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  • 1
    Electronic Resource
    Electronic Resource
    Simulation of reactive ion etching pattern transfer (1989)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 66 (1989), S. 4664-4675 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper describes a model that simulates etching profiles and process latitudes in glow-discharge bombardment-induced reactive-etching processes. Numerical results are presented for the pattern-transfer step in trilayer lithography, but this analysis is applicable to many other pattern-transfer processes. The inputs to the interface-evolution model described here are a kinetic model for the yield per incident energetic particle and a statistical mechanical model that relates the incident-yield-weighted angular distribution to the pressure, sheath thickness, and sheath voltage drop. The kinetic model is based on experimental evidence and assumes that the yield per bombarding particle is proportional to its energy. The resulting interface-evolution equation is mathematically analogous to a free-surface evolution equation in hydrodynamics. This convective partial differential equation is reduced to a coupled set of ordinary differential equations via the method of characteristics and solved numerically. More general energy-dependent yields are easily incorporated in the present formulation, but angle-dependent yields are more difficult and are not treated here. This model describes how shadowing of the surface being etched results in proximity effects in line etching and aspect-ratio-dependent etching rates in trench etching. Simulated profiles are compared to experimental trilayer etching profiles and qualitatively describe their shape and the trends that are observed as pressure or other processing parameters are varied. Simulations showing the effect of angular distributions, line proximity, and trench aspect ratio on process latitudes in trilayer lithography are presented and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.343823
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  • 2
    Electronic Resource
    Electronic Resource
    Nonlocal transport models of the self-consistent potential distribution in a plasma sheath with charge transfer collisions (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 64 (1988), S. 6200-6209 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Plasma sheaths are often assumed to be collision free; however, high-voltage cathode sheaths are typically thicker than the mean free path for charge transfer collisions at pressures encountered in glow discharge processing equipment (greater than 10 mTorr). In this paper, the potential distribution in a plasma sheath is determined by solving Poisson's equation self-consistently using a kinetic theory nonlocal ion transport model for charge transfer collisions. The relationship between the potential distribution, ion flux, and thickness of a plasma sheath is presented for arbitrary values of the sheath thickness relative to the mean free path for charge transfer. The results may be used to estimate the ion flux from measurements of the sheath thickness and potential drop across the sheath. Ion energy distribution functions and a one-parameter approximation to the numerically determined potential distribution are also presented. These results apply to rf discharges in a time-averaged sense when the ion sheath transit time is much longer than the rf cycle time, and they apply to high-voltage cathode sheaths in "abnormal'' dc and low-frequency rf discharges. The present model is compared to earlier self-consistent sheath models, including the collision-free approximation, the local mobility model, and a nonlocal fluid approximation known as the viscous drag model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.342077
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  • 3
    Electronic Resource
    Electronic Resource
    The extensional viscosity and effective thermal conductivity of a dispersion of aligned disks (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 1955-1962 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper discusses the properties of a semidilute suspension of disks, for which nl3(very-much-greater-than)1 and φ(very-much-less-than)1, where n is the number of disks per unit volume, l is their large dimension, and φ is their volume fraction. The effective conductivity of a dispersion of aligned, highly conducting disks is shown to be O[k(nl3)2], where k is the conductivity of the matrix. The extensional viscosity is shown to be O[μ(nl3)2], where μ is the viscosity of the fluid. In addition, similar scaling results are shown to hold for the case of a semidilute suspension of aligned, two-dimensional slabs which are of infinite extent in the direction perpendicular to their plane of cross section. Specifically, for nl2(very-much-greater-than)1, the effective conductivity and the extensional viscosity are shown to be O[k(nl2)2] and O[μ(nl2)2] respectively, where n is now the number of slabs per unit area and l is the width of the slab. Planar extensional flow simulations of a periodic array of aligned slabs confirm the quadratic scaling for stress in the semidilute regime. The simulations also show the crossover from a linear dependence of the stress on particle concentration in the dilute regime to the quadratic, semidilute scaling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868202
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  • 4
    Electronic Resource
    Electronic Resource
    Averaged-equation and diagrammatic approximations to the average concentration of a tracer dispersed by a Gaussian random velocity field (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 887-894 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Approximate methods for predicting the spread of a passive tracer due to a Gaussian random velocity field are examined. Previous methods such as the direct-interaction approximation [J. Fluid Mech. 11, 257 (1961)] and Phythian's short-time expansion [J. Fluid Mech. 67, 145 (1975)] make predictions for the second moment of the concentration that are qualitatively consistent with numerical simulations [Phys. Fluids 13, 22 (1970)]. However, it is shown that the higher moments obtained from these approximations are incorrect. The derivations of the direct-interaction approximation using a diagrammatic expansion and the method of averaged equations are reviewed [Phys. Fluids A 1, 47 (1989)]. A higher-order (two-body) approximation is developed which makes predictions for the fourth moment that are qualitatively correct in both the short- and long-time limits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858268
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  • 5
    Electronic Resource
    Electronic Resource
    The effects of inertia on the viscoelastic Dean and Taylor–Couette flow instabilities with application to coating flows (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2415-2431 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effects of inertia on the elastic instabilities in Dean and Taylor–Couette flows are investigated through a linear stability analysis. The critical conditions and the structure of the vortex flow at the onset of these instabilities are presented. The results reveal that the purely elastic Dean flow is destabilized by inertial effects. It is also found that inertia destabilizes elastic Taylor–Couette flow if the rotation of the inner cylinder is the flow driving force, while it stabilizes the flow driven by rotation of the outer cylinder. The mechanism of destabilization or stabilization of these viscoelastic instabilities is investigated through an examination of the disturbance-energy equation. It is shown that Dean flow is destabilized by two separate mechanisms: a purely elastic mechanism discussed previously (i.e., energy production due to the coupling of a perturbation velocity to the polymeric stress gradient in the base state) [see Phys. Fluids A 3, 1691 (1991)] and a purely inertial mechanism discussed by Dean [Proc. R. Soc. London Ser. A 121, 402 (1928)] (i.e., energy production from Reynolds stresses). It is also shown that, when rotation of the inner cylinder drives Taylor–Couette flow, the Reynolds stresses produce energy, and thus are destablizing, while for the flow driven by the rotation of the outer cylinder alone, the Reynolds stresses dissipate energy, thus stabilizing the flow. The elastic forces remain destabilizing in both modes of operation. In a second study, a pressure-driven viscoelastic coating flow over a curved surface is examined. The results demonstrate the existence of a purely elastic stationary instability in the coating flow on a concave wall which is very similar to that which occurs in viscoelastic Dean flow. It is demonstrated that the mechanisms of instability in Dean flow and the coating flow are the same, again through an examination of the disturbance-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858483
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  • 6
    Electronic Resource
    Electronic Resource
    The conformation change of model polymers in stochastic flow fields: Flow through fixed beds (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1222-1234 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Simulations of the conformation change of model polymers in various steady, anisotropic Gaussian random flow fields are presented. These flow fields have been chosen because they are models for the flow through porous media and have been predicted to be "stochastic strong flows" according to the criteria developed by Shaqfeh and Koch [J. Fluid Mech. 244, 17 (1992)]. To be specific, beyond a certain Deborah number (based on the sampling time of a velocity fluctuation), large average conformation change in the polymer is predicted. In our simulations, the polymers are modeled as dumbbells, but beyond this restriction, the assumptions of the theory by Shaqfeh and Koch are removed. Many realizations of the Gaussian fields are synthesized spectrally following a modified version of the method developed by Kraichnan [Phys. Fluids 13, 22 (1970)]. Moreover, the ratio of the mean "plug" flow to the amplitude of the fluctuations is varied from mean-dominant to fluctuation-dominant flows. The simulated conformation change shows that, in fact, these flows are "strong" in the sense that the average second moment of the end-to-end distance becomes large (relative to equilibrium) beyond a critical value of the fluctuation Deborah number. Although qualitatively capturing these trends, the theory by Shaqfeh and Koch underestimates the strength of the flows and thus overestimates the critical Deborah number. We present a new theory which includes spring relaxation and Brownian motion in the sampling of a velocity fluctuation (two factors which were neglected in the existing theory), thereby breaking the fore–aft symmetry of the sampling, thus increasing the average polymer stretch. The new theory quantitatively predicts the simulation results. To the authors knowledge, this is the first evidence via direct simulation that these random flows can produce large conformation change in model polymer molecules, even when the mean flow would produce no such change. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869262
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  • 7
    Electronic Resource
    Electronic Resource
    Viscoelastic Poiseuille flow through a curved channel: A new elastic instability (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2043-2046 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor–Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbance-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857886
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  • 8
    Electronic Resource
    Electronic Resource
    Viscoelastic Poiseuille flow through a curved channel: A new elastic instability (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1691-1694 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor-Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbande-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858223
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  • 9
    Electronic Resource
    Electronic Resource
    Heat and mass transport in composites of aligned slender fibers (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 3-20 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A theory is presented to describe the time-dependent and steady transport properties of composite media containing randomly placed, aligned slender fibers. The formalism is based on a diagrammatic representation of the multiple scattering expansion for the configurational-averaged Green's function. Several topological reductions are performed on the series to remove long-wavelength singularities and to render the theory self-consistent. Approximations based on partial summation of the renormalized series have structures that are similar to, but distinct from, effective medium theories. The present approach is systematic and retains a unique subset of the multiple scattering series at each level of approximation. The formalism is appliedto the specific cases of steady diffusion-controlled reaction and heat conduction in composites that contain slender, aligned rods. Both the dilute and semidilute regimes are investigated. Theseresults for the diffusion-controlled reaction problem are new, and known results are recovered for heat conduction in the case of highly conductive rods. However, the method has uncovered a new semidilute expansion for the latter problem. The screening of disturbances in fibrous composites is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857546
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  • 10
    Electronic Resource
    Electronic Resource
    A nonlocal theory for the heat transport in composites containing highly conducting fibrous inclusions (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 2405-2425 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A theory is developed to describe the heat transfer in composites containing highly conducting fibrous inclusions under conditions in which the average temperature field scales on lengths comparable to the length of the included fibers. Thus, in contrast to previous developments, the fiber samples the details of a rapidly varying temperature field rather than simply a local linear field. Using the method of averaged equations and slender body theory, the average "extra flux'' created by the presence of the fibers is demonstrated to be an integral of the temperature gradient about any point weighted by a function which is the appropriate nonlocal conductivity. This representation of the thermal transport in the material is derived explicitly for (a) dilute composites in which nf l3(very-much-less-than)1, where nf is the number density of the fiber and l is their length; and (b) semidilute composites in which nfl3(very-much-greater-than)1 but nflb2(very-much-less-than)1, where b is the fiber thickness. In both instances the expressions derived are rigorously valid for fibers that are very long and thin. Associated with the derivation of the semidilute nonlocal theory is the first complete derivation of the semidilute local result, which justifies the arguments made by Batchelor [J. Fluid Mech. 46, 813 (1971)] and demonstrates the mechanisms of "screening'' in these multiparticle systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866594
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