A yield detection model and an acquisition method thereof, and a method for detecting a yield distribution
By applying a yield detection model within the wafer and using a quadratic fitting function to determine the distribution pattern of failed structural units, the problems of manpower consumption and insufficient sensitivity in existing technologies are solved, achieving efficient and accurate identification of failed structural unit distribution and photomask traceability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI HUAHONG GRACE SEMICON MFG CORP
- Filing Date
- 2022-12-09
- Publication Date
- 2026-07-03
AI Technical Summary
In existing technologies, determining the repetitive distribution of failed structural units within the wafer within the exposure area suffers from issues of manpower consumption and insufficient sensitivity, making it impossible to effectively trace the cause of the photomask failure.
This paper provides a yield detection model and its acquisition method. By obtaining the number and distribution relationship of failed structural units in the wafer, the distribution pattern of failed structural units is determined by using a quadratic fitting function, and regular distribution is quickly identified to trace photomask problems.
It improves the accuracy and efficiency of detection, saves manpower, and can quickly identify and solve the problem of repeated distribution of failed structural units in wafers, thereby improving yield.
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Figure CN116092962B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of semiconductor technology, and in particular to a yield detection model and its acquisition method, and a method for detecting yield distribution. Background Technology
[0002] In the wafer fabrication process, a common problem is low yield caused by the repeated distribution of faulty structural units across multiple exposure areas. Because the characteristics of these faulty structural units are readily apparent, once detected, the photomask can be quickly located and the problem resolved.
[0003] Currently, determining whether a wafer has repeatedly distributed faulty structural units within the exposure area relies on engineers visually inspecting each one. This presents two problems: manpower consumption: for a factory, manually monitoring the distribution of fault patterns on tens of thousands of wafers for each test represents a huge waste of manpower; sensitivity: if the number of faulty structural units is very low, it is easy for humans to miss them during inspection, leading to omissions.
[0004] An efficient and accurate method is needed to determine whether there are failed structural units repeatedly distributed within the exposed area of the wafer. Summary of the Invention
[0005] The technical problem solved by this invention is to provide a yield detection model and its acquisition method, and a method for detecting yield distribution, so as to efficiently and accurately determine whether there are failed structural units repeatedly distributed in the exposure area within the wafer.
[0006] To address the aforementioned technical problems, the present invention provides a method for obtaining a yield detection model, comprising: providing a wafer, the wafer including a plurality of first exposure areas and second exposure areas, the plurality of first exposure areas being distributed along a first direction and a second direction, the first direction and the second direction being parallel to the wafer surface and perpendicular to each other, the shape of the first exposure areas including rectangles, the second exposure areas being located in the edge region of the wafer, each of the first exposure areas having a plurality of structural units distributed in an array, the number of structural units in the first exposure area being a first value; obtaining the total number of failed structural units in the plurality of first exposure areas, the total number of failed structural units in the plurality of first exposure areas being a second value; and obtaining the relationship between the actual maximum value of the distribution of the failed structural units in the plurality of first exposure areas in the first exposure areas and the first value and the second value, thereby obtaining the yield detection model.
[0007] Optionally, the yield detection model Y=AX 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units within the first exposure area. n is the second value, m is the first value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
[0008] Optionally, the first coefficient A ranges from -0.08 to -0.06; the second coefficient B ranges from 1.35 to 1.65; and the third coefficient C ranges from 4 to 5.
[0009] Optionally, the first coefficient A is -0.068, the second coefficient B is 1.47, and the third coefficient C is 4.51.
[0010] Optionally, the array-distributed structural units have a first number a in the first direction and a second number b in the second direction, where the first number m = a × b.
[0011] Optionally, based on the first and second values, the relationship between the actual maximum values of several failed structural units distributed within the first exposure area and the first and second values is obtained, including: taking values for the first value within a first range with a first step size; taking values for the second value within a second range with a second step size; obtaining the theoretical maximum values of a second number of failed structural units randomly distributed within the first exposure area based on the known first and second values, wherein the theoretical maximum values correspond to the first and second values; and obtaining the relationship between the actual maximum values of several failed structural units distributed within the first exposure area and the first and second values based on the theoretical maximum values and the corresponding first and second values.
[0012] Optionally, based on the theoretical maximum value and the corresponding first and second values, the relationship between the total number of failed structural units and the actual maximum value distributed within the first exposure area, the first value, and the second value is obtained, including: using the ratio of the second value to the first value as the abscissa and the theoretical maximum value corresponding to the first and second values as the ordinate, to obtain a number of scattered points; performing quadratic fitting on the number of scattered points to obtain the first coefficient, the second coefficient, and the third coefficient, and obtaining the relationship between the actual maximum value distributed within the first exposure area and the first and second values of the number of failed structural units within the first exposure area.
[0013] Optionally, the first step length includes 10, and the first range includes 20 to 200; the second step length includes 20, and the second range includes 50 to 1000.
[0014] Accordingly, the present invention also provides a yield detection model, including: the yield detection model includes: the relationship between the actual maximum value of the distribution of several failed structural units in the first exposure area and the first value and the second value.
[0015] Optionally, the yield detection model Y=AX 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units within the first exposure area. n is the second value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
[0016] Optionally, the first coefficient A ranges from -0.08 to -0.06; the second coefficient B ranges from 1.35 to 1.65; and the third coefficient C ranges from 4 to 5.
[0017] Optionally, the array-distributed structural units have a first number a in the first direction and a second number b in the second direction, where the first number m = a × b.
[0018] Accordingly, the present invention also provides a method for detecting yield distribution, comprising: providing a yield detection model; obtaining the number of structural units in any first exposure area within a wafer; obtaining the total number of failed structural units in several first exposure areas within a wafer; obtaining the theoretical maximum value of the random distribution of the failed structural units in the first exposure area based on the number of structural units in any first exposure area and the total number of failed structural units in several first exposure areas within a wafer; obtaining the actual maximum value of the distribution of the failed structural units in several first exposure areas within the first exposure area based on the number of structural units in any first exposure area, the total number of failed structural units in several first exposure areas within a wafer, and the yield detection model; and determining whether the failed structural units are randomly distributed within the first exposure area based on the comparison result between the theoretical maximum value and the actual maximum value.
[0019] Optionally, the method for determining whether the plurality of failed structural units are randomly distributed within the first exposure area includes: if the actual maximum value is greater than the theoretical maximum value, then the plurality of failed structural units are determined to be regularly distributed within the first exposure area; if the actual maximum value is less than or equal to the theoretical maximum value, then the plurality of failed structural units are determined to be randomly distributed within the first exposure area.
[0020] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:
[0021] The technical solution of the present invention obtains a yield detection model, and then detects each wafer according to the yield detection model to determine whether the failed structural units in the wafer are randomly distributed or regularly distributed in the first exposure area. If they are regularly distributed, the problem can be quickly traced back to the photomask to solve the problem, thereby saving manpower and improving detection accuracy and yield. Attached Figure Description
[0022] Figures 1 to 4 This is a schematic diagram of the yield detection model acquisition process in an embodiment of the present invention;
[0023] Figure 5 and Figure 6 This is a flowchart illustrating the method for obtaining the yield detection model in an embodiment of the present invention;
[0024] Figure 7 This is a flowchart illustrating the method for detecting yield distribution in an embodiment of the present invention. Detailed Implementation
[0025] As described in the background section, there is a need for an efficient and accurate method to determine whether there are failed structural units repeatedly distributed within the exposed area of a wafer.
[0026] Specifically, a wafer can be divided into several complete exposure areas based on photomask information. Each complete exposure area contains several structural units. After electrical testing of these structural units, a summary of the failed structural units on the entire wafer is obtained. The method for manually determining whether there is a repetitive distribution of failed structural units within the exposure areas is to judge whether the distribution pattern of the failed structural units within the exposure areas exhibits a regularity. If a regularity is found, it indicates that the failed structural units are repeatedly distributed within the exposure areas. This method requires a significant amount of manpower.
[0027] However, the condition for a factory to trigger engineers to observe the wafer failure distribution is that the wafer yield is below a certain threshold (the common threshold in factories is 90%-95%). If the repeated distribution of failure structural units occurs, but the wafer yield is not below 90%-95%, without engineer intervention, the repeated distribution of failure structural units will be missed, and it will be impossible to trace the cause of the photomask to solve the problem.
[0028] To address the aforementioned issues, the present invention provides a yield detection model and its acquisition method, as well as a method for detecting yield distribution. By acquiring a yield detection model, each wafer is then inspected according to the model to determine whether the failed structural units within the wafer are randomly or regularly distributed in the first exposure area. If they are regularly distributed, the problem can be quickly traced back to the photomask to resolve the issue, thereby saving manpower and improving detection accuracy and yield.
[0029] To make the above-mentioned objectives, features and beneficial effects of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0030] Figures 1 to 4 This is a schematic diagram of the yield detection model acquisition process in an embodiment of the present invention.
[0031] Figure 5 and Figure 6 This is a flowchart illustrating the method for obtaining the yield detection model in an embodiment of the present invention.
[0032] Please refer to Figure 5 The method for obtaining the yield detection model includes:
[0033] Step S10: Provide a wafer, the wafer including a plurality of first exposure areas and second exposure areas, the plurality of first exposure areas being distributed along a first direction and a second direction, the first direction and the second direction being parallel to the wafer surface and perpendicular to each other, the shape of the first exposure area including rectangle, the second exposure area being located in the edge region of the wafer, each of the first exposure areas having a plurality of structural units arranged in an array, the number of structural units in the first exposure area being a first value;
[0034] Step S20: Obtain the total number of failed structural units in several first exposure areas, where the total number of failed structural units in several first exposure areas is a second value;
[0035] Step S30: Based on the first value and the second value, obtain the relationship between the actual maximum value of the distribution of several failed structural units in the first exposure area and the first value and the second value, and obtain the yield detection model.
[0036] By acquiring a yield detection model, and then detecting each wafer according to the yield detection model, it can be determined whether the failed structural units in the wafer are randomly or regularly distributed in the first exposure area. If they are regularly distributed, the problem can be quickly traced back to the photomask to solve the problem, thereby saving manpower and improving detection accuracy and yield.
[0037] Please combine Figure 1 and Figure 2 Continue to refer to Figure 5 , Figure 1 This is a schematic diagram of wafer 100. Figure 2This is a schematic diagram of a method for a single first exposure region 101. Step S10 is performed: a wafer 100 is provided, the wafer 100 includes a plurality of first exposure regions 101 and second exposure regions 102, the plurality of first exposure regions 101 are distributed along a first direction X and a second direction Y, the first direction X and the second direction Y are parallel to the surface of the wafer 100 and perpendicular to each other, the shape of the first exposure region 101 includes a rectangle, the second exposure region 102 is located in the edge region of the wafer 100, each of the first exposure regions 101 has a plurality of structural units 103 arranged in an array, the number of structural units 103 in the first exposure region 101 is a first value m.
[0038] Several first exposure areas 101 and second exposure areas 102 are divided according to photomask information. A wafer can be continuously divided into several exposure areas by a photomask. The first exposure area 101 is a complete exposure area, and the second exposure area 102 is a non-complete exposure area located at the edge of the wafer. The photomask information in each first exposure area 101 is the same.
[0039] Please continue to refer to this. Figure 2 The array-distributed structural unit 103 has a first number a in the first direction X and a second number b in the second direction Y, where the first number m = a × b.
[0040] Please combine Figure 1 and Figure 2 Continue to refer to Figure 5 Step S20: Obtain the total number of failed structural units 104 in several first exposure areas 101, where the total number of failed structural units 104 in several first exposure areas 101 is a second value n.
[0041] Electrical tests are performed on each structural unit 103 on the wafer 100, and the failed structural units 104 that fail the test are marked to obtain the total number of failed structural units 104 in several first exposure areas 101.
[0042] Please continue to refer to this. Figure 5 Step S30: Based on the first value m and the second value n, obtain the relationship between the actual maximum value Y of the distribution of several failed structural units 104 in the first exposure area 101 and the first value m and the second value n, and obtain the yield detection model.
[0043] Please combine Figure 3 refer to Figure 6In this embodiment, based on the first value m and the second value n, the relationship between the actual maximum value Y of the distribution of several failed structural units 104 within the first exposure area 101 and the first value m and the second value n is obtained, including:
[0044] Step S301: Take a value for the first value m within the first range, using the length of the first step.
[0045] In this embodiment, the first step length includes 10, and the first range includes 20 to 200.
[0046] Step S302: Take a value for the second value n within the second range with a second step size.
[0047] In this embodiment, the second step size includes 20, and the second range includes 50 to 1000.
[0048] The first range of values for the first value m and the second range of values for the second value n are applicable to different structural designs of various semiconductor products.
[0049] Step S303: Based on the known first value m and second value n, obtain the theoretical maximum value union bound of the second value n of the failed structural units 104 randomly distributed in the first exposure area 101, wherein the theoretical maximum value union bound corresponds to the first value m and the second value n.
[0050] According to the theory of random distribution, if n failed structural units 104 are randomly distributed among m structural units 103, then there exists a theoretical maximum value (union bound) for the number of failed structural units 104. Therefore, given the first value m and the second value n, a theoretical maximum value (union bound) will inevitably be obtained, and this theoretical maximum value (union bound) corresponds to the first value m and the second value n.
[0051] exist Figure 3 In the diagram, the second value n of one curve is the same.
[0052] Step S304: Based on the theoretical maximum value union bound and the corresponding first value m and second value n, obtain the relationship between the actual maximum value Y of the distribution of several failed structural units 104 in the first exposure area 101 in the first exposure area 101 and the first value m and the second value n.
[0053] Please refer to Figure 4In this embodiment, based on the theoretical maximum value union bound and the corresponding first value m and second value n, the relationship between the actual maximum value Y of several failed structural units 104 distributed within the first exposure area 101 and the first value m and the second value n is obtained. This includes: using the ratio of the second value n to the first value m as the abscissa and the theoretical maximum value union bound corresponding to the first value m and the second value n as the ordinate to obtain several scattered points; performing quadratic term fitting on the several scattered points to obtain the first coefficient A, the second coefficient B and the third coefficient C, and obtaining the relationship between the actual maximum value Y of several failed structural units 104 distributed within the first exposure area 101 and the first value m and the second value n.
[0054] The quadratic fitting involves fitting the distribution of several scattered points to obtain a univariate quadratic fitting function. The resulting yield detection model is Y = AX. 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units 104 within the first exposure area 101. n is the second value, m is the first value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
[0055] The first coefficient A ranges from -0.08 to -0.06; the second coefficient B ranges from 1.35 to 1.65; and the third coefficient C ranges from 4 to 5.
[0056] In this embodiment, the first coefficient A is -0.068, the second coefficient B is 1.47, and the third coefficient C is 4.51.
[0057] The yield detection model is applicable to a variety of semiconductor products.
[0058] Accordingly, this embodiment of the invention also provides a yield detection model, which includes the relationship between the actual maximum value Y of the distribution of a plurality of failed structural units 104 in the first exposure area 101 and the first value m and the second value n.
[0059] In this embodiment, the yield detection model Y = AX 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units 104 within the first exposure area 101. n is the second value, m is the first value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
[0060] In this embodiment, the first coefficient A ranges from -0.08 to -0.06; the second coefficient B ranges from 1.35 to 1.65; and the third coefficient C ranges from 4 to 5.
[0061] In this embodiment, the array-distributed structural unit 103 has a first number a in the first direction X and a second number b in the second direction Y, where the first number m = a × b.
[0062] Figure 7 This is a flowchart illustrating the method for detecting yield distribution in an embodiment of the present invention.
[0063] Please refer to Figure 7 The method for detecting yield distribution includes:
[0064] Step S100: Provide as follows Figure 5 and Figure 6 The yield detection model described above;
[0065] Step S200: Obtain the number of structural units within any first exposure area of the wafer;
[0066] Step S300: Obtain the total number of failed structural units in several first exposure areas within the wafer;
[0067] Step S400: Obtain the theoretical maximum value of the random distribution of the failed structural units in the first exposure area based on the number of structural units in any first exposure area and the total number of failed structural units in several first exposure areas within the wafer;
[0068] Step S500: Based on the number of structural units in any first exposure area, the total number of failed structural units in several first exposure areas within the wafer, and the yield detection model, obtain the actual maximum value of the distribution of failed structural units in several first exposure areas within the first exposure area.
[0069] Step S600: Based on the comparison between the theoretical maximum value and the actual maximum value, determine whether several of the failed structural units are randomly distributed within the first exposure area.
[0070] Please continue to refer to this. Figure 7 Execution step S100: Provide such as Figure 5 and Figure 6 The yield detection model mentioned above.
[0071] The yield detection model Y=AX 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units 104 within the first exposure area 101. n is the second value, m is the first value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
[0072] Please continue to refer to this. Figure 7 Step S200: Obtain the number m of structural units in any first exposure area within the wafer, where m = a × b.
[0073] Please continue to refer to this. Figure 7 Execute step S300: Obtain the total number n of failed structural units in several first exposure areas within the wafer;
[0074] Please continue to refer to this. Figure 7 Step S400: Based on the number of structural units m in any first exposure area and the total number n of failed structural units in several first exposure areas within the wafer, obtain the theoretical maximum value (union bound) of the random distribution of the failed structural units in the first exposure area.
[0075] Please refer to the process for obtaining the theoretical maximum value of union bound. Figure 5 Step 30 in the process will not be repeated here.
[0076] Please continue to refer to this. Figure 7 Step S500: Based on the number m of structural units in any first exposure area, the total number n of failed structural units in several first exposure areas in the wafer, and the yield detection model, obtain the actual maximum value Y of the distribution of failed structural units in several first exposure areas in the first exposure area.
[0077] The process of obtaining the actual maximum value Y is to substitute the number of structural units m in the first exposure area and the total number n of failed structural units in several first exposure areas in the wafer into the yield detection model to obtain the actual maximum value Y.
[0078] Please continue to refer to this. Figure 7 Step S600: Based on the comparison between the theoretical maximum value union bound and the actual maximum value Y, determine whether several of the failed structural units are randomly distributed within the first exposure area.
[0079] In this embodiment, the method for determining whether a plurality of failed structural units are probabilistically distributed within the first exposure area includes: if the actual maximum value Y is greater than the theoretical maximum value union bound, then the plurality of failed structural units are determined to be regularly distributed within the first exposure area; if the actual maximum value Y is less than or equal to the theoretical maximum value union bound, then the plurality of failed structural units are determined to be randomly distributed within the first exposure area.
[0080] If it is determined that several of the failed structural units are regularly distributed within the first exposure area, the cause of failure can be traced back to the photomask, making it easier to trace the source; if it is determined that several of the failed structural units are randomly distributed within the first exposure area, other causes of failure need to be found.
[0081] Each wafer is inspected according to the yield detection model to determine whether the failed structural units within the wafer are randomly or regularly distributed in the first exposure area. If they are regularly distributed, the problem can be quickly traced back to the photomask to solve the problem, thereby saving manpower and improving detection accuracy and yield.
[0082] While the present invention has been disclosed above, it is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.
Claims
1. A method for obtaining a yield detection model, characterized in that, include: A wafer is provided, the wafer including a plurality of first exposure areas and second exposure areas, the plurality of first exposure areas being distributed along a first direction and a second direction, the first direction and the second direction being parallel to the wafer surface and perpendicular to each other, the shape of the first exposure area including a rectangle, the second exposure area being located in the edge region of the wafer, each of the first exposure areas having a plurality of structural units distributed in an array, the number of structural units in the first exposure area being a first value. Obtain the total number of failed structural units within several first exposure areas, where the total number of failed structural units within several first exposure areas is a second value; Based on the first and second values, the relationship between the actual maximum values of the distribution of several failed structural units in the first exposure area and the first and second values is obtained, and the yield detection model is obtained.
2. The method for obtaining the yield detection model as described in claim 1, characterized in that, The yield detection model Y=AX 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units within the first exposure area. n is the second value, m is the first value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
3. The method for obtaining the yield detection model as described in claim 2, characterized in that, The first coefficient A ranges from -0.08 to -0.06; the second coefficient B ranges from 1.35 to 1.65; and the third coefficient C ranges from 4 to 5.
4. The method for obtaining the yield detection model as described in claim 3, characterized in that, The first coefficient A is -0.068, the second coefficient B is 1.47, and the third coefficient C is 4.
51.
5. The method for obtaining the yield detection model as described in claim 2, characterized in that, The array-distributed structural units have a first number a in the first direction and a second number b in the second direction, where the first number m = a × b.
6. The method for obtaining the yield detection model as described in claim 2, characterized in that, Based on the first and second values, the relationship between the actual maximum values of several failed structural units distributed within the first exposure area and the first and second values is obtained, including: taking values for the first value within a first range with a first step size; taking values for the second value within a second range with a second step size; obtaining the theoretical maximum values of a second number of failed structural units randomly distributed within the first exposure area based on the known first and second values, wherein the theoretical maximum values correspond to the first and second values; and obtaining the relationship between the actual maximum values of several failed structural units distributed within the first exposure area and the first and second values based on the theoretical maximum values and the corresponding first and second values.
7. The method for obtaining the yield detection model as described in claim 6, characterized in that, Based on the theoretical maximum value and the corresponding first and second values, the relationship between the total number of the failed structural units and the actual maximum value distributed within the first exposure area, the first value, and the second value is obtained, including: using the ratio of the second value to the first value as the abscissa and the theoretical maximum value corresponding to the first and second values as the ordinate, to obtain a number of scattered points; performing quadratic fitting on the number of scattered points to obtain the first coefficient, the second coefficient, and the third coefficient, and obtaining the relationship between the actual maximum value distributed within the first exposure area and the first and second values of the failed structural units within the first exposure area.
8. The method for obtaining the yield detection model as described in claim 6, characterized in that, The first step length includes 10, and the first range includes 20 to 200; the second step length includes 20, and the second range includes 50 to 1000.
9. A yield detection model, characterized in that, include: The yield detection model obtained by the method according to any one of claims 1 to 8 includes: the relationship between the actual maximum value of the distribution of a plurality of failed structural units in the first exposure area and the first value and the second value.
10. The yield detection model as described in claim 9, characterized in that, The yield detection model Y=AX 2 +BX+C, where Y is the actual maximum value of the distribution of several failed structural units within the first exposure area. n is the second value, m is the first value, A is the first coefficient, B is the second coefficient, and C is the third coefficient.
11. The yield detection model as described in claim 10, characterized in that, The first coefficient A ranges from -0.08 to -0.06; the second coefficient B ranges from 1.35 to 1.65; and the third coefficient C ranges from 4 to 5.
12. The yield detection model as described in claim 10, characterized in that, The array-distributed structural units have a first number a in the first direction and a second number b in the second direction, where the first number m = a × b.
13. A method for detecting yield distribution, characterized in that, include: Provide a yield detection model as described in any one of claims 9 to 12; Obtain the number of structural units within any first exposure area of the wafer; Obtain the total number of failed structural units within several first exposure areas of the wafer; The theoretical maximum value of the random distribution of the failed structural units in the first exposure area is obtained based on the number of structural units in any first exposure area and the total number of failed structural units in several first exposure areas within the wafer. Based on the number of structural units in any first exposure area, the total number of failed structural units in several first exposure areas in the wafer, and the yield detection model, the actual maximum value of the distribution of several failed structural units in the first exposure area is obtained. Based on the comparison between the theoretical maximum value and the actual maximum value, it is determined whether several of the failed structural units are randomly distributed within the first exposure zone.
14. The method for detecting yield distribution as described in claim 13, characterized in that, The method for determining whether a plurality of failed structural units are randomly distributed within the first exposure area includes: if the actual maximum value is greater than the theoretical maximum value, then the plurality of failed structural units are determined to be regularly distributed within the first exposure area; if the actual maximum value is less than or equal to the theoretical maximum value, then the plurality of failed structural units are determined to be randomly distributed within the first exposure area.