrays and crystal planes, which consistently explains both the high penetration of particles into the lattice and the anomalous Rutherford scattering under channeling conditions [2, 3]. Detailed discussion is carried out for <111> and (100) Si crystals and electron energy E=(1.0–1.5) MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 29–35, July, 1978.     

On purely radiative space-times

The existence of space-times representing pure gravitational radiation which comes in from infinity and interacts with itself is discussed. They are characterized as solutions of Einstein's vacuum field equations possessing a smooth structure at past null infinity which forms the future null cone at past timelike infinity with complete generators. The pure radiation problem is analysed where free initial data for Einstein's field equations are prescribed on the null cone at past time-like infinity. It is demonstrated how the pure radiation problem can be formulated as a local initial value problem for the symmetric hyperbolic system of reduced conformal vacuum field equations. Its solutions are uniquely determined by the free data.Work supported by a Heisenberg-fellowship of the Deutsche Forschungsgemeinschaft     

Additivity of vector gleason measures

We study the degree of additivity of orthogonal Hilbert-space-valued measures on the latticeL(H) of all projections acting on a Hilbert spaceH. We present criteria for such measures to be completely additive and we establish the connection between the additivity of orthogonal measures and the size of almost disjoint families on dimH. [For example, we show that everyH-valued orthogonal measure is weakly-additive iff (dimH) > dim H]. As a corollary we see that finitely additive orthogonal measures distinguish dimensions of Hilbert spaces (this can be viewed as a generalization of a theorem by Kruszynski). As a further corollary, we obtain that, for cardinals, with >,3, there is no Jordan homomorphism from a typeI -factor into a typeI -factor. Finally, we show that every latticeL(H) with (dimH) = dimH admits a nonzero free orthogonal measure with values inH. Our results contribute to the noncommutative probability theory and also may find applications in the theory of the representation ofC ^*-algebras.     

The paramagnetic state (μ+e−) in silicon and tellurium at high temperature

The paramagnetic state (⁺e^–) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: _Si = 1.45(3) s, _Te = 12.5(8) s at 290 K, _Te = 12(2) s at 250 K.     

Investigation of the radiation damage to a single crystal of KCl using the method of backward scattering and chaneling of hydrogen and helium ions

The method of channeling and backward scattering of H⁺ and He⁺ ions has been used to analyze the radiation defects in a single crystal of KCl when the crystal is irradiated with H⁺ and He⁺ ions with energies of 1 MeV. The position of the displaced atoms in the crystal lattice was determined and the value of the cross section for the formation of radiation defects and their rate of formation as a function of the radiation dose and orientation of the bombarded beam with respect to the 100 crystallographic axes of the crystal are found. The effect of an external electric field on the formation of the radiation defects was investigated. The effects of irradiation with H⁺ and He⁺ ions are compared with one another. It is shown that mechanisms connected with ionization and excitation of the crystal atoms make the main contribution to the formation of defects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 49–53, March, 1980.     

Cluster calculations of the interactions of μ+ with lattice defects in Li

Using the Hartree-Fock Roothaan scheme we have carried out molecular cluster calculations to study the interaction of positive muon with host metal atoms and intrinsic lattice defects in lithium. The total ground state energies of the clusters are calculated selfconsistently for various assumed impurity-host configurations. From the minimum in the total energy curve, we are able to determine the equilibrium lattice constant, the relaxation of first near neighbors around the impurity, the binding energy of the muon to a lattice trap and the activation energy for muon diffusion. Extension of the present method to treat ⁺-defect complexes in other metallic hosts are discussed.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Escape times in interacting biased random walks

The dynamics ofN particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on theN sites of the lattice closest to the wall. ForN=1 the leading behavior of the first passage timeT _FP to a distant sitel is known to follow the Kramers escape time formulaT _FP ^l where is the ratio of hopping rates toward and away from the wall. ForN > 1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes toT _FR ^IN. First passage times for the other particles are studied as well. A second question that is studied pertains to survival timesT _s in the presence of an absorbing barrier placed at sitel. In contrast to the first passage time, it is found thatT _s follows the leading behavior independent ofN.     

Interaction between recoil-implanted111In impurities and radiation damage in silver

We report a study of the impurity-radiation damage interaction for In in silver. Time-differential perturbed angular correlation experiments were carried out on¹¹¹Cd, the radioactive daughter of¹¹¹In produced and recoiled in Ag following the¹⁰⁹Ag(, 2n)¹¹¹In nuclear reaction. All irradiations were performed at 80 K. The dose-rate and annealing temperature dependences of the defect-induced quadrupole interaction on¹¹¹Cd were investigated. Clear differences are observed between the effects of correlated damage (the impurity interacting with the damage created by its own recoil) and uncorrelated damage (where the impurity is submitted to the influence of other damage cascades). In the former case (low dose-rate experiments), about 6% of the¹¹¹In impurities are subject to a well-defined quadrupole interaction which is ascribed to a near-neighbor vacancy. This proportion is temperature-independent up to 500 K, but the amplitude of the quadrupole frequency is reduced by a factor of three between 300 and 400 K. Assuming vacancy release by the impurity, this would lead to a binding energy of 0.34(15) eV. The remainder of the¹¹¹In nuclei are subject to a distribution of quadrupole interactions presumably due to a statistical repartition of lattice defects at some distance from the impurities. The width of the distribution changes upon annealing: a clear transition takes place at 200 K, which is the divacancy mobility threshold in Ag deduced from resistivity experiments. When cascade overlap occurs (high dose-rate experiments), no impurity-defect trapping is evidenced but a distribution of quadrupole interactions due to surrounding damage is still found. From these experiments, an order of magnitude of the damage cascade size is deduced. Our results are discussed in terms of available information on the impurity-damage interaction in various hosts; a compilation of all results on the impurity-vacancy interaction known to us is also presented in the paper.This work is part of a Ph.D. Thesis submitted by L. Thomé to Université Paris-Sud.     

Correction: New stiff matter solutions are really not stiff

Four new solutions in general relativity have recently been derived as representing static spherically symmetric stiff matter,=p. It is pointed out that the equation of state is, in fact,+p=0. It is further shown that two of the solutions are physically reasonable, turning out to represent the vacuum, one of them with a term.     

Spectral duality for planar billiards

For a bounded open domain with connected complement inR ² and piecewise smooth boundary, we consider the Dirichlet Laplacian- on and the S-matrix on the complement ^c . We show that the on-shell S-matricesS _k have eigenvalues converging to 1 askk ₀ exactly when-- has an eigenvalue at energyk ₀ ² . This includes multiplicities, and proves a weak form of transparency atk=k ₀. We also show that stronger forms of transparency, such asS _{k 0} having an eigenvalue 1 are not expected to hold in general.