Methods for identifying sources of patterns in processing effects in manufacturing

A method of detecting processing effects on products manufactured in a manufacturing process comprising:

• ordering a set of products in a first sequence for a first process step in the manufacturing process;
• ordering the set of products in a second sequence for a second process step in the manufacturing process, the second sequence being different from the first sequence;
• extracting site-specific data regarding responses of the products to the process steps in the manufacturing process;
• converting the site-specific data to distance factor scores and angle factor scores for each product, the distance factor scores being representative of patterns in the data independent of a rotation angle with respect to a fixed position on the product and the angle factor scores being representative of the rotation angle of patterns in the data;
• correlating the distance factor scores and angle factor scores with the first processing sequence and the second processing sequence and analyzing the correlated distance factor scores and angle factor scores.

An arrangement for detecting processing effects on products manufactured in a manufacturing process comprising:

• a product handler that arranges the products in a processing sequence;
• a processing apparatus that performs a processing step on the products;
• a detector that detects site-specific response variables of the products;
• a processor that processes the site-specific response variables to determine distance factor scores and angle factor scores for each product, the distance factor scores being representative of patterns in the response variables independent of a rotation angle with respect to a fixed position on the product and the angle factor scores being representative of the rotation angle of patterns in the response variables and correlates the distance factor scores and angle factor scores with the processing sequence.

A method of detecting a pattern within products manufactured in a manufacturing process comprising:

• ordering a set of products in a first sequence for a first process step in the manufacturing process;
• systematically rotating the set of products such that each product in the first sequence is rotated more than the preceding product in the first sequence;
• ordering the set of products in a second sequence for a second process step in the manufacturing process, the second sequence being different from the first sequence;
• systematically rotating the set of products such that each product in the second sequence is rotated more than the preceding product in the second sequence;
• extracting site-specific data regarding responses of the products to the process steps in the manufacturing process;
• and
• displaying the site-specific data for each product, the displays ordered according to the first sequence and according to the second sequence.

A method of detecting processing effects on products manufactured in a manufacturing process comprising:

• ordering a set of products in a first sequence for a first process step in the manufacturing process;
• ordering the set of products in a second sequence for a second process step in the manufacturing process, the second sequence being different from the first sequence;
• extracting site-specific data regarding responses of the products to the process steps in the manufacturing process;
• computing a distance matrix from the site-specific data, the element of the distance matrix corresponding to a first product and a second product corresponding to the similarity in pattern of the site-specific data from the first product and the second product;
• computing a first similarity index from the distance matrix and a first wafer-to-wafer distance matrix, the elements of the first wafer-to-wafer distance matrix being the difference in sequence number for the wafers in the first sequence, and computing a second similarity index from the distance matrix and a second wafer-to-wafer distance matrix, the elements of the second wafer-to-wafer distance matrix being the difference in sequence number for the wafers in the second sequence;
• and
• comparing the first similarity index and the second similarity index with a distribution of indices for wafers in random sequence to identify processing effects.