Method for comparing distribution of measurement values between wafers

Abstract

The application discloses a kind of comparison methods of the distribution of measurement value between wafers, comprising: step one, the same area division is carried out to 2 wafers needing comparison.Step two, the regional average of the measurement value of each area of each wafer and total average are calculated respectively.Step three, the k value is calculated, and the calculation formula of k value is:Step four, the k obtained by calculation and k0 are compared;When k is less than k0, then judge the matching of the distribution of measurement value between two wafers;When k is greater than or equal to k0, then it is not matched.The present application can realize automatic comparison, with high efficiency and good reproducibility.

Description

TECHNICAL FIELD

[0001] The present application relates to a semiconductor integrated circuit, in particular to a method for comparing distribution maps of measurement values between wafers. BACKGROUND

[0002] With the development of semiconductor manufacturing technology, the critical dimension of chips gradually decreases, the amount of measurement data gradually increases, and the difficulty of data processing and comparison gradually increases.

[0003] The distribution map formed by the distribution of measurement data on the wafer is generally referred to as a map distribution. At present, the industry mainly plots the measurement data of different wafers according to their positions on the wafer to obtain a map distribution, and manually compares whether the map distributions match. This method has the problems of large workload and poor reproducibility, and it is difficult to realize full automation due to the need for human judgment. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a method for comparing distribution maps of measurement values between wafers, which can realize automatic comparison and has high efficiency and good reproducibility.

[0005] To solve the above technical problems, the method for comparing distribution maps of measurement values between wafers provided by the present application comprises the following steps:

[0006] Step one, divide the same regions for two wafers to be compared.

[0007] Step two, calculate the regional average value and the total average value of the measurement values of each region of each wafer.

[0008] Step three, calculate k, the calculation formula of k is:

[0009]

[0010] Wherein, k represents a matching parameter, n represents the number of regions divided by each wafer, i represents the serial number of each region of the wafer, A i is the regional average value of the i-th region of the first wafer, B i is the regional average value of the i-th region of the second wafer, is the total average value of the first wafer, is the total average value of the second wafer.

[0011] Step four, compare the calculated k and k0; when k is less than k0, it is judged that the distribution maps of measurement values between the two wafers match; when k is greater than or equal to k0, it is judged that the distribution maps of measurement values between the two wafers do not match.

[0012] k0 is a matching parameter preset value set according to matching requirements, the higher the matching requirements, the smaller k0.

[0013] Further improvement is that in step one, the area division is performed according to actual requirements.

[0014] Further improvement is that in step one, the area division forms areas with equal or unequal areas.

[0015] Further improvement is that the area division includes: dividing the wafer in a concentric circle manner, each area is a circular area surrounded by the innermost concentric circle and an annular area between each concentric circle.

[0016] Further improvement is that the areas are equal in area.

[0017] Further improvement is that in step four, k0 is less than or equal to 0.005.

[0018] Further improvement is that in step one, semiconductor devices are formed on the wafer; the measurement values include size measurement values or electrical parameter measurement values of each semiconductor device.

[0019] Further improvement is that the measurement of the wafer has been completed before step one.

[0020] Further improvement is that steps one to four are automatically realized by software.

[0021] Further improvement is that steps one to four are repeated to realize two-by-two comparison between multiple wafers.

[0022] The present application can quantify the matching relationship between the measurement values between the wafers, the quantization formula is obtained by referring to the standard deviation formula, and finally the matching relationship between the measurement values between the wafers can be judged by comparing the quantized k value and the pre-set k0 parameter, so the present application can be realized by data processing, without manual comparison, so as to realize automatic comparison, with high efficiency and good reproducibility. BRIEF DESCRIPTION OF DRAWINGS

[0023] The present application will be further described in detail below in combination with the drawings and specific embodiments:

[0024] Figure 1 is a flowchart of the comparison method of the wafer measurement value distribution graph of the embodiment of the present application;

[0025] Figure 2A is a schematic diagram of one area division in the comparison method of the wafer measurement value distribution graph of the embodiment of the present application;

[0026] Figure 2B is a calculationFigure 2A a schematic diagram of the area average of one region in

[0027] Figures 3A-3C is a distribution diagram of measurement values of 3 wafers to be compared in the method of the embodiment of the present application. DETAILED DESCRIPTION

[0028] As shown in Figure 1 is a flow chart of the method for comparing the distribution diagrams of measurement values between wafers in the embodiment of the present application; the method for comparing the distribution diagrams of measurement values between wafers in the embodiment of the present application comprises the following steps:

[0029] Step one, divide the same regions for 2 wafers to be compared.

[0030] In the embodiment of the present application, the region division is made according to actual needs, such as determining the number and area of the regions formed by the region division according to actual needs.

[0031] The area of each region formed by the region division is equal or unequal.

[0032] As shown in Figure 2A is a schematic diagram of one region division in the method for comparing the distribution diagrams of measurement values between wafers in the embodiment of the present application; the region division comprises: dividing the wafer 101 in the form of concentric circles, and each concentric circle is represented by a mark 102. Each region 103 is a circular region surrounded by the innermost concentric circle 102 and an annular region between each concentric circle 102. Figure 2A In the embodiment, the n regions 103 are also represented by region 1, region 2 to region n respectively. Figure 2A In the embodiment, the area of each region 103 is equal.

[0033] The wafer is formed with semiconductor devices; the measurement values include size measurement values or electrical parameter measurement values of each semiconductor device.

[0034] The measurement of the wafer has been completed before step one and the distribution diagram of measurement values has been formed.

[0035] Step two, calculate the area average of measurement values of each region and the total average of each wafer respectively.

[0036] As shown in Figure 2B is a schematic diagram of calculating the area average of one region in Figure 2A , the region i is represented by a mark 103a alone, and the average of measurement values of region i, i.e. the area average of the i-th region, is: Figure 2B

[0037] ​

[0038] wherein A i is Figure 2B the area average value of the i-th region, i.e., region i, in the first wafer; a ix represents the x-th measurement value in region i, the number of measurement values in region i is j, and x is a value in the range of 1 to j.

[0039] Step three, calculate the value of k, and the calculation formula of k is:

[0040]

[0041] wherein k represents a matching parameter, n represents the number of regions divided by each wafer, i represents the serial number of each region of the wafer, A i is the area average value of the i-th region of the first wafer, B i is the area average value of the i-th region of the second wafer, is the total average value of the first wafer, is the total average value of the second wafer.

[0042] Step four, compare the calculated k and k0; when k is less than k0, it is judged that the distribution map of measurement values between the two wafers matches; when k is greater than or equal to k0, it is judged that the distribution map of measurement values between the two wafers does not match.

[0043] k0 is a preset value of a matching parameter set according to a matching requirement, and the higher the matching requirement, the smaller k0.

[0044] In some embodiments, k0 is less than or equal to 0.005. In a preferred embodiment, k0 is equal to 0.005.

[0045] Steps one to four are automatically realized by software; for example, programming or excel macro can be combined with automatic office software to realize automation, which has the advantages of high efficiency and good reproducibility.

[0046] Steps one to four are repeated to realize pairwise comparison between multiple wafers.

[0047] The embodiment of the present application can quantify the matching relationship between the measurement values between the wafers, the quantification formula is obtained by referring to the standard deviation formula, and finally the matching relationship between the measurement values between the wafers can be judged by comparing the quantified k value and the preset k0 parameter, so the embodiment of the present application can be realized by data processing, without manual comparison, so that automatic comparison can be realized, which has high efficiency and good reproducibility.

[0048] In the embodiment of the present application, the calculation formula (1) of k is obtained by deforming the standard deviation formula, and the derivation process is as follows:

[0049] The standard deviation formula is:

[0050]

[0051] In formula (3), σ is the standard deviation, n represents the number of data in the data set, Ai represents the i-th data value of the data set, represents the average value of the data.

[0052] The formula (3) is transformed to obtain:

[0053]

[0054] The formula (4) is simplified to obtain formula (1).

[0055] It can be seen that the formula (1) in the embodiment of the application is based on the formula of the widely used standard deviation; at the same time, the formula (1) normalizes the mean value, only compares the map distribution, and the mean value of the measured value has no effect on the calculation result.

[0056] As shown in Figures 3A-3C is the measured value distribution diagram of the three wafers to be compared in the method of the embodiment of the application, Figures 3A-3C The three wafers are marked as 101a, 101b and 101c respectively. The matching of the measured value distribution diagrams between the wafer 101a and the wafer 101b and the wafer 101a and the wafer 101c is realized by using the method of the embodiment of the application.

[0057] As shown in Figure 3A , it can be seen that the measured value distribution diagram of the wafer 101a includes a plurality of measured values, and the measured value here is the critical dimension of the semiconductor device. The mean value is 30.7 nm, 3-sigma represents 3σ, i.e. 3 standard deviations, and the range represents the deviation of the maximum value and the minimum value.

[0058] Figure 3B and Figure 3C also show a plurality of measured values, a mean value, 3-sigma and a range in the measured value distribution diagram of the wafer 101b and the wafer 101c respectively.

[0059] Comparing Figures 3A-3C each measured value distribution diagram alone cannot easily determine the matching degree of each measured value distribution diagram.

[0060] Using the method of the embodiment of the application, as shown in Figure 3A , the wafer 101a is divided into a plurality of regions. When comparing two by two between the wafers, the corresponding k value can be calculated, and

[0061] The k value between the wafer 101a and the wafer 101b is 0.00175, which is less than 0.005, and the map distribution between the wafer 101a and the wafer 101b is basically matched.

[0062] The k value between the wafer 101a and the wafer 101c is 0.21956, which is greater than 0.005, and the map distribution between the wafer 101a and the wafer 101c is not matched.

[0063] The above has been described in detail through specific embodiments, but these do not constitute a limitation on the present application. Many modifications and improvements can be made by those skilled in the art without departing from the principles of the present application, and these should also be considered as within the scope of protection of the present application.

Claims

1. A method of comparing metrology value profiles between wafers, characterized by, The method comprises the following steps: Step one, dividing the two wafers to be compared into the same regions; Step two, calculating the regional average and the total average of the measurement values of each region of each wafer; Step three, calculating k, the formula of which is: wherein k represents a matching parameter, n represents the number of regions divided by each of the wafers, i represents the serial number of each region of the wafer, A i is the region average value of the i-th region of the first wafer, B i is the region average value of the i-th region of the second wafer, is the total average value of the first wafer, is the total average value of the second wafer; Step four, comparing k and k0; when k is less than k0, it is determined that the distribution of the measurement values of the two wafers matches; when k is greater than or equal to k0, it is determined that the distribution of the measurement values of the two wafers does not match; k0 is a preset value of a matching parameter set according to a matching requirement, and the higher the matching requirement is, the smaller k0 is.

2. The method of claim 1, wherein: In step one, the regions are divided according to actual requirements.

3. The method of claim 2, wherein: In step one, the areas of the regions formed by the region division are equal or unequal.

4. The method of claim 3, wherein: The region division comprises dividing the wafers in a concentric manner, and each region is a circular region surrounded by the innermost concentric circle and an annular region between the concentric circles.

5. The method for comparing measurement distribution maps between wafers as described in claim 4, characterized in that: The areas of the regions are equal.

6. The method of claim 1, wherein: In step four, k0 is less than or equal to 0.

005.

7. The method for comparing measurement distribution maps between wafers as described in claim 1, characterized in that: In step one, semiconductor devices are formed on the wafers, and the measurement values comprise size measurement values or electrical parameter measurement values of the semiconductor devices.

8. The method for comparing measurement distribution maps between wafers as described in claim 7, characterized in that: The measurement of the wafers has been completed before step one.

9. The method for comparing measurement distribution maps between wafers as described in claim 1, characterized in that: Steps one to four are automatically realized by software.

10. The method for comparing measurement distribution maps between wafers as described in claim 1, characterized in that: Steps one to four are repeated to realize pairwise comparison between multiple wafers.

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