Non-planar Interface Research Articles

Three-dimensional effects due to the field oxide in MOS devices analyzed with MINIMOS 5

The MINIMOS simulation program has been extended to three dimensions to investigate the parasitic effects at the channel edge on MOSFET device characteristics. The box integration method after Forsythe has been applied for discretization. This method is suitable for nonplanar interfaces. The most important nonplanar interface occurs at the transition of the gate oxide to the field oxide called the bird's beak. Approximating this interface as a rectangular shape leads to unrealistic results. The oxide-body is defined by analytical functions, so it is easy to investigate a wide range of applications. An automatic grid-refinement algorithm is used to generate the specific grid. The simulation shows that the influence of the channel edge is not negligible for channel widths less than 2 mu m. The total drain current for narrow channel MOSFETs is either increased or decreased by parasitic three-dimensional effects compared to wide channel (two-dimensional) MOSFETs depending on the bias conditions. >

Numerical Modeling of Energy-Beam Induced Localized Melting of Thin SI Films

ABSTRACTWe have developed a quantitative model, based on a two-dimensional finite difference enthalpy method, which accounts for the localized melting behavior of thin Si films on substrates. The model incorporates radiative and conductive heat flow components and takes account of the phase changes that occur during zone-melting recrystallization. Emphasis is placed on the effects resulting from the differences in reflectivity and emissivity between solid and liquid Si. The model provides quantitative information concerning the temperature profile of the Si film and the configuration of the solid-liquid interface. Results of the analysis indicate that there exist two distinct types of transition behavior: i) reflectivity-change dominated and ii) emissivity-change dominated. Partial melting and a nonplanar solid-liquid interface are characteristics of the reflectivity-change dominated behavior. The emissivity-change dominated behavior, on the other hand, can be characterized by explosive-like melting and a planar solid-liquid interface. The conditions and physical factors which give rise to these behaviors are discussed.

The Adhesion of Growing Oxides to Metallic Substrates

AbstractThere are several possible descriptions of the nature of the adhesion between an oxide and a metal substrate, some of which are formally equivalent. These include electrostatic interactions connected with the development of space charge regions, chemical bonding across the interface, van der Waals forces, and mechanical interactions associated with a nonplanar interface. However, the detailed mechanism must also be consistent with the growth process and the associated evolution of the interface for an oxide growing on a metal substrate. The problem is further complicated by the nature of the failure at or near the interface which leads to a phenomenological definition of adhesion which is not necessarily identical to the formal definition, and involves other parameters such as the growth stresses in the oxide, the plasticity of the oxide or the surface metal, and the effect of thermal cycling when the coefficients of thermal expansion of the two phases differ. In this paper, an attempt is made to describe these different aspects of the problem, and to refer to some of the more important ways of modifying the adhesion of an oxide, including the reactive element effect and the segregation of impurities to the interface and the modification of the morphology of the interface.

Nonplanar interface morphologies during unidirectional solidification of a binary alloy: II. Three-dimensional computations

Three-dimensional steady-state solutions for nonplanar interface morphologies are computed numerically by using finite differences. A linear temperature field is assumed, corresponding to the case of equal thermal properties in the crystal and melt, with negligible latent heat release. The solute field in the melt and the unknown crystal-melt interface position are obtained self-consistently. For a model of an aluminum-chromium alloy with distribution coefficient greater than one, steady-state solutions corresponding to two-dimensional bands and three-dimensional hexagonal nodes are obtained, as well as solutions with rectangular interface planforms. The stability of the computed steady-state solutions is suggested by the behavior of the iterative scheme used in the calculation: successive iterates may be viewed as evolving in a time-like manner as determined by a set of governing equations that depend on an artificial time. Near the onset of instability the calculations predict hexagonal nodes, which is consistent with weakly nonlinear theory.

TEM Study of Interdiffusion and Interfaces in Mo/Pd/Si Thin Films

Cross‐sectional transmission electron microscopy was performed on annealed samples of the Mo/Pd/Si thin films to determine microstructure and interface morphologies following annealing at 450° and 550°C. A sample annealed at 450°C for 0.5h shows the formation of a uniformly thick , and planar and interfaces. In contrast, a sample annealed at 550°C for 0.5h shows formation of a uniform but wavy layer along with a nonuniform layer. The interface is planar, but a nonplanar interface between and Si is produced. A mechanism is proposed to explain these morphological changes. It is shown that these morphologies can lead to changes in the Pd and Si edges in Rutherford backscattering spectra of annealed samples of the Mo/Pd/Si.

Anisotropic surface free energy and the roughening transition of the diffuse crystal-liquid interface.

An explicit expression for the surface free energy of a nonplanar diffuse crystal-liquid interface is derived in terms of microscopic parameters starting from a free-energy functional for a nonuniform crystal. The broken symmetries of the crystal lattice manifest themselves in this effective surface Hamiltonian as an anisotropic surface tension, plus its derivatives with respect to orientation, and as contributions that vary periodically upon translation of the interface. The amplitudes of these latter components, expressed in terms of the bulk Debye-Waller factors and the intrinsic interfacial width, are related to the roughening temperature. A variational treatment is carried out upon a discrete Gaussian model involving two periodic potentials and, hence, two competing length scales, which displays families of commensurate arrays of ledges.

Local intrinsic modes: Layer with nonplanar interface

Laterally inhomogeneous layered media serve as models for realistic propagation environments in electromagnetics, optics, underwater acoustics, seismology and other disciplines. When the inhomogeneities extend over long distances compared to the local wavelength, general methods (like those based on integral equations) for these nonseparable boundary value problems become intractable. For weak lateral variations, the propagation process can be localized around intrinsic modal fields, which are synthesized by plane wave spectra capable of describing propagation properties uniformly in guiding, cutoff and radiating regions. These local intrinsic modes, specified by modal invariants, traverse the medium along lateral trajectories, which may refract and form caustics similar to those for ordinary ray fields in an inhomogeneous environment. In the present investigation, these concepts are applied to a single homogeneous layer separated from a homogeneous half space by an interface with arbitrary but slowly changing surface profile, as exemplified by a shallow ocean waveguide. The previously derived intrinsic modes for a two-dimensional wedge geometry (J.M. Arnold and L.B. Felsen, “Intrinsic modes in a nonseparable ocean waveguide”, Journal of Acoustical Society of America 76, 850–860 (1984)), serve as the prototype for the construction of the wave spectra, first, for the two-dimensional configuration with nonplanar interface, and then for the general three-dimensional case.

On the tunneling hypothesis for ray reflection and transmission at a concave dielectric boundary

When a ray field is incident on a concave boundary confining a dielectric medium, total reflection is perturbed by leakage due to surface curvature. The resulting modification of the conventional Fresnel ray reflection coefficient, including its uniform transition through critical incidence, has previously been addressed by the so-called hypothesis, which is based essentially on the behavior of a corresponding peripherally guided whispering gallery or leaky modal field; the former exhibits evanescent decay (tunneling) away from the boundary in the exterior region but eventually gives rise to radiation from a caustic whereon the modal phase speed equals the speed of light. It is shown here that inferring local ray field properties from global mode field properties has limited validity. The demonstration is based on a rigorous analysis of the two-dimensional Green's function for a circular boundary. Asymptotic solutions are constructed for the various ray-optical domains, and for the transition regions near caustics and especially near the critically refracted ray. Examination of the reflected and transmitted fields reveals that the tunneling hypothesis holds only near the critically refracted ray. Elsewhere, the transmitted ray field may deviate markedly from that predicted by the tunneling model. The results clarify not only the ray field behavior but also the mechanism of local energy reflection and transmission for a nonplanar interface.

Nonplanar interface morphologies during unidirectional solidification of a binary alloy

During directional solidification of a binary alloy, a planar solid-liquid interface may become unstable and develop into a cellular non-planar interface, exhibiting periodic structure transverse to the growth direction. Steady state two-dimensional temperature, solute concentration, and interface shapes are calculated numerically and the solute inhomogeneity (microsegregation) in the solidified material obtained. Specific results are presented for an aluminum alloy containing silver for solidification velocities of 0.01 and 1.0 cm/s, which correspond to the constitutional supercooling and absolute stability regimes, respectively.

Non-planar solid phase epitaxial growth processes in ion-implanted GaAs

High resolution ion channelling and reflection electron diffraction techniques have been used to examine details of epitaxial regrowth in Ar +-ion-implanted GaAs(100) at furnace anneal temperatures of 400°C or less. In particular, we have investigated the nature and extent of epitaxial regrowth during both isothermal and isochronal annealing for various implant energies and for implant doses above and below the amorphous threshold. Our results indicate the development of a non-planar growth interface during annealing which may lead, ultimately, to complex near-surface crystallization processes. Consistently with our observations and recent results from other laboratories, we propose a model for the epitaxial regrowth of amorphous GaAs layers based upon non-uniform growth rates along the amorphous-crystalline interface which could arise from local stoichiometry imbalance.

Finite Elenent Analysis of The Effect of a Non-Planar Solid-Liquid Interface on The Lateral Solute Segregation During Unidirectional Solidification.

ABSTRACTThe effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly non-planar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Non-Planar Solid Phase Epitaxial Growth Processes in Ion-Implanted GaAs

High resolution ion channelling and reflection electron diffraction techniques have been used to examine details of epitaxial regrowth in Ar+-ion-implanted GaAs(100) at furnace anneal temperatures of 400°C or less. In particular, we have investigated the nature and extent of epitaxial regrowth during both isothermal and isochronal annealing for various implant energies and for implant doses above and below the amorphous threshold. Our results indicate the development of a nonplanar growth interface during annealing which may lead, ultimately, to complex near-surface crystallization processes. Consistently with our observations and recent results from other laboratories, we propose a model for the epitaxial regrowth of amorphous GaAs layers based upon non-uniform growth rates along the amorphous-crystalline interface which could arise from local stoichiometry imbalance.

The seismic response of sediment-filled valleys. Part 2. The case of incidentPandSVwaves

abstractWe present the extension to incident P and SV waves of our previous study (Bard and Bouchon, 1980) concerning the seismic response of sediment-filled bidimensional valleys to incident SH transient signals. The reliability of the Aki-Larner method is briefly discussed and the domain is estimated within which it provides accurate results. Then we investigate the response of three different valleys, having various geometrical and elastic parameters, to vertically incident P and SV waves, in both the frequency and time domains. The behavior of the valleys is shown to be qualitatively similar to their behavior for SH waves: the nonplanar interface causes surface waves (here Rayleigh waves) to be generated on valley edges, and to propagate laterally inside the basin. The amplitude of these Rayleigh waves depends greatly on the velocity contrast, the valley shape, and the incident wave type (P or SV), but it may be significantly higher than the disturbance associated with the direct incident signal. The frequency and direction of incident motion determine partly whether the fundamental or first higher mode will be predominantly excited, depending on the main component (vertical or horizontal) of the Rayleigh mode motion. Although the reflections of these Rayleigh waves on valley edges do not appear as clearly as in the SH case, a very long duration of the ground shaking inside the valley is still observed. In deep valleys, these laterally propagating Rayleigh waves may degenerate into a lateral resonance pattern, involving high-amplitude surface motion. These latter resonance modes, however, begin to appear in shallower valleys for incident SV waves than for incident P ones.

The seismic response of sediment-filled valleys. Part 1. The case of incidentSHwaves

abstractIn this study is presented the extension to time domain calculations of the Aki-Larner method (Aki and Larner, 1970), developed to investigate the scattering of plane waves at irregular interface. Seismograms computed at the surface of a soft basin for SH waves vertically incident are compared with results obtained by finite difference, finite element, and asymptotic ray theory methods. The method is then applied to a study of the seismic response of sediment-filled valleys to incident SH waves. Various geometries and rheological parameters are considered. The study shows the important role played by the nonplanar interface, which, when the incident wavelengths are comparable to the depth of the valley, results in the generation of Love waves which may have much larger amplitude than the disturbance associated with the direct incident signal. In the presence of a high-velocity contrast between the sediments and the underlying bedrock, these local surface waves can be reflected several times at the edges of the valley, resulting in a long duration of the ground shaking in the basin. In the case of a lower impedance contrast, these waves may produce disturbances on the outer sides of the valley.

Some properties of multi-fluid stokes flows

The solution of Stokes' equations for a rotating axisymmetric body which possesses reflection symmetry about a planar interface between two infinite immiscible quiescent viscous fluids is shown to be independent of the viscosities of the fluids and identical with the solution when the fluids have the same viscosity. The result is generalized to a rotating axisymmetric system of bodies which possesses reflection symmetry about each interface of a plane stratified system of fluids. An analogous result for two-fluid systems with a nonplanar static interface is also derived. The effect on torque reduction produced by the presence of a second fluid layer adjacent to a rotating axisymmetric body is considered and explicit calculations are given for the case of a sphere. A proof of uniqueness for unbounded multi-fluid Stokes' flow is given and the asymptotic far field structure of the velocity field is determined for axisymmetric flow caused by the rotation of axisymmetric bodies.

Microstructure and mechanical properties of unidirectionally solidified Al-Si-Ni ternary eutectic

Al-10.98 pct Si-4.9 pct Ni ternary eutectic alloy was unidirectionally solidified at growth rates from 1.39μm/sec to 6.95μm/sec. Binary Al-Ni and Al-Si eutectics prepared from the same purity metals were also solidified under similar conditions to characterize the growth conditions under the conditions of present study. NiAl3 phase appeared as fibers in the binary Al-Ni eutectic and silicon appeared as irregular plates in the binary Al-Si eutectic. However, in the ternary Al-Si-Ni eutectic alloy both NiAl3 and silicon phases appeared as irregular plates dispersed in α-Al phase, without any regular repctitive arrangement. The size and spacing of NiAl3 and Si platelets in cone shaped colonies decreased with an increase in the growth rate of the ternary eutectic. Examination of specimen quenched during unidirectional solidification indicated that the ternary eutectic grows with a non-planar interface with both Si and NiAl3 phases protruding into the liquid. It is concluded that it will be difficult to grow regular ternary eutectic structures even if only one phase has a high entropy of melting. The tensile strength and modulus of unidirectionally solidified Al-Si-Ni eutectic was lower than the chill cast alloys of the same composition, and decreased with a decrease in growth rate. Tensile modulus and strength of ternary Al-Si-Ni eutectic alloys was greater than binary Al-Si eutectic alloy under similar growth conditions, both in the chill cast and in unidirectionally solidified conditions.

The directional solidification of Pb-Sn-Cd alloys

The growing interest in composite structures for new material applications makes it necessary to determine just how generally we can apply existing solidification theory to controlled three-phase ternary solidification. The Pb-Sn-Cd ternary eutectic system was used as a suitable model system to completely map the phase morphology as a function of G/R and compositions. By carefully controlling the freezing rate and the thermal gradient in the liquid ahead of the solid-liquid interface (in the range 400 to 500 C/cm) the following areas of interest were investigated: 1) the effect of growth velocity and composition on coupled structures, 2) ternary impurities and their effect on the minimum G/R for coupled growth in a binary system, 3) the effect of growth velocity and composition on the nonplanar interface structures, and 4) the adaptability of present theories (the constitutional supercooling criterion and Cline’s binary analysis) in predicting the region of coupled growth in a three-component eutectic system growing at steady-state. It was found that much of the one and two-phase directional solidification theory and terminology can be directly extended to a ternary eutectic system. This suggests a further extension to n-phase, m-component systems (m ≥ n) with at least a qualitative understanding of the solidification process.

The structure of directionally solidified two-phase Sn-Cd peritectic alloys

The structure of Sn-Cd two-phase peritectic alloys directionally solidified at various values ofG/υ (temperature gradient in the liquid divided by growth rate) is reported. The minimum value of G/υ as a function of composition required for the solidification of two-phase peritectic alloys with a planar liquid-solid interface is estimated using a simple constitutional supercooling stability criterion. At a value ofG/υ just below this minimum value, these alloys solidify with a nonplanar interface consisting of cells of α (the high temperature phase) and intercellularβ (the low temperature phase). This produces a coarse rod-like microstructure consisting of rods of α phase imbedded in aβ matrix. At a value ofG/υ above this minimum value, these alloys solidify with a planar interface which alternately deposits bands of α andβ transverse to the growth direction. No coupled growth of α andβ at a planar interface is observed in Sn-Cd two-phase peritectic alloys as was expected. To understand this, an analysis of coupled (eutectic-like) growth of two-phase peritectic alloys is presented and contrasted with the results of the Jackson-Hunt theory of lamellar eutectic growth. This calculation indicates that the coupled growth of two-phase peritectic alloys is unlikely on theoretical grounds.

Controlled solidification of a dilute binary alloy: I. Theory

A discussion of the steady controlled solidification of a dilute binary alloy is presented. A solution of the solute diffusion equation is obtained for an infinite paraboloidal dendrite, moving in a fixed temperature gradient. The behaviour of a group of dendrites is approximately accounted for by truncating the dendrite at a self-consistent boundary limit, and a unique solution of the solute diffusion equation in front of a nonplanar interface is obtained by invoking an extremum principle based in nonquilibrium thermodynamics. The effects of varying growth velocity and temperature gradient on the dendrite tip concentration and radius are then predicted theoretically; computed numerical results for an Fe-8wt% Ni alloy are presented.

Inhomogeneities in Optical Crystals Resulting from Nonplanar Solid-Melt Interface during Growth

An approximate two-dimensional model is presented which shows that nonunique growth directions along a nonplanar interface can lead to significant variations in the actual growth rates along the interface. Such growth-rate variations can be the source of appreciable chemical inhomogeneity in directions normal to the mechanically imposed crystal growth direction. Numerical estimates are made for the magnitude of this radial chemical gradient in CaWO4:Nd3+ crystals under typical growth conditions and with hemispherically shaped solid-melt interfaces during growth. These estimates are in good agreement with the measured optical quality of typical CaWO4:Nd3+ crystals in which laser beam divergences of at least 10 times the diffraction limit for a 7-mm aperture are common.