A method for measuring and evaluating the uniformity of periodic high-density cylindrical objects

Abstract

The present invention provides a method for measuring and evaluating the uniformity of a periodic high-density cylindrical object, comprising step S1: obtaining height and coordinate data of the periodic high-density cylindrical object using a microscope, and organizing the data into a data matrix; step S2: reconstructing and drawing the original morphology of the periodic high-density cylindrical object based on the acquired data matrix, calculating the average height of the periodic high-density cylindrical object, and setting a relative height for calculating uniformity; step S3: determining the coordinates of the center of each periodic high-density cylindrical object contained in the data matrix; step S4: calculating the cross-sectional area of ​​each periodic high-density cylindrical object at a set relative height, and storing the result in a cross-sectional area data matrix; step S5: performing statistical analysis on the cross-sectional area data matrix; and step S6: drawing a cross-sectional diagram of the periodic high-density cylindrical object at the set relative height based on the calculation result of step S4.

Description

Technical Field

[0001] The present invention relates to the technical field of material detection and evaluation, and in particular to a method for measuring the average height and uniformity of a high-density columnar object. Background Art

[0002] High-density cylindrical objects are primarily used for interconnecting area array and linear semiconductor optoelectronic chips with integrated circuits. For example, indium pillar flip-flop solder connections and copper-copper interconnects are used in camera manufacturing. Therefore, the growth quality of these cylindrical objects, including height and uniformity, directly impacts the performance of the interconnected devices. Poor uniformity in the cylindrical objects used for interconnection prevents proper signal output from each pixel, significantly impacting device yield and blind pixel rate.

[0003] Currently, conventional methods for detecting cylindrical objects include observations using microscopes, laser confocal microscopes, and SEMs. After observing the sample or taking images, the height of periodic high-density cylindrical objects within the field of view can be manually measured using simple measurement software provided by some microscopes. However, measuring the number of periodic high-density cylindrical objects relies entirely on manual operation, and measuring them one by one is very inefficient. It is impossible to quickly and uniformly analyze all periodic high-density cylindrical objects within the field of view, and it is impossible to analyze the uniformity and fullness of high-density cylindrical objects. Therefore, the existing methods are qualitative rather than quantitative in their evaluation of high-density cylindrical objects, and are subjective rather than observable. Furthermore, they are unable to obtain parameters such as the uniformity and fullness of the entire periodic high-density cylindrical object, which are crucial for interconnection. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for measuring and evaluating the uniformity of periodic high-density columnar objects that can be quickly and quantitatively tested for uniformity, and quickly determine whether they meet the requirements for the next step of process implementation.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for measuring and evaluating the uniformity of a periodic high-density cylindrical object is provided, and includes the following steps:

[0007] Step S1: using a microscope to obtain the height and coordinate data of periodic high-density cylindrical objects and organize them into a data matrix;

[0008] Step S2: reconstructing and drawing the original morphology of the periodic high-density columnar object according to the collected data matrix, calculating the average height of the periodic high-density columnar object, and setting the relative height for which uniformity needs to be calculated;

[0009] Step S3: determining the coordinates of the center of each periodic high-density cylindrical object included in the data matrix;

[0010] Step S4: for each periodic high-density cylindrical object, calculate its cross-sectional area at a set relative height, and store the result in a cross-sectional area data matrix;

[0011] Step S5: performing statistical analysis on the cross-sectional area data matrix, including calculating the mean, standard deviation, and coefficient of variation to evaluate uniformity;

[0012] Step S6: Based on the calculation result of step S4, a cross-sectional view of the periodic high-density cylindrical object at a set relative height is drawn.

[0013] Preferably, the step S2 of calculating the average height of the periodic high-density columnar objects comprises the following specific steps:

[0014] Step S21: Bottom area calculation: Set a step value in the bottom area, calculate the number of data points contained in each bottom step value, find the step interval with the largest number of data points, and average the height values ​​z of all data points in this interval. The resulting value is used as the bottom z value of the cylindrical object;

[0015] Step S22: Top area calculation: Determine the step value in the top area, calculate the number of data points contained in each top step value, find the step interval with the largest number of data points, and average the height values ​​z of all data points in this interval. The average value is used as the top z value of the cylindrical object.

[0016] Step S23: Average height of the periodic high-density columnar object: the difference between the z value at the top and the z value at the bottom of the columnar object is the average height of the periodic high-density columnar object.

[0017] Preferably, in step S3, determining the coordinates of the center of each periodic high-density cylindrical object contained in the data matrix includes using the contour function in MATLAB to obtain a contour function matrix at half the average height, which contains the data point coordinates of all the periodic high-density cylindrical objects at half the average height, and averaging the x value and y value of the coordinates of each data point of the periodic high-density cylindrical object to obtain the coordinates of the center of each periodic high-density cylindrical object.

[0018] Preferably, the specific steps of step S3 include:

[0019] Step S31: Determine half the average height of the periodic high-density cylindrical object calculated in step S2.

[0020] Step S32: Using the contour function in MATLAB, extract z=h based on the data matrix mid The contour data matrix ContourMatrix;

[0021] This matrix contains the coordinates (x, y) of all the data points of the periodic high-density cylindrical objects at half the average height;

[0022] Step S33: separating the data point sets belonging to each of the periodic high-density cylindrical objects from the ContourMatrix;

[0023] Step S34: For each set of data points of the periodic high-density cylindrical object, calculate the average values ​​of its x and y coordinates:

[0024]

[0025] Where N is the number of data points belonging to the periodic high-density cylindrical object, and the coordinates (x center ,y center ).

[0026] Preferably, in step S4, for each periodic high-density cylindrical object, its cross-sectional area is calculated at a set relative height, and the result is stored in a cross-sectional area data matrix, including the coordinates of the center obtained in step S3. Based on the periodic spacing between the periodic high-density cylindrical objects, the initial height and coordinate data matrix of all cylindrical objects is divided into a separate height and coordinate data matrix for each periodic high-density cylindrical object. A contour function is applied to each periodic high-density cylindrical object to obtain a contour function matrix for each periodic high-density cylindrical object at a given height, which contains the coordinates of the data points of the periodic high-density cylindrical object at the given height. The polyarea function is used to obtain the cross-sectional area of ​​each periodic high-density cylindrical object at the given height, and the result is stored in the cross-sectional area matrix for the periodic high-density cylindrical object at a given height.

[0027] Preferably, the specific steps of step S4 include:

[0028] Step S41: Using the center coordinates of each of the periodic high-density cylindrical objects obtained in step S3, the initial data matrix is ​​divided into independent sub-matrices according to the periodic spacing d between the periodic high-density cylindrical objects, where each sub-matrix corresponds to the height and coordinate data of one of the periodic high-density cylindrical objects;

[0029] Step S42: For each independent sub-matrix of the periodic high-density cylindrical object, use the contour function in MATLAB to extract the height and coordinate sub-matrix at the specified relative height z=h relative Contour line data at the height, obtaining the contour point (x, y) of the periodic high-density cylindrical object at the height;

[0030] Step S43: Calculate the cross-sectional area A of the contour points (x, y) in the contour data using the polyarea function in MATLAB:

[0031] A = polyarea(x, y).

[0032] Preferably, in step S5, the cross-sectional area data matrix is ​​statistically analyzed, including calculating the mean, standard deviation and coefficient of variation to evaluate uniformity, including using the cross-sectional area data matrix of all the periodic high-density cylindrical objects at a given height obtained in step S4 to calculate the mean, standard deviation and coefficient of variation of the cross-sectional area at a given height, and generate an analysis report.

[0033] Preferably, the step S5 specifically includes:

[0034] Step S51: Using the cross-sectional area data matrix of all the periodic high-density cylindrical objects at a given height obtained in step S4, AreaMatrix=[A1, A2, ..., A n ], where A i represents the cross-sectional area of ​​the i-th periodic high-density cylindrical object;

[0035] Step S52: Calculate the mean μ:

[0036]

[0037] Where n is the total number of cylindrical objects;

[0038] Standard deviation σ:

[0039]

[0040] Coefficient of variation CV:

[0041]

[0042] Step S53: Organize the statistical results into a report, including the following information:

[0043] Given height h relative , the mean, standard deviation and coefficient of variation of the cross-sectional area data matrix AreaMatrix and simple visualization of the data include bar charts, histograms or box plots to intuitively present the cross-sectional area distribution.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] (1) The present invention realizes the fully automatic measurement and analysis of all cylindrical objects in a single field of view or multiple fields of view through a high-precision microscope combined with algorithm analysis, greatly improving the detection efficiency and meeting the needs of rapid evaluation of large-scale high-density cylindrical objects.

[0046] (2) Based on three-dimensional height and coordinate data, this invention uses an algorithm to accurately calculate parameters such as the average height, cross-sectional area at different heights, standard deviation, and coefficient of variation of the cylinder, thereby achieving quantitative analysis of the growth quality of cylindrical objects. The results are objective and consistent, providing a reliable basis for interconnection process optimization.

[0047] (3) By calculating the mean, standard deviation, and coefficient of variation of the cross-sectional area, this method can comprehensively evaluate the uniformity and fullness of cylindrical objects. These indicators directly reflect whether the growth quality meets interconnect requirements, helping to reduce the blind element rate of the device and improve the yield rate.

[0048] (4) The present invention supports unified analysis of all cylindrical objects within a single field of view or multiple fields of view to obtain overall uniformity, fullness, and growth quality parameters, providing a global reference for device performance evaluation.

[0049] (5) The present invention accurately analyzes indicators such as column growth height and uniformity, timely discovers process defects and provides feedback on optimization directions, effectively improves the yield of the device, reduces the blind pixel rate, and ensures the stable output of each pixel signal after interconnection.

[0050] (6) The present invention realizes automatic analysis report generation based on computer algorithms, including data statistics, chart display and parameter summary, providing an efficient and convenient tool for R&D and quality control. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A program interface for qualitative analysis of high-density cylindrical objects provided by an embodiment of the present invention;

[0052] Figure 2 A periodic high-density cylindrical object restoration diagram provided by an embodiment of the present invention;

[0053] Figure 3A cross-sectional view of a high-density cylindrical object when the height is set to 50% according to an embodiment of the present invention;

[0054] Figure 4 An analysis report is provided for an embodiment of the present invention.

[0055] Figure 5 Flowchart of the method of the present invention. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0057] like Figure 5 As shown in FIG, a method for measuring and evaluating the uniformity of a periodic high-density cylindrical object provided by this embodiment, the specific steps are as follows:

[0058] Step S1: First, use a confocal microscope, white light microscope or other instruments to capture and obtain periodic high-density cylindrical object images, and export and save their height and coordinate data files.

[0059] like Figure 1 Open the program interface as shown, fill in the necessary parameters, click start, and a pop-up window will pop up to select the file path to be calculated, and then the automatic calculation will begin.

[0060] Step S2: Figure 2 As shown, restore and draw its original morphology and then calculate the average height of the cylinder. The specific steps are as follows:

[0061] Step S21: Bottom area calculation: Set a step value in the bottom area, calculate the number of data points contained in each bottom step value, find the step interval with the largest number of data points, and average the height values ​​z of all data points in this interval. The resulting value is used as the bottom z value of the cylindrical object;

[0062] Step S22: Top area calculation: Determine the step value in the top area, calculate the number of data points contained in each top step value, find the step interval with the largest number of data points, and average the height values ​​z of all data points in this interval. The average value is used as the top z value of the cylindrical object.

[0063] Step S23: Average height of the periodic high-density columnar object: the difference between the z value at the top and the z value at the bottom of the columnar object is the average height of the periodic high-density columnar object.

[0064] Step S3: Then determine the coordinates of the center of each cylindrical object included in the data matrix. The specific steps are as follows:

[0065] Step S31: Determine half the average height value of the periodic high-density cylindrical object calculated in step S2.

[0066] Step S32: Using the contour function in MATLAB, extract z=h based on the data matrix mid The contour data matrix ContourMatrix;

[0067] This matrix contains the coordinates (x, y) of all the data points of the periodic high-density cylindrical objects at half the average height;

[0068] Step S33: separating the data point sets belonging to each of the periodic high-density cylindrical objects from the ContourMatrix;

[0069] Step S34: For each set of data points of the periodic high-density cylindrical object, calculate the average values ​​of its x and y coordinates:

[0070]

[0071] Where N is the number of data points belonging to the periodic high-density cylindrical object, and the coordinates (x center ,y center ).

[0072] Step S4: Then calculate the cross-sectional area of ​​each cylindrical object at a given relative height and store it in a cross-sectional area data matrix. The specific method is as follows:

[0073] Step S41: Using the center coordinates of each of the periodic high-density cylindrical objects obtained in step S3, the initial data matrix is ​​divided into independent sub-matrices according to the periodic spacing d between the periodic high-density cylindrical objects, where each sub-matrix corresponds to the height and coordinate data of one of the periodic high-density cylindrical objects;

[0074] Step S42: For each independent sub-matrix of the periodic high-density cylindrical object, use the contour function in MATLAB to extract the height and coordinate sub-matrix at the specified relative height z=h relative Contour line data at the height, obtaining the contour point (x, y) of the periodic high-density cylindrical object at the height;

[0075] Step S43: Calculate the cross-sectional area A of the contour points (x, y) in the contour data using the polyarea function in MATLAB:

[0076] A = polyarea(x, y).

[0077] Draw as Figure 3 The given height cross-sectional view is shown and stored in the given height cross-sectional area matrix of the cylinder.

[0078] Step S5: Finally, based on the cross-sectional area data matrix of each cylinder at a given height, the mean, standard deviation, and coefficient of variation of the cross-sectional area at a given height are calculated. The specific steps are as follows:

[0079] The cross-sectional area data matrix of all the periodic high-density cylindrical objects at a given height obtained in step S4 is AreaMatrix=[A1, A2, ..., A n ], where A i represents the cross-sectional area of ​​the i-th periodic high-density cylindrical object;

[0080] Step S52: Calculate the mean μ:

[0081]

[0082] Where n is the total number of cylindrical objects;

[0083] Standard deviation σ:

[0084]

[0085] Coefficient of variation CV:

[0086]

[0087] Step S53: Figure 4 The statistical results are organized into a report, including the following information:

[0088] Given height h relative , the mean, standard deviation and coefficient of variation of the cross-sectional area data matrix AreaMatrix and simple visualization of the data include bar charts, histograms or box plots to intuitively present the cross-sectional area distribution.

[0089] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like to indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0090] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature identified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0091] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for measuring and evaluating the uniformity of a periodic high-density cylindrical object, for measuring and evaluating a periodic high-density cylindrical object, characterized in that: The steps include: Step S1: using a microscope to obtain the height and coordinate data of periodic high-density cylindrical objects and organize them into a data matrix; Step S2: reconstructing and drawing the original morphology of the periodic high-density cylindrical object based on the collected data matrix, calculating the average height of the periodic high-density cylindrical object, and setting the relative height for which uniformity needs to be calculated; Step S3: determining the coordinates of the center of each periodic high-density cylindrical object included in the data matrix; Step S4: for each periodic high-density cylindrical object, calculate its cross-sectional area at a set relative height, and store the result in a cross-sectional area data matrix; Step S5: performing statistical analysis on the cross-sectional area data matrix, including calculating the mean, standard deviation, and coefficient of variation to evaluate uniformity; Step S6: based on the calculation result of step S4, drawing a cross-sectional diagram of the periodic high-density cylindrical object at a set relative height; The specific steps of step S2 include: Step S21: Bottom area calculation: Set a step value in the bottom area, calculate the number of data points contained in each bottom step value, find the step interval with the largest number of data points, and average the height values ​​z of all data points in this interval. The resulting value is used as the bottom z value of the cylindrical object; Step S22: Top area calculation: Determine the step value in the top area, calculate the number of data points contained in each top step value, find the step interval with the largest number of data points, and average the height values ​​z of all data points in this interval. The average value is used as the top z value of the cylindrical object. Step S23: Average height of the periodic high-density columnar object: the difference between the top z value and the bottom z value of the columnar object is the average height of the periodic high-density columnar object; The specific steps of step S3 include: Step S31: Determine half the average height of the periodic high-density cylindrical object calculated in step S2. Step S32: Using the contour function in MATLAB, extract z=h based on the data matrix mid The contour data matrix ContourMatrix; This matrix contains the coordinates (x, y) of all the data points of the periodic high-density cylindrical objects at half the average height; Step S33: separating the data point sets belonging to each of the periodic high-density cylindrical objects from the ContourMatrix; Step S34: For each set of data points of the periodic high-density cylindrical object, calculate the average values ​​of its x and y coordinates: Where N is the number of data points belonging to the periodic high-density cylindrical object, and the coordinates (x center ,y center ); The specific steps of step S4 include: Step S41: Using the center coordinates of each of the periodic high-density cylindrical objects obtained in step S3, the initial data matrix is ​​divided into independent sub-matrices according to the periodic spacing d between the periodic high-density cylindrical objects, where each sub-matrix corresponds to the height and coordinate data of one of the periodic high-density cylindrical objects; Step S42: For each independent sub-matrix of the periodic high-density cylindrical object, use the contour function in MATLAB to extract the height and coordinate sub-matrix at the set relative height z=h relative Contour line data at , obtaining the contour points (x, y) of the periodic high-density cylindrical object at relative height; Step S43: Calculate the cross-sectional area A of the contour points (x, y) in the contour data using the polyarea function in MATLAB: A=polyarea(x,y).

2. The method for measuring and evaluating the uniformity of a periodic high-density cylindrical object according to claim 1, characterized in that: In step S5, the cross-sectional area data matrix is ​​statistically analyzed, including calculating the mean, standard deviation, and coefficient of variation to evaluate uniformity, including using the cross-sectional area data matrix of all the periodic high-density cylindrical objects at the set relative height obtained in step S4 to calculate the mean, standard deviation, and coefficient of variation of the cross-sectional area at the set relative height, and generating an analysis report.

3. The method for measuring and evaluating the uniformity of a periodic high-density cylindrical object according to claim 2, characterized in that: The specific steps of step S5 include: Step S51: Utilize the cross-sectional area data matrix of all the periodic high-density cylindrical objects at the set relative height obtained in step S4: AreaMatrix=[A1, A2, ..., A n ], where A i represents the cross-sectional area of ​​the i-th periodic high-density cylindrical object; Step S52: Calculate the mean μ: Where n is the total number of cylindrical objects; Standard deviation σ: Coefficient of variation CV: Step S53: Organize the statistical results into a report, including the following information: Set relative height h relative , the mean, standard deviation and coefficient of variation of the cross-sectional area data matrix AreaMatrix and simple visualization of the data include bar charts, histograms or box plots to intuitively present the cross-sectional area distribution.

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