Method for assessing data worth for analyzing yield rate
View Patent ↗A method for assessing data worth for analyzing yield rate includes: getting measured data with data points that corresponds to control variables of semiconductor manufacturing; transforming the data points into a distance matrix with matrix distances corresponding to differences of the data points under the control variables; expressing sample differences recorded in the distance matrix by two-dimension vectors and calculating similarity degrees of the two-dimension vectors and the distance matrix so as to take loss information as a conversion error value; calculating discriminant ability of the transformed two-dimension data and expressing the discriminant ability by an error rate of discriminant; and taking the conversion error value and the error rate of discriminant as penalty terms and calculating a quality score corresponding to the measured data. Thereby, before analyzing the yield rate of semiconductor manufacturing, analysts can determine whether data includes information affecting the yield rate based on the quality score.
1. A method for assessing data worth for analyzing a yield rate of wafers in a semiconductor manufacturing process based on a quality score, comprising the steps of:
measuring physical properties and electrical properties of the wafers, which are represented in terms of data points in a multi-dimension matrix, wherein each of the data points is a multi-dimension vector corresponding to a controlled factor;
transforming the plurality of the data points corresponding to the physical properties and the electrical properties of the wafers into a distance matrix with matrix distances, and the matrix distances representing differences of the plurality of the data points;
expressing the differences between the data points recorded in the distance matrix using two-dimension vectors and calculating similarity degrees of the two-dimension vectors and the distance matrix so as to retrieve loss information as a conversion error value corresponding to the distance matrix among the data points;
calculating discriminating ability of the transformed two-dimension vectors and expressing the discriminating ability by an error rate of a discriminate; and
taking the conversion error value and the error rate of discriminant as penalty terms and calculating the quality score corresponding to the physical properties and the electrical properties of the wafers;
wherein the quality score is used for assessing distinguish-ability of the data points, with the higher quality score corresponding to the higher distinguish-ability of the data points under the controlled factors.
2. The method as claimed in claim 1 , wherein the distance matrix is a two-dimension matrix.
3. The method as claimed in claim 2 , wherein the matrix distances are equal to Euclidean distances between the plurality of the data points.
4. The method as claimed in claim 2 , wherein the matrix distances are equal to City-Block Distances between the plurality of the data points.
5. The method as claimed in claim 1 , wherein the conversion error value is expressed as C=Σ i<k Σ(d ik −{circumflex over (d)} ik ) 2 /Σ i<k Σ(d ik ) 2 , wherein i=1,2, . . . N, k=1,2, . . . N, and {circumflex over (d)} ik denotes a monotonic function of the distance d ik between two data points of the distance matrix.
6. The method as claimed in claim 1 , wherein the quality score is expressed as Q=(1−C)×(1−ε), wherein ε denotes the error rate of the discriminate and C denotes the conversion error value.
7. The method as claimed in claim 6 , wherein the quality score is between 0 and 1, and the closer the quality score Q approaches 1, the greater the probability that the measured physical properties and electrical properties are influential and significant on the yield rate and the closer the quality score Q approaches 0, the less the probability that the measured physical properties and electrical properties are influential and significant on the yield rate.