Development of approximate growth models to control thin-film deposition using stochastic differential equations

Amit Varshney, Antonios Armaou

Research output: Contribution to conferencePaper

Abstract

Thin film deposition is an important process in semiconductor manufacturing. Lately,considerable research effort is being directed towards development of optimization and control strategies based on detailed macroscopic and microscopic models. However, high computational requirements associated with these models have led to development of reduced, "computational friendly", process models [2, 3], to perform these tasks. We focus on the development of computationally efficient dynamic process models for the evolution the microscopic properties during thin-film growth. Specifically, we derive a set of coupled stochastic differential equations (SDEs) for the temporal evolution of the dominant surface characteristics during the deposition process. These SDEs are an approximation of kMC-based detailed process descriptions and capture the dominant traits of the surface of the growing film. The motivation behind this approach is to develop a predictive microscopic optimization and control methodology based on reduced process models that circumvent the computational issues related to direct atomistic simulations such as kMC or MD. The variables that capture the dominant traits of the film surface can be categorized based on the nature of the information contained within them, i.e., statistical or spectral. The variables linked to statistical information describe the unavailable discrete lattice height distribution function and are obtained from Charlier Series B type expansion based on Poisson distribution. The variables linked to the spectral information describe the lateral correlation between lattice locations and are derived from a number of two-point correlation functions. The issue of uniqueness of surfaces having a given set of statistical and spectral parameters with respect to kMC simulations is also discussed, and we demonstrate that by incorporating a su±cient amount of statistical and spectral information through a finite (and small) number of parameters, the dominant growth dynamics can be adequately captured. For the identification of the state-space model, we employ Carlemann Linearization in conjunction with Maximum Likelihood Estimation [1] and derive a set of SDEs that govern the dynamic behavior of system. The proposed approach is employed towards the control of a conceptual deposition process which describes film growth under adsorption and surface diffusion with first neighbor interactions. A reduced SDE-based process model is constructed from the data obtained through kMC simulations of this deposition process under a wide range of macroscopic process conditions (e.g., wafer temperature and flux of reactants). Subsequently, the reduced process model is successfully employed as a basis for controller synthesis to control the roughness of the thin-film during deposition process.

Original languageEnglish (US)
Number of pages1
StatePublished - Dec 1 2005
Event05AIChE: 2005 AIChE Annual Meeting and Fall Showcase - Cincinnati, OH, United States
Duration: Oct 30 2005Nov 4 2005

Other

Other05AIChE: 2005 AIChE Annual Meeting and Fall Showcase
CountryUnited States
CityCincinnati, OH
Period10/30/0511/4/05

Fingerprint

Differential equations
Thin films
Film growth
Poisson distribution
Surface diffusion
Maximum likelihood estimation
Linearization
Distribution functions
Identification (control systems)
Surface roughness
Semiconductor materials
Fluxes
Adsorption
Controllers

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Varshney, A., & Armaou, A. (2005). Development of approximate growth models to control thin-film deposition using stochastic differential equations. Paper presented at 05AIChE: 2005 AIChE Annual Meeting and Fall Showcase, Cincinnati, OH, United States.
Varshney, Amit ; Armaou, Antonios. / Development of approximate growth models to control thin-film deposition using stochastic differential equations. Paper presented at 05AIChE: 2005 AIChE Annual Meeting and Fall Showcase, Cincinnati, OH, United States.1 p.
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Varshney, A & Armaou, A 2005, 'Development of approximate growth models to control thin-film deposition using stochastic differential equations', Paper presented at 05AIChE: 2005 AIChE Annual Meeting and Fall Showcase, Cincinnati, OH, United States, 10/30/05 - 11/4/05.

Development of approximate growth models to control thin-film deposition using stochastic differential equations. / Varshney, Amit; Armaou, Antonios.

2005. Paper presented at 05AIChE: 2005 AIChE Annual Meeting and Fall Showcase, Cincinnati, OH, United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Development of approximate growth models to control thin-film deposition using stochastic differential equations

AU - Varshney, Amit

AU - Armaou, Antonios

PY - 2005/12/1

Y1 - 2005/12/1

N2 - Thin film deposition is an important process in semiconductor manufacturing. Lately,considerable research effort is being directed towards development of optimization and control strategies based on detailed macroscopic and microscopic models. However, high computational requirements associated with these models have led to development of reduced, "computational friendly", process models [2, 3], to perform these tasks. We focus on the development of computationally efficient dynamic process models for the evolution the microscopic properties during thin-film growth. Specifically, we derive a set of coupled stochastic differential equations (SDEs) for the temporal evolution of the dominant surface characteristics during the deposition process. These SDEs are an approximation of kMC-based detailed process descriptions and capture the dominant traits of the surface of the growing film. The motivation behind this approach is to develop a predictive microscopic optimization and control methodology based on reduced process models that circumvent the computational issues related to direct atomistic simulations such as kMC or MD. The variables that capture the dominant traits of the film surface can be categorized based on the nature of the information contained within them, i.e., statistical or spectral. The variables linked to statistical information describe the unavailable discrete lattice height distribution function and are obtained from Charlier Series B type expansion based on Poisson distribution. The variables linked to the spectral information describe the lateral correlation between lattice locations and are derived from a number of two-point correlation functions. The issue of uniqueness of surfaces having a given set of statistical and spectral parameters with respect to kMC simulations is also discussed, and we demonstrate that by incorporating a su±cient amount of statistical and spectral information through a finite (and small) number of parameters, the dominant growth dynamics can be adequately captured. For the identification of the state-space model, we employ Carlemann Linearization in conjunction with Maximum Likelihood Estimation [1] and derive a set of SDEs that govern the dynamic behavior of system. The proposed approach is employed towards the control of a conceptual deposition process which describes film growth under adsorption and surface diffusion with first neighbor interactions. A reduced SDE-based process model is constructed from the data obtained through kMC simulations of this deposition process under a wide range of macroscopic process conditions (e.g., wafer temperature and flux of reactants). Subsequently, the reduced process model is successfully employed as a basis for controller synthesis to control the roughness of the thin-film during deposition process.

AB - Thin film deposition is an important process in semiconductor manufacturing. Lately,considerable research effort is being directed towards development of optimization and control strategies based on detailed macroscopic and microscopic models. However, high computational requirements associated with these models have led to development of reduced, "computational friendly", process models [2, 3], to perform these tasks. We focus on the development of computationally efficient dynamic process models for the evolution the microscopic properties during thin-film growth. Specifically, we derive a set of coupled stochastic differential equations (SDEs) for the temporal evolution of the dominant surface characteristics during the deposition process. These SDEs are an approximation of kMC-based detailed process descriptions and capture the dominant traits of the surface of the growing film. The motivation behind this approach is to develop a predictive microscopic optimization and control methodology based on reduced process models that circumvent the computational issues related to direct atomistic simulations such as kMC or MD. The variables that capture the dominant traits of the film surface can be categorized based on the nature of the information contained within them, i.e., statistical or spectral. The variables linked to statistical information describe the unavailable discrete lattice height distribution function and are obtained from Charlier Series B type expansion based on Poisson distribution. The variables linked to the spectral information describe the lateral correlation between lattice locations and are derived from a number of two-point correlation functions. The issue of uniqueness of surfaces having a given set of statistical and spectral parameters with respect to kMC simulations is also discussed, and we demonstrate that by incorporating a su±cient amount of statistical and spectral information through a finite (and small) number of parameters, the dominant growth dynamics can be adequately captured. For the identification of the state-space model, we employ Carlemann Linearization in conjunction with Maximum Likelihood Estimation [1] and derive a set of SDEs that govern the dynamic behavior of system. The proposed approach is employed towards the control of a conceptual deposition process which describes film growth under adsorption and surface diffusion with first neighbor interactions. A reduced SDE-based process model is constructed from the data obtained through kMC simulations of this deposition process under a wide range of macroscopic process conditions (e.g., wafer temperature and flux of reactants). Subsequently, the reduced process model is successfully employed as a basis for controller synthesis to control the roughness of the thin-film during deposition process.

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Varshney A, Armaou A. Development of approximate growth models to control thin-film deposition using stochastic differential equations. 2005. Paper presented at 05AIChE: 2005 AIChE Annual Meeting and Fall Showcase, Cincinnati, OH, United States.