Cost analysis and risk assessment for metrology applications

Historically, the significance of an accurate and precise metrology tool has been determined by rules of thumb such as the Gagemaker's Rule. However, with the advent of statistical process control of IC manufacturing, it has become practical to statistically determine the probability of a product being misclassified during metrology. Several parameters, such as the process distribution, the precision and accuracy of the metrology tool, the measurement strategies, etc., determine the probability that a good product is classified as bad and vice versa. The probability function can subsequently be converted to a number equivalent to the percentage of product misclassified. From this number, the cost of misclassification can be calculated, which is a function of the precision, the accuracy, and the measurement strategy used. This cost can be used in making decisions involving justification of new metrology capability, better measurement strategies, or to decide whether metrology is needed at all. Examples have been generated to illustrate the actual cost involved in using a poor metrology tool, and strategies have been suggested to contain the cost of misclassification.