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## Modeling and Model Reduction for Control and Optimization of Epitaxial Growth in a Commercial Rapid Thermal Chemical Vapor Deposition Reactor (1998)

Citations: | 3 - 3 self |

### Citations

710 |
Principal component analysis in linear systems: Controllability, observability, and model reduction,”
- Moore
- 1981
(Show Context)
Citation Context ...box" input--output models of the system. 3.4 Balancing In response to concerns regarding the POD method, we considered an alternative approach based on the method of balanced realizations (see, e=-=.g., [12, 33]-=-). In this method, a coordinate transformation is computed which allows state components to be ranked according to their influence on the input--output behavior of the system as measured by the Hankel... |

610 |
Low-dimensional procedure for the characterization of human faces.
- Kirby
- 1987
(Show Context)
Citation Context ... same dimension (see, e.g., [19]). Application The attractive properties of the POD have led to success in applying it to areas such as turbulence modeling (e.g., [19]) and pattern recognition (e.g., =-=[46]-=-). Recently, much work has been done to study its use for RTCVD model reduction (e.g., [1, 2, 3, 4, 36, 50]). We have performed a similar study toward finding a low--order approximation to (52). To ge... |

471 |
All optimal Hankel-norm approximations of linear multivariable systems and their Loo-error bounds",
- GLOVER
- 1984
(Show Context)
Citation Context ...box" input--output models of the system. 3.4 Balancing In response to concerns regarding the POD method, we considered an alternative approach based on the method of balanced realizations (see, e=-=.g., [12, 33]-=-). In this method, a coordinate transformation is computed which allows state components to be ranked according to their influence on the input--output behavior of the system as measured by the Hankel... |

148 |
The growth of crystals and the equilibrium structure of their surfaces
- Burton, Cabrera, et al.
- 1951
(Show Context)
Citation Context ...mately the quality of the film for its intended purpose [27]. One framework for studying atomic mechanisms of crystal growth is the terrace--ledge--kink model introduced by Burton, Cabrera, and Frank =-=[7]-=-. The general idea is illustrated in Figure 34. In this framework, arriving atoms land on the surface which contains terraces, steps, vacancies, and kinks. Atoms can evaporate, move on the terrace, cr... |

111 |
Thermal Radiation Heat Transfer, Hemisphere,
- Siegel, Howell
- 1981
(Show Context)
Citation Context ... Epsilon--1 reactor for use in high fidelity models of epitaxial growth. Methodology The analytical approach we take to determine the heat flux spatial profiles is based on the concept of view factor =-=[37, 45]-=- which describes the radiation exchange between two or more surfaces separated by a nonparticipating medium that does not absorb, emit, or scatter radiation. The view factor between two surfaces repre... |

102 |
Turbulence and the Dynamics of Coherent Structures, Part I: Coherent Structures,”
- Sirovich
- 1987
(Show Context)
Citation Context ... One approach to finding a basis for the desired coordinate transformation is application of the POD, which is based on the classical Karhunen--Loeve decomposition of a stochastic process (see, e.g., =-=[14, 18, 35, 47]-=-). The POD is also known as the method of empirical eigenfunctions, or principal components analysis (PCA). The POD is a statistical pattern analysis technique for finding the dominant structures in a... |

97 | Balancing for nonlinear systems
- Scherpen
- 1993
(Show Context)
Citation Context ...is for the balanced realization is readily accomplished by use of matrix operations and decompositions. A general theory and procedure for balancing of a class of nonlinear systems has been presented =-=[43]-=-, but in contrast to the linear case, algorithms for performing the required computations do not currently exist. We note that development of such algorithms is a topic of current research being under... |

53 |
Reckeweg, private communication,
- Meyer, O
- 2004
(Show Context)
Citation Context ... pressure (RP). Choice of pressure mode will a#ect deposition kinetics. Furthermore, flow can be turbulent in the AP regime [51], although it has been observed to always be laminar in the ASM reactor =-=[29]-=-. 3. Transport of reactant species to the wafer surface occurs via multi--component di#usion and convection. Hence, complicated gas flows and boundary layer e#ects enter into the deposition kinetics e... |

23 | Model Reduction Via the Karhunen-Loeve Expansion Part 1: An Exposition,”
- Newman
- 1996
(Show Context)
Citation Context ... One approach to finding a basis for the desired coordinate transformation is application of the POD, which is based on the classical Karhunen--Loeve decomposition of a stochastic process (see, e.g., =-=[14, 18, 35, 47]-=-). The POD is also known as the method of empirical eigenfunctions, or principal components analysis (PCA). The POD is a statistical pattern analysis technique for finding the dominant structures in a... |

22 |
Alternative approaches to Karhunen–Lo<eve decomposition for model reduction and data analysis.
- Graham, Kevrekidis
- 1991
(Show Context)
Citation Context ... One approach to finding a basis for the desired coordinate transformation is application of the POD, which is based on the classical Karhunen--Loeve decomposition of a stochastic process (see, e.g., =-=[14, 18, 35, 47]-=-). The POD is also known as the method of empirical eigenfunctions, or principal components analysis (PCA). The POD is a statistical pattern analysis technique for finding the dominant structures in a... |

15 |
A Schur method for balanced truncation model reduction,”
- Safonov, Chiang
- 1989
(Show Context)
Citation Context ...that are almost impossible to produce using the available control inputs. Schur Method For Balancing In order to alleviate the numerical di#culties, we use a procedure presented by Safanov and Chiang =-=[40]-=- for calculating a realization of a kth--order reduced model. The reduced model is not necessarily balanced, but has transfer function b G(s) which is exactly the same as that obtainable by applying M... |

14 |
Nonlinear model reduction for simulation and control of rapid thermal processing.
- Aling, Banerjee, et al.
- 1997
(Show Context)
Citation Context ...d to success in applying it to areas such as turbulence modeling (e.g., [19]) and pattern recognition (e.g., [46]). Recently, much work has been done to study its use for RTCVD model reduction (e.g., =-=[1, 2, 3, 4, 36, 50]-=-). We have performed a similar study toward finding a low--order approximation to (52). To generate empirical time series data, i.e., snapshots of the wafer temperature field, the system (52--54) was ... |

13 |
Thermal and stress analysis of semiconductor wafers in a rapid thermal processing oven
- Lord
- 1988
(Show Context)
Citation Context ... r=R w r=0 Figure 10: Wafer with coordinates and measurements used in the heat transfer model. 2.3.3 Wafer Heat Transfer The model for wafer heat transfer is a modified version of models presented in =-=[2, 8, 28, 41, 42]-=-. It is based on an energy balance for a heat conducting solid which emits and absorbs heat radiation at its boundary surfaces. The model takes into account simplified e#ects of conductive, radiative ... |

7 |
Application of a nonlinear model reduction method to rapid thermal processing reactors,”
- Aling, Ebert, et al.
- 1996
(Show Context)
Citation Context ...d to success in applying it to areas such as turbulence modeling (e.g., [19]) and pattern recognition (e.g., [46]). Recently, much work has been done to study its use for RTCVD model reduction (e.g., =-=[1, 2, 3, 4, 36, 50]-=-). We have performed a similar study toward finding a low--order approximation to (52). To generate empirical time series data, i.e., snapshots of the wafer temperature field, the system (52--54) was ... |

7 |
A model for rapid thermal processing: Achieving uniformity through lamp control
- Gyurcsik, Riley, et al.
- 1991
(Show Context)
Citation Context ... on the wafer surface requires either an empirically determined heat flux intensity profiles (using experimental data and further analysis), a ray--trace algorithm, or a view factor model (see, e.g., =-=[16, 24]-=-). Any analytical approach needs to be verified experimentally. 10. Heat transfer to and from the wafer includes conductive, convective, and radiative transport mechanisms. Heat energy is exchanged am... |

7 |
Chemical vapor deposition processes
- Kleijn
- 1995
(Show Context)
Citation Context ...surface--reaction controlled. This modeling e#ort provides a foundation for a series of minor and major enhancements. 2.1 Modeling Overview The general modeling scheme is illustrated in Figure 4 (see =-=[26]-=- for a similar approach). The two main components of the modeling e#ort are a macroscopic level process and equipment model, and a microscopic level feature scale model. These two components cooperate... |

6 |
Re-engineering silicon: Si{Ge heterojunction bipolar technology
- Cressler
- 1995
(Show Context)
Citation Context ...as of September 1997. Some of the contents of this report are contained in [34]. 1.1 Objectives Epitaxial growth of Si--Ge heterostructures on a silicon substrate is an area of great current interest =-=[9, 15, 17, 32]-=-. This is mainly due to the superior electrical performance and manufacturing economies associated with Si--Ge devices [9, 49]. One such epitaxial growth process of immediate interest to Northrop Grum... |

6 |
Thermal Modeling of Wafer in a Rapid Thermal Processor,”
- Dilhac, Ganibal, et al.
- 1995
(Show Context)
Citation Context ...ment in the reactor under consideration was axisymmetric about the wafer center. This situation is, however, not the case in the ASM Epsilon--1 reactor. Hence, our analysis is similar to that used in =-=[10]-=-, where the authors consider the chamber geometry from a three-- dimensional point of view. However, in that paper, as in this paper, the e#ect of reflectors is not included. Scope In this report, rad... |

6 | Bistable conditions for lowtemperature silicon epitaxy - Meyerson, Himpsel, et al. - 1990 |

5 |
Growth of epitaxial germanium-silicon heterostructures by chemical vapour deposition
- Greve
- 1993
(Show Context)
Citation Context ...as of September 1997. Some of the contents of this report are contained in [34]. 1.1 Objectives Epitaxial growth of Si--Ge heterostructures on a silicon substrate is an area of great current interest =-=[9, 15, 17, 32]-=-. This is mainly due to the superior electrical performance and manufacturing economies associated with Si--Ge devices [9, 49]. One such epitaxial growth process of immediate interest to Northrop Grum... |

5 |
Three-zone rapid thermal processor system
- Kiether, Fordham, et al.
- 1994
(Show Context)
Citation Context ... on the wafer surface requires either an empirically determined heat flux intensity profiles (using experimental data and further analysis), a ray--trace algorithm, or a view factor model (see, e.g., =-=[16, 24]-=-). Any analytical approach needs to be verified experimentally. 10. Heat transfer to and from the wafer includes conductive, convective, and radiative transport mechanisms. Heat energy is exchanged am... |

5 |
Modeling and model reduction for epitaxial growth,”
- Newman, Krishnaprasad, et al.
- 1997
(Show Context)
Citation Context ... techniques to reduce the model complexity, leading to faster simulation and facilitating the use of standard control and optimization strategies. Some of the contents of this report are contained in =-=[34]-=-. # This research was supported by grants from the Northrop Grumman Foundation, the National Science Foundation's Engineering Research Centers Program: NSFD CDR 8803012 and NSF Grant EEC-9527576, and ... |

5 |
Low-order modeling and dynamic characterization of rapid thermal processing
- Schaper, Cho, et al.
- 1992
(Show Context)
Citation Context ... r=R w r=0 Figure 10: Wafer with coordinates and measurements used in the heat transfer model. 2.3.3 Wafer Heat Transfer The model for wafer heat transfer is a modified version of models presented in =-=[2, 8, 28, 41, 42]-=-. It is based on an energy balance for a heat conducting solid which emits and absorbs heat radiation at its boundary surfaces. The model takes into account simplified e#ects of conductive, radiative ... |

4 | RTCVD model reduction: A collocation on empirical eigenfunctions approach
- Adomaitis
- 1995
(Show Context)
Citation Context ... r=R w r=0 Figure 10: Wafer with coordinates and measurements used in the heat transfer model. 2.3.3 Wafer Heat Transfer The model for wafer heat transfer is a modified version of models presented in =-=[2, 8, 28, 41, 42]-=-. It is based on an energy balance for a heat conducting solid which emits and absorbs heat radiation at its boundary surfaces. The model takes into account simplified e#ects of conductive, radiative ... |

3 |
Rapid thermal process model reduction via empirical eigenfunctions: A collocation approach
- Adomaitis
- 1995
(Show Context)
Citation Context ...d to success in applying it to areas such as turbulence modeling (e.g., [19]) and pattern recognition (e.g., [46]). Recently, much work has been done to study its use for RTCVD model reduction (e.g., =-=[1, 2, 3, 4, 36, 50]-=-). We have performed a similar study toward finding a low--order approximation to (52). To generate empirical time series data, i.e., snapshots of the wafer temperature field, the system (52--54) was ... |

3 |
Eect of silicon source gas on silicongermanium chemical vapor deposition kinetics at atmospheric pressure
- Kamins, Meyer
- 1992
(Show Context)
Citation Context ...ies concentration at the downstream end of the flow) may also occur. 4. Deposition rates are a#ected by germanium content in the reactant gases. This phenomenon is the subject of much recent research =-=[22, 23, 25, 31]-=-, which provides empirical data and rules of thumb but no explicit mathematical models. E#ects of multiple reactant gases complicate the deposition kinetics models. 5. Reaction kinetics are sensitive ... |

3 |
Atom Motion on Surfaces
- Lagally
- 1993
(Show Context)
Citation Context ...on the surface of a wafer during the deposition process largely determines the arrangement of these atoms in terms of crystal structure and ultimately the quality of the film for its intended purpose =-=[27]-=-. One framework for studying atomic mechanisms of crystal growth is the terrace--ledge--kink model introduced by Burton, Cabrera, and Frank [7]. The general idea is illustrated in Figure 34. In this f... |

3 |
Cooperative growth phenomena in silicon/germanium lowtemperature epitaxy
- Meyerson
- 1988
(Show Context)
Citation Context ...ies concentration at the downstream end of the flow) may also occur. 4. Deposition rates are a#ected by germanium content in the reactant gases. This phenomenon is the subject of much recent research =-=[22, 23, 25, 31]-=-, which provides empirical data and rules of thumb but no explicit mathematical models. E#ects of multiple reactant gases complicate the deposition kinetics models. 5. Reaction kinetics are sensitive ... |

3 |
Heat Transer: A Basic Approach
- Ozisik
- 1985
(Show Context)
Citation Context ...we have assumed a constant uniform gas temperature. In order to estimate h v , we assume flow in the process chamber is a laminar flow along a flat plate. The mean heat transfer coe#cient is given in =-=[37]-=- pp. 233--235 as h v = 2 [0.332 k g P r 1/3 (Re 1/2 /L)] (15) where k g denotes the gas thermal conductivity, P r denotes the gas Prandtl number, Re denotes the gas Reynolds number, and L denotes the ... |

3 |
Various private communications. Northrop Grumman ESSS
- Ponczak, Knight, et al.
- 1998
(Show Context)
Citation Context ...n will not be valid when high operating temperatures are used. However, Northrop Grumman ESSD performs some low temperature epitaxial growth of undoped silicon at temperatures between 600 C and 800 C =-=[38]-=-. In that portion of our work where this assumption is invoked, we can essentially ignore the gas flow dynamics which control convective transport of species to the wafer surface. Instead, we can assu... |

3 |
Thermal model validation for RTCVD of polysilicon
- Schaper, Kailath
- 1996
(Show Context)
Citation Context |

2 |
Private communication. Northrop Grumman ESSD
- Brabant
- 1997
(Show Context)
Citation Context ...nd 1 micron can be and were measured by the available ellipsometer and nanospec. Previous work by Brabant has shown growth rates for epitaxial and polycrystalline silicon to be approximately the same =-=[6]-=-. Procedure Thin films of polycrystalline silicon were deposited from a silane precursor over a five minute period at reduced pressure (20 Torr). Deposition was performed under a combination of operat... |

2 |
Golubovic and Robijn Bruinsma. Surface di#usion and fluctuations of growing interfaces
- Leonardo
- 1991
(Show Context)
Citation Context ...technology, because of its influence on the film morphology, i.e., roughness [27]. One useful model for our purposes here is the "Eden model" for growth of interfaces relaxing by surface di#=-=usion. In [13]-=-, an evolution equation for film growth is given under the assumption that the growth rate depends only on the local surface morphology through rotational invariants (such as curvature), #h #t = -K(# ... |

2 |
Introduction to Microelectronic Fabrication, chapter 6
- Jaeger
- 1993
(Show Context)
Citation Context ...ates and germanium fraction are a#ected by pattern pitch and closeness to pattern edges [23]. 6. The type of growth (epitaxial, polycrystalline, or amorphous) is sensitive to the operating conditions =-=[20, 30, 39, 44, 51]-=-, most importantly temperature, pressure, flow rate, and type and concentration of reactant species. It is also strongly influenced by the properties of the substrate surface [29]. The literature prov... |

2 |
Kinetics of selective epitaxial deposition of Si 1-x Ge x
- Kamins, Vook, et al.
- 1992
(Show Context)
Citation Context ...ies concentration at the downstream end of the flow) may also occur. 4. Deposition rates are a#ected by germanium content in the reactant gases. This phenomenon is the subject of much recent research =-=[22, 23, 25, 31]-=-, which provides empirical data and rules of thumb but no explicit mathematical models. E#ects of multiple reactant gases complicate the deposition kinetics models. 5. Reaction kinetics are sensitive ... |

2 | Low pressure chemical vapor deposition of Si 1-x Ge x films using Si2H6 and GeH4 source gases
- Kim, Ryu, et al.
- 1996
(Show Context)
Citation Context |

2 |
High speed silicon germanium electronics
- Meyerson
- 1994
(Show Context)
Citation Context ...as of September 1997. Some of the contents of this report are contained in [34]. 1.1 Objectives Epitaxial growth of Si--Ge heterostructures on a silicon substrate is an area of great current interest =-=[9, 15, 17, 32]-=-. This is mainly due to the superior electrical performance and manufacturing economies associated with Si--Ge devices [9, 49]. One such epitaxial growth process of immediate interest to Northrop Grum... |

2 |
Low temperature atomospheric pressure chemical vapor deposition for epitaxial growth of Si--Ge bipolar transistors
- Sedgwick, Grutzmacher
- 1995
(Show Context)
Citation Context ...ates and germanium fraction are a#ected by pattern pitch and closeness to pattern edges [23]. 6. The type of growth (epitaxial, polycrystalline, or amorphous) is sensitive to the operating conditions =-=[20, 30, 39, 44, 51]-=-, most importantly temperature, pressure, flow rate, and type and concentration of reactant species. It is also strongly influenced by the properties of the substrate surface [29]. The literature prov... |

2 |
RTCVD growth and applications of epitaxial Si 1-x Ge x alloys
- Sturm
- 1991
(Show Context)
Citation Context ...tures on a silicon substrate is an area of great current interest [9, 15, 17, 32]. This is mainly due to the superior electrical performance and manufacturing economies associated with Si--Ge devices =-=[9, 49]-=-. One such epitaxial growth process of immediate interest to Northrop Grumman ESSD is Si--Ge co-- deposition on a patterned silicon substrate. The deposition is performed using a commercial RTCVD reac... |

1 |
Model identification in RTP systems
- Cho, Kailath
- 1993
(Show Context)
Citation Context |

1 |
SiGe HBT technology: Device and application issues
- al
- 1995
(Show Context)
Citation Context |

1 |
Pattern sensitivity of selective Si 1-x Ge x chemical vapor deposition: Pressure dependence
- Kamins
- 1993
(Show Context)
Citation Context ...n kinetics are sensitive to patterns (microfeatures) on the wafer surface. For example, it has been shown experimentally that thickness dependence on an oxide pattern is a strong function of pressure =-=[21]-=- and deposition rates and germanium fraction are a#ected by pattern pitch and closeness to pattern edges [23]. 6. The type of growth (epitaxial, polycrystalline, or amorphous) is sensitive to the oper... |

1 |
Evanghelos Zafiriou. Model reduction for optimization of RTCVD systems
- Theodoropoulou, Adomaitis
- 1996
(Show Context)
Citation Context ...lex manner. High--fidelity models require incorporation of chamber wall geometry and material properties for computation of radiative terms due to reflections and nonuniformity in ambient temperature =-=[50]-=-. 11. Material properties are functions of the process variables, whose time evolution in turn depend on the material properties. For example, heat transfer in the wafer depends on the mass density, h... |