Feedback control of growth rate and surface roughness in thin film growth

Lou, Yifei; Christofides, Panagiotis D.

doi:10.1002/aic.690490818

Cited by 69 publications

(26 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This averaging technique has been used in previous works to reduce the noise produced by smaller KMC lattices. 35,64 As shown in Figure 4, the noise in the coverage of species A using the averaged 30 3 30 lattices is comparable to the noise of the result obtained from a 100 3 Figure 3. The gap-tooth scheme for the catalytic surface of the reactor.…”

Section: Lattice Size Determination and Solution Approachmentioning

confidence: 48%

Distributional uncertainty analysis and robust optimization in spatially heterogeneous multiscale process systems

2016

View full text Add to dashboard Cite

in Wiley Online Library (wileyonlinelibrary.com) Multiscale models have been developed to simulate the behavior of spatially-heterogeneous porous catalytic flow reactors, i.e., multiscale reactors whose concentrations are spatially-dependent. While such a model provides an adequate representation of the catalytic reactor, model-plant mismatch can significantly affect the reactor's performance in control and optimization applications. In this work, power series expansion (PSE) is applied to efficiently propagate parametric uncertainty throughout the spatial domain of a heterogeneous multiscale catalytic reactor model. The PSE-based uncertainty analysis is used to evaluate and compare the effects of uncertainty in kinetic parameters on the chemical species concentrations throughout the length of the reactor. These analyses reveal that uncertainty in the kinetic parameters and in the catalyst pore radius have a substantial effect on the reactor performance. The application of the uncertainty quantification methodology is illustrated through a robust optimization formulation that aims to maximize productivity in the presence of uncertainty in the parameters.

show abstract

Section: Lattice Size Determination and Solution Approachmentioning

confidence: 48%

Distributional uncertainty analysis and robust optimization in spatially heterogeneous multiscale process systems

2016

View full text Add to dashboard Cite

show abstract

“…Control is currently used in fabricating small electronic devices for computing [3], but as device size shrinks toward the size of individual atoms, continuum models of the processing dynamics are no longer valid [4,5]. Plant models instead require consideration of discrete atoms and their interactions, using molecular dynamics, Monte Carlo simulations, or quantum mechanics [6]. The atomicscale models must also couple to macroscopic models of the process equipment, resulting in multiscale simulations [7][8][9].…”

Section: Introductioncontrasting

confidence: 38%

Reduction and identification methods for Markovian control systems, with application to thin film deposition

Gallivan

Murray

2003

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYDynamic models of nanometer-scale phenomena often require an explicit consideration of interactions among a large number of atoms or molecules. The corresponding mathematical representation may thus be high dimensional, nonlinear, and stochastic, incompatible with tools in nonlinear control theory that are designed for low-dimensional deterministic equations. We consider here a general class of probabilistic systems that are linear in the state, but whose input enters as a function multiplying the state vector. Model reduction is accomplished by grouping probabilities that evolve together, and truncating states that are unlikely to be accessed. An error bound for this reduction is also derived. A system identification approach that exploits the inherent linearity is then developed, which generates all coefficients in either a full or reduced model. These concepts are then extended to extremely high-dimensional systems, in which kinetic Monte Carlo (KMC) simulations provide the input-output data. This work was motivated by our interest in thin film deposition. We demonstrate the approaches developed in the paper on a KMC simulation of surface evolution during film growth, and use the reduced model to compute optimal temperature profiles that minimize surface roughness.

show abstract

“…This can be caused by adsorbed molecules which have not yet merged into stable islands. Some works [2][3][4][5] provided a theoretical description of formation of stable nuclei and their growth from gaseous phase. However, it is difficult to identify such gaseous phase molecules visually, because their interaction with the electron beam in the electron microscope is very weak due to their low density.…”

Section: Introductionmentioning

confidence: 40%

Phase composition of amorphous Se island layers

Montrimas¹,

Rinkūnas²

2005

Lith. J. Phys.

View full text Add to dashboard Cite

Results of investigations of island amorphous selenium layers evaporated upon a carbon film are presented. The layers were heated at various temperatures. In all cases, selenium formed islands of almost perfectly hemispherical shape with various diameters. Such well-defined shape of the islands made it possible to calculate total mass of the islands. Experimental data indicates that heating of the layer causes an increase of the mass of islands up to 7 times in comparison with their mass prior to thermal processing. This is possible only if the islands grow by accepting atoms of the same kind adsorbed on the substrate. It follows that a part of the layer mass is accumulated in the gas adsorbed on the substrate. This part depends on the layer temperature, substrate material, evaporation rate, etc. Investigation of distribution of island diameters immediately after layer evaporation and during thermal processing of the layer allowed determination of conditions that are needed in order to be able to estimate defect density in the substrate from the measured density of the islands.

show abstract

Feedback control of growth rate and surface roughness in thin film growth

Cited by 69 publications

References 31 publications

Distributional uncertainty analysis and robust optimization in spatially heterogeneous multiscale process systems

Distributional uncertainty analysis and robust optimization in spatially heterogeneous multiscale process systems

Reduction and identification methods for Markovian control systems, with application to thin film deposition

Phase composition of amorphous Se island layers

Contact Info

Product

Resources

About