David S. Soong

A mathematical model for spin coating of polymer resists

The success of lithographic processes in microelectronics fabrication depends on the reproducible generation of desired polymer resist film thickness and profile uniformity. Numerous process variables affect the outcome of spin coating of resists on wafers. A thorough understanding of the intricate interdependence of process parameters is essential to guide future process design and improvement. A mathematical model is derived to elucidate the dominant mechanisms governing film formation. The non‐Newtonian character of the resist solution is taken into account, as well as the changes in resist viscosity and solvent diffusivity with changing polymer concentration. Results obtained from this model show that polymer film thickness is controlled by convective radial flow of the resist solution and solvent evaporation. The former process governs film thickness during the early stages of the process, while the latter becomes significant in later stages. The model accurately describes the experimentally observed...

An in situ study of dissolution and swelling behavior of poly‐(methyl methacrylate) thin films in solvent/nonsolvent binary mixtures

A single‐element rotating‐polarizer ellipsometer (psi‐meter) was used for in situ characterization of the thermodynamic and kinetic behavior of poly‐(methyl methacrylate), PMMA, thin films (1.2 μm) in solvent/nonsolvent binary mixtures of methyl ethyl ketone/isopropanol (MEK/IPA) and methyl isobutyl ketone/methanol (MIBK/MeOH). Thermodynamic effects were inferred from equilibrium behavior by the degree of swelling and polymer‐solvent solubility. A sharp transition between complete solubility and almost total insolubility was observed in a narrow concentration range near 50:50 (by volume) solvent/nonsolvent for both MEK/IPA and MIBK/MeOH. In the insoluble regime, the polymer was found to swell up to three times the initial thickness. At 50:50 MEK/IPA, a temperature decrease from 24.8 to 18.4 °C caused a change from complete dissolution to combined swelling/dissolution behavior and rendered the PMMA film only 68% soluble. Kinetic effects were determined by dissolution and penetration rate measurements. A co...

A model for structured fluids

Steady-state and time-dependent non-Newtonian properties of structurally complex systems, such as suspensions and foodstuffs, are simulated by the extension of a recently developed fluid model. This model accommodates the concept of structure variation induced by flow via a kinetic approach similar to the treatment of reversible chemical reactions. Purely viscous and viscoelastic responses are considered, entailing different equations for the computation of their contribution to the overall stress sustained by the systems. The model successfully describes pseudoplastic and thixotropic behavior, with or without yield stress.

Yield stress determination of styrene-butadiene-styrene triblock copolymer solutions

Abstract Conventional methods of yield stress determination involve extrapolation of shear stress data to zero shear rate, and are thus susceptible to errors. This paper reports the application of a quasi-static technique for direct yield stress measurement, which obviates data extrapolation. Yield stresses of 38%, 42%, and 46% (by weight) SBS block copolymer solutions in a mixed solvent of tetrahydrofuran and methyl ethyl ketone (9:1 by volume) were obtained with a modified Fisher Autotensiomat Surface Tension Analyzer. Values obtained via extrapolation of viscometric data were compared with and found to differ significantly from those measured with the Autotensiomat. Arrhenius plots of the yield stress give straight lines, from which energy barriers to induce breakdown of the phase-separated morphologies are determined. These activation energies increase with solution concentration. The effect of repeated shearing on the apparent yield stress of the solutions was also determined at different temperatures.

Control of drug release from polymer matrices impregnated with magnetic beads —a proposed mechanism and model for enhanced release

Abstract The need to regulate drug release rates in applications such as suppression of diabetic symptoms and birth control has previously led to the development of delivery systems containing small magnetic beads uniformly imbedded within drug-laden polymer matrices. An oscillating magnetic field imposed on such systems triggers a significant increase in release rate. A mechanism for enhanced release is proposed here, which draws upon the similarity between the observed increase in mass transfer by pulsation, e.g., promotion of axial diffusion in a cylinder with pulsed (but zero net) flow and enhanced drug release by the oscillating field. A mathematical model is derived based on this analogy. Its predictions are consistent with general observations and provide correlations of release rates with the frequency and amplitude of the oscillating magnetic field and the intrinsic drug diffusivity.

Binary Blends of Monodisperse Polymers: Use of a Kinetic Network Model for Nonlinear Shear Stress Predictions in Entangled Polymer Fluids

A molecular network theory incorporating the concept of entanglement disruption and regeneration was previously developed to describe not only steady‐state but also transient rheological properties of monodisperse polymer melts and concentrated solutions. The viscoelastic responses of these systems are dominated by a rapid segmental motion at short times and a more sluggish, structure‐dependent network relaxation process at long times. In a binary blend of monodisperse fractions, the entangled network is composed of chains of two different lengths. The chain dynamics, and thus the characteristic response time, of each component in such a system is influenced by the presence of the coexistent component. This interaction is accommodated by a simple mixing assumption, which leads to accurate predictions of composition‐dependent linear viscoelastic properties, such as zero‐shear viscosity. In addition, the model gives an excellent description of the shear‐rate‐dependent viscosity curves of binary blends of va...

Plasma polymerization of ethane. I: Experimental studies of effluent gas composition and polymer deposition rates

The plasma polymerization of ethane was studied in a flow reactor of rectangular cross section. The plasma was sustained between parallel-plate electrodes by an RF generator operating at 13.56 MHz. The composition of the gas leaving the reactor was analyzed by gas chromatography. Polymer deposition rates were measured as a function of axial position in the reactor, using a quartz-crystal microbalance. The effluent gas is composed primarily of unreacted C2H6 and H2. Significant concentrations of CH4, C2H4, C2H2, and C3H8, and small amounts of C3H6, i-C5H12, and n-C5H12, are also observed. The distribution of these products is a strong function of the discharge power and of the gas pressure and residence time in the plasma. These experimental variables also affect both the rate of polymer deposition and the shape of the deposition profile along the reactor axis.

Plasma polymerization of ethane. II. Theoretical analysis of effluent gas composition and polymer deposition rates

A theoretical model has been developed to describe the deposition of polymer occurring in a capacitatively coupled, low-pressure, RF discharge sustained in ethane. The reaction mechanism chosen for this model assumes that polymer formation is controlled by the formation of free radicals in the plasma and the subsequent reaction of these species at the surface of the electrodes used to sustain the plasma. Convective and diffusive transport is taken to occur in the direction parallel to the electrodes. Diffusive transport perpendicular to the electrodes is considered to be rapid, and hence the gradients in this direction are taken to be negligible. Both the composition of the gas leaving the plasma reactor and the axial profile of polymer deposition rate within the reactor, observed experimentally, are predicted accurately by the model. Results obtained from the model have also been used to estimate the kinetic chain length and degree of unsaturation in the polymer. Both predictions are found to be in reasonable agreement with experimental observations.

Degradation of poly(methyl methacrylate) in CF4 and CF4/O2 plasmas

The degradation of poly(methyl methacrylate) films exposed to CF4 and CF4/O2 plasmas in a parallel plate reactor is investigated by means of gel permeation chromatography. Profile results indicate that degradation is high in the top few thousand angstroms, although reductions in molecular weight are observed throughout the 1.5 μm films. Oxygen additions to CF4 generate increases in PMMA etch rates, but molecular weight profiles suggest that degradation is still confined to the film surface. The shifts in molecular weight distribution obtained from plasma degradation experiments are simulated by a random scissioning model.

A model for laser marking of thin organic data storage layers by short intense pulses

A mathematical model is developed to describe the pit formation process in thin (∼0.1 μm) organic layers induced by short (<100 ns), intense laser pulses. The basic premise is an ablation‐driven viscous flow, in which the reactive pressure gradient due to polymer decomposition causes fluid motion. Contrary to the case of thick layers (∼1 μm) and long (∼500 ns), weak pulses, here surface tension gradients are shown to be too small to promote material flow in the short time span of laser exposure. The derived closed‐form expressions for temperature profile and pit contour allow expedient calculation of threshold energies and prediction of functional relationships among imposed (e.g., pulse energy and width) and measured (e.g., pit width) system variables. Model predictions compare favorably with experimental observations of such interrelations.