The Combination of Equipment Scale and Feature ScaleModels for Chemical Vapor Deposition Via aHomogenization Technique

Gobbert, Matthias K.; Cale, Timothy S.; Ringhofer, Christian

doi:10.1155/1998/24073

Cited by 5 publications

(4 citation statements)

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“…The extension to parameterized surfaces (allowing overhangs on the feature sides) is contained in Ref. 6. Following that, the numerical method used in the simulations is presented.…”

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confidence: 99%

Mesoscopic Scale Modeling of Microloading during Low Pressure Chemical Vapor Deposition

Gobbert

Ringhofer

Cale

1996

J. Electrochem. Soc.

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A model designed to deal with pattern dependences of deposition processes is discussed. It is a mesoscopic scale model in the sense that it deals with spatial scales on the order of lO to 10-2rn which is intermediate between reactor scale and feature scale. This model accounts for the effects of the microscopic surface structure via suitable averages obtained by a homogenization technique from asymptotic analysis. Two studies on the low pressure chemical vapor deposition of silicon dioxide from tetraethoxysilane are presented to demonstrate the mesoscopic scale model. The first study shows the effects of microloading in regions of higher feature density. The second study shows the effects of varying operating conditions on loading and introduces a generalized Damkoehler number, which includes information about the surface patterns, for quantifying the degree of transport limitations. Some thoughts on how this model can be used to bridge reactor scale and feature scale models are presented. InfroductionThe trend toward single-wafer reactors (SWR) for deposition and etch processes in the microelectronics industry is expected to continue as wafer size continues to increase. To make SWRs more economically attractive, deposition and etch processes are being run at high rates to maintain reasonable throughputs. High rates can lead to nonunif ormities on the wafer scale because of depletion of reactants and transport limitations. Reactor scale models (RSIVI) for flow, heat transfer, and chemical reactions are well devel-

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“…The extension to parameterized surfaces (allowing overhangs on the feature sides) is contained in Ref. 6. Following that, the numerical method used in the simulations is presented.…”

mentioning

confidence: 99%

Mesoscopic Scale Modeling of Microloading during Low Pressure Chemical Vapor Deposition

Gobbert

Ringhofer

Cale

1996

J. Electrochem. Soc.

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“…Based on analytic work in [2,5,6,8,11], the authors and coworkers have previously introduced [7,12] a mesoscopic scale model on a length scale intermediate to those of the classical reactor scale and feature scale models, which was designed to provide information on the effects of feature clustering on a length scale of about 1.0 cm at comparably high pressures of at least 1 torr (where 760 torr = 1 atm). In that regime, the mean free path of the gas molecules was well inside the domain size, and the gas flow could be modeled as diffusion-dominated [8,9,11,12,18].…”

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confidence: 99%

“…In that regime, the mean free path of the gas molecules was well inside the domain size, and the gas flow could be modeled as diffusion-dominated [8,9,11,12,18]. While [8,11] derive the homogenized model formally for the concrete problem of interest, [2,5,6] handle the analysis rigorously for a more general class of models.…”

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confidence: 99%

“…We remark that in the previous work [2,5,6,8,11], where the flow was assumed to be Maxwellian inside the features as well, the only information needed about the surface geometry was the ratio of surface areas between the microstructured surface and the flat surface. This ratio is now replaced by the integral kernelã, which contains much more information about the actual shape of the surface and is necessary for the non-Maxwellian picture.…”

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confidence: 99%

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A Homogenization Technique for the Boltzmann Equation for Low Pressure Chemical Vapor Deposition

Ringhofer

Gobbert²

2003

SIAM J. Appl. Math.

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Abstract. We present a homogenization technique for rarefied gas flow over a microstructured surface consisting of patterns of periodic features. The length scale of the model domain is comparable to the mean free path of the molecules, while the scale of the surface patterns is much smaller. The flow is modeled by a system of linear Boltzmann equations with a diffusive boundary condition at the patterned surface. The resulting homogenized boundary condition holds at a virtual flat surface and incorporates the microscopic geometry information about the surface structure on the macroscopic level. Numerical results validate the approach. The setup models low pressure chemical vapor deposition processes in the manufacturing of integrated circuits. 1. Introduction. Low pressure chemical vapor deposition is used in the manufacturing of integrated circuits to deposit a thin layer of material onto the surface of a silicon wafer. The deposition surface necessarily involves a microstructure given by the electrical components of the future microchip. Classical models for this process include reactor scale models [17] with a typical length scale of over 10 cm, which model the gas flow throughout the chemical reactor, and feature scale models [3] with a typical length scale of under 1 µm, which focus on the evolution of the film profile inside an individual feature.In more detail, the process works as follows. Molecules of the species to be deposited are carried inside the chemical reactor by an inert carrier gas to a microstructured surface, where they are partially absorbed and partially reflected at a certain rate. The length scale of the surface structure is several orders of magnitude smaller than that of the reactor and therefore cannot be reasonably resolved on the reactor scale. On the other hand, this structure will influence the gas flow through the boundary conditions; i.e., adsorption on the microstructured surface will result in a different behavior of the gas flow than adsorption on a flat surface, even on the macroscopic reactor scale. We therefore have to solve a homogenization problem at the boundary by deriving a boundary condition for the flow problem which incorporates the microscopic geometric information about the surface structure into the macroscopic flow picture.

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Mesoscopic Scale Modeling for Chemical Vapor Deposition in Semiconductor Manufacturing

Gobbert

Ringhofer

2004

Dispersive Transport Equations and Multiscale Models

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The Combination of Equipment Scale and Feature ScaleModels for Chemical Vapor Deposition Via aHomogenization Technique

Cited by 5 publications

References 1 publication

Mesoscopic Scale Modeling of Microloading during Low Pressure Chemical Vapor Deposition

Mesoscopic Scale Modeling of Microloading during Low Pressure Chemical Vapor Deposition

A Homogenization Technique for the Boltzmann Equation for Low Pressure Chemical Vapor Deposition

Mesoscopic Scale Modeling for Chemical Vapor Deposition in Semiconductor Manufacturing

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