The Study On Model And Algorithm Of Process Capability Evaluation For Modern Electronic Elements

In the field of modern microcircuit manufacturing, because process and equipments are becoming more and more complicated, the function of electronic devices is becoming more perfect and users bring more requirements to process, it is necessary that we should pay more attention to evaluating and controlling technologies of process. At the same time, all factories which produce electronic device for army equipment are required to adopt systemically process evaluating technologies; and in order to keep abreast of time and compete with international companies, domestic companies begin to implement technologies of quality management and process evaluation. So, their implement are of important significant.In the dissertation, process capability index is chosen as research object, many main problems which come from using process evaluating technologies are solved though setting up relevant model and algorithm. Such research works include studying relationship between process capability index and yield, building model and algorithm of process capability index for non-normal distribution, building model and algorithm of process capability index for multivariate, getting more precise value of normal distribution and relationship between sample numbers with process capability index analysis. The major achievements are listed as followed:1. After analyzing relationship between process capability index Cp and yield, the reason that Cpk value alone is not sufficient to determine the yield are pointed out, then using intermediate variable and setting the ratio of the difference of mean and median to half of specification width, the equation about Cpk and yield is developed successfully. Last, relationship about process capability index and yield when concerning 6σdesign technology is analyzed.2. Model and algorithm of process capability index for non-normal distribution are built successfully. It is common to compute process capability index for non-normal data when concerning the level of semiconductor process. Firstly, analyzing several main process capability indexs which have been already presented, their advantages and disadvantages are presented. Then, based on Chebyshev-Hermite polynomials, a model for computing process capability index for non-normal is given when regarding the fact that these four moments, i.e. mean, standard deviation, skewness, and kurtosis, are suitable to approximately characterize the data distribution properties , which also work effectively even data deviation to normal distribution is large. In order to evaluate modern process, a probability distribution family named Pearson distribution is introduced and its three types of probability density function are deeply analyzed. Based on the study of distribution's central moments and origin moments, the parameters of the distribution are obtained and fitting method is presented.3. Model and algorithm of process capability index for multivariate based on yield are built successfully. The model connects process capability index with yield, which makes user understand process capability index meaning easier. When variables are independent, the model is built according to relationship between single variable yield and total yield. The model is still effective when variable number is much large, and can deduce single process capability index interval according to process level class. When variable is not independent, the model is built successfully after using multi-dimension function integral.4. Model and algorithm of process capability index for multivariate based on weighting Coefficient are built successfully. After analyzing factor analysis and using principal component analysis to compute load matrix, then considering all public factors and contributing ratio, the model is presented, which has not requirement of variable number and of variable correlation. An example of calculating process capability index for multivariate is given. Real application shows that the method presented is effective and actual. A system scheme computing process capability index for multivariate is given when also considering process capability index for multivariate based on yield.5. At PPM(Parts Per Million) level, using process evaluation needs high accuracy distribution function value. As for one-dimension normal distribution, after using relationship between normal distribution function and error function, adopting continued-fraction expansion and Taylor series expansion for exponential term, algorithm of high range of integration and accuracy of normal distribution is built successfully.As for two-dimension normal distribution, algorithm for fitting relative coefficient and getting high precise two-dimension normal distribution value are presented. The dissertation puts forward a way of testing two-dimension normality using testing marginal distribution and data figure, and analyzes important significance of relative coefficient on two-dimension normal distribution value. It needs high precise function value of normal distribution. After building big data storage structure and constructing decimal code array, an algorithm for high-accuracy value of two-dimensional normal distribution is built through using Laguerre Polynomial expansion, and accelerating operation with Compound Simpson formula, Compound Cotes formula and Romberg formula. At last result is gotten.6. Sample number has much influence on computing process capability index. When sample number is large, the cost will be also large and it will waste more time and cost; when sample number is small, it is possible the precise process capability index value can not be gotten. The dissertation discusses the influence of sample number to process capability evaluation in two cases which are full sample number and non-full sample number. Last curve about sample number and process capability index is gotten, from which users can determine sample number according to their need.7. At last, based on the models and algorithms discussed above, the computer-aid process capability evaluation software is developed. The software system not only performs common process capability index computation, common distribution function computation and curve fitting, but also has the function especially for computing process capability index for non-normal distribution and multivariate. The software offers an effective analysis tool for electronic element evaluation.