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Volume 72, Issue 7, 01 October 1992

On the image brightness of the trench bottom surface in a scanning electron microscope
View Description Hide DescriptionTrajectories of secondary electrons (SEs) as an image signal in scanning electron microscopy are studied analytically in high‐aspect‐ratio submicron wide infinite trenches. It is found that the SE collection efficiency ξ, which is defined as the ratio of the number of SEs exiting the trench top surface divided by that emitted from the trench bottom surface, has the following dependencies on magnetic flux density B _{ z } generated by an objective lens and electric fieldE _{ z }. Here, B _{ z } and E _{ z } are the components perpendicular to the wafer surface. For a low B _{ z } region corresponding to a usual operation condition, ξ decreases gradually but is almost constant at about 0.15 with increasing B _{ z } for trenches 0.5 μm wide and 5 μm deep. For a high B _{ z } region over 3 T, ξ increases with increasing B _{ z }, since the cyclotron radius is fairly small compared with the trench width. A special superconducting magnet is necessary to reach the high B _{ z } region. An external electric fieldE _{ z } brings about the larger increase of ξ for the smaller SE energy ε_{ s }. For ε_{ s }=1 eV, E _{ z } as large as 10^{6} V/m is necessary to realize a 50% increase of ξ compared with the case of E _{ z }=0 V/m, whereas for ε_{ s }=0.1 eV, only about E _{ z }=10^{5} V/m is sufficient to realize the increase of 50%. On the other hand, experiments show that an electric field as large as 10^{5} V/m is effective to achieve bright and clear observations of the bottom image.

A theoretical model of neutron thermalization in a medium
View Description Hide DescriptionA simple theoretical model is developed to explain neutron thermalization properties. Assuming that a fast neutron source is located at the origin, the neutron distribution is described as a function of distance from the source. Based on the continuous slowing‐down model, it is shown that the thermal neutron flux is a simple function of the diffusion constant D, the reciprocal length κ, and the Fermi age τ of a moderator material. Several points are noteworthy from calculation of the thermal neutron flux. First, theoretical results for polyethylene moderator agree remarkably well with simulation data obtained from a Monte Carlo simulation. Second, the thermal neutron flux at the origin is proportional to the square of moderator density. Third, the volume of the large thermal neutron flux increases drastically as the Fermi age increases. Finally, we also note that theoretical results agree reasonably well with experimental data for a broad range of physical parameters. A simple analytical expression of the thermalization factor of a moderator material is derived and it is found that its theoretical values agree rather closely with measured values.

An analytical model for longitudinally pumped continuous‐wave laser
View Description Hide DescriptionAn analytical model for a longitudinally end‐pumped laser is developed using the circulating photon flux approach, and the threshold pump intensity and slope efficiency are expressed with the laser parameters. The thermal population in the lower laser level is included in the model. The threshold pump intensity decreases as the absorption cross section increases. The model shows that the threshold pump intensity increases as the length of the laser rod increases over the optimum value. The slope efficiency of the system depends on the laser rod length, the absorption cross section, and the reflectance of the output mirror. When the model is applied to a GaAlAs diode laser pumped Nd:YAG laser, the achievable slope efficiency reaches up to 76%, which is the ultimate quantum efficiency, at the output mirror reflectance lower than 50% with a laser crystal of loss coefficient 0.1%/cm. The experimental results of 946 nm Nd:YAG laser by Fan and Byer, Opt. Lett. 12, 809 (1987) are compared with the present model, and shows a good agreement with calculations.

Properties of proton exchange waveguides in lithium tantalate
View Description Hide DescriptionThe characteristics and properties of proton exchange and annealed proton exchange waveguides in lithium tantalate are investigated. Planar waveguides are first studied using secondary‐ion mass spectrometry (SIMS) to obtain the hydrogen‐ and lithium‐ion concentration profiles. From this data, accurate exchange and anneal diffusion coefficients are calculated. Optical propagation constants are also measured and used in conjunction with the SIMS results to calculate the change in the extraordinary refractive index at λ=0.6328 and 0.829 μm. Infrared‐absorption measurements are also taken to monitor the exchange process. In addition, the surface damage due to proton exchange of the x facet of lithium tantalate is qualitatively investigated. Channel waveguides are also characterized. A parameter space study to determine the fabrication conditions necessary to achieve low‐loss, single‐mode waveguides at λ=0.829 μm is carried out. Mode near‐field sizes and the fiber‐to‐output insertion losses are characterized as a function of anneal time. The polarization extinction ratio and optical damage threshold for typical waveguides are also measured.

Implantation of Li^{+} and Na^{+} into PbTeSe for current confinement in PbTeSe/PbSnTe ridge waveguide lasers
View Description Hide DescriptionIon implantation of both Li^{+} and Na^{+} into n‐type PbTe_{0.92}Se_{0.08} has been used to convert this material to p‐type. Li^{+}‐implanted samples achieved carrier‐type conversion without annealing, while Na^{+}implanted samples required an anneal at 350 °C before carrier conversion was attained. Hall measurements at 77 K on Li^{+}‐implanted, n‐type PbTe_{0.92}Se_{0.08}, annealed at 250 °C, indicated an estimated activation efficiency of 11%, and achievement of a hole concentration of 5×10^{18}/cm^{3}. The implantation of Li^{+} into the top layer of a PbTe_{0.92}Se_{0.08}(n)/PbTe_{0.82}Se_{0.18}Te(p) /PbTe_{0.92}Se_{0.08}(p) double heterostructurelaser diode test structure resulted in a factor of 20 increase in series resistance at 200 mV, when compared to the series resistance of a similar unimplanted structure at the same bias voltage. The implanted structure did not exhibit breakdown until voltages exceeding 800 mV had been applied. These results suggest that ion implantation of Li^{+} into the top cladding layer of PbTeSe/PbSnTe laser diodes can be used to significantly reduce current spreading.

Hot carriers and the frequency response of quantum well lasers
View Description Hide DescriptionA simple analytical model is obtained to describe the effect of carrier heating on the frequency response of a quantum well laser. The principal factors are taken to be injection heating, recombination heating, and hot phonons. The model is applied to the GaAs/GaInAs strained layer system and is shown to qualitatively account for many of the nonideal features observed. The nonlinear effects cannot be described satisfactorily by a single phenomenological ‘‘gain suppression’’ factor. However, at low drives the conventional gain suppression factor can be expressed in terms of the phonon lifetime and the temperature‐relaxation time. The response is mediated by several time constants which, in our example, combine to give an effective time constant of about 10 ps. The modulation frequency response becomes seriously impaired when the differential gain is lowered by a factor of 2 and the time constants describing scattering and phonon lifetime are increased by a factor of 2.

Excitation of guided elastic wave modes in hollow cylinders by applied surface tractions
View Description Hide DescriptionThe problem of the generation of guided elastic wave modes in infinite hollow circular cylinders by loading applied to the boundaries of the cylinder, apart from being an interesting problem in itself, has important applications in the field of nondestructive evaluation. Hollow cylinders are commonly used in the nuclear industry in heat exchangers and hence must be inspected for defects regularly to ensure continued safe operation. An exact, closed‐form solution is given for the amplitude with which any propagating waveguide mode is generated due to the application of prescribed (time harmonic) surface tractions. Instead of using classical integral transform techniques to solve the problem, the normal mode expansion technique is used. In this technique, analogous to the expansion of a function in terms of an orthogonal (and complete) set of functions, the fields generated in the cylinder due to the application of the surface loading are expanded in terms of the normal modes of the cylinder. The general results are then specialized to loading configurations of practical importance in nondestructive testing.

Thermal interface crack problems in dissimilar anisotropic media
View Description Hide DescriptionThe fundamental nature of an interface crack between dissimilar anisotropic media under the uniform heat flux is studied. Based on the Hilbert problem formulation and a special technique of analytical continuation, a simple and compact version of general solutions for the thermal field are given. The temperature gradients or heat fluxes are found to possess the characteristic inverse square‐root singularity in terms of the radial distance from the crack tip. Due to this singular behavior, the heat flux intensity factor is then introduced to quantify the thermal energy cumulated in the neighborhood of the crack tip. Some numerical examples are given for the application of the final results to the intensity factor of heat flux as well as the full field solutions of temperature. It is very interesting to see that the solutions associated with the dissimilar media can be easily obtained from the corresponding problem associated with the homogeneous media by a simple substitution of their own material properties. In general, the system possesses the symmetric properties of the thermal conductivity coefficients which can make the heat flux intensity factor smaller. Consequently, the thermal energy intensification is diminished.

Numerical simulation of cylindrical converging shocks in solids
View Description Hide DescriptionCylindrically converging shock waves in solids have been analyzed by the random choice method (RCM). A Riemann solver for fluidlike solids with the Grüneisen‐type equation of state is constructed and incorporated into the RCM. It is then applied to the cylindrical shock tube problems for solid copper with driving pressures of 20 and 200 GPa. The numerical results are compared with those of the finite difference method (FDM). The shock speed is smaller and the discontinuity at the shock front is smeared out due to the artificial viscosity in the FDM calculation. Spatial distributions of pressure, density, and particle velocity calculated by the RCM show that the steepness at the shock front is maintained both in the converging and reflecting stages. It is shown that the pressure on the shock front and the total energy contained in the central circular area are much larger in the reflecting stage than in the focusing stage. The dimensional analysis has shown that the similarity solution exists; however the numerical result shows that the flow does not fall within the similarity regime in the region of calculation. It suggests that the self‐similar flow is only limited in extreme proximity to the axis.

Cross‐property relations for momentum and diffusional transport in porous media
View Description Hide DescriptionCross‐property relations linking the fluid permeability k associated with viscousflow through a porous medium to effective diffusion properties of the medium have recently been derived. Torquato [Phys. Rev. Lett. 64, 2644 (1990)] found that k≤Dφ_{1}τ, where τ is the ‘‘mean survival time’’ associated with steady‐state diffusion of ‘‘reactants’’ in the fluid region of diffusion coefficient D and porosity φ_{1} of a porous medium containing absorbing walls (i.e., trap boundaries). Subsequently, Avellaneda and Torquato [Phys. Fluids A 3, 2529 (1991)] related k to the electrical formation factor F (inverse of the dimensionless effective electrical conductivity) and the principal (largest) diffusionrelaxation timeT _{1} associated with the time‐dependent trapping problem, namely, k≤DT _{1}/F. In this study, we compute the aforementioned bounds, using an efficient first‐passage‐time algorithm, for grain‐consolidation models of porous media and compare them to exact results for these models. We also conjecture a new relation connecting k to τ and F for a wide class of porous media, namely, k≤Dτ/F, and show that it gives the sharpest permeability estimate among the existing bounds. The importance of this relation lies not only in its usefulness as an estimator of the permeability but that it involves the diffusional parameters τ and F which can be measured in situ.

Hydrodynamic analysis of electron motion in the cathode fall using a Monte Carlo simulation
View Description Hide DescriptionThe exact mass, momentum, and energy conservation equations for electron transport in a dc glow are derived from the Boltzmann equation. A Monte Carlo particle simulation is used to explicitly calculate the individual terms of the moment equations, and to gain insight into the behavior of the electron distribution function (EDF) moments such as density and average velocity. Pure forward scattering and isotropic scattering are considered as two limiting scattering mechanisms. When forward scattered, the electron fluid shows the maximum change in properties and in transport mechanisms at the field transition point between the cathode fall (CF) and the negative glow. Isotropic scattering, however, results in property changes a short distance inside the sheath. Diffusion of the low‐energy, high‐density, bulk plasma electrons into the CF causes dilution of the low‐density, high‐energy beam from the CF before the beam actually arrives at the low‐field region. The applicability of commonly used closure relations which yield a fluid description of the system is evaluated. Use of fluid equations to characterize this system with no a priori knowledge of the EDF is limited by kinetic effects, such as heat flow against the temperature gradient, especially in the forward‐scattered case where the EDF is very anisotropic. The description of inelastic rates by Arrhenius kinetics is found to be surprisingly accurate with both scattering mechanisms. However, while temperature is an adequate gauge of the characteristic energy under isotropic scattering, the energy of the bulk electron motion must be included under forward scattering. Also, Arrhenius kinetics sometimes produce a spurious double peak in the inelastic rate profile which is not reproduced by the Monte Carlo simulation. The anisotropy of the EDF under the forward‐scatter assumption makes it difficult to justify the use of the mobility and heat conduction closure relations. Under isotropic scattering, however, electron inertia is negligible. In that case, under the discharge conditions used here, the drift‐diffusion approximation to the flux is good to within a factor of 2. Classical heat conduction theory overestimates the heat flux by a factor of 4 at the sheath edge.

The effect of molecular ions on the plasma parameters in a medium pressure rare gas radio frequency discharge positive column
View Description Hide DescriptionA rare gas positive column plasma theory that takes into account the effect of various chemical processes on the production, loss, and interconversion of metastable and ion species is developed and compared with experimental results. The experimental measurements have been made in a 4 cm i.d. radio frequency (rf)discharge tube for He, Ne, and Ar. An electrostatic triple probe was used to monitor the electron temperature and plasma density, and a mass spectrometer was used to analyze the ion species. The results show that the molecular ion becomes important when gas pressure is above 1 Torr in the Ar and Ne plasmas. For a He plasma, the molecular ion always plays an important role in the plasma process. Good agreement has been observed between present model and experiments.

Absolute H‐atom concentration profiles in continuous and pulsed rf discharges
View Description Hide DescriptionAbsolute concentrations of ground state atomic hydrogen are determined by two‐photon absorption laser‐induced fluorescence in a pure hydrogen rf discharge. Axial concentration profiles obtained across the interelectrode space show a relatively constant concentration (of the order of 10^{14} atoms/cm^{3}) in the region around the center of the discharge until it decreases sharply within 3–4 mm of each metalelectrodesurface. In addition, the temporal evolution of the atomic concentration is monitored by means of a pulsed discharge from short times to the establishment of a steady‐state concentration. We present a model according to which the formation and decay of the distribution of atomic hydrogen is dominated by diffusion from the production regions towards both the center of the discharge and the metallic electrodesurfaces where H atoms are absorbed.

Tungsten etching mechanisms in low‐pressure SF_{6} plasma
View Description Hide DescriptionA detailed study of tungsten low‐pressure etching in a helicon source reactor was performed. In correlation with surface analyses (transmission electronic microscope,Rutherford backscattering, nuclear reaction analysis), a complete parametric study of the plasma and etching parameters versus the macroscopic parameters [gas pressure, radio frequency (rf) power, substrate bias voltage) has been carried out. Using a model developed by Hoffman and Heinrich for silicon etching (Proceedings of the 9th ISPC, Pugnochiuso, Italy, 1989, p. 1003), and taking into account the experimental results, it has been shown that tungstenetching mechanisms can be expressed by the formation and destruction of a low‐density reactive top layer. Sputtering of this layer under argon‐ion bombardment has been studied by optical emission spectroscopy. Consequently, the tungstenetch rate can be expressed as an analytical function of the macroscopic parameters such as gas pressure, rf power, and substrate bias voltage.

Two‐dimensional modeling of electron cyclotron resonance plasma production
View Description Hide DescriptionFor the numerical simulation of electron cyclotron resonanceplasma production, a two‐dimensional model that describes wave propagation and plasma transport is developed. The modeling code calculates profiles of electromagnetic wave fields, power absorption of electrons, and temporal evolution of plasma densities in a bounded, inhomogeneous, cylindrical system. The calculation of the plasma production in a mirrormagnetic field shows that the plasma productionproperty is very sensitive to the antenna location.

Crystallographic alignment analysis of Nd_{2}Fe_{14}B materials using standard x‐ray powder diffraction spectra
View Description Hide DescriptionThe crystallographic alignment quality of anisotropic magneticmaterials made from die‐upset Nd_{2}Fe_{14}B (MQ‐III) materials was determined using a phenomenological analysis of θ‐2θ x‐ray diffraction spectra. This analysis consisted of fitting a calculated diffraction spectrum for aligned Nd_{2}Fe_{14}B to an observed spectrum collected on a bulk MQ‐III slab oriented with the c‐axis alignment parallel to the direction normal to the surface of the slab. The calculated spectrum was then used as a standard for intensity shifts of diffraction peaks corresponding to crystallographic reorientation from random to c‐axis alignment. Intensity shifts for other samples for Nd_{2}Fe_{14}B materials having various degrees of c‐axis alignment were determined and compared to the standard shifts giving an alignment factor representing the nature and extent of the crystallographic alignment in the sample.

Calorimetric and morphological studies of mechanically alloyed Al‐50 at. % transition metal prepared by the rod‐milling technique
View Description Hide DescriptionThe mode of amorphization and crystallization of mechanically alloyed Al‐TM (TM; Zr, Nb, and Ta) has been studied by means of differential thermal analysis,differential scanning calorimetry, optical metallography, scanning electron microscopy, and transmission electron microscopy. The mechanical alloying process via the rod‐milling technique is classified into three stages of milling. At the early stage of milling, the elemental powders of Al and TM are grown to form layered‐composite particles of a larger diameter as a result of cold welding. At the intermediate stage, a complete crystalline‐to‐amorphous transformation occurs at around 700 K, by heating the well‐arranged layered particles in a differential thermal analyzer under an Ar atmosphere. This transformation occurs due to a thermally assisted solid‐state amorphization between the layers of the elemental starting material in the composite particles. At the final stage of milling, an amorphous phase is formed by the mechanical driving force which is generated by the rods. The amorphization and crystallization properties of Al‐50 at. % TM alloys are presented.

Defects in low‐temperature electron‐irradiated p‐type silicon
View Description Hide DescriptionDefects in monocrystalline silicon have been studied in the past, in particular, defects induced by room‐temperature electron and protonirradiations on both n‐ and p‐type materials, and most of the corresponding defects have been tentatively identified. However, there are still several questions which remain to be answered such as the nature and behavior of the defects introduced in the range 4–300 K. In this work Czochralski‐grown p‐type material has been irradiated at three different temperatures (90, 200, and 300 K) and characterized by deep‐level transient spectroscopy (DLTS) and lifetime measurements. The data show that the defects created after irradiations at 90 and 200 K are different from those reported in the literature for irradiations at 4, 77, and 300 K, showing that three annealing steps exist between 4 and 300 K. These defects are characterized and a tentative identification of them is made. Finally, an attempt to detect the defects responsible for the lifetime, i.e., the recombination centers, not observed by DLTS, using spin‐dependent recombination is described.

Discrete conductance fluctuations in silicon emitter junctions due to defect clustering and evidence for structural changes by high‐energy electron irradiation and annealing
View Description Hide DescriptionObservations of discrete conductance fluctuations are reported at voltages well below the breakdown voltage in selected reverse‐biased p ^{+}‐n ^{++} base‐emitter junctions originating from gate turn‐off thyristors. The occurrence of the phenomenon is attributed to the presence of defect clusters at the p‐n junctions. The defect clusters introduce field confinements which activate tunneling processes that would not otherwise be present in these nonabrupt p‐n junctions. The fluctuating reverse current was only observed in voltage and temperature regions where the total reverse current was influenced by tunneling‐related conduction mechanisms. The experimental observations concerning the voltage and temperature dependences of the fluctuation amplitude and rate deviate from earlier reports on decisive points. Both the amplitude and the switching rate of the observed fluctuations were unstable in time and influenced by the measurement procedure itself. This instability is attributed to small structural changes of the defect clusters. Furthermore, the unstable behavior of the defect clusters also influences the static reverse current‐voltage characteristic. Distinct changes were found in the static reverse current‐voltage characteristics of selected samples due to high‐energy electron irradiation and annealing at 200 °C. A clearly increased uniformity of the reverse current‐voltage characteristics between the gate‐cathode junctions of gate‐turn off thyristors was also found as a result of electron irradiation. The changes observed are interpreted as evidence of structural changes of the defect clusters.

Site transfer of Si in GaAs after heavy ion MeV implantation and annealing
View Description Hide DescriptionThe electrical and optical properties of n‐type and p‐type epitaxial GaAs layers have been studied after MeV implantation of heavy (Xe and Er) ions. All implanted layers were highly resistive immediately after implantation.Annealing to only moderate temperature (725 °C) recovered the as‐grown electrical properties of beryllium‐doped p‐type layers. However, after annealing silicon‐doped n‐type layers, we observe a dramatic change from the as‐grown carrier profiles. After anneal, the silicon‐doped, n‐type layers became conductive but the carrier profiles were markedly different from the as‐grown material. A significant thickness of the implanted portion of the epitaxial layers shows distinct p‐type conductivity after annealing. We have correlated this p‐type activity with a transfer of silicon from the gallium sublattice (Si_{Ga}) to the arsenic sublattice (Si_{As}). The site transfer is viewed to result from the altered thermodynamics governing site occupancy during annealing of Si in GaAs under the unique damage conditions produced by heavy ion MeV implantation. Additionally, the observed thermal stability of the site transfer process above 875 °C may have implications for implantation isolation techniques.