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Response Surface Methodology and Its Application in Optimizing the Efficiency of Organic Solar Cells Rajab Suliman South Dakota State University

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Response Surface Methodology and Its Application in Optimizing the Efficiency of Organic Solar Cells Rajab Suliman South Dakota State University South Dakota State University Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange Theses and Dissertations 2017 Response Surface Methodology and Its Application in Optimizing the Efficiency of Organic Solar Cells Rajab Suliman South Dakota State University Follow this and additional works at: http://openprairie.sdstate.edu/etd Part of the Statistics and Probability Commons Recommended Citation Suliman, Rajab, "Response Surface Methodology and Its Application in Optimizing the Efficiency of Organic Solar Cells" (2017). Theses and Dissertations. 1734. http://openprairie.sdstate.edu/etd/1734 This Dissertation - Open Access is brought to you for free and open access by Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange. For more information, please contact [email protected]. RESPONSE SURFACE METHODOLOGY AND ITS APPLICATION IN OPTIMIZING THE EFFICIENCY OF ORGANIC SOLAR CELLS BY RAJAB SULIMAN A dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy Major in Computational Science and Statistics South Dakota State University 2017 iii ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor Dr. Gemechis D. Djira for accepting me as his advisee since November 2016. He has helped me to successfully bring my Ph.D. study to completion. In particular, he has helped me to develop simultaneous inferences for stationary points in quadratic response models. I also worked with Dr. Yunpeng Pan for three years. I appreciate his guidance and support. I could not have imagined successfully completing of my Ph.D. study without their continuous support, motivation, patience, and enthusiasm, especially through difficult times, to achieve my long-sought goal. Dr. Pan also facilitated our collaboration with the Department of Electrical Engineering and Computer Science. In this regard, I would also like to express my sincere thanks to Dr. Qiquan Qiao and Mr. Abu Farzan Mitul from Electrical Engineering and Computer Science Department for their assistance in generating the data we used for the organic solar cell experiment. They have provided an excellent environment that will foster to carry on my future independent research. I would also gratefully acknowledge Dr. Kurt Cogswell, Head of the Mathematics and Statistics Department, and Dr. Donald Vestal, graduate program coordinator in the Department of Mathematics and Statistics, for their support. I am also grateful to all of my Ph.D. advisory committee members including Dr. Gary Hatfield and Thomas Roe from the Department of Mathematics and Statistics, and my graduate school representative Dr. Jane Mort from the College of Pharmacy. They provided me with constructive comments which greatly improved the quality of my dissertation. iv My especially thanks goes to the Ministry of Higher Education, Libya, for sponsoring my Ph.D. study abroad through Libyan North American Scholarship Program (LNASP). My research is also partially benefitted by the NSF CAREER (ECCS- 0950731) , and NASA EPSCoR (NNX13AD31A) grants used for the organic solar cell experiment. I also sincerely acknowledge all faculty members in the Department of Statistics at Misurata University for their encouragement. I am also indebted to Dr. Yasmina Faqih, and Dr. Hussain Kaiba who was a great mentor. I want to thank him post hum for his support. Last but not least, my sincere thanks to my family, especially to my mother, wife, brothers, and son, for their love, sacrifices, and encouragement that helped me to complete my research. Finally, I must say that in the journey of my life I am indebted to so many of my family members, friends, and well-wishers who have provided invaluable advice during uncertain and challenging times and helped me to keep my dream alive. I wish I could thank every individual person, but nevertheless, they are always in my heart. v TABLE OF CONTENTS LIST OF FIGURES ........................................................................................................... ix LIST OF TABLES ............................................................................................................ xii ABSTRACT ..................................................................................................................... xiv GENERAL INTRODUCTION ............................................................................................1 INTRODUCTION TO RESPONSE SURFACE METHODOLOGY .................................3 2.1 Introduction ....................................................................................................................3 2.2 Overview and stages for RSM application ....................................................................3 2.3 Screening experiment.....................................................................................................6 2.4 Empirical model building ..............................................................................................6 2.5 Encoding of input variable levels ................................................................................12 2.6 First-order model .......................................................................................................12 2.6.1 Two-level factorial designs .......................................................................................12 2.6.2 Two-level fractional factorial designs ......................................................................13 2.7 Blocking in response surface designs ..........................................................................14 2.8 Steepest ascent .............................................................................................................16 2.9 A second-order experimental design ..........................................................................21 2.9.1 Full 3K factorial designs ............................................................................................21 2.9.2 Box–Behnken designs (BBD) ...................................................................................22 2.9.3 The central composite design (CCD) ........................................................................23 vi 2.9.4 Doehlert design .........................................................................................................25 2.10 Lack-of-fit test ...........................................................................................................27 2.11 Variance dispersion graph.......................................................................................29 2.12 The Common design properties .................................................................................32 2.12.1 Orthogonality ..........................................................................................................32 2.12.2 Rotatability ..............................................................................................................32 2.12.2.1 Design moment matrix .........................................................................................33 2.12.2.2 Rotatable conditions for first-order design ..........................................................35 2.12.2.3 Rotatability conditions for a second-order design ...............................................36 2.12.2.4 Rotatability of the CCD .......................................................................................37 2.13 Uniform precision ......................................................................................................38 MODELING OF ORGANIC SOLAR CELL USING RESPONSE SURFACE METHODOLOGY ............................................................................................................39 3.1 Introduction and background .......................................................................................40 3.1 Materials, device fabrication and characterization ......................................................44 3.1.1 Materials ...................................................................................................................44 3.1.2 Single-junction device fabrication ............................................................................45 3.1.3 Current density – voltage (J-V) characterization ......................................................45 3.2 Experimental design.....................................................................................................46 3.3 Result and discussion ...................................................................................................48 vii 3.3.1. Model fitting for first order design ..........................................................................48 3.3.2 Moment matrix and rotatability conditions ...............................................................51 3.4. Augmenting further to fit a quadratic response surface ..............................................52 3.5. Device structure ..........................................................................................................57 3.6. Residual analysis for fitted quadratic model ...............................................................59 SIMULTANEOUS INFERENCE FOR THE LOCATION OF A STATIONARY POINT ..........................................................................................................................................
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