2006-1009: Experiential Learning of Design of Experiments Using a Virtual Cvd Reactor

Presently there is a need for more effective ways to integrate statistical methodologies such as Design of Experiments (DOE) into the engineering curriculum. We have developed a virtual chemical vapor deposition (CVD) reactor based on a numerical simulation where students learn and then actually apply DOE. Associated educational materials are also being developed. The simulation of the Virtual CVD reactor is based on fundamental principles of mass transfer and chemical reaction, obscured by added “noise.” However, rather than having access to the entire output of model, the film thicknesses are given to students only at the select points within the wafer and from wafer to wafer that they have decided to “measure”. This package is all housed within a three-dimensional (3D) graphical user interface where students are placed in a simulated clean room environment. Student assessment is based not only on the ultimate reactor performance but also on the cost of experimentation. This learning tool represents an innovative use of computers and simulation in integrating statistics into engineering education. Students are given a “capstone” experience in which they have the opportunity to synthesize engineering science and statistics principles to optimize reactor performance. Since the simulation is from first principles, students can interpret the outputs given by the DOE in terms of the chemical and physical phenomena in the system. The Virtual CVD reactor allows students a broader and more realistic experience in using the DOE methodology for process improvement as if they were operating an actual industrial reactor. The project scope also includes development and implementation of an assessment plan to evaluate the effectiveness of this tool in promoting higher order thinking skills. The Northwest Regional Educational Laboratory is providing support for the project evaluation and assessment. A five-member advisory committee consists of engineers and statisticians from academia (Oregon State University, University of Oregon) and industry (LSI Logic, Intel, WaferTech). The VirtualCVD Learning Platform is available now for use in approved courses. Instructors who are interested in adopting this software into their curriculum can go to the following web page for information: http://che.oregonstate.edu/research/VirtualCVD Motivation Proficiency with statistical methodologies such as Design of Experiments (DOE) is an increasingly essential skill for engineers. This requires not only knowledge of statistical concepts related to DOE, but also the ability to integrate this methodology with fundamental engineering principles toward designing and understanding experiments. However, current engineering curriculums have not fully adapted to this need in the engineering industry. In the 1970s and 1980s, the absence of sound statistical methods in the engineering work place led to a crisis in US industry where a large percentage of the market share went overseas. This crisis was first reflected in the manufacture of automobiles and then in the process-oriented manufacture of integrated circuits. Only with the industrial investment towards quality, largely through the systematic training and implementation of statistical methodologies, has the United States regained competitiveness. Indeed, a survey of OSU ChE alumni found that statistics presented the largest discrepancy between the preparation at the university relative to the importance in employment. This result is typical of curricula throughout the country. The most ubiquitous and powerful of these statistical techniques is Design of Experiments (DOE). DOE is a method for systematic planning and conducting experiments in which multiple input variables are systematically changed to observe changes in the outputs of a process. Historically, both science and engineering curricula have emphasized one-factor-at-a-time experiments where one variable (factor) is changed while the others are held fixed. This approach is wasteful and the results can be misleading. However, statistically designed experiments provide a more effective and efficient way to learn about and optimize a process. By combining the settings of several factors simultaneously in design arrays, it is possible to isolate the effects of each factor individually. A designed experiment usually requires fewer resources for the amount of information obtained, and the results are more precise since more measurements are used to determine the effect of a given factor. Moreover, the interactions between the factors, i.e., the effect of one factor on another can be quantified. Presently, DOE is largely taught to entry-level engineers by industry through in house training programs. Such skills are more appropriate to teach at the university where an educational approach emphasizing fundamentals could provide students with greater depth and adaptability in applying these methods. One constraint, however, is that the curriculum is full and, by in large, successful. The educational challenge then becomes how to integrate statistics-based topics such as DOE so that they compliment the existing educational curriculum and can be fit in; more effective methods are needed to allow students to integrate statistics and DOE into their engineering studies. Numerous computer resources have been developed to reinforce knowledge and understanding of statistics. These applications have evolved from forms that are quite similar to conventional printed material to the development of interactive simulations that give students a hands-on learning experience of specific statistics concepts, e.g., the central limit theorem or sampling distributions. In the classroom, process simulation is typically used for analysis where students are either asked to use commercial simulations, e.g., SUPREM-IV or FLOODS or use simplified code to predict reactor performance. However, process engineers in industry rely largely on empirical techniques to develop process recipes that optimize performance. No tool is more critical in this process than DOE. The undergraduate laboratory has been demonstrated to provide an effective means of teaching DOE through experiential learning. However, lab experiments are expensive and time consuming; hence, there is a constraint on the proportion of topics in the curriculum that can realistically be introduced in the lab. University teaching labs can also be limited by their equipment capability. Ideally, a student would have a rich experience in DOE before entering senior lab, and then could reinforce it by creatively applying these methods to real measurements. Often, however, the bridge between what is taught in an engineering statistics class and what is required in the lab is weak. In an attempt to meet the need for a “capstone” experience that integrates engineering and statistics, we have developed a virtual chemical vapor deposition (CVD) reactor based on a numerical simulation where students learn and then actually apply DOE. The Virtual CVD reactor uses fundamental process simulation in a new and innovative way. Students will use the virtual reactor in exactly the same manner as they would a reactor in industry. They will be tasked with improving and optimizing reactor performance based on DOE. In completing this task, they will need to choose the parameters for each of the runs they perform and choose what measurements they want to make. Their choices have a cost associated with them so there is a realistic economic constraint. The most effective performance will be a balance between optimization of performance and cost. Not only must students learn how to apply DOE, they must also determine when their results are good enough and the reactor is ready for production. Educational objectives The complete experimental design process is depicted in the flowchart shown in Figure 1. The first step is to select a response/dependent variable (variables) that will provide information about the problem under study and the proposed measurement method for this response variable, including an understanding of the measurement system variability. The next step is to select the independent variables/factors to be investigated in the experiment. After the dependent and independent variables are selected, then an appropriate experimental design should be selected that will allow the experimental questions to be answered once the data is collected and analyzed. The experiment is then performed. Collecting data is a critical stage in DOE. The data are then analyzed using the appropriate statistical model insuring that attention is paid to checking the model accuracy by validating underlying assumptions associated with the model. Based on the results of the analysis, conclusions about the results and the physical meaning of these results are inferred. Finally the practical significance of the findings are determined, and recommendations for a course of action, including further experiments, are made. The intent of the Virtual CVD Learning Platform is to allow students to experience this process, from start to finish. Specifically, the Virtual CVD reactor is an intervention designed to achieve the following educational objectives: 1. Design experiments to optimize the performance of a CVD reactor. o Identify key reactor inputs and determine relationship between input levels and achieved thin film uniformity. Select response/ dependent variable(s) Select the independent variables/ factors Choose an appropriate experimental design Perform the experiment (collect data) Analyze the data using appropriate statistical methods Draw conclusions/ inferences Figure 1. Overview of DOE Methodology o Design appropriate statistical methodology to optimize the uniformity. 2. Perform virtual experiments, analyze and interpret the results. o Explain resulting film uniformity in terms of chemical and physical phenomena. o Analyze film uniformity during experimentation and iteratively modify the experimental design to account for any surprises. Explain why any adjustments in experimental design were made and their effect. 3. Synthesize and toggle between statistics and engineering science concepts while applying both in a real-world simulation. 4. Synthesize results in the form of a final written and oral report. The Virtual CVD Learning Platform The Virtual CVD Learning Platform is available now for use in approved courses. Instructors who are interested in adopting this software into their curriculum can go to the following web page for information: http://che.oregonstate.edu/research/VirtualCVD The Virtual CVD Learning Platform contains several components: • Mathematical model • 3D graphical student interface (3D client) • Instructor web interface • Database The deposition of silicon nitride, Si3N4, films by chemical vapor deposition (CVD) was chosen as a model system to provide students experience with applying DOE. This system has sufficient complexity to warrant a methodological design approach, but also can be qualitatively considered in terms of engineering science fundamentals such as mass transport and reaction kinetics. The deposition of silicon nitride is usually performed from ammonia and dichlorosilane (DCS). The overall reaction is given as follows: 3 2 2 3 4 4 2 10NH (gas) 3SiH Cl (gas) Si N (solid) 6NH Cl(gas) 6H (gas) + → + + The Virtual CVD reactor is based on an industrial scaled vertical reactor, as illustrated in Figure 2. The process is carried out at low pressure (less than 1 torr) to enhance the diffusion of gaseous components involved in the reaction at temperatures ranging from 600°C to 800°C. The mixture of gases flows through the annular space between the wafer edges and liner while the two reactants diffuse into the space between adjacent wafers where the deposition reaction takes place. As the reactant gases flow through the annular space, their concentrations decrease due to depletion in the deposition reaction. To compensate for decreasing reactant concentrations, it is common to raise the reactor temperature towards its exit. The increased temperature increases the deposition rate. The reactor furnace typically has five heating zones used to adjust the reaction temperature profiles. Because diffusion is the main mechanism for supplying the two reactant gases into the space between two adjacent wafers, the deposition rate around the wafer perimeter is naturally higher than that at the center. To minimize deposition thickness variations across wafers and from wafer to wafer, it is essential to determine proper feed rates of NH3 and SiCl2H2 under proper temperature settings of individual heating zones as well as the reactor operating pressure in addition to the time for the reactor operation. Thus, there are a total of 9-10 parameters in operating a CVD reactor. It is an extremely important and difficult task for an engineer to find the optimum conditions using a minimum number of trial settings of the operating parameters. DOE is inevitably an essential tool to accomplish this task. The simulation of the Virtual CVD reactor is based on a mathematical model that describes both the mass transfer and chemical reaction that take place simultaneously in a CVD reactor and predicts the local thickness of silicon nitride deposit at all radial locations on any wafer. The mathematical model is described in detail in Appendix A. Since real systems do not deterministically adhere to fundamental models, random process and measurement variation are incorporated. The Virtual CVD reactor front-end is a three-dimensional (3D) graphical interface that provides the look-and-feel of a typical semiconductor manufacturing environment. From here, the students can make reactor runs, take measurements that they specify, get output data and determine the cost of their experiments. Figure 3 displays screen-shots of this interface. This front-end goes beyond simply providing a method for students to access the simulation. It also allows students to become familiar with the appearance of a cleanroom. The similarity of the 3D interface to popular video games allows this learning platform to feel familiar and nonthreatening to the student. Figure 2. Schematic diagram of typical CVD reactor Furnace