Reactor Scale Model Research Articles

Impact of Thermodiffusion on Carbon Nanotube Growth by Chemical Vapor Deposition

Thermal diffusion, the process by which a multicomponent mixture develops a concentration gradient when exposed to a temperature gradient, has been studied in order to understand if its inclusion is warranted in the modeling of single-wall carbon nanotubes (SWNTs) synthesis by thermal chemical vapor deposition (CVD). A fully coupled reactor-scale model employing conservation of mass, momentum, species, and energy equations with detailed gas phase and surface reaction mechanisms has been utilized to describe the evolution of hydrogen and hydrocarbon feed streams as they undergo transport, as well as homogeneous and heterogeneous chemical reaction within a CVD reactor. Steady state velocity, temperature, and concentration fields within the reactor volume are determined, as well as concentrations of adsorbed species and SWNT growth rates. The effect of thermodiffusion in differing reactor conditions has been investigated to understand the impact on SWNT growth. Thermal diffusion can have a significant impact on SWNT growth, and the first approximation of the thermal diffusion factor, based on the Chapman–Enskog molecular theory, is sufficient for modeling thermophoretic behavior within a CVD reactor. This effect can be facilitatory or inhibitory, based on the thermal and mass flux conditions. The results of this investigation are useful in order to optimize model and reactor designs to promote optimal SWNT deposition rates.

Modeling the effect of Pt dispersion and temperature during anaerobic regeneration of a lean NO x trap catalyst

A crystallite-scale model is incorporated into a reactor-scale model to study the effect of Pt dispersion and temperature during the regeneration of a lean NO x trap (LNT) comprising a Pt/BaO catalyst. The current study is based on a recent experimental study [R.D. Clayton, M.P. Harold, V. Balakotaiah, C.Z. Wan, Appl. Catal. B 90 (2009) 662]. The model shows that an increase in the Pt dispersion for a fixed Pt loading increases the interfacial perimeter between Pt and Ba, and has a significant effect on the regeneration kinetics. The transient product distribution displayed by three catalysts having varied Pt dispersions (3.2%, 8% and 50%) is explained by the localized stored NO x gradients in the Ba phase. A rate determining process during the regeneration is found to be the diffusion of stored NO x within the Ba phase towards the Pt/Ba interface. Temperature-dependent NO x diffusivities in the Ba phase are used to predict the breakthrough profiles of H 2, N 2 and NH 3 over a range of catalyst temperatures. Finite gradients in the stored NO x concentration are predicted in the Ba phase, thus showing that the nitrate ions are not sufficiently mobile at lower temperatures for the low dispersion catalysts. The model predicts that the highest amount of NH 3 is produced by the low dispersion catalyst (3.2% dispersion) at high temperatures, by the high dispersion catalyst (50% dispersion) at low temperatures, and by the intermediate dispersion catalyst (8% dispersion) at intermediate temperatures, consistent with the experimental data. It is found that the net NH 3 generation is favored under conditions when NO x transport to the Pt/Ba interface is the rate determining process. The model considers the consumption of chemisorbed oxygen on Pt by H 2, which is used to predict the low effluent N 2 concentration for the 50% dispersion catalyst as compared to the 8% dispersion catalyst. Finally, a novel design is proposed to maximize the amount of NH 3 in the effluent of a LNT, which can be used as a feed to a selective catalytic reduction (SCR) unit placed downstream of the LNT.

Multi-scale Simulations for Plasma Processing of Thin Films

An inherent challenge to achieving improvements in thin film deposition processes is that requirements at the feature scale have to be somehow "tuned in" by modifying reactor scale geometry and process parameters. The simulation approach described allows for the solution of species fluxes and energies at the wafer surface as a function of process parameters. The reactor scale model addresses coupled flow, chemistry and plasma physics such as power deposition, volumetric reactions, species transport and deposition on chamber walls. The feature scale model computes growth of the film inside a trench. The objective of this work is to develop a comprehensive model for the high-density plasma chemical vapor deposition of silicon dioxide films in an inductively coupled plasma reactor. Using gas phase and surface reaction mechanisms from literature, trends in deposition characteristics with process variables such as inductive power are compared to experimental data in a commercial reactor.

Mechanisms for plasma etching of HfO2 gate stacks with Si selectivity and photoresist trimming

To minimize leakage currents resulting from the thinning of the insulator in the gate stack of field effect transistors, high-dielectric constant (high-k) metal oxides, and HfO2 in particular, are being implemented as a replacement for SiO2. To speed the rate of processing, it is desirable to etch the gate stack (e.g., metal gate, antireflection layers, and dielectric) in a single process while having selectivity to the underlying Si. Plasma etching using Ar/BCl3/Cl2 mixtures effectively etches HfO2 while having good selectivity to Si. In this article, results from integrated reactor and feature scale modeling of gate-stack etching in Ar/BCl3/Cl2 plasmas, preceded by photoresist trimming in Ar/O2 plasmas, are discussed. It was found that BCln species react with HfO2, which under ion impact, form volatile etch products such as BmOCln and HfCln. Selectivity to Si is achieved by creating Si–B bonding as a precursor to the deposition of a BCln polymer which slows the etch rate relative to HfO2. The low ion energies required to achieve this selectivity then challenge one to obtain highly anisotropic profiles in the metal gate portion of the stack. Validation was performed with data from literature. The effect of bias voltage and key reactant probabilities on etch rate, selectivity, and profile are discussed.

Application of dynamic flux balance analysis to an industrial Escherichia coli fermentation

We have developed a reactor-scale model of Escherichia coli metabolism and growth in a 1000L process for the production of a recombinant therapeutic protein. The model consists of two distinct parts: (1) a dynamic, process specific portion that describes the time evolution of 37 process variables of relevance and (2) a flux balance based, 123-reaction metabolic model of E. coli metabolism. This model combines several previously reported modeling approaches including a growth rate-dependent biomass composition, maximum growth rate objective function, and dynamic flux balancing. In addition, we introduce concentration-dependent boundary conditions of transport fluxes, dynamic maintenance demands, and a state-dependent cellular objective. This formulation was able to describe specific runs with high-fidelity over process conditions including rich media, simultaneous acetate and glucose consumption, glucose minimal media, and phosphate depleted media. Furthermore, the model accurately describes the effect of process perturbations—such as glucose overbatching and insufficient aeration—on growth, metabolism, and titer.

Simulating the Dynamics of Gas−Solid Flows in a Multichannel Microcirculating Fluidized Bed

The dynamics of gas−solid flows and distribution in monolithic multichannel microcirculating fluidized-bed reactors was analyzed using a computational fluid dynamics (CFD) modeling approach. A 2D Euler−Euler multiphase model with the kinetic theory of granular flow has been solved for the detailed monolithic packing geometry. The assemblage of monolithic structured packings with through-flow gas-particulate flows is globally considered in the simulation to capture the dominant mechanisms contributing to the final overall aero/granular dynamics. Due to the complex nature of the interactions between gas and particulate phases and the stationary monolith backbone, one of the challenges in the design and operation of the monolith reactors is the prevention of flow maldistribution. The work presented in this paper forms the basis for a comprehensive reactor-scale model for exploring the intriguing possibilities that the proposed process intensification concept offers for chemical reactions of energy/environmental relevance such as biomass gasification and combustion.

Feature profile evolution during shallow trench isolation etch in chlorine-based plasmas. II. Coupling reactor and feature scale models

A two-dimensional numerical fluid model was developed to investigate the effects of reactor design on the radial profiles of plasma species, namely, etch products and positive ions, during shallow trench isolation etching in Cl2∕O2∕Ar inductively coupled plasmas. Specifically, the dual-coil and dual gas-feed designs of the reactor were examined. The former parameter was determined to be effective in tailoring the radial ion flux profile at pressures higher than 20mT, while the latter parameter was shown to alter the etch product transport in the convection-dominant flow regime. Coupling of the reactor scale model to a feature scale model allowed investigation of minor center to edge variations in the etched feature profile. This hybrid model suggests that the general radial decrease in the etch depth seen from a set of design of experiments is caused by an inherent decrease in the spatial distribution of chlorine radicals. In addition, the increase in the silicon sidewall angle from center to edge can be qualitatively explained by the radial profile of the etch products.

Feature profile evolution during shallow trench isolation etch in chlorine-based plasmas. I. Feature scale modeling

The authors developed a cellular based Monte Carlo (MC) feature scale model capable of direct coupling to the dominant plasma species ratios from a reactor scale model in order to simulate the profile evolution of shallow trench isolation etch in chlorine-based plasmas and its variation from the center to the edge of the wafer. Carefully planned experiments along with scanning electron microscopy (SEM) were used to calibrate the MC model, where one to two plasma parameters were systematically varied. Simulated feature profiles were found to agree well with experimental observations, capturing details such as microtrenching, faceting, tapering, and bowing. The particle counts used to achieve these fits agreed well with those estimated from SEM, corroborating the chemistry and physics used in the feature scale model. In addition, the feature scale model uses a novel surface representation that eliminates the artificial flux fluctuations originating from the discrete cells used in the simulation and enables a much more precise calculation of the surface normal, which dictates the trajectory of reflected species.

Modeling of the carbon nanotube chemical vapor deposition process using methane andacetylene precursor gases

Chemical vapor deposition of carbon nanotubes (CNTs) in a horizontal tube-flow reactorhas been investigated with a fully coupled reactor-scale computational model. The modelcombined conservation of mass, momentum, and energy equations with gas-phase andsurface chemical reactions to describe the evolution of a hydrogen and hydrocarbonfeed-stream as it underwent heating and reactions throughout the reactor. Investigationwas directed toward steady state deposition onto iron nanoparticles via methane andhydrogen as well as feed-streams consisting of acetylene and hydrogen. The modeldetermines gas-phase velocity, temperature, and concentration profiles as well as surfaceconcentrations of adsorbed species and CNT growth rate along the entire length of thereactor. The results of this work determine deposition limiting regimes for growth viamethane and acetylene, demonstrate the need to tune reactor wall temperatureto specific inlet molar ratios to achieve optimal CNT growth, and demonstratethe large effect that active site specification can have on calculated growth rate.

A shrinking core model for the electro-deoxidation of metal oxides in molten halide salts

A shrinking core model is developed and applied to the electro-deoxidation of metal oxides (such as TiO 2, SiO 2, NiO, Cr 2O 3 and Nb 2O 3). Among these the reduction of TiO 2 is the most complex due to reduction by formation of a number of lower oxides and perovskite formation under certain experimental conditions. Hence, TiO 2 is chosen as the model material for this reduction. First, a single stage model is adopted for the reduction of TiO 2 to Ti and it is shown that an additional term for the oxygen concentration in the shell must be added to get the accurate values of oxygen concentration unless the concentration at the exterior of the grain is zero. Subsequently, a multi-stage model for the successive reduction of titanium oxides to titanium is proposed. It uses a shrinking core of the oxides in the order starting from TiO 2 to Ti 3O 5 to Ti 2O 3 to TiO to Ti. An analytical solution is developed for the transient differential equation resulting in a series solution for the concentration of oxygen in the lower oxides. Subsequently, a solution based on the pseudo-steady assumption is also developed. It is shown that for the parameters chosen, at certain values of dimensionless applied current density, I d, (∼0.1) the transient and pseudo-steady state solutions agree in terms of the dimensionless time it takes for the core to shrink completely. The proposed model could be applied to other metal oxides such as SiO 2, NiO, Cr 2O 3, Nb 2O 3 and other metal oxides that are reduced using the Fray–Farthing–Chen (FFC) process mechanism. This can be used for a reactor scale model or for performing a parametric study of the current density and the grain size.

Design and modeling of equipment used in electrochemical processes for microelectronics

This paper presents an overview of the design of electrochemical processing equipment for semiconductor and related microelectronic manufacturing as well as a review of publications that are applicable to electrochemical wafer process equipment. We discuss several types of electrochemical processes applicable to wafer processing and the considerations that go into automated equipment for these processes. The design of such equipment is considered from a general perspective, as well as specifically with respect to several electrochemical processes. We also present results from reactor-scale modeling of several associated systems. The modeling results have been used to understand the effects of process parameters and hardware design on the results achieved.

Computational Analysis and Optimization of a Chemical Vapor Deposition Reactor with Large-Scale Computing

A computational analysis and optimization is presented for the chemical vapor deposition (CVD) of silicon in a horizontal rotating-disk reactor. A three-dimensional reactor-scale model for the gas flow, heat transfer, and mass transfer in a CVD reactor is coupled to a simple transport-limited surface reaction mechanism for the deposition of epitaxial silicon from trichlorosilane. The model is solved to steady state for the deposition rate profile over the 8-in. silicon wafer using an unstructured-grid finite-element method and a fully coupled inexact Newton method on parallel computers. Because a high degree of spatial uniformity in the deposition rate is desired, parameter continuation runs for six key operating parameters, including the inlet flow rate and the rotation rate of the substrate, were performed and their individual effects analyzed. Finally, optimization runs were performed that located operating conditions that predict nonuniformity as low as 0.1%.

A Model of Silicon Nanocrystal Nucleation and Growth on SiO2 by CVD

ABSTRACTSilicon nanocrystals can be used in non-volatile memory devices to reduce susceptibility to charge loss via tunnel oxide defects, allowing scaling to smaller sizes than possible with conventional Flash memory technology. In order to optimize device performance, it is desirable to maximize the nanocrystal density and surface coverage, while maintaining sufficient inter-crystallite separation to limit electron tunneling between adjacent crystallites. Ideally, crystallite densities in excess of 1012cm-2 with relatively narrow particle size distributions must be obtained, posing a significant challenge for process development and control. In order to facilitate development of such a process, a rate-expression-based model has been developed for the nucleation and growth of silicon nanocrystals on SiO2 in a CVD process. The model addresses the phenomena of nucleation, growth, and coalescence and includes the effects of exclusion zones surrounding the growing nuclei. The model uses a phenomenological expression to describe the nucleation rate and assumes that following nucleation, crystallite growth is dominated by gas-phase deposition processes, analogous to CVD of polycrystalline silicon. The model-predicted time-evolutions of crystallite densities and crystallite size distributions are consistent with experimental distributions as measured by Scanning Electron Microscopy (SEM). By coupling the model to a reactor-scale model of polysilicon CVD, it is possible to predict variations in the crystallite size distributions at various locations across a wafer as a function of reactor settings (temperature, pressure, flow rates, etc…). This in turn can be used for process control and optimization in order to ensure uniform deposition of nanocrystals in a large-scale manufacturing environment.

Determination of Ti+-flux and Ar+-flux of ionized physical vapor deposition of titanium from multiscale model calibration with test structures

In this article we determine physical parameters characterizing the ionized physical vapor deposition of titanium in a Hollow Cathode Magnetron by comparing experimental results obtained from suitable submicron test structures with a multiscale model. The model includes the reactor scale, the plasma sheath and presheath scale, and the feature scale. The reactor scale model delivers the energy and angular distribution of the neutral sputtered particles from the reactor geometry and an energy dependent collision model. The sheath and presheath model calculates the energy and angular distribution of the ions from the reactor model and a subsequent scattering model describes collisions in the presence of magnetic fields. The levelset-based feature scale simulator propagates the front according to local growth velocities which are calculated from Monte Carlo particle flux and reaction kinetics (derived from molecular dynamics calculation). The calibration is performed in two steps with help from bottle-shaped test structures as well as technologically relevant structures. First, hi-fill and ultra-hi-fill magnetron sputter processes of titanium are investigated in order to verify the transport model for the neutral particles. Second, a Hollow Cathode Magnetron sputter process of titanium is analyzed in order to verify the transport model for postionized particles. This analysis is performed for a floating substrate process and a process with rf-driven substrate bias. The postionized flux fraction of titanium in this technology is not calculated from a plasma model but treated as a free parameter. The prediction of the model and the comparison with the experimental data allow us to determine this value as 0.7±0.1 under a standard condition. The ionized flux of argon relative to the ionized flux of titanium is determined as 2. The results show that the bottom and sidewall coverage of the process depends significantly on the angular dependence of the ionized component which is essentially a result of processes in the presheath. The validity of the model covers a variety of plasma and process conditions. It can be applied to other reactor concepts and materials.

Modeling of the Fischer–Tropsch synthesis in slurry bubble column reactors

A multicomponent one-dimensional dynamic mathematical model for the reacting slurry systems with a change in gas flow rate due to the chemical reaction is developed. A change in gas flow rate caused by the chemical reaction is modeled using the overall gas mass balance. Thus, all relevant chemical species are included in the model. Linear first-order reaction kinetics is considered. The gas phase is modeled using the two-bubble class hydrodynamic model. The interaction between small and large bubbles is included as the cross-flow. Suspension of liquid and solids is assumed to form a pseudo slurry phase. Back-mixing in all of the three considered phases, small bubbles, large bubbles and slurry, is accounted for using the axial dispersion model (ADM). Energy balance of the slurry phase is also included in the model. The developed general reacting slurry system model is used to simulate the performance of the Fischer–Tropsch (FT) slurry bubble column (SBC) reactor. Performance of the developed ADM based model is compared with the reactor scale models in which the reactor back-mixing is represented using some combination of the two limiting ideal reactor models of, complete stirred or plug flow.

Modeling high power magnetron copper seed deposition: Effect of feature geometry on coverage

The deposition of copper using a high power magnetron (HPM) has been studied using reactor and feature scale models. Discussed are results for Cu seed HPM deposition on trench, via, and dual inlaid features with different geometries (aspect ratio and side wall angles). At low wafer powers the Cu seed feature coverage is characterized by geometric shadowing due to the broad angular distribution of the dominant Cu athermal. At high wafer powers the metal deposited at feature bottom is sputtered by Ar+ and redistributed to the side walls. The deposition rate within a feature is nonlinear with time as metal deposited at the feature opening obstructs incoming metal from reaching the inside of the feature. Competing trends of higher copper flux at wafer center versus edge and higher Ar+ flux at wafer center versus edge result in a transition of the field thickness heights from edge>center at low wafer powers to center<edge at high wafer powers. The type and geometry of a feature in which metal is being deposited plays a major role in the final metal coverage. Vias have less coverage than trenches given the smaller opening for incoming metal to enter. For instance trenches with aspect ratio (AR) equal to 4 still have more Cu side wall coverage than vias of AR=1. In the dual inlaid geometry studied the via inner side wall and trench bottom corners are the most difficult regions to deposit a Cu seed. Both side wall angle and AR can have equal control of a thickness change. For instance in a via a similar side wall thickness decrease (at low wafer power) can be achieved with AR=4 and θvia=4°–0° or AR=1–4 and θvia=4°.

A multiscale study of the selective MOVPE of Al xGa 1− xAs in the presence of HCl

The selective deposition of Al x Ga 1− x As films on (1 0 0) substrates patterned with a SiN x mask is simulated at multiple length and time scales. First, gas-phase and surface kinetic schemes are developed to describe GaAs, AlAs and Al x Ga 1− x As deposition from TMGa, TMAl and AsH 3 in the presence of HCl. Unknown reaction kinetic constants are determined by quantum chemistry calculations of energy and structure followed by application of transition state theory. These estimated kinetic parameters and experimental values are then incorporated in finite element computations of flow, temperature, and species concentration fields in different MOVPE reactor configurations. The predicted local growth rates and gas-phase compositions are in good agreement with experimental data. The selective deposition on patterned substrates with different mask/feature ratios is also investigated with a feature scale model, coupled to the reactor scale model by imposing continuity of gas-phase concentrations and fluxes at the boundaries. The experimentally observed growth rate enhancement is reproduced quantitatively.

Multiscale modeling of plasma etch processing

This paper presents an overview of the recent developments in simulation capabilities of the plasma-assisted processes. Different scale-related models are considered. A reactor-scale model produces electric fields, ion and neutral densities as a function of position, and ion and neutral fluxes incident on to the wafer. A sheath model represents the spatial distributions of fields and fluxes at gas–solid boundaries as well as particle energy and angular distributions for ions and neutrals striking the wafer and other solid surfaces. A feature-scale model uses Monte Carlo (MC) or ballistic integral methods to evolve an etched profile based on the fluxes and particle energy-angular distributions generated by the sheath model. The effect of pattern density on the etch-induced feature profile is considered as an example of the implementation of multi-scale plasma simulation.

Integrated multiscale three-dimensional simulation approach in local interconnect gap-fill optimization

An integrated three-dimensional (3D) simulation approach for the optimization of multistep process modules is developed. A link between a 3D finite volume reactor-scale model and a developed 3D cell topography feature-scale model allows the prediction of uniformity distribution for a sequence of process steps on an entire wafer surface. As an example, an across-wafer gap-fill is simulated using a combination of simulation tools to capture a variety of nonuniformities that exist in all steps involved in the local interconnect tungsten-fill process flow. Across-wafer variations in Ti flux density, angular distributions in Ti and TiN physical vapor deposition fluxes, as well as nonuniformities in precursor fluxes in TiN and W chemical vapor deposition are taken into consideration. Across wafer blanket layer thickness variations as well as bottom and sidewall thickness variations inside interconnect features are determined for all deposited layers. Across-wafer metal stack thickness distributions, wafer edge effect, and key-hole formation inside the features are simulated. Experimentally extracted parameters are employed for the calibration of the simulation results.

Role of sidewall scattering in feature profile evolution during Cl2 and HBr plasma etching of silicon

Coupling reactor-scale models of plasma etching equipment to device-scale models of feature profile evolution offers the potential for increased levels of virtual design of both capital equipment and process recipes. In this article, a combined reactor-and feature-scale model of crystalline silicon feature profile evolution is described, and simulation results of isolated trench and isolated line etching with Cl2 and HBr plasmas are compared to experimental data. By incorporating reactor-scale predictions of plasma properties along with assumptions concerning the details of energetic particle scattering from surfaces, we are able to predict both the etch rate and the shape of evolving features. Important in the comparison to experiment is the proper prediction of “microtrench”-free high aspect ratio trench etching in the case of HBr, contrasted with the occurrence of deep microtrenching when Cl2 plasmas were used. These results suggest that a thorough knowledge of the details of energetic ion scattering from all evolving surfaces is required before accurate feature profile evolution predictions can be made.