A surface topography data resampling method and wafer thickness measurement method

Abstract

The present invention discloses a surface morphology data resampling method and a wafer thickness measurement method, the surface morphology data resampling method comprises the following steps: preprocessing the original morphology data of the object to be measured, removing abnormal data, and obtaining the preprocessed sampling data; performing regional segmentation on the preprocessed sampling data to obtain segmented grid data; based on the original sampling relative height value of the sampling points around each grid point and its contribution weight to the grid point, obtaining the relative height value of each grid point by weighted calculation; generating a resampling point array covering the object to be measured according to the resampling interval; based on each resampling point in the resampling point array, using the relative height values ​​of the four grid points around it and their corresponding contribution weights, calculating the relative height value of each resampling point. The method can realize effective denoising and data distribution uniformity of the original morphology data of the object to be measured, and accurately reflect the true morphology of the object to be measured.

Description

Technical Field

[0001] The present invention relates to the field of measurement technology, and in particular to a surface topography data resampling method and a wafer thickness measurement method. Background Art

[0002] The existing collection of semiconductor wafer morphology data mainly relies on high-precision distance sensors and high-precision motion platforms. The optical characteristics of the distance sensor determine that when it collects data, it is easily affected by factors such as ambient light and sampling point angle, resulting in some noise or abnormal data. Different sampling process settings, such as spiral sampling and concentric circle sampling, will result in different data distributions. Directly using raw data or performing conventional filtering processing cannot effectively remove abnormal data, and will be affected by data non-uniformity, resulting in the measurement results being unable to accurately reflect the wafer morphology. Summary of the invention

[0003] The technical problem to be solved by the present invention application is to provide a surface morphology data resampling method and a wafer thickness measurement method, so as to achieve effective denoising and data distribution uniformity of the original wafer morphology data, and accurately reflect the true morphology of the semiconductor wafer.

[0004] A surface topography data resampling method comprises the following steps:

[0005] Preprocess the original shape data of the object to be measured, remove abnormal data, and obtain the preprocessed sampling data Data_nr (X_nr, Y_nr, Z_nr);

[0006] Performing regional segmentation on the preprocessed sampling data Data_nr to obtain segmented grid data Data_grid (X_grid, Y_grid);

[0007] Based on the original sampled relative height value Z_nr[pi] of the sampling points around each grid point and its contribution weight W to the grid point pi , the relative height value Z of each grid point is obtained by weighted calculation grid [P];

[0008] Generate a resampling point array Data_co (X_q, Y_q) covering the object under test according to the resampling interval;

[0009] Based on each resampling point in the resampling point array, the relative height values ​​Z of the four grid points around it are used P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q, calculate the relative height value Z_q of each resampling point, and thus generate the resampled data Data_rs(X_q,Y_q ， Z_q).

[0010] In one embodiment, the method of preprocessing the original shape data of the measured object, removing abnormal data, and obtaining the preprocessed sampling data Data_nr (X_nr, Y_nr, Z_nr) includes the following steps:

[0011] Calculate the global mean Z of the sampled data mean and standard deviation Z std ;

[0012] Eliminate relative height values ​​Z_nr that are not in range Z mean ±n×Z std Abnormal data within, where n is 1-3.

[0013] In one embodiment, the method of preprocessing the original shape data of the measured object, removing abnormal data, and obtaining the preprocessed sampling data Data_nr (X_nr, Y_nr, Z_nr) includes the following steps:

[0014] Count the number of sampling points within the neighborhood of radius R_n for each sampling point;

[0015] If the number of sampling points in the neighborhood of a sampling point is less than the preset threshold N_min, the sampling point is removed.

[0016] In one embodiment, the contribution weight W of the sampling point to the grid point is pi The calculation includes:

[0017] According to the distance between the sampling point and the grid point, use any method of bilinear interpolation, Gaussian function or Sigmoid function to calculate the contribution weight W of the sampling point to the grid point. pi .

[0018] In one embodiment, the relative height value Z of each grid point is obtained by weighted calculation. grid [P] Includes:

[0019] By weighted averaging, the original sampled relative height value Z_nr[pi] of the sampling points around the grid point is added to its contribution weight W pi Combined, the relative height value Z of each grid point is calculated grid [P].

[0020] In one embodiment, generating a resampling point array Data_co(X_q, Y_q) covering the measured object according to the resampling interval includes the following:

[0021] For each resampled point (X_i, Y_i) generated, calculate the distance d_i between the point and the center point (0,0);

[0022] If d_i≤R, keep the sampling point;

[0023] If d_i>R, the point is considered to be outside the object being measured and is removed;

[0024] Wherein, R is the radius of the object being measured.

[0025] In one embodiment, the method is based on each resampling point in the resampling point array, using the relative height values ​​Z of the four grid points around it. P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q , calculate the relative height value Z_q of each resampling point, and also include the following steps:

[0026] Calculate the relationship between each resampled point q(X_q,Y_q) and its surrounding four vertices P1(x P1 ,y P1 ),P2(x P2 ,y P2 ),P3(x P3 ,y P3 ),P4(x P4 ,y P4 ) between the two sides;

[0027] If the condition X_q-x is met P1 >0 and X_q-x P2 ≤0, and Y_q-y P1 >0 and Y_q-y P3 ≤0, then the resampling point q is located at the four vertices P1(x P1 ,y P1 ),P2(x P2 ,y P2 ),P3(x P3 ,y P3 ),P4(x P4 ,y P4 ) within the grid formed by .

[0028] In one embodiment, the contribution weights W of the four grid points around the resampling point to the resampling point are: q The calculation includes:

[0029] According to the distance between the resampling point and the grid point, use any method of bilinear interpolation, Gaussian function or Sigmoid function to calculate the contribution weight W of the four grid points around the resampling point to the resampling point. q .

[0030] In one embodiment, the method is based on each resampling point in the resampling point array, using the relative height values ​​Z of the four grid points around it. P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q , calculate the relative height value Z_q of each resampling point, including the following steps:

[0031] Calculate the relative distances d_x and d_y between the resampled point and the four surrounding grid points;

[0032] Use the relative height values ​​Z of the four grid points P1 ,Z P2 ,Z P3 ,Z P4 As well as the relative distances d_x and d_y of the resampling points, the relative height value Z_q of the resampling point q is calculated by bilinear interpolation. The calculation formula is as follows:

[0033] Z_q=[Z P1 *(X step -d_x)*(Y step -d_y)+Z P2 *d_x*(Y step -d_y)+Z P3 *d_x*d_y+Z P4 *(X step -d_x)*d_y] / (X step *Y step )

[0034] in:

[0035] X step and Y step are the step sizes of the grid in the X and Y directions respectively.

[0036] Z P1 ,Z P2 ,Z P3 ,Z P4 The relative height values ​​of the four vertices of the mesh.

[0037] A wafer thickness measurement method comprises the following steps:

[0038] Measure the topographic data Data_chuck_nr and Data_wafer_nr of the upper surface of the carrier and the upper surface of the wafer respectively;

[0039] Resample Data_chuck_nr and Data_wafer_nr respectively using the surface topography data resampling method to obtain resampled data Data_chuck_rs and Data_wafer_rs;

[0040] Data_wafer_rs is subtracted from Data_chuck_rs point by point to obtain the wafer thickness data of the wafer topography.

[0041] The above-mentioned surface morphology data resampling method mainly includes preprocessing of the original morphology data, grid point division, and recalculation of relative height information, which realizes effective denoising and data distribution uniformity of the original morphology data of the measured object, and accurately reflects the true morphology of the measured object. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of a surface topography data resampling method in one embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of the original wafer morphology data;

[0044] Figure 3 It is a schematic diagram of the original morphological data after preprocessing;

[0045] Figure 4 This is a schematic diagram after the grid points are divided;

[0046] Figure 5 Schematic diagram of grid point weight calculation;

[0047] Figure 6 is a schematic diagram of the resampling point array;

[0048] Figure 7 A schematic diagram for calculating the relative height value of the resampling point;

[0049] Figure 8 A schematic diagram of the resampled data. DETAILED DESCRIPTION

[0050] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and understandable, the specific implementation methods of the present invention are described clearly and completely below in conjunction with the accompanying drawings. Obviously, the specific details described below are only part of the embodiments of the present invention, and the present invention can also be implemented in many other embodiments different from those described herein. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the protection scope of the present invention.

[0051] In this document, when an element is referred to as being "fixed to" another element, it may be directly on the other element or there may be an intermediate element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be an intermediate element at the same time. The directional words such as front, back, top, and bottom involved are defined by the positions of the parts in the drawings and the positions of the parts relative to each other, just for the clarity and convenience of expressing the technical solution. It should be understood that the use of the directional words should not limit the scope of protection claimed in the present invention.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0053] The input of the present invention is the original wafer topography data Data_origin collected by the sensor, which includes the horizontal coordinate X_origin, the vertical coordinate Y_origin, and the relative height value Z_origin of each data collection point. Figure 2 shown.

[0054] See also Figure 1 In one embodiment of the present invention, a surface topography data resampling method comprises the following steps:

[0055] Step S1: data preprocessing.

[0056] The goal of data preprocessing is to effectively remove global and local abnormal data generated during semiconductor wafer topography measurement, thereby improving the accuracy of subsequent data processing. This step includes global 3sigma filtering and / or neighborhood filtering. The following is a detailed description of each step:

[0057] Step S1-1: Global 3sigma filtering

[0058] The purpose of global 3sigma filtering is to remove global abnormal data caused by equipment errors or wafer edge shape during wafer topography measurement. The specific implementation method is as follows:

[0059] Step S1-1-1: Calculate the relative height mean and standard deviation

[0060] Perform statistical analysis on the relative height data Z of all sampling points and calculate the relative height mean Z of the relative height values mean and standard deviation Z std .

[0061]

[0062] Where n is the total number of sampling points, Z i is the relative height value of the i-th sampling point.

[0063] Step S1-1-2: Eliminate global abnormal data

[0064] For each sampling point, the relative height value Z i , determine whether it falls within the range Z mean ±n×Z std Within, wherein n is 1-3, and further, n is 2 or 3. If the relative height value of a sampling point exceeds this range, the point is considered to be a global abnormal point and is removed. This step is mainly used to remove abnormal values ​​caused by wafer edge fillets or non-measurement areas.

[0065] Step S1-1-3: Output intermediate data

[0066] After removing the global abnormal data, the remaining data set is recorded as Data_3sigma, which contains the coordinates and relative height information of all sampling points after 3sigma filtering:

[0067] Data_3sigma=(X_3sigma,Y_3sigma,Z_3sigma)

[0068] Among them, X_3sigma, Y_3sigma are the coordinates of the sampling points, and Z_3sigma is the relative height value after global 3sigma filtering.

[0069] Step S1-2: Neighborhood filtering

[0070] The purpose of neighborhood filtering is to remove local abnormal sampling data caused by the measurement environment. This step determines whether there is a local anomaly by evaluating the density of sampling points in the neighborhood around each sampling point. The specific implementation method is as follows:

[0071] Step S1-2-1: Neighborhood sampling point statistics

[0072] For each sampling point P i (X i ,Y i ,Z i), with this point as the center, define a radius R n Count the number of all sampling points within the spherical range, denoted as N i This neighborhood statistics process is performed by calculating the neighborhood i The Euclidean distance is used to determine whether the neighborhood contains other sampling points.

[0073] For all sampling points Pj(X j ,Y j ,Z j ), calculate P by the following formula j With P i The Euclidean distance d between ij :

[0074]

[0075] Among them, X j is the sampling point P j The horizontal axis, X i is the sampling point P i The horizontal axis, Y j is the sampling point P j The vertical coordinate, Y i is the sampling point P i The vertical coordinate of .

[0076] If a sampling point P j With the center point P i The distance d ij Less than R n , then P j Counted in P i In the neighborhood sampling point set of i .

[0077] Step S1-2-2: Eliminate local abnormal sampling points

[0078] For each sampling point, if the number of sampling points in its neighborhood is N i Less than the set number threshold N min , then the sampling point is considered as a local outlier and is removed.

[0079] Step S1-2-3: Output intermediate data

[0080] After removing local outliers, the remaining valid data set is recorded as Data_nr, which contains the coordinates and relative height information of the sampling points after neighborhood filtering:

[0081] Data_nr=(X_nr,Y_nr,Z_nr)

[0082] Among them, X_nr, Y_nr are the coordinates of the sampling points after neighborhood filtering, and Z_nr is the corresponding relative height value.

[0083] Through the combination of global 3sigma filtering and neighborhood filtering, the present invention can effectively remove global and local abnormal data that appear during the wafer topography measurement process. Global 3sigma filtering is mainly aimed at abnormal values ​​caused by structures such as wafer edges, while neighborhood filtering is aimed at abnormal points caused by local environmental interference. The final output Data_nr data set can provide high-precision basic data for subsequent wafer topography reconstruction, effectively improving the reliability of the measurement results. The preprocessed sampled data such as Figure 3 .

[0084] Step S2: Grid point division

[0085] The purpose of grid point division is to evenly divide the preprocessed sampled data Data_nr into multiple regular grid areas to provide anchor points for subsequent data resampling. This division process is performed on the XY plane. By setting a suitable step size, the entire sampling area is divided into equally spaced grids and the height values ​​of the grid points are initialized. The specific implementation method is as follows:

[0086] Step S2-1: Determine the range of sampling data

[0087] First, calculate the X-coordinate range and Y-coordinate range of the sampled data Data_nr after preprocessing to remove outliers, which are:

[0088] X min =min(Xnr),X max =max(Xnr)

[0089] Y min =min(Ynr),Y max =max(Ynr)

[0090] These values ​​represent the minimum and maximum coordinates of the sampled data on the X-axis and Y-axis, respectively.

[0091] Step S2-2: Determine the step size of the grid

[0092] According to application requirements, set the step size in the X direction and Y direction, denoted as X step and Y step The step size defines the spacing between grid points. The step size directly affects the density of the grid. The smaller the step size, the denser the grid. The choice of step size can be adjusted according to the distribution of sampling points and the measurement accuracy requirements.

[0093] Step S2-3: Generate grid point coordinates

[0094] Centered at (0,0), based on X step and Y step Generate an equally spaced grid in the X and Y directions. The range of the grid should be able to completely cover the minimum range of all sampling points, that is:

[0095] X grid ={X min ,X min +X step ,…,X max}

[0096] Y grid = {Y min ,Y min +Y step ,…,Y max}

[0097] The coordinates of the grid points are marked (X grid ,Y grid ), which form a regular grid structure in the XY plane.

[0098] Step S2-4: Initialize the height value of the grid point

[0099] For each generated grid point, initialize its height value Z grid The purpose of initialization is to provide a data anchor point for subsequent resampling. The height value Z of the grid point grid It will be updated in subsequent recalculation steps to ensure that the heights of the grid points reflect the actual measured topography information.

[0100] Step S2-5: Output grid data

[0101] After the grid division is completed, the output grid data set Data_grid contains the X coordinates, Y coordinates and initial height value Z of all grid points:

[0102] Data_grid={(X_grid,Y_grid,Z_grid)}

[0103] Where X_grid and Y_grid are the X-axis and Y-axis coordinates of the equally spaced grid points, and Z_grid is the corresponding initial height value.

[0104] like Figure 4 As shown in the figure, the grid point division effect shows uniformly distributed grid points, covering the entire range of the sampling area. By mapping the sampling points to these regular grids, the impact of uneven distribution of sampling points on subsequent topography measurements can be eliminated. Ultimately, grid point division provides a basis for resampling relative height information and data homogenization.

[0105] Step S3: Calculation of grid point weights

[0106] The grid point weight calculation aims to accurately estimate the relative height value Z of each grid point by using the information of the surrounding sampling points. grid [P] to ensure that the morphological information of the grid points can accurately reflect the actual morphology of the semiconductor wafer. This process uses a weight-based interpolation method, and the weights can be calculated in a variety of ways such as bilinear interpolation, Gaussian function or Sigmoid function. The specific implementation is as follows:

[0107] Step S3-1: Collection of sampling points

[0108] First, the sampling points in the preprocessed sampling data Data_nr are divided into corresponding grid areas according to their coordinates. For each grid point P(x, y), the sampling points pi falling around the grid are collected (usually the four nearest sampling points in the grid). The original sampled relative height value Z_nr[pi] of the sampling point pi will be used to calculate the relative height value Zgrid[P] of the grid point P.

[0109] Step S3-2: Calculate the distance and weight of the sampling points

[0110] For each grid point P(x,y), according to the X and Y distances D of the surrounding sampling points pi(X_i,Y_i) x and D y , calculate the contribution weight W of each sampling point to the grid point pi .

[0111] Step S3-2-1: Calculate distance

[0112] See Figure 5 , for the distance between each sampling point pi and the grid point P:

[0113] D x =|x-X_i|,D y =|y-Y_i|

[0114] Among them, x and y are the coordinates of the grid point P, and X_i and Y_i are the coordinates of the sampling point pi.

[0115] Step S3-2-2: Calculate weight

[0116] When computing the weights, different methods can be used to evaluate the contribution of each sample point to the grid point P.

[0117] Here are three common weight calculation methods:

[0118] 1. Bilinear interpolation weight calculation

[0119] Bilinear interpolation is based on the distance between the sampling point and the grid point in the X and Y directions, with weight Wpi The calculation formula is:

[0120]

[0121] Among them, X step and Y step is the mesh step size.

[0122] 2. Gaussian function weight calculation

[0123] The Gaussian function uses the square of the distance as input and the weight W pi The calculation formula is:

[0124]

[0125] Here, δ is the standard deviation parameter of the Gaussian distribution, which can be set according to specific needs, for example, δ=0.6 or δ=0.3.

[0126] 3. Sigmoid function weight calculation

[0127] The Sigmoid function combines the Euclidean distance between the sampling point and the grid point, and the weight W pi The calculation formula is:

[0128]

[0129] This formula smoothes the distance through the nonlinear mapping of the Sigmoid function.

[0130] Note: The weight calculation method is not limited to the above three methods, and other interpolation or weighting functions can be used according to specific application requirements.

[0131] Step S3-3. Calculate the relative height value of the grid point

[0132] After calculating the weight W of each sampling point to the grid point P pi After that, the relative height value Zgrid[P] of the grid point P can be calculated by weighted average. The formula is as follows:

[0133]

[0134] in:

[0135] Z_nr[pi] is the original sampled relative height value of sampling point pi;

[0136] W pi is the contribution weight of sampling point pi to grid point P;

[0137] N is the number of sampling points around the grid point.

[0138] Through the above calculation, the relative height value Z of the grid point grid [P] can reflect the morphological characteristics within the sampling area, and because of the use of weight calculation, it can fully consider the spatial relationship between the sampling points and the grid points, making the estimated morphological data more accurate.

[0139] Step S3-4: Complete the calculation of all grid points

[0140] The above calculation method is applied to each grid point until the relative height value Z of all grid points is grid All calculations are completed. The resulting grid data set Data_grid contains the coordinates of each grid point (X grid ,Y grid ) and the corresponding relative height value Z grid , these data will be used for further analysis and reconstruction of semiconductor wafer morphology.

[0141] Step S4: Resampling point setting

[0142] The purpose of setting the resampling points is to generate a regular sampling point array Data_co according to the set sampling interval Sample_interval, which covers the entire surface area of ​​the semiconductor wafer and trims the edges according to the specific specifications of the wafer to ensure that the sampling point array only covers the effective wafer area.

[0143] Step S4-1: Resampling point array generation

[0144] Step S4-1-1: Set the resampling point interval

[0145] First, the density of the resampling points is determined according to the preset sampling interval Sample_interval. The sampling interval defines the distance between each resampling point, and the size of the interval will affect the distribution density and measurement accuracy of the sampling points.

[0146] Step S4-1-2: Determine the coverage of the wafer

[0147] Semiconductor wafers are usually circular, so the resampling point array needs to cover the entire circular area. Let the radius of the wafer be R, with (0,0) as the center, and the range of the resampling points be:

[0148] -R≤x≤R,-R≤y≤R

[0149] Based on this range, resampled points covering the entire wafer are generated in the X-axis and Y-axis directions.

[0150] Step S4-1-3: Generate a regular resampling point array

[0151] The coordinates of the resampling points are generated in a regular grid array with an interval of Sample_interval, covering the entire wafer range. The generated resampling point coordinates are:

[0152] X_rs={-R,-R+Sample_interval,…,R}

[0153] Y_rs={-R,-R+Sample_interval,…,R}

[0154] These points form a regular array of sampling points centered at (0,0).

[0155] Step S4-2: Edge trimming

[0156] Since the wafer is circular and the generated resampled point array covers a rectangular area, the array needs to be edge trimmed to ensure that only the resampled points that fall within the wafer range are retained.

[0157] Step S4-2-1: Determine whether the sampling point is inside the wafer

[0158] For each resampled point (X_i, Y_i) generated, calculate the distance between the point and the center point (0,0):

[0159]

[0160] If the distance d_i≤R, the sampling point is retained; otherwise, the point is considered to be outside the wafer and is removed.

[0161] Step S4-2-2: Generate a trimmed resampled point dataset

[0162] After edge trimming of the data set, the resulting resampled point array Data_co contains all resampled points within the wafer range:

[0163]

[0164] In this way, the resampled point array covers the entire active area of ​​the wafer and removes points beyond the wafer boundary.

[0165] like Figure 6 As shown in the figure, the final resampling point array is a regular dot matrix, which covers the entire semiconductor wafer. By adjusting Sample_interval, the density of the sampling points can be controlled to ensure that each area on the wafer surface can be evenly sampled, thereby providing high-quality resampling data for subsequent topography measurement.

[0166] Step S5: Resampling

[0167] Based on each resampling point in the resampling point array, the relative height values ​​Z of the four grid points around it are used P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q , calculate the relative height value Z_q of each resampling point, and thus generate the resampled data Data_rs(X_q,Y_q ， Z_q).

[0168] Similarly, according to the distance between the sampling point and the grid point, any method of bilinear interpolation, Gaussian function or Sigmoid function is used to calculate the contribution weight Wq of the four grid points around the resampling point to the resampling point. The bilinear interpolation method is used as an example for explanation.

[0169] Resampling calculates the relative height value of each resampling point through a bilinear interpolation algorithm, and finally obtains accurate resampling data Data_rs. This process will use the grid data of the sampling point to interpolate the topography data of each resampling point to ensure that the relative height value of each point accurately reflects the topography information of the wafer.

[0170] Step S5-1: Determine the grid where the resampling point is located

[0171] For each resampled point q(X_q,Y_q), we first need to determine the grid it is in. The grid consists of four vertices P1(x P1 ,y P1 ),P2(x P2 ,y P2 ),P3(x P3 ,y P3 ),P4(x P4 ,y P4 ) is surrounded by. Figure 7 The resampled points q are shown to lie within a quadrilateral grid.

[0172] The vertex coordinates of the mesh are determined by the following conditions:

[0173] X_q-x P1 >0 and X_q-x P2 ≤0 (the resampling point is between P1 and P2)

[0174] Y_q-y P1 >0 and Y_q-y P3 ≤0 (the resampling point is between P1 and P3)

[0175] After determining the grid to which the resampled point q belongs, the relative height values ​​Z of the four vertices of the grid P1 ,Z P2 ,ZP3 ,Z P4 Will be used for interpolation calculations.

[0176] Step S5-2: Calculate the relative distance between the resampling point and the grid point

[0177] For a given grid, calculate the relative distances d_x and d_y of the resampled point q relative to the vertex P1 in the X and Y directions:

[0178] d_x=X_q-xP1,d_y=Y_q-yP1

[0179] in:

[0180] d_x is the distance of point q relative to P1 in the X direction.

[0181] d_y is the distance of point q relative to P1 in the Y direction.

[0182] Step S5-3: Bilinear interpolation calculation

[0183] Use the relative height values ​​Z of the four grid points P1 ,Z P2 ,Z P3 ,Z P4 As well as the relative distances d_x and d_y of the resampling points, the relative height value Z_q of the resampling point q is calculated by bilinear interpolation. The calculation formula is as follows:

[0184] Z_q=[Z P1 *(X step -d_x)*(Y step -d_y)+Z P2 *d_x*(Y step -d_y)+Z P3 *d_x*d_y+Z P4 *(X step -d_x)*d_y] / (X step *Y step )

[0185] in:

[0186] X step and Y step are the step sizes of the grid in the X and Y directions respectively.

[0187] Z P1 ,Z P2 ,Z P3 ,Z P4 The relative height values ​​of the four vertices of the mesh.

[0188] Step S5-4: Complete the calculation of all resampling points

[0189] According to the above steps, bilinear interpolation is performed on each resampling point to obtain the data Data_rs of all resampling points. This data set contains the coordinates (X_q, Y_q) of all resampling points and the corresponding relative height value Z_q. The resampled data is as follows Figure 8 .

[0190] The present invention application also discloses a wafer thickness measurement method, comprising the following steps:

[0191] Step S21: measuring the topographic data Data_chuck_nr and Data_wafer_nr of the upper surface of the carrier and the upper surface of the wafer respectively;

[0192] Step S22: resample Data_chuck_nr and Data_wafer_nr respectively using the surface topography data resampling method in the above embodiment to obtain resampled data Data_chuck_rs and Data_wafer_rs;

[0193] Step S23: Data_wafer_rs is subtracted from Data_chuck_rs point by point to obtain wafer thickness data of wafer topography. Then, the relevant parameters are calculated according to the measurement standard and the wafer topography image is output.

[0194] The surface topography data resampling method of the present invention has the following beneficial effects:

[0195] 1. Outlier removal and homogenization processing: It can effectively remove outliers in wafer data, achieve data homogenization processing, and reduce uncertainty in measurement.

[0196] 2. Accurate morphological data: Through the improved resampling method, data that accurately reflects the surface morphology of the wafer can be quickly obtained, thereby improving the measurement accuracy.

[0197] 3. Reduce the impact of data sparsity: The resampled data can significantly reduce the impact of the sparsity of the original sampled data on the measurement accuracy, ensuring that the measurement results are more reliable.

[0198] 4. Alignment and resampling of carrier and wafer data: The carrier and wafer data at different sampling points can be resampled to achieve the correspondence of data points, thereby simplifying the calculation process of wafer thickness.

[0199] 5. Easy to implement: You only need to input the original data collected by the sensor, and through simple settings, the entire resampling process can be automatically completed. It is easy to use and reduces human intervention.

[0200] 6. High compatibility: This method is compatible with the resampling of morphological data of semiconductor wafers not less than 12 inches, and is suitable for the resampling of surface three-dimensional data of products of any shape, and has a wide range of applications.

[0201] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A surface topography data resampling method, characterized in that: The following steps are involved: Preprocess the original shape data of the object to be measured, remove abnormal data, and obtain the preprocessed sampling data Data_nr (X_nr, Y_nr, Z_nr); Performing regional segmentation on the preprocessed sampling data Data_nr to obtain segmented grid data Data_grid (X_grid, Y_grid) with equal spacing in the same direction; Based on the original sampled relative height value Z_nr[pi] of the sampling points around each grid point and its contribution weight W to the grid point pi , the relative height value Z of each grid point is obtained by weighted calculation grid [P]; Generate a resampling point array Data_co (X_q, Y_q) covering the object under test according to the resampling interval; Based on each resampling point in the resampling point array, the relative height values ​​Z of the four grid points around it are used P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q , calculate the relative height value Z_q of each resampling point, and thus generate the resampled data Data_rs(X_q,Y_q ， Z_q).

2. The surface topography data resampling method according to claim 1, characterized in that: The method of preprocessing the original shape data of the measured object, removing abnormal data, and obtaining the preprocessed sampling data Data_nr (X_nr, Y_nr, Z_nr) includes the following steps: Calculate the global mean Z of the sampled data mean and standard deviation Z std ; Eliminate the relative height value Z_nr that is not in the range Z mean ±n×Z std Abnormal data within, where n is 1-3.

3. The surface topography data resampling method according to claim 1, characterized in that: The method of preprocessing the original shape data of the measured object, removing abnormal data, and obtaining the preprocessed sampling data Data_nr (X_nr, Y_nr, Z_nr) includes the following steps: Count the number of sampling points within the neighborhood of radius R_n for each sampling point; If the number of sampling points in the neighborhood of a sampling point is less than the preset threshold N_min, the sampling point is removed.

4. The surface topography data resampling method according to claim 1, characterized in that: The contribution weight W of the sampling point to the grid point pi The calculation includes: According to the distance between the sampling point and the grid point, use any method of bilinear interpolation, Gaussian function or Sigmoid function to calculate the contribution weight W of the sampling point to the grid point. pi .

5. The surface topography data resampling method according to claim 1, characterized in that: The relative height value Z of each grid point is obtained by weighted calculation grid [P] Includes: By weighted averaging, the original sampled relative height value Z_nr[pi] of the sampling points around the grid point is added to its contribution weight W pi Combined, the relative height value Z of each grid point is calculated grid [P].

6. The surface topography data resampling method according to claim 1, characterized in that: The generating of the resampling point array Data_co(X_q, Y_q) covering the measured object according to the resampling interval includes the following: For each resampled point (X_i, Y_i) generated, calculate the distance d_i between the point and the center point (0,0); If d_i≤R, keep the sampling point; If d_i>R, the point is considered to be outside the object being measured and is removed; Wherein, R is the radius of the object being measured.

7. The surface topography data resampling method according to claim 1, characterized in that: The method is based on each resampling point in the resampling point array, using the relative height values ​​Z of the four grid points around it. P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q , calculate the relative height value Z_q of each resampling point, and also include the following steps: Calculate the relationship between each resampled point q(X_q,Y_q) and its surrounding four vertices P1(x P1 ,y P1 ),P2(x P2 ,y P2 ),P3(x P3 ,y P3 ),P4(x P4 ,y P4 ) between the two sides; If the condition X_q-x is met P1 >0 and X_q-x P2 ≤0, and Y_q-y P1 >0 and Y_q-y P3 ≤0, then the resampling point q is located at the four vertices P1(x P1 ,y P1 ),P2(x P2 ,y P2 ),P3(x P3 ,y P3 ),P4(x P4 ,y P4 ) within the grid formed by .

8. The surface topography data resampling method according to claim 1, characterized in that: The contribution weights W of the four grid points around the resampling point to the resampling point q The calculation includes: According to the distance between the resampling point and the grid point, use any method of bilinear interpolation, Gaussian function or Sigmoid function to calculate the contribution weight W of the four grid points around the resampling point to the resampling point. q .

9. The surface topography data resampling method according to claim 8, characterized in that: The method is based on each resampling point in the resampling point array, using the relative height values ​​Z of the four grid points around it. P1 ,Z P2 ,Z P3 ,Z P4 and its corresponding contribution weight W q , calculate the relative height value Z_q of each resampling point, including the following steps: Calculate the relative distances d_x and d_y between the resampled point and the four surrounding grid points; Use the relative height values ​​Z of the four grid points P1 ,Z P2 ,Z P3 ,Z P4 As well as the relative distances d_x and d_y of the resampling points, the relative height value Z_q of the resampling point q is calculated by bilinear interpolation. The calculation formula is as follows: Z_q=[Z P1 *(X step -d_x)*(Y step -d_y)+Z P2 *d_x*(Y step -d_y)+Z P3 *d_x*d_y+Z P4 *(X step -d_x)*d_y] / (X step *Y step ) in: X step and Y step are the step sizes of the grid in the X and Y directions respectively; Z P1 ,Z P2 ,Z P3 ,Z P4 The relative height values ​​of the four vertices of the mesh.

10. A wafer thickness measurement method, characterized in that: The steps include: Measure the topographic data Data_chuck_nr and Data_wafer_nr of the upper surface of the carrier and the upper surface of the wafer respectively; Resample Data_chuck_nr and Data_wafer_nr respectively using the surface topography data resampling method as claimed in any one of claims 1 to 9 to obtain resampled data Data_chuck_rs and Data_wafer_rs; Data_wafer_rs is subtracted from Data_chuck_rs point by point to obtain the wafer thickness data of the wafer topography.

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