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Volume 61, Issue 4, 15 February 1987

A two‐dimensional theory for high‐frequency vibrations of piezoelectric crystal plates with or without electrodes
View Description Hide DescriptionTwo‐dimensional equations of motion of successively higher‐order approximations for piezoelectric crystal plates with triclinic symmetry are deduced from the three‐dimensional equations of linear piezoelectricity by expansion in series of trigonometric functions of the thickness coordinate of the plate. These equations, complemented by two additional relations: one, the usual relation of face tractions to the mass of electrodes, and the other relating face charges to face potentials and face displacements, can accommodate either the traction and charge boundary conditions at the faces of the plate without electrodes or the traction and potential boundary conditions at the faces of the plate with electrodes. Dispersion curves are obtained from the first‐ to fourth‐order approximate plate equations for a rotated 45° Y‐cut lithiumtantalate plate without electrodes, and these curves are compared with those from the frequency equation of the three‐dimensional equations with close agreement. Solutions of forced vibrations of an AT‐cut quartz plate with electrodes are obtained from the first‐order plate equations complemented by the two additional relations. It is shown that cutoff frequencies of the fundamental thickness‐shear vibrations from the approximate equations are identical to the ‘‘exact’’ ones obtained from the three‐dimensional equations.

Characterization of periodic composites by laser‐beam diffraction
View Description Hide DescriptionA method has been developed for deriving the characteristic lengths of periodic composites by diffracting a laser beam from their surface and analyzing the diffraction pattern. This method has been applied to two directionally solidified lamellar eutectics and to a fibrous composite produced by wire drawing. From the diffraction pattern the periodicity length, the width of the bright phase, and the effective fluctuation of these two lengths have been computed. The latter fluctuation characterizes the perfection of the composite.

Studies of microwave radiation from a low‐energy rotating electron beam in a multiresonator magnetron cavity
View Description Hide DescriptionThe generation of microwave radiation at high harmonics of the cyclotron frequency by a low‐energy annular rotating electron beam (27 kV, 1 A, 3 μs) via interaction with the modes of a magnetron‐type conducting boundary has been studied experimentally. Details of producing the axis‐encircling E layer by magnetic cusp injection are presented. Narrow‐band microwave radiation has been obtained from the device at power levels of 9.1 kW at 6.78 GHz (eighth cyclotron harmonic) and 2.2 kW at 8.85 GHz (tenth cyclotron harmonic). Measurements of the radiated power spectra and confining magnetic field have allowed identification of operating waveguide modes and instability mechanisms. An experimental comparison with respect to threshold beam power is presented between waveguide structures operating in the π mode and the 2π mode.

Calibration of aspirator‐type ion counters and measurement of unipolar charge densities
View Description Hide DescriptionThe characterization of a parallel plate apparatus which can produce a unipolar charge density that is suitable for calibrating aspirator‐type ion counters operating in the ground plane is described. The influence of a dcelectric field, air motion, Coulomb repulsion, and diffusion on the transport of ions into the ion counter are examined to determine their effects on instrument calibration and measurements in the vicinity of high‐voltage dc transmission lines. A charge density which is known with an uncertainty of less than ±9% is used to check the performance of an ion counter with and without a duct at its entrance.

Anode plasma ionization due to sheath heating in magnetically insulated ion diodes
View Description Hide DescriptionWe show that anodeplasma sheathheating can cause undesirable i n s i t uionization of the anodeplasma in magnetically insulated ion diodes. We find that extremely high electron energies will occur in the anodeplasma sheath due to an increasing magnetic field at the anodesurface during the diode pulse. These high‐energy electrons can collisionally ionize the plasma ions to an unwanted ionization state. Multiply ionized anodeplasma ions represent a beam contaminant that may cause undesired preheat in inertial confinement fusion(ICF) capsules. The fraction of unwanted higher ionization states increases with anodeplasma density. Therefore, this effect places an upper limit on the anodeplasma density that can be used in an ICF application. As an example, we estimate the fraction of Li^{+} ^{+} generated by sheathheating in the PBFA‐II Applied‐B ion diode as a function of the initial Li^{+}anodeplasma density and obtain an upper limit for a lithium anodeplasma density of approximately 1×10^{1} ^{6} cm^{−} ^{3}. At anodeplasma densities of 1×10^{1} ^{6} cm^{−} ^{3} or less there will be substantial motion of the ion emitting surface during the diode pulse. We discuss the advantages and disadvantages of this plasma motion.

Formation, optical properties, and laser operation of F^{−} _{2} centers in LiF
View Description Hide DescriptionFormation conditions, optical properties, and lasing behavior of F^{−} _{2} color centers in LiF crystals are investigated. The optical pumping cycle of the three‐electron defect is found to involve intermediate transitions of small efficiency into some metastable energy levels (having a lifetime of several seconds). This process could either be intrinsic to the F^{−} _{2} defects (e.g., intersystem crossing into quartet states) or it could be caused by (low efficiency) optical ionization of F^{−} _{2} centers and electron capture in unstable traps. While cw laser oscillation is prevented by a resulting bottleneck, efficient tunable pulsed laser operation in the 1.1–1.2‐μm range is possible at room temperature.

Piezoresistance response of ytterbium foil gauges shocked to 45 kbar in fused silica matrix
View Description Hide DescriptionResistance change at peak stress and the residual resistance change of ytterbium foil gauges embedded at different depths in fused silica matrix were determined under shock loading to a stress of 45 kbar. The results show that for a given peak stress, the gauge response was unchanged for an order of magnitude variation (10^{3}–10^{4} kbar/μs) in the loading rate. Measured resistance change at peak stress and upon unloading agree very well with the analytic model calculations for stresses up to 30 kbar in the fused silica. Peak resistance change values in the present work have been reconciled with earlier ytterbium data in a polymethylmethacrylate (PMMA) matrix on the basis of differences in longitudinal stress in the gauge foils for the two materials (polymethylmethacrylate and fused silica) and differences in the electromechanical constants of the two sets of foils. Above 30 kbar stress in the fused silica, measured resistance values are lower than the calculated values. This difference is attributed to changes in the ytterbium as a result of the initiation of the fcc to bcc phase transition. The resistance change‐time profile from the 45‐kbar experiment shows a strongly time‐dependent behavior suggesting that a significant fraction of the material has been transformed.

Stability enhancement of a low initial density hollow gas‐puff z pinch by e ^{−} beam preionization
View Description Hide Descriptione ^{−} beam preionization of the initial gas column of the hollow gas‐puff z pinch at the University of California, Irvine is shown to decrease the amplitude of Rayleigh–Taylor instabilities which disrupt the imploding plasma shell of low initial density (<1×10^{1} ^{7} cm^{−} ^{3}) helium pinches. A 5‐ns pulsed nitrogen laser Mach–Zehnder interferometer compares the plasma density profile at various times during the implosion for preionized and unpreionized pinches. Also, a B‐dot current probe compares the plasma induction fluctuations of the pinched state. Numerical calculations of the effects of the Rayleigh–Taylor growth for our geometry are discussed.

Electron‐density distribution in a laser tube with a hyperboloid of revolution boundary
View Description Hide DescriptionThe electron‐density distribution is determined in a laser tube that is formed by a hyperboloid of revolution and spherical end surfaces. Calculations are made assuming different symmetrical optical resonator configurations ranging from near‐planar to near‐confocal. The tube geometry is specified in terms of the optical resonator parameters: resonator length L, mirror radius of curvature, R, and optical spot size at the mirrorsurface. The active medium is assumed to be a low‐temperature, weakly ionized plasma.Schottkyboundary conditions are assumed and the electron temperature is taken to be independent of position. The particle‐diffusion equation is solved using oblate spheroidal coordinates. The oblate spheroidal angular dependence (which in the cylindrical limit corresponds to the variation perpendicular to the axis of the cylinder) of the density is found to be that of a zero‐order Bessel function. The oblate spheroidal radial dependence (which in the cylindrical limit corresponds to the axial dependence) is obtained by means of numerical methods. Radial density profiles are calculated, assuming L=1.0 m, for various R/L ratios. The position Z _{ p } of the peak radial density is found to depend on the R/L ratio; as R/L decreases Z _{ p } is observed to move towards the end walls of the tube.

3D computer simulation of the primary electron orbits in a magnetic multipole plasma source
View Description Hide DescriptionPerformance characteristics of the magnetic multipole plasma source depend strongly on the structure of the line‐cusp magnetic fields and the behavior of the primary electrons. In order to design and improve the plasma source efficiently, we developed a computer code which can simulate primary electron orbits in the three‐dimensional magnetic field generated in the source. Using this code, we compared the orbits of the primary electrons in the arc discharges with and without the mode‐flip phenomenon. The result indicates that the trapping of the primary electrons in a local magnetic mirror fields causes the mode flip due to the reduction of the effective anode area. Trapping also degrades the spatial uniformity of the sourceplasma density, due to local arc discharge. The structure of the magnetic field can be optimized so that the primary electrons fill the center region of the source. The 3D simulation of the electron orbits turned out to be effective and useful in designing a multipole source.

Impurity induced layer disordering of Si implanted Al_{ x }Ga_{1−x }As‐GaAs quantum‐well heterostructures: Layer disordering via diffusion from extrinsic dislocation loops
View Description Hide DescriptionExtensive data are presented on impurity‐induced layer disordering (IILD) of Al_{ x }Ga_{1−x }As‐GaAs quantum‐well heterostructures and superlattices that are Si implanted and annealed (Si^{+}‐IILD) at three different implant doses. We show that impurity activation is not critical to the layer disordering process and that Si diffusion from the implanted profile initiates Si^{+}‐IILD. When the implant dose is as high as φ≥5×10^{1} ^{3}/cm^{2} (n _{Si} ≥2×10^{1} ^{8}/cm^{3}), Si interstitial loops (Si‐ILs) form by diffusion and agglomeration of the implanted Si atoms during the initial stages of annealing. If a source of Ga vacancies is provided (e.g., via an As overpressure or SiO_{2} encapsulation), the Si‐ILs dissociate and supply Si atoms for diffusion and hence Si^{+}‐IILD during the latter stages of annealing. If a Si_{3}N_{4} encapsulant is employed, however, fewer Si‐ILs form and Si diffusion is inhibited. For an implantation dose as low as φ=1×10^{1} ^{2}/cm^{2} (n _{Si} =3×10^{1} ^{6}/cm^{3}), extensive Si^{+}‐IILD is realized via capless annealing and Si‐ILs are not observed. It is significant for device applications that the layer‐disordered material operates as a cw 77 K photopumped laser, which indicates that the layer averaging (IILD) does not damage the crystal.

Strain in GaAs by low‐dose ion implantation
View Description Hide DescriptionThe production of strain in (100) GaAs by low‐dose ion implantation has been investigated. Implantations were conducted at room temperature with ions of He, B, C, Ne, Si, P, and Te. Energies were between 100 and 500 keV, and each species was implanted over a range of doses sufficient to create perpendicular strain below 0.3%. The perpendicular strains ε ^{⊥} were measured by x‐ray double‐crystal diffractometry about the (400) Bragg condition. Detailed depth profiles of ε^{⊥} were obtained by fitting the resulting rocking curves with a kinematic model for the diffraction. For all implantations the maximum in the ε^{⊥} distribution was found approximately from the separation of the lowest‐angle prominent oscillation from the substrate peak. The depth profiles of perpendicular strain had the same shape as the calculated profiles of energy deposited per ion by nuclear collisions, F _{ D }. The maximum perpendicular strains scaled linearly with the dose φ of the implanted ions for all ion species. Also the ratio of maximum strain to dose was found to vary linearly with F _{ D } over more than 2 orders of magnitude in F _{ D }. We therefore conclude that ε^{⊥}=KφF _{ D } at all depths, where K is a constant. The value of K was found to be (5±1)×10^{−} ^{2} Å^{3}/eV. Our results suggest that this holds for any ion species in the mass range 4–128 amu, with energy in the hundreds of keV, implanted into (100) GaAs at room temperature, provided the maximum strain is less than 0.3%.

Determination of dopant and deep imperfection profiles in p‐type CdTe by improved constant capacitance‐voltage transient measurements
View Description Hide DescriptionBy constant capacitance‐voltage transient measurements we are able to determine the dopant and deep imperfection density versus distance profiles, regardless of either the absolute density of imperfection levels, or their density relative to the dopant density. The data analysis of the method is similar to the well‐known capacitance versus voltage measurement, which is very convenient compared to other imperfection profiling methods.

Particle size distribution from small‐angle scattering data: A histogram technique
View Description Hide DescriptionA method of reparametrizing small‐angle scattered intensity spectra I(q) in terms of the q=0 contributions from populations of spheres of discrete radii I _{0}(r) is described. The minimal assumptions are made that the scattering from a particulate system can be parameterized as a distribution of sizes of solid spheres, and that the particle positions are uncorrelated. The calculated size distribution can be used to define either the multimodal size distributions of spherical particles or the shape of monodisperse, nonspherical particles. In any case, its usefulness is limited at high concentrations where the particle–particle correlation function has significant structure. The applicability of this technique is demonstrated with calculated spectra and experimental results from water‐in‐oil microemulsions.

Range and shape factors, damage, regrowth, and redistribution for Ag implants in (100) and (111) Si
View Description Hide DescriptionThe nature of regrowth of implantation‐damaged (100) and (111) Si was investigated by measuring the depth distribution of implanted Ag atoms following annealing at 550 °C for fluences of 1×10^{1} ^{2} to 1×10^{1} ^{5} cm^{−} ^{2}. Cross‐section transmission electron microscopemeasurements were made for a few conditions to compare damage depth distributions. Other factors studied were anneal time, Si growth technique, Ag atom densities, and the transition region between amorphous and crystalline Si. Ranges and profile shape factors are reported for 150, 300, 450, and 600 keV Ag implants into Si.

Amorphous Ti‐Si alloy formed by interdiffusion of amorphous Si and crystalline Ti multilayers
View Description Hide DescriptionReactions upon rapid thermal annealing of sputtered Ti‐Si multilayers have been studied by cross‐section and through‐foil transmission electron microscopy, glancing‐angle Rutherford backscattering, and x‐ray diffraction. The compositions of the samples are 40 at. % Ti, 60 at. % Si and 60 at. % Ti, 40 at. % Si, and the bilayer periodicity is about 10 nm. The silicon layers in the as‐deposited films are amorphous; the titanium layers are polycrystalline hcp. After a 30‐s anneal at 455 °C, significant interdiffusion occurs and we observed the formation of an amorphous Ti‐Si alloy by interfacial reaction. The metastable disilicide, C49 TiSi_{2}, nucleated along with a small amount of TiSi in the sample with higher silicon content (60%) upon annealing at 550 °C for 10 s, but the amorphousalloy remained as the only product of reaction in the 40‐at. % Si sample.

Onset of runaway nucleation in aerosol reactors
View Description Hide DescriptionThe onset of homogeneous nucleation of new particles from the products of gas phase chemical reactions was explored using an aerosol reactor in which seed particles of silicon were grown by silane pyrolysis. The transition from seed growth by cluster deposition to catastrophic nucleation was extremely abrupt, with as little as a 17% change in the reactant concentration leading to an increase in the concentration of measurable particles of four orders of magnitude. From the structure of the particles grown near this transition, it is apparent that much of the growth occurs by the accumulation of clusters on the growing seed particles. The time scale for cluster diffusion indicates, however, that the clusters responsible for growth must be much smaller than the apparent fine structure of the product particles.

Effects of dielectric encapsulation and As overpressure on Al‐Ga interdiffusion in Al_{ x }Ga_{1−x } As‐GaAs quantum‐well heterostructures
View Description Hide DescriptionData are presented showing that the Al‐Ga interdiffusion coefficient (D _{Al‐Ga}) for an Al_{ x }Ga_{1−x }As‐GaAs quantum‐well heterostructure, or a superlattice, is highly dependent upon the crystal encapsulation conditions. The activation energy for Al‐Ga interdiffusion, and thus layer disordering, is smaller for dielectric‐encapsulated samples (∼3.5 eV) than for the case of capless annealing (∼4.7 eV). The interdiffusion coefficient for Si_{3}N_{4}‐capped samples is almost an order of magnitude smaller than for the case of either capless or SiO_{2}‐capped samples (800≤T≤875 °C). Besides the major influence of the type of encapsulant, the encapsulation geometry (stripes or capped stripes) is shown, because of strain effects, to be a major source of anisotropic Al‐Ga interdiffusion.

Effects of ion‐implantation damage on two‐dimensional boron diffusion in silicon
View Description Hide DescriptionModel two‐dimensional distributions of implantedboron and implantation‐induced displacement damage near a mask edge are used to calculate the two‐dimensional redistribution of boron resulting from a typical short‐time anneal. The damage is removed during annealing by releasing vacancies which enhance the diffusion of boron. The effect is that boron preferentially redistributes further into the bulk. Such considerations become increasingly important as metal‐oxide‐semiconductor field‐effect transistors become smaller.

Effects of vanadium and chromium on aluminum electromigration
View Description Hide DescriptionA systematic study was made of electromigration in homogeneous Al‐V and Al‐Cr thin films. V and Cr concentrations were varied in the range of 0–2 wt. %, and films were prepared both with and without 1% Si. The addition of as little as 0.1% V caused significant improvements in lifetime relative to pure Al. In the most concentrated alloy studied, the activation energy of mass transport had increased from 0.54 eV for pure Al to 0.92 eV for Al‐1.1% V. For the Al‐Cr alloys, a maximum in lifetime was found at 0.4% Cr. Higher concentrations of Cr resulted in a gradual degradation of the enhanced lifetime. Lifetimes were reduced when 1% Si was added to either alloy system. Alloy microstructure was examined using transmission electron microscopy. Contrary to results for other Al alloys, lifetimes were reduced in films with extensive precipitation.