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Identifier	Thesis 1833
Author	Gagne, Ann-Marie F., 1976-
Title	Surface Fitting by Minimizing the Root Mean Squares Error and Application of Clamped Cubic Spline
Publisher	Central Connecticut State University
Date	2006
Resource Type	Master's Thesis
Notes	Surface Fitting is useful to researchers in fields from engineering to medicine. The expertise of mathematicians is needed to help with the analysis of data to help the experts in those fields draw appropriate conclusions. The research that this thesis is analyzing comes from an electrical engineer at Texas Instrument Incorporated. The data and questions being answered were provided from research on polycrystalline silicon films, which are used in manufacturing cell phones. The questions that are being answered are: The first section will answer, 'Find an analytic model of the surface thickness that the data represents' and the second section will answer, 'What is the relationship between deposition time and temperature?' In the first section, the question 'Find an analytic model of the surface thickness that the data represents' will be answered by approximating the thickness of polycrystalline silicon films by minimizing the root mean squares error. The polycrystalline silicon films deposition in the integrated tool is carried out in a single-wafer rapid thermal chemical vapor deposition chamber. Typically, a silane-based process is used. The polycrystalline silicon films are produced in such a system that has two manufacturing difficulties: across wafer thickness uniformity and surface topology. This process, if not optimized, can negatively impact film production. The engineers at Texas Instrument Incorporated recently reported an enhanced manufacturability of the polycrystalline silicon films process with disilane-based process. The surface is approximated by generalizing the least squares method of minimizing the root mean squares error to estimate a surface, F(x,y) = Ax2+By2+Cxy+Dx+Fy+G. The thesis demonstrates the process of determining the matrix needed to estimate the surface and the Matlab commands needed to produce the surface. The surfaces produced allow the engineers at Texas Instrument Incorporated to understand the uniformity of the thickness of the films produced. In the second section, the question "What is the relationship between deposition time and temperature?" will be answered by approximating the deposition rate of the silane and disilane processes as a function of heater temperature for polycrystalline silicon films by estimating a clamped cubic polynomial spline. Due to the request from the researchers at Texas Instrument Incorporated, the silane process must be analyzed separately from the disilane process. The researchers at Texas Instrument Incorporated recently reported an enhanced manufacturability of polycrystalline silicon films using the disilane process, based on the disilane process being less sensitive to temperature.
Subject	Least squares Spline theory
Department	Department of Mathematical Sciences
Advisor	Chen, Yuanquian
Type	Text
Digital Format	application/pdf
Language	eng
OCLC number	713733940
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