Aluminium diffusion in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained (B ₊ films) film structures, respectively, have been examined as diffusion barriers for preventing aluminium diffusion. The aluminium diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) at temperatures up to 550° C. The diffusivity from 300° C to 550° C is: D[m²s^–1]=3×10^–18 exp[–30/(RT)] in B ₀ layers and D[m²s^–1]=1.4×10^–16 exp[–48/(RT)] in B ₊ TiN layers. The activation-energy values determined indicate a grain boundary diffusion mechanism. The difference between the diffusion values is determined implicitly by the microstructure of the layers. Thus, the porous B ₀ layers contain a considerable amount of oxygen absorbed in the intercolumnar voids and distributed throughout the film thickness. As found by AES depth profiling, this oxygen supply allows the formation of Al₂O₃ during annealing the latter preventing the subsequent diffusion of the aluminium atoms.     

Diffusion of silicon in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained film structure (B ₊ films) have been examined as diffusion barriers, preventing the silicon diffusion in silicon devices. The silicon diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) after annealing at temperatures up to 900° C, in view of application of high-temperature processes. The diffusivity from 400 to 900° C: D (m² s^–1)=2.5×10^–18 exp[–31 kJ/mol/(RT)] in B ₀ layers and D (m² s^–1)=3×10^–19 exp[–26 kJ/mol/(RT) in B ₊ TiN layers. The diffusivities determined correspond to grain boundary diffusion, the difference being due to the different microstructure. The very low diffusivity of silicon in B ₊ TiN layer makes it an excellent high-temperature barrier preventing silicon diffusion.     

Magnetic- and stress-fields of cylindrical non-uniform current density superconducting coils

Superconducting coils with an inhomogeneous current density distribution yield more field for less volume of superconductor. The advantages of these systems are lower costs and an improved cooling. The latter is important for high field magnets. Mechanical stresses induced by the electromagnetic forces are the limiting factor in designing such coils. The inhomogeneous current field is produced by a set of concentric subcoils. The radial and tensile stresses and the radial displacements in the subcoils are calculated. This calculation requires the field-shape in the coils. An exact calculation shows a linear decrease of the field with the radius in each subcoil. Thus the stress-calculations are very simple and one does not need a computer. As an example this method is applied to a 10 T-magnet with three subcoils. In this case the results of our exact calculation differ from the approximation of Kilbet al., Steklyet al. and from the magnetic pressure estimateB ²/2μ ₀ up to a factor of three.     

The filling of neutron star magnetospheres with plasma: Dynamics of the motion of electrons and positrons

We consider the motion of charged particles in the vacuum magnetospheres of rotating neutron stars with a strong surface magnetic field, B ≳ 10¹² G. The electrons and positrons falling into the magnetosphere or produced in it are shown to be captured by the force-free surface E · B = 0. Using the Dirac-Lorentz equation, we investigate the dynamics of particle capture and subsequent motion near the force-free surface. The particle energy far from the force-free surface has been found to be determined by the balance between the power of the forces of an accelerating electric field and the intensity of curvature radiation. When captured, the particles perform adiabatic oscillations along the magnetic field lines and simultaneously move along the force-free surface. We have found the oscillation parameters and trajectories of the captured particles. We have calculated the characteristic capture times and energy losses of the particles through the emission of both bremsstrahlung and curvature photons by them. The capture of particles is shown to lead to a monotonic increase in the thickness of the layer of charged plasma accumulating near the force-free surface. The time it takes for a vacuum magnetosphere to be filled with plasma has been estimated.     

Self-consistent equilibria in a cylindrical reversed-field pinch

Summary A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma+gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions:a) to the lowest order, the turbulent dynamo electric fieldE ^t is expressed as a homogeneous function of degree 1 of the magnetic fieldB, sayE ^t =α·B, with α being a 2nd-rank tensor, homogeneous of degree 0 inB, and generally depending on the plasma state;b)E ^t does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both α and the plasma resistivity η are isotropic and constant, the magnetic field turns out force-free with constant abnormality αμ₀/η for vanishing axial electric fieldE _z . This case has also been solved analytically, for whateverE _z , under circular, besides cylindrical, symmetry.     

Magnetic dipole moment of127Sb by NMR/ON

The technique of NMR on oriented nuclei has been applied to¹²⁷Sb to measure the magnetic dipole moment of the¹²⁷Sb ground state. Resonant destruction of gamma-ray anisotropy from¹²⁷Sb^g (I =7/2⁺) has been observed at 139.6(2) MHz forB _app=0.30(1) T andat 138.7(1) MHz forB _app=0.25(1) T. The deduced magnetic moment is ||=2.697(6) µ_N.     

Excited Muonic Atom Scattering: New Adiabatic Approach

New results on the applied field dependence of the NMR of ⁷⁵Se implanted in pure iron and oriented at millikelvin temperatures are reported. They yield the magnetic hyperfine field acting on Se nuclei present as dilute impurities in the iron matrix and the magnetic dipole moment of the 5/2⁺ ground state of ⁷⁵Se with significantly improved precision. The results are B _hf(SeFe) =+67.9(10)T and ||(⁷⁵Se) =0.683(10)_N. The improved value of the hyperfine field, with data from[2], gives the magnetic dipole moment of the 9/2⁺ ground state of ⁷³Se as ||=0.892(13)_N.     

Calculation of magnetic field in the region of the superconducting winding of window frame dipole for particle accelerators

The necessity of simulations in design of superconducting dipole magnets is due to the following circumstances. First, the critical current as a function of the magnetic field I _c(B) for the multicore superconducting cable which drops strongly requires the knowledge of the value of maximum magnetic field “felt” by its coils for estimation of the working current of the magnet. Second, for choosing the optimal number of coils of the winding (1 or 2) and the working current of the magnet, the ratio of B _max for the inner and outer layers of the dipole magnet winding should be known. Since usually the length of the dipole magnet exceeds many times its transverse size, in this work all calculations of B(x, y) are performed in the transverse plane crossing the center of the magnet. The field at the central point is chosen to be B(0, 0) = 2 T (this is the characteristic working value close to the maximum value in the dipole magnet of this type). In this work, the results of calculation of B(x, y) for single-and double-layered windings with 8 and 16 coils from circular hollow cable are presented.     

Crystal-field splitting and temperature dependence of two-dimensional antiferromagnetism in the high-Tc compound DyBa2Cu4O8

By means of a quantitative analysis of extensive elastic neutron scattering experiments performed on theT _c =78 K superconductor DyBa₂Cu₄O₈ it is shown that two-dimensional (2D) antiferromagnetic Dy ordering in the (a,b)-plane remains stable in the whole temperature range fromT _N =(1.10±0.02) K down to 7 mK. The magnetic difference pattern with good angular resolution fits well to the Warren equation for scattering on 2D systems with powder averaging. Consequently, the fitted sublattice magnetisation is found to have a 2D Ising character. Moreover, the Dy³⁺ crystal-field levels were determined by inelastic neutron scattering. From the resulting crystal-field parameters we calculate the sublattice magnetisation of Dy³⁺ at saturation to be _Dy,CEF=6.0 _B in good agreement with _Dy,obs=(5.9±0.5) _B as measured by neutron diffraction.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Electron mobility in compensated VPE GaAs films

Electron Hall mobilities were measured on a series of intentionally compensated vapor phase epitaxy (VPE) GaAs layers. Using Sn and Zn as dopants, compensation ratiosK=(N_D+N_A)/(N_D-N_A) as high as 50 were obtained. Already for samples with the lowestK values the 300 K mobilities are higher than the 77 K values. In the range 20<T<100 [K] the data may be represented by μ∼T ^α with α increasing from 0.6 to 1.1 with compensation. The experimental μ values are smaller than those predicted from current models in all cases. It appears that scattering at ionized impurities is the dominant process also at temperatures well above 77 K, and that this scattering process is quantitatively underestimated in current models.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

Perpendicular magnetic anisotropy of FePt film on Si substrate with SiO2 underlayer and B4C interlayers

FePt multilayer composite films with and without B₄C interlayer have been prepared by magnetron sputtering, respectively, and subsequent annealing in vacuum. It was found that the B₄C layers effectively serve as spacers to separate the FePt layers, enhancing (0 0 1) orientation of FePt alloy. Our results show that highly (0 0 1) oriented FePt/B₄C films have significant potential as perpendicular recording media.     

Magnetic Moment of the 3/2− Ground State of 185W

Nuclear magnetic resonance measurement have been performed for ¹⁸⁵W oriented at 8 mK in an Fe host. The magnetic hyperfine splitting frequency at an external magnetic field of 0.1 T was determined to be 196.6(2) MHz. With the known hyperfine field of B _hf = −71.4(18) T, the nuclear magnetic moment of ¹⁸⁵W is deduced as μ(¹⁸⁵W) = +0.543(14) μ_N.     

Spectral Ellipsometry of Multilayer ZnS/ZnSe Heterostructures

By the method of spectral ellipsometry with binary modulation of the polarization state the dispersions of the refractive index n, absorption coefficient k, and layer thickness in ZnS/ZnSe multilayer structures grown by the chemical gasphase deposition method from heteroorganic compounds on GaGaAssubstrates with ZnSe buffer layers have been determined. The efficiency of local ellipsometric measurements (with a light beam size less than 150 × 500 m) permitting mapping of the parameters of structures with A²B⁶ layers up to a few microns thick has been demonstrated. The optical properties of oxide layers formed on the zinc selenide surface have been investigated. Multilayer structures (ZnSe/ZnS) _n /ZnSe/GaAs with a pronounced exciton absorption and specific features in the reflection spectra coinciding in energy with exciton transitions, as well as Bragg mirrors with a reflection coefficient up to 99% in the blue region of the spectrum, have been studied.     

Hadronic equation of state and the onset of kaon condensation

An equation of state is presented which takes the finite size of baryons and of mesons consistently into account and incorporates the contributions of both nonstrange and strange hadrons. All extensive quantities (energy, particle number, entropy) are modified by a factor taking into account the excluded volume due to baryon repulsion. Intensive quantities (pressure) are not modified. This is achieved by introducing a baryon chemical potential, _B, which is shifted from its point-like value, _B ⁰ , by a term proportional to the finite volume of a hadron,V ₀, as follows: _B= _B ⁰ + V₀[P⁰(T, _B ⁰ )–P⁰(T, 0)], whereP ⁰ is the pressure for pointlike particles. The last term is necessary to conserve baryon number at the phase transition point. The differences between the new equation of state and those considered previously in the literature are discussed. It is shown that kaon condensation sets in only in the mixed phase of the transition, where hadrons, quarks and gluons are present simultaneously in thermodynamical equilibrium.     

Evidence for complex magnetic order in U2Zn17: A μ+ SR studySR study

μ⁺ SR-measurements in transversally applied magnetic fields of 2000 G and 4000 G on heavy-electron single crystal U₂Zn₁₇ are presented. They reveal that at least two types of interstitial sites are occupied by the positive muons. One of these sites (1/3, 2/3, 5/6) could be identified via induced local dipolar fields which aboveT _N=9.7 K can exactly be derived from the magnetic susceptibility. The corresponding component of the μ⁺-signal exhibits a steplike decrease by about 40% atT _N which is caused by the onset of a very broad distribution of static internal magnetic fields (ΔB≈1000 G) with zero average. Such a field distribution is in distinct contrast to dipolar-field calculations performed for the simple antiferromagnetic structure deduced from neutron diffraction. The remaining 60% of the muons contributing to this component belowT _N are subject to a narrow static field distribution (ΔB≈1 G). The induced dipolar fields at the site (1/3, 2/3, 5/6) are temperature-independent belowT _N. A weak dipolar coupling to the U-moments renders similar observations for muons occupying the second type of interstitial impossible.     

Two successive magnetic transitions in Y2Cu2O5 studied by μSR

Zero field muon spin rotation and magnetic susceptibility experiments on investigation of magnetic properties of cuprateY ₂Cu₂O₅ have been performed in the temperature range 4.2–30 K. Transverse fieldSR-experiments have been also carried out in order to obtain accurate information about transition temperature and to study the influence of the external magnetic field. Our data show that two magnetic phase transitions occur inY ₂Cu₂O₅ with lowering temperature. Upper Neel temperatureT _N=13 K is consistent with previous experimental data. We obtained the temperature dependence of the local magnetic field on the muonB (T) in the antiferromagnetic phase.B (T) reveals a peculiarity (some change of the slope) near the temperatureT _N=7.5 K, which can be interpreted as an additional magnetic phase transition caused by a change in magnetic ordering of the copper subsystem. Applying a small external magnetic field 50 Oe leads to smearing of the peculiarity inB (T) dependence.     

Domain-wall energy in sintered Nd15Fe77B8 permanent magnet

From measurements of the magnetic domain widthsD versus grain thicknessL, we have determined the domain wall energy in the demagnetized state for a sintered Nd₁₅Fe₇₇B₈ magnet: = 56 erg/cm². Using this wall energy and the published magnetocry-stalline constantK ₁=4.9×10⁷ erg/cm³, we have calculated the exchange constantA=4.0×10^–6 erg/cm, domain wall thickness _B=89 Å, and the critical diameter for single domain particlesD _c=0.67 m.     

Statistical mechanics of braided Markov chains: I. Analytic methods and numerical simulations

We investigate numerically and analytically the statistics of Markov chains on so-called braid (B _n ) and locally free (ℒℱ _n ) groups. Namely, we compute the mean length 〈μ〉 and the variance 〈μ²〉−〈μ〉² of the shortest word which remains after applying of all group relations to the randomly generatedN-letter word (Markov chain). We express the conjecture (numerically justified) that the mean value 〈μ〉 for the random walk on the groupB _n (n≫1) coincides with high accuracy with the same value for the random walk on the “locally free group weth errors” if the number of errors is of order of 20%.