JPH0535769A - Correlation analyzing device - Google Patents

Abstract

PURPOSE:To provide a correlation analyzing device by which calculation is easy, precision analysis is obtained even if correation and the presence of the correlation are not clear between two kinds of measuring items, and, the correlation is easily decided and both the gathering of measuring points indicating abnormal correlation and the position of measuring plane are definitely presented. CONSTITUTION:In measuring plane of the object to be measured which is uniformly formed over plural measuring points, two kinds of measuring items are measured among other. This device is constituted of a measured value inputting part 21 in which the values obtained by measuring are inputted, a difference calculating part 22 which calculates a difference between the measured values of two measuring points, a partial differentiation calculating part 23 which calculates the differential ratio of two kinds of measuring items, a correlational index calculating part 24 which calculates correlational index, an abnormal correlation point extracting part 25 which extracts abnormal correlation points and an analyzing result outputting part 26 which outputs analyzing result.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a correlation analysis device, and more particularly to a correlation analysis device 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 analysis apparatus. (Step 41) The measuring apparatus inputs measured values for two desired types of measurement items for which the 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 square method. Here, X and Y are measured values of 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 the total sum. The constants a and b when the total sum becomes minimum and the The total sum (hereinafter referred to as error) is calculated. (Step 43) The two constants a and b obtained as described above and the error are displayed on the display screen of the display device,
Output to printer.

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

[0004]

However, since the conventional correlation analysis apparatus approximates all measured values by a specific function using the least squares method, the calculation process is complicated and the time required for the calculation process is long. Become. Further, the correlation between the two types of measurement items is not clear. Therefore, if an appropriate function to be used for the least squares method is not clear, the error becomes large and it becomes difficult to determine the presence or absence of the correlation. further,
The method of determining the abnormal correlation measurement points is not clear, and the correlation analysis is performed without excluding the abnormal correlation measurement points, and the correlation index is calculated, so the accuracy of the correlation analysis deteriorates. At the same time, there is a problem that it is not possible to accurately specify the existence of an abnormal measurement point of correlation.

The present invention has been made in view of the above points,
Correlation between two types of measurement items on the measurement plane of the object to be measured that is formed so as to be formed uniformly Even if the presence or absence of the correlation is not clear, simply enter the measured values of the measurement items to simplify the process. Analyze and easily determine the presence or absence of correlation anomaly between the two types of measurement items at the measurement points provided on the measurement plane, and exclude the measurement points determined to have correlation anomaly and the measurement values at the measurement points. Then, it aims at providing the correlation analysis apparatus which can analyze a correlation accurately.

[0006]

[Means for Solving the Problems] On a measurement plane of an object to be measured formed so as to be uniformly formed over a plurality of measurement items, two kinds of measurement items are measured and obtained by the measurement. Enter the measured value
In a correlation analyzer that analyzes the correlation between different types of measurement items, select two types of measurement items to be analyzed, and select multiple measurement points common to the two types of measurement items in the measurement plane of the measured object. Individually set, extract all the sets consisting of two different measurement points from the measurement points, input the measured values in the set, and analyze all the sets 2
The difference calculation unit that calculates the difference between the types of measurement items, and all the sets of two measurement points whose differences are not zero are all extracted, and the extracted sets are set as the set of analysis target measurement points, and the same analysis target measurement point is set. Of the partial differential value which is the ratio of the difference between the two types of measurement items in the set, the partial differential value of the set of all the analysis target measurement points, and the partial differential value of all the sets. A correlation index calculation unit that calculates the average and standard deviation as a correlation index that represents the correlation of the measurement target of the two types of measurement items in the measurement plane, and stores the calculation result in the storage device.
And an analysis result output unit for outputting the correlation index as an analysis value.

Further, in the above correlation analysis device,
Define the allowable range using the average and standard deviation of the partial derivatives, exclude the values of the partial derivatives that deviate from the allowable range, extract the set with the values of the excluded partial derivatives, and include it in the extracted set. A correlation abnormal point extraction unit that calculates the appearance frequency of the measured measurement points and extracts the measurement points whose appearance frequencies exceed a predetermined allowable appearance frequency as the correlation abnormal points. Also, the correlation index is calculated by excluding the set including the measurement points extracted as correlation abnormal points from the set of analysis target measurement points, and the allowable range is calculated using the correlation index. It includes an iterative means for repeating a series of procedures for extracting a correlation abnormal point by using.

[0008]

The present invention basically measures two kinds of measurement items at a plurality of measurement points provided in the measurement plane of the object to be measured, and measures the 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 derivative, and the value of the partial derivative is obtained for all the pairs of the two measurement points extracted from all the measurement points. To calculate the average and standard deviation of the partial differential values,
Since the calculated partial differential, the average of the partial differential, and the standard deviation are used as a correlation index representing the correlation between two types of measurement items, there is an advantage that 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 measurement values of the measurement items are input to perform simple analysis, and the two points at the measurement points provided on the measurement plane are measured. It is possible to easily determine whether or not there is a correlation abnormality between types of measurement items.

Further, the allowable range is defined by using the average and standard deviation of the partial differentials, the partial differential values out of the allowable range are excluded from the calculated partial differential values, and the excluded partial differential values. All the sets consisting of two measurement points with is extracted, the frequency of the measurement points included in the extracted set is calculated, the measurement point with high frequency is determined as the correlation abnormal point, and the measurement determined as the correlation abnormal point is performed. You can exclude points.

Further, by repeating the procedure of calculating the correlation index such as the average and standard deviation of the partial differential and determining / excluding the correlation abnormal point using the correlation index, all correlation abnormal points are determined / excluded, and thereby the correlation It is possible to clearly present the set of measurement points indicating the abnormality and the position in the measurement plane, and it is possible to calculate the correlation index with high accuracy.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT FIG. 1 shows the configuration of a correlation analysis apparatus according to the present invention. The correlation analysis device comprises a measuring device 1, a 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 the measurement plane of the measured object. Furthermore, at the measurement point, measure two types of measurement items to be analyzed,
From all of the set measurement points, all sets of two different measurement points are extracted. The extracted set is the electronic computer 2
To enter.

The electronic computer 2 is obtained from the measuring device 1.
The difference between the measured values of the two measurement points that make up the set of three different measurement points is defined as the difference. The difference between the two types of measurement items is calculated for all the sets. Further, all sets of two measurement points in which the differences between the two types of measurement items are not zero are all extracted, and the extracted sets are defined as sets 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 values of all the sets of analysis target measurement points and the partial differential values of all the sets are defined. The average and the standard deviation are defined as a correlation index indicating the correlation between the two types of measurement items in the measurement target 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 is output to the output device 5.

FIG. 2 is a block diagram for explaining the functional configuration of the correlation analysis apparatus of one embodiment of the present invention. Further, FIG. 3 is a flow chart for explaining a correlation analysis procedure in the correlation analysis apparatus of the embodiment of the present invention. The correlation analysis procedure of this embodiment will be described with reference to FIGS. 2 and 3. (Step 31) The measurement value input unit 21 selects a desired measurement item measured at a plurality of measurement points set in the measurement plane of the object to be measured which is formed to uniformly form a plurality of measurement items. Enter 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 sets the two measurement points between the two measurement points constituting the set. The difference (difference) between the measured values of is calculated for each of the two types of measurement items for all the sets.

For example, assuming that two measurement points are i and j, and the measurement 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 The difference between the two types of measurement items in the set consisting of _j is calculated as K _i −K _j and L _i −L _j . (Step 33) Further, the difference calculation unit 22 sets the set of two measurement points (hereinafter, the difference between the two types of measurement items is not zero).
Set of analysis target measurement points) Example) All K _i −K _j ≠ 0 and L _i −L _j ≠ 0 are extracted. (Step 34) The partial differential calculation unit 23 calculates the ratio (partial differential) of the difference between the above-mentioned two types of measurement items for each set of measurement points to be analyzed. In the example shown in step 32, the partial differentiation at the two measurement points i and j is (K _i −K _j ) / (L _i −L _j ), or (L _i −
It is calculated as L _j ) / (K _i −K _j ). (Step 35) The correlation index calculation unit 24 calculates the average and standard deviation of the partial differential values calculated for all the sets of analysis target measurement points. (Step 36) The correlation index calculating unit 24 calculates the allowable width by multiplying the preset variable constant by the standard deviation. (Step 37) The correlation index calculation unit 24 calculates the upper limit value by adding the allowable width to the calculated average value of the partial differentials, while calculating the lower limit value by subtracting the allowable width from the average value, and the lower limit value. Above, the range of values below the upper limit is defined and calculated as the allowable range. (Step 38) The correlation abnormal point extraction unit 25 extracts all the sets of the analysis target measurement points having the values of the partial differential out of the allowable range of the step 37 among the values of the partial differentials in all the sets of the analysis target measurement points. It All the measurement points included in all the extracted sets are extracted, and the appearance frequency in the extracted sets of measurement points is calculated, and the appearance frequency exceeds the preset allowable changeable appearance frequency. Is defined as a correlation abnormal point and is extracted. (Step 39) The correlation abnormal point extraction unit 25 determines whether or not there is a correlation abnormal point. If it exists according to the determination, the process proceeds to step 40, and if it does not exist, step 41
Move to. (Step 40) The correlation abnormal point extraction unit 25 excludes a set including a correlation abnormal point from the set of analysis target measurement points, and the step 35
Move to. (Step 41) The analysis result output unit 26 determines the position in the measurement plane of the measurement point and the set of measurement points determined to be the correlation abnormal points,
The partial differential values of all the sets of the measurement points to be analyzed, which are defined as the correlation index between the two types of measurement items, and the average value and standard deviation of the partial differential values of all the sets are stored in the storage device 3 and displayed. Either it is displayed on the display screen of the device 4 or it is printed out on the output device 5 and the correlation analysis process is terminated.

Since the correlation analyzing apparatus of the present invention has the above-mentioned functions, for example, the surface of a silicon wafer is used as a measurement plane, and measurement is performed on a plurality of MOS transistors formed under the same conditions on the surface of the wafer. Set the point. For example, the gate length and threshold voltage of the MOS transistor or the leak current between the source and drain is used as the measurement item.
It is effective for selecting and measuring, analyzing the correlation, and calculating the change in the threshold voltage and the leak current with respect to the change in the gate length.

[0017]

According to the correlation analysis apparatus of the present invention, even if the measurement plane of the object to be measured is formed so as to be uniformly formed for a plurality of measurement items, the measurement plane is generated due to the fluctuation occurring in the formation process. In many cases, the measured values are different for each of the measurement points provided on the. In addition, even if the measurement value differs at each measurement point due to the above fluctuation, the measurement plane of the measured object is formed so as to be formed uniformly, so that a normal correlation is maintained between the two types of measurement items. Is formed,
The characteristic that the rate of change of the measured value between the two types of measurement items near the measurement point is almost constant is used.

This is because the difference between the measured values between two measuring points is defined and calculated as the difference, and the difference between the two measuring points is the same.
By defining and calculating the ratio of the difference between the types of measurement items as the partial differential, and using the partial differential value, the average value of the partial differential values, and the standard deviation as the correlation index representing the correlation, the calculation process is simple. The time required for calculation processing is short. Further, even if the correlation between the above-mentioned two types of measurement items and the presence or absence of the correlation are not clear, the analysis can be performed accurately and the presence or absence of the correlation can be easily determined.

Further, since it is possible to extract a measurement point at which the correlation between the above-mentioned two types of measurement items is abnormal, by excluding the measurement point at which the correlation is abnormal,
It is possible to analyze the correlation more accurately, and it is possible to clearly present the set of measurement points indicating the abnormal correlation and the position of the set in the measurement plane.

[Brief description of drawings]

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

FIG. 2 is a block diagram for explaining a functional configuration of a correlation analysis device 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 the exemplary 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 analysis device.

[Explanation of symbols]

1 Measuring device 2 electronic calculator 3 storage devices 4 display device 5 Output device 21 Measurement value input section 22 Difference calculator 23 Partial differential calculator 24 Correlation index calculation unit 25 Correlation abnormal point extraction unit 26 Analysis result output section

Claims (3)

[Claims] 1. A measurement plane of an object to be measured formed so as to be formed uniformly over a plurality of measurement items,
In the correlation analysis device that measures two types of measurement items out of the measurement items, inputs the measurement values obtained by the measurement, and analyzes the correlation between the two types of measurement items, the two types to be analyzed Measurement items are 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. Then, 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 where the differences are not zero. A set of partial differentials that are the ratios of the differences between the two types of measurement items in the same set of analysis target measurement points Derivative calculation unit and all the above-mentioned analysis The value of the partial differential of the set of phantom measurement points, the average and the standard deviation of the values of the partial differential of all the sets are calculated as the correlation index indicating the correlation between the two types of measurement items of the measured object in the measurement plane. Then, the correlation analysis device, comprising: a correlation index calculation unit that stores the calculation result in a storage device; and an analysis result output unit that outputs the correlation index as an analysis value. 2. The correlation analysis apparatus, wherein an allowable range is defined by using an average and a standard deviation of the partial differentials, values of the partial differential outside the allowable range are excluded, and the excluded partial differentials are excluded. A correlation abnormal point extraction unit that extracts a set having a value, calculates an appearance frequency of measurement points 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 device according to claim 1, wherein 3. A correlation index is calculated by excluding a set including the measurement points extracted as the correlation abnormal points from the set of measurement points to be analyzed, and an allowable range is calculated using the correlation index, 3. The correlation analysis apparatus according to claim 1, further comprising repeating means for repeating a series of procedures for extracting a correlation abnormal point using the allowable range and the allowable appearance frequency.