R. L. Sani

Simulation of Shape Evolution during Electrodeposition of Copper in the Presence of Additive

Shape evolution during electrodeposition of copper in microtrenches was studied numerically by a model which incorporates adaptive meshing capabilities. Filling of trenches with copper without creating a void was related to plating additives in solution. The shape-change behavior of this system resulting from variation of the features aspect ratio bulk composition, and level of additive components was investigated. The operating window of bath conditions for void-free electrodeposition was studied in the range of 0.25 × 10 -4 to 10 -4 M bulk concentration of additive in a 0.25 M CuSO 4 + 0.2 M H 2 SO 4 plating solution and for aspect ratios (depth:width) from 0.5 to 4. The mathematical model includes fluid flow, transport by diffusion, migration and convection, multiple species, and reactions in complex geometries.

Linear stability theory model for finger formation in asymmetric membranes

Abstract Various features of asymmetric membrane morphology are studied via a linear stability theory model which is corroborated by experimental studies. This model concerns the formation of spatial structures in a stationary liquid layer containing a nonvolatile and a volatile component; the volatile component is assumed to undergo unsteady-state, one-dimensional mass transfer into an adjacent immiscible and inviscid phase. The system is predicted to be unstable whenever random perturbations of the interface result in lowering of the local interfacial tension, due to very steep concentration profiles of the components near the interface. When applied to the description of precipitating polymer/solvent systems, the model predicts the spacing of the largest-scale spatial structures to be 4.2 times the final membrane thickness. This corroborates well with observations of finger spacing in cross-sections of asymmetric membranes. The model explains qualitatively the formation of both small-scale fingers and nodules observed in many asymmetric membranes.

Theoretical study of the transport processes occurring during the evaporation step in asymmetric membrane casting

Abstract A mathematical model is developed for the evaporation step in asymmetric membrane casting which allows for the convective transport induced by local film shrinkage because of both solvent loss and the excess volume of mixing effect. Realistic boundary conditions account for the gas phase mass transfer characteristics. Predictions for the cellulose acetate/acetone system are presented for the instantaneous concentration profiles, film thickness, and time required for the interface to skin. The results are presented in the form of dimensionless correlations which allow predicting the behavior during evaporative casting for generalized operating conditions. The predictions are compared with limited data for cellulose acetate/acetone. The model suggests that once the polymer/solvent system has been selected, the most influential process parameter is the gas phase mass transfer coefficient and that inadequate control of this parameter may account for the variability in membranes cast in similar devices operated under ostensibly the same conditions.

Predicting Electrode Shape Change with Use of Finite Element Methods

A method of numerical calculation is developed for predicting two‐dimensional shape changes at a cathode during electrodeposition. The calculation uses finite element methods to obtain the secondary potential field distribution in an electrolysis cell. The cathode shape initially consists of parallel metal strips which are separated by, and coplanar with, insulating strips; the anode is at a fixed distance from the cathode. Transient numerical calculations provide a complete time history of cathode shape during deposition. Results are obtained in order to compile dimensionless shape change dependence on coulombs passed, polarization parameter, applied potential, and initial cathode shape.

Modeling of Charge Carrier Transport in Photoetching of Gallium Arsenide

Wet photoelectrochemical etching of GaAs was investigated with the use of a numerical model that calculated electron, hole, and potential distributions in a selectively illuminated semiconductor. The Galerkin finite element method was used to solve the Poisson equation for the potential and the species transport equations for holes, and electrons in two dimensions. The transport equations included generation, recombination, diffusion, and migration terms. A technique was developed for examining the sensitivity of the distribution of holes, electrons, and the potential to the parameters of the system including the surface reaction rate constant, diffusion coefficients, doping concentration, light intensity, wavelength, and the recombination length. The sensitivity analysis technique facilitated identification of parameters for which the behavior of this complex, nonlinearly coupled system is most sensitive.

Studies of convective transport in evaporative casting of dense polymer films

Although several models have been developed to describe the evaporative casting of dense polymer films, none of them has included the convective transport terms which arise owing to the densification which occurs. In this paper we first describe a new finite element solution to the binary nonisothermal evaporative casting process which is used to confirm the predictions of the finite difference solution recently developed by Shojaie et al. (J. Mater. Process. Manu. Sci., 1 (1992) 181). This comparison then establishes that systematic deviations between experimental measurements and the model predictions of Shojaie et al. do not arise because of any inaccuracies in the numerical solution methodology. We then explore whether these deviations arise owing to omission of the convective transport terms by Shojaie et al. and all other modeling efforts. We employ a scaling analysis to demonstrate that convective transport effects can be significant in the evaporative casting process. The convective transport terms then are incorporated into the nonisothermal evaporative casting model of Shojaie et al. for the cellulose acetate/acetone system. The model predictions both with and without convective transport are compared to real-time gravimetric and surface-temperature data. This study indicates that ignoring convective transport can result in differences as large as 40% in the model predictions. The model predictions incorporating convective transport are in quantitative agreement with real-time data at short evaporation times, but progressively deviate at longer times. This deviation is thought to be due to the use of an equilibrium equation-of-state for the solution density as a function of concentration.

Flow and Transport in Systems with Shape Change: Mass Transfer in Electrochemical Systems

There are many important technological and engineering science applications in which a free and/or moving fluid and/or solid interface play a dominant role. Such systems encompass general static and dynamic applications encountered, for example, in capillarity, crystal growth, electrochemical plating and and corrosion, coating and polymer technology, separation processes, metal and glass forming processes and many other areas of engineering and science. Specifically, the equilibrium shape and stability of menisci between pairs of immiscible fluids in containers; coating flows in which a viscous fluid is deposited on a rigid, or flexible, substrate as commonly encountered in the manufacturing of photographic films and plate glass or the coating of paper; solidification processes which are commonly encountered in the material science of crystal growth, e.g., in open boat configuration, Czochralski or floating zone methods; extrusion of liquid from nozzles as encountered in the continuous production of fibers or curtain coating operations; domain shape changes associated with elect rod eposition and chemical etching processes. A quantitative description and solution of such problems has been allusive even in the simplest cases because of firstly, the inherent nonlinearities in the continuum equations and secondly, heat and/or mass (and sometimes concomitant heat) transport which often play a decisive role in the process.

On the Finite Element Modeling of the Scalar Transport Equation

ABSTRACT This material was presented (by RL.S.) as part of a three hour lecture on finite element modeling of incompressible and Boussinesq flows at the summer school organized by IUSTI, Universite de provence.