SIMPAR: A Versatile Technology Independent Parameter Extraction Program Using a New Optimized Fit-Strategy

1989

J. Electrochem. Soc.

The purpose of this paper is to demonstrate and evaluate the parameter uncertainty in most of the proposed analytical oxidation models (1-6). First, the concept of the e-indifference range, i.e., IR(O) -R(0*) I -< e 2, is introduced. Then the problem of the determination of the parameters' uncertainty is converted into the determination of the e-indifference range. Methods are introduced to determine the e-indifference range, resulting in the parameter uncertainty range. The correlation matrices of the parameters for a number of models are given in this paper. The analytical results of this paper show that most of the analytical oxidation model parameters (1-6) are interdependent within a wide data-fitting and parameterextraction range, and as such suffer from a quite large uncertainty. Therefore, some physical mechanisms of oxidation which are concluded from, or proven by data-fitting only can be critically questioned and debated.

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Section: Determining the E-indifference Regionmentioning

confidence: 99%

Section: Modification Of the Ellipsoid Techniquementioning

confidence: 99%

The Implementation of the Response Surface Techniques to the Analytical Oxidation Model Evaluation

1989

J. Electrochem. Soc.

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“…Of course, if the ellipsoid at T2 is on the e-ellipsoid position, there has to be some nonlinear dependence and new physical interpretations are encouraged. To carry out this parameter extraction strategy, a subroutine SEAPAR was written and connected to the program SIMPAR (12). Indeed, we do not offer a new technique-to extract parameters more "precisely" from the numerical point of view, which would be only an exercise in parameter fitting, but it is a global strategy consideration where the physics are kept as simple and transparent as possible.…”

Section: A New Parameter Extraction Strategymentioning

confidence: 99%

“…The model of Eq. [9] (with the SEAPAR extracted parameter set of B/A = 2.58 A/rain, B = 3.4 x V) is used as the input of the SIMPAR package (12) to fit the Mass0ud's Si (100) data grown at T = 900~ The following parameters are extracted: X, = 9.46A, Ki = 1.215 x 104 A/rain, T~ = 0.90 min, K2 = 3.27 x 10 a a2/min, and % = 16.6 min. By using these parameters in Eq.…”

Section: Ambiguity In the Kinetics Studymentioning

confidence: 99%

Sensitivity Analysis of the Deal‐Grove Model Parameters: Problem Definition and Strategy Considerations

1988

J. Electrochem. Soc.

In this work the Deal-Grove (DG) oxidation model, being the key ingredient in many current oxidation models, has been examined in detail from the physical and numerical point of view. It is clearly proven that for a rather broad range of (B/A, B) combinations the fitting error is smaller than the experimental error. So there exists a wide range of allowable parameters of the Deal-Grove model to satisfy different physical explanations. This means that a good fit alone is not a sufficient criterion to validate a possible physical model. It is also demonstrated that the existence of breakpoints in the temperature behavior could be seen as an artifact of the model parameters extraction procedure normally used. Therefore, a new and efficient parameter extraction strategy, which carefully considers the influence of experimental errors, is suggested in this work. As an example, a physically acceptable expression for the parameters in the HCl-oxidation is found as a substitute for the look-up table used in SUPREM-3.The Deal-Grove model (1) has been used over more than twenty years to describe the silicon oxidation process. This model is based on an equilibrium process between the. diffusion of the oxidizing species through the oxide layer and the reaction of this species at the interface, resulting in both a parabolic and a linear growth rate component.Although th!s model is widely being used to describe the oxidation process, it suffers from a lack of accuracy mainly for the description of the growth of thin layers. To modify this model in the initial phase of dry oxidation, a lot of models were proposed over the last decade: e.g., oxide charge effects (2), chemisorption (3), structural channels (4), stress effects (5), parallel independent diffusion mechanisms of the oxidizing species in the oxide film (6, 7), and interface potential effects (8).Nearly all of these models exhibit a quite good data fitting, although they are based on some different physical assumptions and in most cases exclude each other implicitly. The .data fitting and the observations of the variation of the linear-rate constant B/A and the parabolic-rate constant B of the Deal-Grove model as a function of some factors (e.g., temperature, 02 pressure, HCI%...), are the usual way to provide evidence for the proposed models. For example, some authors have observed breakpoints in the In (B/A) vs. 1/KT and in (B) vs. 1/KT plots, and to explain these breakpoints the stress effect has been proposed (5).However, in this work, it will be indicated that there exists an inherent problem with the Deal-Grove model parameters (linear-parabolic law) which may raise some questions about a number of physical phenomena which are used to explain some observed effects. In effect, it turns out that the "exact" values of the parameters B/A and B are quite insensitive to the Deal-Grove model, especially when the oxide fitting range is getting smaller. Namely, by allowing a domain of sets of (B/A, B) values, the fitting error for many (B/A, B) combinations is less than th...

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Modeling of the Oxide Growth in a Chlorine Ambient

The Physics and Chemistry of SiO2 and the Si-SiO2 Interface

1988