JP2855590B2 - Correlation analyzer - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a correlation analyzer, and more particularly to a correlation analyzer for analyzing a correlation between two types of measurement items on a measurement plane of an object to be measured.

[0002]

2. Description of the Related Art FIG. 4 is a flowchart showing a processing procedure for analyzing a correlation between two types of measurement items in a conventional correlation analyzer. (Step 41) The measurement device inputs measurement values for two desired types of measurement items whose correlation is to be analyzed. (Step 42) The correlation between the input measurement items is analyzed using regression analysis. For example, the correlation between two types of measurement items is approximated by a linear function Y = aX + b using the least squares method. Here, X and Y are measured values of the measurement items, and a and b are constants. At this time, the square of the difference between the left side and the right side of the linear function at each measurement point is calculated, and all the calculated values are added to obtain a sum. The constants a and b when the sum becomes a minimum are obtained. The sum (hereinafter error) is obtained. (Step 43) The two constants a and b and the error obtained as described above are displayed on the display screen of the display device,
Output to printer.

The linear function obtained as described above, or two constants and an error included in the function, are used as a correlation index indicating a correlation between two types of measurement items.

[0004]

However, the conventional correlation analyzer uses the least squares method to approximate all measured values by a specific function, so that the calculation process is complicated and the time required for the calculation process is long. Become. In addition, when the correlation between the two types of measurement items is not clear, and therefore, when an appropriate function to be used in the least squares method is not clear, an error increases or it becomes difficult to determine whether there is a correlation. further,
The accuracy of the correlation analysis deteriorates because the correlation analysis is performed and the correlation index is calculated without excluding the measurement method of the measurement point having the abnormal correlation and without excluding the measurement point having the abnormal correlation. In addition, there is a problem that it is not possible to accurately specify the existence of a measurement point having an abnormal correlation.

[0005] The present invention has been made in view of the above points,
Even if it is not clear whether there is a correlation between two types of measurement items on the measurement plane of the object to be measured formed so as to be formed uniformly, it is easy to input the measurement value of the measurement item. Analyze, easily determine the presence or absence of a correlation abnormality between the two types of measurement items at the measurement points provided on the measurement plane, and exclude the measurement points determined to have a correlation abnormality and the measurement values at the measurement points It is another object of the present invention to provide a correlation analysis device capable of accurately analyzing a correlation.

[0006]

On a measurement plane of an object to be measured formed so as to be uniformly formed over a plurality of measurement items, two types of measurement items are measured and the measurement results are obtained. Enter the measured value
In a correlation analyzer for analyzing the correlation between the types of measurement items, two types of measurement items to be analyzed are selected, and a plurality of measurement points common to the two types of measurement items are arranged in a measurement plane of the object to be measured. A measurement value input unit for setting all the sets, extracting two sets of two different measurement points from the measurement points, and inputting the measurement values in the set, and analyzing all the sets 2
A difference calculation unit for calculating the difference between the types of measurement items, and all pairs of two measurement points whose differences are not zero are all extracted, and the extracted set is set as a set of analysis target measurement points. A partial differential calculation unit that calculates the value of the partial differential that is the ratio of the difference between the two types of measurement items, and the partial differential values of all the pairs of measurement points to be analyzed and the partial differential values of all the pairs. A correlation index calculating unit that calculates the average and the standard deviation as a correlation index indicating a correlation between the two types of measurement items in the measurement plane of the measured object, and stores the calculation result in a storage device;
An analysis result output unit that outputs the correlation index as an analysis value.

In the above correlation analyzer,
Define an allowable range using the average and standard deviation of partial derivatives, exclude partial derivative values that fall outside of the allowable range, extract sets with excluded partial differential values, and include them in the extracted sets. A correlation abnormal point extraction unit that calculates an appearance frequency of the measurement point to be measured and extracts a measurement point whose appearance frequency exceeds a predetermined allowable appearance frequency as a correlation abnormal point. In addition, a correlation index is calculated by excluding a set including a measurement point extracted as a correlation abnormal point from a set of analysis target measurement points, an allowable range is calculated using the correlation index, and an allowable range and an allowable appearance frequency are calculated. And iterative means for repeating a series of procedures for extracting a correlation abnormal point by using.

[0008]

The present invention basically measures two types of measurement items at a plurality of measurement points provided on a measurement plane of an object to be measured, and obtains a measurement value between the two measurement points for each measurement item. The difference is defined as the difference, the ratio of the difference between the two types of measurement items at the two measurement points is defined as the partial differential, and the value of the partial differential is calculated for all the pairs of the two measurement points extracted from all the measurement points. Is calculated, and the average and standard deviation of the values of the partial derivatives are calculated,
Since the calculated partial differential, the average of the partial differential, and the standard deviation are used as correlation indices indicating the correlation between the two types of measurement items, the calculation is easy and the time required for the calculation is short.

Further, even when the correlation between two types of measurement items and the presence or absence of the correlation are not clear, the analysis can be easily performed by inputting the measured values of the measurement items, and the two points at the measurement points provided on the measurement plane are measured. It is possible to easily determine the presence or absence of a correlation abnormality between types of measurement items.

Further, an allowable range is defined by using the average and the standard deviation of the partial derivatives, the values of the partial derivatives that are out of the allowable range are excluded from the calculated partial differential values, and the excluded partial differential values are calculated. Extract all the pairs of two measurement points with, calculate the frequency of the measurement points included in the extracted set, determine the most frequent measurement points as correlation abnormal points, and determine the measurement points as correlation abnormal points Points can be excluded.

Further, by repeating the procedure of calculating a correlation index such as the average and standard deviation of partial derivatives and judging / eliminating a correlation abnormal point using the correlation index, all correlation abnormal points are judged / excluded to obtain a correlation. A set of measurement points indicating anomalies and a position in the measurement plane can be clearly presented, and a correlation index can be calculated with high accuracy.

[0012]

FIG. 1 shows the configuration of a correlation analysis apparatus according to the present invention. The correlation analysis device includes a measurement device 1, an electronic computer 2, a storage device 3, a display device 4, and an output device 5. The measuring apparatus 1 selects two types of measurement items to be analyzed, and sets a plurality of common measurement points for measuring these two types of measurement items in a measurement plane of the object to be measured. Furthermore, at the measurement point, two types of measurement items to be analyzed are measured,
All sets of two different measurement points are extracted from all the set measurement points. Electronic computer 2
To enter.

The electronic computer 2 obtains the data obtained from the measuring device 1.
The difference between the measured values between the two measurement points forming the set of two different measurement points is defined as a difference. The difference between the two types of measurement items is calculated for all sets. Further, all pairs of two measurement points whose differences between the two types of measurement items are not zero are all extracted, and the extracted pair is defined as a set of analysis target measurement points. In the same set of analysis target measurement points, the ratio of the difference between the two types of measurement items is defined as partial differential, and the partial differential value of all pairs of the analysis target measurement point and the partial differential value of all pairs are defined. The average and the standard deviation are defined as correlation indices indicating the correlation between two types of measurement items in the measurement plane of the measured object.
This correlation index is calculated and stored in the storage device 3. Also,
The data is displayed on the display device 4 as output data or output to the output device 5.

FIG. 2 is a block diagram for explaining the functional configuration of the correlation analyzer according to one embodiment of the present invention. FIG. 3 is a flowchart for explaining a correlation analysis procedure in the correlation analysis apparatus according to one embodiment of the present invention. The analysis procedure of the correlation according to the present embodiment will be described with reference to FIGS. (Step 31) The measurement value input unit 21 is configured to set a desired one of the measurement items measured at a plurality of measurement points set in the measurement plane of the object to be measured that is formed so as to uniformly form the plurality of measurement items. Input the measured values of the two types of measurement items. (Step 32) The difference calculation unit 22 extracts all sets of two different measurement points from all the measurement points set in the measurement plane of the object to be measured, and extracts the two measurement points between the two measurement points. Are calculated for each of the two types of measurement items for all sets.

For example, assuming that two measurement points are i and j, and the measured values of two kinds of measurement items at each measurement point are K _i , L _i and K _j , L _j , these two measurement points i and j two differential measurement items in the set consisting of j is and K _i -K _j, is calculated as L _i -L _j. (Step 33) Further, the difference calculation unit 22 sets a pair of two measurement points (hereinafter, referred to as a pair) in which the difference between the two types of measurement items is not zero.
Analysis set of target measurement points) Example) K _i -K _j ≠ 0 and extracts all L _i -L _j ≠ 0. (Step 34) The partial differential calculation unit 23 calculates the ratio (partial differential) of the difference between the above two types of measurement items for each set of analysis target measurement points. In the example shown in step 32, the partial derivative at the two measurement points i and j is (K _i −K _j ) / (L _i −L _j ) or (L _i −
L _j ) / (K _i −K _j ). (Step 35) The correlation index calculation unit 24 calculates the average and the standard deviation of the partial differential values calculated for all the sets of the analysis target measurement points. (Step 36) The correlation index calculation unit 24 calculates an allowable range by multiplying a preset changeable constant by the standard deviation. (Step 37) The correlation index calculation unit 24 calculates an upper limit by adding an allowable range to the calculated average value of the partial derivatives, and calculates a lower limit by subtracting the allowable range from the average value. The range of values below the upper limit is defined and calculated as an allowable range. (Step 38) The correlation abnormal point extracting unit 25 extracts all sets of analysis target measurement points having partial differential values that are out of the allowable range of step 37 among the partial differential values in all the sets of analysis target measurement points. You. All the measurement points included in all the extracted sets are extracted, and the frequency of appearance of the measurement points in the extracted group is calculated. Is defined as a correlation abnormal point and extracted. (Step 39) The abnormal correlation point extraction unit 25 determines whether or not there is an abnormal correlation point. If it is determined, the process proceeds to step 40, and if not, the process proceeds to step 41.
Move to (Step 40) The correlation abnormal point extracting unit 25 excludes the set including the correlation abnormal point from the set of analysis target measurement points, and
Move to. (Step 41) The analysis result output unit 26 determines the position of the measurement point and the set of measurement points determined as the correlation abnormal point in the measurement plane,
The partial differential values of all pairs of the analysis target measurement points defined as the correlation index between the two types of measurement items, the average value and the standard deviation of the partial differential values of all the pairs are stored in the storage device 3 and displayed. The image is displayed on the display screen of the device 4 or printed out to the output device 5 to terminate the correlation analysis processing.

Since the correlation analysis apparatus of the present invention has the above-described functions, for example, the measurement is performed on a plurality of MOS transistors formed under the same conditions on the surface of a silicon wafer as a measurement plane. Set points. For example, a gate length and a threshold voltage of a MOS transistor or a source-drain leakage current are measured as measurement items.
The correlation is analyzed by selecting / measuring and it is effective to calculate the change in the threshold voltage or the leak current with respect to the change in the gate length.

[0017]

According to the correlation analyzing apparatus of the present invention, even if the measurement plane of the object to be measured is formed so as to form a plurality of measurement items uniformly, the measurement plane is not affected by the fluctuation occurring during the formation process. In many cases, the measured value differs for each of the measurement points provided in. In addition, even if the measured value differs for each measurement point due to the fluctuation, the measurement plane of the object to be measured is formed so as to be formed uniformly, so that a normal correlation is maintained between the two types of measurement items. If formed
The characteristic that the rate of change of the measured value between the two types of measurement items near the measurement point is substantially constant is used.

In this method, a difference between measured values between two measurement points is defined and calculated as a difference, and a difference between two identical measurement points is calculated.
The ratio of the difference between the types of measurement items is defined and calculated as partial differential, and the partial differential value, the average value of the partial differential values, and the standard deviation are used as correlation indices indicating the correlation. The time required for the calculation process is short. Furthermore, even when the correlation between the two types of measurement items and the presence or absence of the correlation are not clear, the analysis can be performed with high accuracy, and the presence or absence of the correlation can be easily determined.

Further, since it is possible to extract measurement points indicating an abnormal correlation between the above two types of measurement items, by excluding the measurement points indicating an abnormal correlation,
The analysis of the correlation can be performed with higher accuracy, and a set of measurement points showing abnormal correlation and a position of the set in the measurement plane can be clearly presented.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of a correlation analysis apparatus of the present invention.

FIG. 2 is a block diagram illustrating a functional configuration of a correlation analysis apparatus according to an embodiment of the present invention.

FIG. 3 is a flowchart for explaining a correlation analysis procedure in the correlation analysis apparatus according to one embodiment of the present invention.

FIG. 4 is a flowchart showing a processing procedure for analyzing a correlation between two types of measurement items in a conventional correlation analyzer.

[Explanation of symbols]

 REFERENCE SIGNS LIST 1 measuring device 2 computer 3 storage device 4 display device 5 output device 21 measured value input unit 22 difference calculating unit 23 partial differential calculating unit 24 correlation index calculating unit 25 correlation abnormal point extracting unit 26 analysis result output unit

Claims (3)

(57) [Claims] 1. A measurement plane of an object to be measured formed so as to be uniformly formed over a plurality of measurement items,
A correlation analyzer that measures two types of the measurement items, inputs a measurement value obtained by the measurement, and analyzes a correlation between the two types of the measurement items. Is selected, a plurality of measurement points common to the two types of measurement items are set in the measurement plane of the object to be measured, and all sets of two different measurement points are extracted from the measurement points. A measurement value input unit for inputting a measurement value in the set, a difference calculation unit for calculating a difference between the two types of measurement items to be analyzed for all the sets, and two measurement points whose differences are not zero. And extracting the extracted set as a set of analysis target measurement points, and calculating a partial differential value that is a ratio of a difference between the two types of measurement items in the same set of analysis target measurement points. Differential calculation unit, all the analysis The partial differential value of the set of elephant measurement points, the average and the standard deviation of the partial differential values of all the sets are calculated as correlation indices indicating the correlation of the two types of measurement items in the measurement plane of the measured object. A correlation analysis device, comprising: a correlation index calculation unit that stores a calculation result in a storage device; and an analysis result output unit that outputs the correlation index as an analysis value. 2. The correlation analyzer, wherein an allowable range is defined using an average of the partial derivatives and a standard deviation, a value of the partial derivative that is out of the allowable range is excluded, and a value of the excluded partial differential is calculated. A correlation abnormal point extracting unit that extracts a set having a value, calculates an appearance frequency of a measurement point included in the set, and extracts the measurement point whose appearance frequency exceeds a predetermined allowable appearance frequency as a correlation abnormal point. The correlation analysis apparatus according to claim 1, wherein: 3. A correlation index is calculated by excluding a set including a measurement point extracted as the correlation abnormal point from the set of analysis target measurement points, and an allowable range is calculated using the correlation index. 3. The correlation analysis apparatus according to claim 1, further comprising an iterative unit that repeats a series of procedures for extracting a correlation abnormal point using the allowable range and the allowable appearance frequency.