A Hybrid Boundary Element Method for Elliptic Problems with Singularities

The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local behavior of the singularity. The method is fitted into the framework of the widely used boundary element method (BEM), forming a hybrid technique, with the BEM computing the solution away from the singularity. Results of the hybrid technique are reported for the Motz problem and compared with the results of the standalone BEM and Galerkin/finite element method (GFEM). The comparison is made in terms of the total flux (i.e. the capacitance in the case of electrostatic problems) on the Dirichlet boundary adjacent to the singularity, which is essentially the integral of the normal derivative of the solution. The hybrid method manages to reduce the error in the computed capacitance by a factor of 10, with respect to the BEM and GFEM

Experimental and computational investigation of chemical vapor deposition of Cu from Cu amidinate

Experiments and computations are performed for the CuMOCVD fromcopper(I) N,N′-di-isopropylacetamidinate [Cu(iPr–Me–amd)]2 or [Cu(amd)]2 where amd = CH(CH3)2NC(CH3)NCH(CH3)2. The a priori choice of this precursor is dictated mainly by its oxygen and halogen–free ligands allowing co-deposition with oxophilic elements such as Al and by its ability to provide conformal Cu films in atomic layer deposition processes. The nucleation delay and the deposition rate as a function of deposition temperature and the evolution of the deposition rate along the radius of the substrate holder are experimentally determined with depositions performed at 1333 Pa in a vertical, warm wall, MOCVD reactor. With the aim to propose a kinetic scenario for Cu deposition, based on recently published experimental results for the decomposition of [Cu(amd)]2, a predictive 3D model of the process is built, based on the mass, momentum, energy and species transport equations. In agreement with the previously mentioned experimental results, it is demonstrated that a single surface reaction is responsible for the deposition of Cu. Two surface kinetics expressions are implemented depending on the deposition regime; a simple Arrhenius type expression in the reaction limited regime and a Langmuir–Hinshelwood type expression prevailing in the transport limited regimewhich takes into account the inhibition effects. The two different kinetics designate a modification in the surface reaction mechanism. The results show good agreement between experiments and computations. Complementary computations are performed, in order to compare the deposition rates of the Cu films deposited via the [Cu(amd)]2 and the (hfac)Cu(VTMS) and Cu(hfac)2 so as to determine relative advantages and disadvantages of Cu MOCVD from [Cu(amd)]2

A comprehensive insight in the MOCVD of aluminum through interaction between reactive transport modeling and targeted growth experiments

Growth experiments and reactive transport modeling were combined to formulate a comprehensive predictive model for aluminum growth from dimethylethylamine alane. The growth-rate profile was experimentally investigated as a function of substrate temperature. The reactive transport model, built under the computational fluid dynamics software PHOENICS, was used to reproduce the experimental measurements and to contribute to the understanding of the aluminum growth process, under sub-atmospheric pressure conditions. The growth mechanism of aluminum films was based on well established in literature reaction order and activation energy of homogeneous and heterogeneous chemical reactions. The reactive transport model was used further to investigate the effect of some key operating parameters on the process output. Simulation results are suggestive of modifications in the operating parameters that could enhance the growth rate and the spatial uniformity of the film thickness

Combined Macro/Nanoscale Investigation of the Chemical Vapor Deposition of Fe from Fe(CO)5

Experiments and computations are performed to model the chemical vapor deposition of iron (Fe) from iron pentacarbonyl (Fe(CO)5). The behavior of the deposition rate is investigated as a function of temperature, in the range 130–250 °C, and pressure in the range 10–40 Torr. Furthermore, the evolution of the surface roughness is correlated with the deposition temperature. By combining previously published mechanisms for the decomposition of Fe(CO)5, a predictive 3D macroscale model of the process is built. Additionally, a nanoscale and a multiscale framework are developed for linking the evolution of the surface of the film with the operating conditions at the reactor scale. The theoretical predictions from the coupled macro/nanoscale models are in very good agreement with experimental measurements indicating poisoning of the surface from carbon monoxide and decrease of the film roughness when temperature increases

Shape optimization of a showerhead system for the control of growth uniformity in a MOCVD reactor using CFD-based evolutionary algorithms

A steady state, laminar flow coupled with heat transfer, gas-phase and surface chemistry, is numerically solved for the optimal design of a showerhead gas delivery system in an axis-symmetrical MOCVD reactor. The design method involves an evolutionary algorithm based on CFD simulations. A finite-volume CFD code for aluminum growth provides the numerical predictions of the growth rate and its spatial variation over the substrate. A multilevel evolutionary algorithm is used to continuously adjust the shape of the shower plate so as to minimize the spatial variation of the growth rate. A 5-variable parameterization of the shower plate is investigated and a near-optimal solution is proposed and compared to the original configuration of the shower plate