Including: Kerri Skowron, Michael G. Blosser, Brett Rogers, Mark Diodato, and Joe Freed

Sponser: Jeff McKeveny     University Prof : Dr. David Cannon

Project Title: Laminate Chip Carrier Yield Modeling

                                                              

Text Box: IBM has supplied Team Yield with data from prototype manufacturing runs of their new laminate chip carrier. Team Yield has modeled the resultant yield data against product attributes in order to supply IBM a basis for understanding the limitations of their manufacturing process. By understanding the manufacturing process, IBM seeks to gain a better means of scheduling production lot sizes, purchasing raw materials, and most importantly estimating manufacturing costs.  

 

 

Text Box: Team Yield has provided IBM an understanding about the effects that product design has on manufacturing yield. To understand resultant yield effects from product design in both a qualitative and quantitative manner Team Yield has generated both graphical and numerical analysis measuring the effect of product design on manufacturing yield at various stages in the manufacturing process. Furthermore, Team Yield has provided an in depth analysis explaining how results were obtained, the perceived meaning of the results, and the limits of the results due to statistical variation in the data. Finally, Team Yield constructed a  C++ program to predict yield results for new products, based on product attributes defined by the user. The program also contains a procedure for updating the yield model as more data is collected from the manufacturing process.

 

 

 

 

 

Background and Problem Statement

Text Box: IBM’s new process is a laminated chip carrier that is manufactured layer by layer. At each level of manufacturing, there are defects that occur. A less complex design with less risk will produce increased yields as opposed to a highly complex product. IBM needs to account for these expected differences in yield performance because they must be able to accurately predict the finished yield given a specific beginning production lot size. Team Yield has computed a model that predicts, as accurately as possible, the yield at internal and finished points in the manufacturing process. The model was accomplished by collecting data from prototypical manufacturing runs at the IBM Microelectronics facility in Endicott, NY. This data included characteristics of the product, as defined by the engineering design, and the true yield observed in the process.    

 

 

 

 

 

 

Why Yield Modeling Benefits IBM?

 

 

 

 

 

 

 

 

 

Solution Method

 

 

 

 

 

Text Box: Regression lines were used at each layer of manufacturing to predict yield losses. Then these subsequent regression lines were incorporated into a C++ file that prompts the user for types of attributes that are included as variables in the regression lines. The program then completed tedious number crunching indicating how many parts are needed to achieve the level of desired parts. The following is the method used to predict regression lines at each layer of manufacturing

 

 

 

Text Box: Prediction Interval – This is very similar to the Confidence interval. The only difference being that this term is applied to a single sample value and not the mean value. So if trying to predict the yield loss of a single batch of chips the prediction interval would be used. Text Box: Confidence Interval – This is a range of values that the mean of a given sample is expected to fall with a specified significance level. For this investigation, a 95% confidence interval was used. This means that if IBM runs 10 different batches of chips and has a certain percent yield loss in each batch, it is possible to develop a confidence interval in which the mean yield loss for all 10 batches would be expected to fall. Text Box: Cp - In general we look for models where Cp is small and is close to p. If the model is adequate, then the expected value of Cp is approximately equal to p, the number of parameters in the model. A small value of Cp indicates the model has small variance in estimating the true regression coefficients and predicting future responses. Text Box: R-sq – The R-squared value represents the percentage of variation of the response variable that can be attributed to the predictor variables. For example, if a regression equation has an R-sq value of 75%, then 75% of the change in the response variable can be explained by the predictor variables. Likewise, 25% of the change in the response variable is caused by another factor that is not being considered.

 

 

 

 

The Method

Text Box: The first step in the analysis was to gain a general idea of how different chip attributes affected percent yield loss. This was done through the use of basic scatter plots like the one found to the left.                                   

Text Box: After the general indication of the influence that each variable had on yield loss was determined, fitted line plots were constructed along with the corresponding R-sq values, confidence intervals, and prediction intervals. An example of one of these graphs can be seen to the left.                            

Text Box: When choosing the best regression model, it is desirable to get the best possible combination of Cp and R-sq values. This process is often subjective, as many combinations are very similar. To help clarify the decision, a stepwise regression was run using MINITAB. This program uses an algorithm to determine the suggested best model. This was an insurance plan to determine if the right regression model was chosen. Text Box: After the most influential attributes were determined and their affects analyzed, MINITAB was used to perform a Best Subsets Regression, which performs regression on every combination of attributes and outputs the R-sq and C-p values for the most appropriate models. Sample out put from this can be seen in the table to the left.              

 

 

Sample Program

 

Text Box: The following sample program was developed using Microsoft Visual C++. It prompts the user for the relevant chip characteristics, and using the regression equations as determined through the above methodology outputs data on the expected yield and suggested production rates.