Method for evaluating edge profile of wafer

Abstract

Provided is a method for evaluating an edge profile of a wafer, which is capable of quantitatively evaluating a degree of similarity between edge profiles at two locations. The edge profiles at the two locations are measured (step S1). X-Y coordinates of two items of edge profile data are acquired (step S2). The X-Y coordinates are converted into Rθ polar coordinates (step S3). The two items of edge profile data are displayed on an Rθ orthogonal coordinate plane with the horizontal axis as θ and the vertical axis as R (step S4). On the Rθ orthogonal coordinate plane, the average value of each R is subtracted from each item of edge profile data (step S5). On the Rθ orthogonal coordinate plane, a difference R' of R is taken between the two items of edge profile data (step S6). As an example, a root mean square RMS of R' is calculated (step S7). The degree of similarity between the edge profiles is evaluated on the basis of the RMS (step S8).

Description

Method for Evaluating End Face Shape of Wafer

[0001] The present invention relates to a method for evaluating the end face shape of a wafer.

[0002] There is known and commercially available an end face shape measuring device for measuring the end face shape of a wafer as described in Patent Document 1, which is also called an edge profiler. In this end face shape measuring device, the end face shape of the wafer is measured at an arbitrary position in the circumferential direction on the outer peripheral portion of the wafer. For example, with the thickness center line of the wafer as the X-axis and the thickness direction of the wafer as the Y-axis, the end face shape (edge profile) is displayed on the XY orthogonal coordinate plane.

[0003] Japanese Patent Application Laid-Open No. 2019-36700

[0004] In various wafers such as silicon wafers serving as substrates for manufacturing semiconductor devices, there are various requirements from customers regarding the end face shape. For example, it is a natural requirement to make the end face shape uniform in the circumferential direction on the outer peripheral portion of the wafer.

[0005] Also, there may be a case where it is required to align the end face shape at the notch (V-shaped groove formed to indicate the crystal orientation) of the wafer with the end face shape at a position other than the notch (referred to as "edge" in this specification). In this case, the end face shape at the notch and the end face shape at the edge are measured with an end face shape measuring device, and the two end face shapes (edge profiles) are superimposed and displayed on the above-mentioned XY orthogonal coordinate plane, and an evaluator visually confirms this to evaluate whether the two end face shapes are similar. When it is evaluated that the two end face shapes are not similar, the conditions for grinding or polishing the end face can be adjusted.

[0006] Furthermore, there are cases where a wafer is required to have the same edge shape as a given wafer. In this case as well, the edge shape of the given wafer and the edge shape of the manufactured wafer can be measured using an edge shape measuring device, and the two edge shapes (i.e., one on each wafer) can be superimposed and displayed on the XY Cartesian coordinate plane. An evaluator can then visually check this and evaluate whether the two edge shapes are similar or not. If the two edge shapes are evaluated as not being similar, the grinding or polishing conditions for the edge of the manufactured wafer can be adjusted.

[0007] However, this evaluation method has the drawback that it cannot quantify the degree of similarity of the end face shapes, raising concerns about variability in evaluations depending on the evaluator.

[0008] In view of the above-mentioned problems, the present invention aims to provide a method for evaluating the edge shape of a wafer that can quantitatively evaluate the degree of similarity between the edge shapes of two locations.

[0009] To solve the above problems, the inventors have conducted diligent research and discovered the following method that can quantitatively evaluate the degree of similarity between two end face shapes. First, the end face shapes of the two locations are measured. Then, the XY coordinates of the two end face shape data are converted to Rθ polar coordinates. Next, the two end face shape data are displayed on an Rθ Cartesian coordinate plane with θ on the horizontal axis and R on the vertical axis. Then, on the Rθ Cartesian coordinate plane, the average value of R for each end face shape data is subtracted from each end face shape data. Next, on the Rθ Cartesian coordinate plane, the difference R' between the two end face shape data is taken. Then, as an example, the root mean square RMS of R' is calculated. Finally, the degree of similarity between the end face shapes is evaluated based on the calculated RMS. With this method, the smaller the RMS (i.e., the closer it is to zero), the higher the similarity between the two end face shapes can be evaluated.

[0010] The gist of the present invention, completed based on the above findings, is as follows: [1] A step of measuring the edge shape of the first wafer at a first position on the outer periphery of the first wafer and acquiring first edge shape data; A step of measuring the edge shape of the second wafer at a second position on the outer periphery of the second wafer and acquiring second edge shape data; A step of acquiring the XY coordinates of the first edge shape data and the second edge shape data, with the thickness centerlines of the first and second wafers as the X axis and the thickness direction of the first and second wafers as the Y axis; A step of converting the acquired XY coordinates of the first edge shape data and the second edge shape data into Rθ polar coordinates, with the origin of the XY Cartesian coordinate plane as the pole and the X axis as the starting line; A step of superimposing the Rθ polar coordinates of the first edge shape data and the second edge shape data on an Rθ Cartesian coordinate plane with the horizontal axis as θ and the vertical axis as R, and displaying them to obtain a first edge shape graph and a second edge shape graph, respectively. A method for evaluating the edge shape of a wafer, comprising: a step of obtaining a first edge shape correction graph and a second edge shape correction graph, respectively, by subtracting the average value of R in each graph from the R values ​​of each data point included in the first edge shape graph and the second edge shape graph on the Rθ orthogonal coordinate plane; a step of obtaining a difference graph with the horizontal axis as θ and the vertical axis as the difference of R R' by taking the difference of R at the same θ on the Rθ orthogonal coordinate plane with respect to the first edge shape correction graph and the second edge shape correction graph; a calculation step of calculating the arithmetic mean of the absolute values ​​of R', or the 2nth root of the arithmetic mean of the values ​​obtained by raising R' to the power of 2n (where n is a natural number) from the difference graph; and a step of evaluating the degree of similarity between the edge shape of the first wafer at the first position and the edge shape of the second wafer at the second position based on the calculated value.

[0011] [2] The method for evaluating the end face shape of a wafer according to [1], wherein the first wafer and the second wafer are the same wafer, and the first position and the second position are different circumferential positions.

[0012] [3] The method for evaluating the edge shape of a wafer according to [2] above, wherein the first position is the position of a notch and the second position is a position other than a notch.

[0013] [4] The method for evaluating the edge shape of a wafer according to [1] above, wherein the first wafer and the second wafer are different wafers.

[0014] [5] The method for evaluating the edge shape of the wafer according to [4] above, wherein both the first position and the second position are positions other than a notch.

[0015] [6] The method for evaluating the edge shape of wafers according to [4], wherein the first wafer and the second wafer have different thicknesses.

[0016] [7] The method for evaluating the edge shape of a wafer according to any one of the above items [1] to [6], wherein in the calculation step, n=1 and the root mean square of R' is calculated.

[0017] The wafer edge shape evaluation method according to the present invention makes it possible to quantitatively evaluate the degree of similarity between the edge shapes of two locations.

[0018] This is a flowchart illustrating a method for evaluating the edge shape of a wafer according to one embodiment of the present invention. This figure shows an example of the measurement position of the edge shape in one embodiment of the present invention. This is an example of the edge shape (edge ​​profile) on the XY Cartesian coordinate plane for two locations in Figure 2. This is an edge shape graph shown on the Rθ Cartesian coordinate plane by converting the XY coordinates in Figure 3A to Rθ polar coordinates. This is an edge shape correction graph obtained by subtracting the average value of R in each graph from the R value of each data point included in the edge shape graph in Figure 3B. This is a difference graph obtained by taking the difference of R at the same θ for the edge shape correction graph in Figure 3C. This figure shows the measurement position of the edge shape in Examples 1 and 2. This is the edge shape (edge ​​profile) on the XY Cartesian coordinate plane in Example 1. This is the edge shape (edge ​​profile) on the XY Cartesian coordinate plane in Example 2.

[0019] A method for evaluating the edge shape of a wafer according to one embodiment of the present invention will be described below with reference to Figures 1, 2, and 3A to 3D.

[0020] In the wafer edge shape evaluation method according to this embodiment, the degree of similarity between the edge shape at a first position on the outer periphery of the first wafer and the edge shape at a second position on the outer periphery of the second wafer is evaluated. Here, the first wafer and the second wafer are the same wafer, and the first position and the second position are different circumferential positions. More specifically, as shown in Figure 2, this embodiment will be explained using the case where the first position is a notch position and the second position is an edge (a position other than a notch) as an example.

[0021] [Step S1] First, in step S1 of Figure 1, the edge shape at two locations is measured. Specifically, the edge shape (edge ​​profile) of the first wafer is measured at a first position in the circumferential direction on the outer periphery of the first wafer, and the first edge shape data is obtained. Also, the edge shape (edge ​​profile) of the second wafer is measured at a second position on the outer periphery of the second wafer, and the second edge shape data is obtained. In the example shown in Figure 2, the edge shape of the notch and the edge of the same wafer are measured. Note that "edge shape at a predetermined position on the outer periphery of the wafer" means the shape of the wafer edge in a cross-section in the thickness direction passing through the in-plane center of the wafer and the predetermined position on the outer periphery.

[0022] [Step S2] Next, in step S2 of Figure 1, the XY coordinates of the two end face shape data are obtained. That is, the XY coordinates of the first end face shape data and the second end face shape data are obtained with the thickness centerlines of the first and second wafers as the X axis and the thickness direction of the first and second wafers as the Y axis. With respect to the XY coordinates of the first end face shape data, the position X=0 is set as the origin, located half the thickness of the first wafer inward from the outermost edge in the X direction of the first wafer, and the position Y=0 is set as the midpoint of the thickness of the first wafer. Similarly, with respect to the XY coordinates of the second end face shape data, the position X=0 is set as the origin, located half the thickness of the second wafer inward from the outermost edge in the X direction of the second wafer, and the position Y=0 is set as the midpoint of the thickness of the second wafer. Figure 3A shows the notch end face shape and edge end face shape of the same wafer superimposed on the XY Cartesian coordinate plane, as in the example shown in Figure 2. In Figure 3A, since two end face shapes of the same wafer are displayed, it can be seen that the position of the outermost edge in the X direction coincides for the two end face shapes, and that their thicknesses are also equal. Note that the distance from the outermost edge in the X direction of each wafer to X=0 is not limited to half the thickness of the wafer, as long as the entire end face shape of the chamfered portion is displayed on the XY Cartesian coordinate plane.

[0023] In the method where evaluators visually inspect Figure 3A and evaluate whether the two end face shapes are similar, the degree of similarity of the end face shapes cannot be quantified, raising concerns about variability in evaluations depending on the evaluator. Therefore, in this embodiment, the degree of similarity of the two end face shapes is quantitatively evaluated by performing the following steps.

[0024] [Steps S3, S4] Next, in step S3 of Figure 1, the XY coordinates are converted to Rθ polar coordinates. That is, the XY coordinates of the first end face shape data and the second end face shape data obtained in step S2 are converted to Rθ polar coordinates, with the origin in the XY Cartesian coordinate plane as the pole and the X-axis as the starting line.

[0025] Next, in step S4 of Figure 1, two end face shape data are displayed on the Rθ Cartesian coordinate plane, where the horizontal axis is θ and the vertical axis is R. That is, the Rθ polar coordinates of the first end face shape data and the second end face shape data are superimposed on the Rθ Cartesian coordinate plane, where the horizontal axis is θ and the vertical axis is R, to obtain the first end face shape graph and the second end face shape graph, respectively. Figure 3B is an end face shape graph shown on the Rθ Cartesian coordinate plane after converting the XY coordinates of Figure 3A to Rθ polar coordinates. The range of θ is not particularly limited as long as the entire end face shape of the chamfered portion is displayed on the Rθ Cartesian coordinate plane, but considering the position of the origin of the XY Cartesian coordinate plane shown in Figure 3A, it is preferable to set it to -90° ≤ θ ≤ 90°.

[0026] [Step S5] Next, in step S5 of Figure 1, the average value of R is subtracted from each end face shape data on the Rθ Cartesian coordinate plane. That is, on the Rθ Cartesian coordinate plane, the average value of R in each graph is subtracted from the R value of each data point included in the first end face shape graph and the second end face shape graph to obtain the first end face shape correction graph and the second end face shape correction graph, respectively. Figure 3C is an end face shape correction graph obtained by subtracting the average value of R in each graph from the R value of each data point included in the end face shape graph of Figure 3B. That is, the notch end face shape correction graph is obtained by subtracting the average value of R in the end face shape graph from the R value of each data point included in the notch end face shape graph of Figure 3B. Similarly, the edge end face shape correction graph is obtained by subtracting the average value of R in the end face shape graph from the R value of each data point included in the edge end face shape graph of Figure 3B. As a result, the reference value of R is aligned to zero in each end face shape correction graph. The average value of R in the first and second end face shape graphs is calculated by dividing the sum of the R values ​​for all data points included in each graph by the number of data points.

[0027] [Step S6] Next, in step S6 of Figure 1, the difference R' of R is taken between the two end face shape data on the Rθ Cartesian coordinate plane. That is, with respect to the first end face shape correction graph and the second end face shape correction graph, the difference of R at the same θ is taken on the Rθ Cartesian coordinate plane to obtain a difference graph with θ on the horizontal axis and the difference R' of R on the vertical axis. Figure 3D is a difference graph (notch-edge difference graph) obtained by taking the difference of R at the same θ with respect to the end face shape correction graph of Figure 3C. Note that the value of R in the second end face shape correction graph may be subtracted from the value of R in the first end face shape correction graph, or the value of R in the first end face shape correction graph may be subtracted from the value of R in the second end face shape correction graph.

[0028] [Step S7] Next, in step S7 (calculation process) of Figure 1, as an example, the root mean square RMS of R' is calculated from the difference graph. RMS is calculated as shown in the following formula, where each value (x １ , x ２ ,...x ｎ It is defined as the square root of the arithmetic mean of the values ​​obtained by squaring ( ). Therefore, the root mean square RMS is calculated from each R' value that makes up the difference graph.

[0029] As shown in Figure 3D, the difference graph may contain both positive and negative ranges for R'. However, by calculating the root mean square (RMS) of R', an index based on the magnitude of the absolute value of R' across the entire range can be calculated, regardless of whether the value of R' at each point is positive or negative. This allows RMS to be used as an index of similarity in end face shapes.

[0030] Furthermore, the index of similarity of end face shapes is not limited to RMS, as long as it is an index based on the magnitude of the absolute value of R'. For example, the arithmetic mean of the absolute values ​​of R' can be calculated from the difference graph and used as an index of similarity. Alternatively, the 2nth root of the arithmetic mean of the values ​​obtained by raising R' to the power of 2n (where n is a natural number) can be calculated from the difference graph and used as an index of similarity. When n=1, the above RMS will be calculated.

[0031] [Step S8] Next, in step S8 of Figure 1, the degree of similarity of the end face shapes is evaluated based on RMS. Not limited to RMS, the degree of similarity between the end face shape at the first position of the first wafer and the end face shape at the second position of the second wafer is evaluated based on the value calculated in the calculation step of step S7. In this embodiment, the smaller the calculated value (i.e., the closer to zero), the higher the similarity between the two end face shapes can be evaluated.

[0032] [Technical Significance of the Invention] The first feature of the present invention is the conversion of XY coordinates to Rθ polar coordinates for two end face shape data (conversion from Figure 3A to Figure 3B by steps S3 and S4). In the XY Cartesian coordinate plane of Figure 3A, the upper part of the X-axis represents the difference in the end face shape of the upper half of the wafer, and the lower part of the X-axis represents the difference in the end face shape of the lower half of the wafer. In this case, at a certain position on the X-axis, the difference in the end face shape of the upper half and the difference in the end face shape of the lower half are displayed simultaneously, making it difficult to set an index for the similarity of the end face shapes. In contrast, in the Rθ Cartesian coordinate plane of Figure 3B obtained after conversion to Rθ polar coordinates, the range of -90°≦θ≦0° represents the difference in the end face shape of the lower half of the wafer, and the range of 0°≦θ≦90° represents the difference in the end face shape of the upper half of the wafer. In this case, the difference in the end face shape of the upper half of the wafer and the difference in the end face shape of the lower half of the wafer can be separated on the θ axis. Therefore, by steps S5 to S7 described above, an index of similarity of end face shapes can be set.

[0033] If the only requirement is to separate the differences in the upper and lower end face shapes, one could consider taking the difference in the X-axis direction on the XY Cartesian coordinate plane shown in Figure 3A. However, in this case, when comparing the end face shapes between two wafers of different thicknesses, there will be a range where the difference cannot be calculated, making accurate shape comparison difficult. In contrast, according to the present invention, which converts to Rθ polar coordinates, it is possible to accurately evaluate the similarity of the end face shapes even when comparing the end face shapes between two wafers of different thicknesses.

[0034] The second feature of the present invention is that step S5, which subtracts the average value of R, sets the reference value of R to zero in the edge shape correction graph. This makes it possible to evaluate that the closer the calculated RMS is to zero, the higher the similarity of the edge shapes. If RMS is calculated without performing step S5, a large RMS value will be calculated regardless of whether the edge shapes are similar or not, making it difficult to accurately evaluate the similarity. Furthermore, by performing step S5, it is possible to accurately evaluate the similarity of the edge shapes even when comparing the edge shapes of two wafers with different thicknesses.

[0035] [Other Evaluation Methods] Figures 2 and 3A to 3D show examples of evaluating the similarity between the notch end face shape and the edge end face shape on the same wafer, but the present invention is not limited thereto. For example, the similarity between the end face shapes of two different edges in the circumferential direction on the same wafer may be evaluated.

[0036] Furthermore, the first wafer and the second wafer may be different wafers. That is, the similarity of the edge shapes of two different wafers can also be evaluated. For example, the edge shape of one wafer can be compared with the edge shape of a different wafer. In this case, the first wafer and the second wafer may have different thicknesses.

[0037] [Wafer] In this embodiment, the wafer to be evaluated may be a polished wafer obtained by grinding and / or polishing a wafer cut from a single-crystal ingot, or it may be an annealed wafer obtained by further annealing. These wafers are preferably single-crystal silicon wafers.

[0038] We prepared silicon wafers with two different end face shapes (round and short bevel).

[0039] [Example 1] For a round-shaped silicon wafer, the end face shape was measured with an edge profiler at three locations shown in Fig. 4 (taking the notch position as 0°, the positions of 0°, 135°, and 180°). Fig. 5 shows the end face shape (edge profile) on the XY orthogonal coordinate plane.

[0040] For the combination of the end face shape at the 180° position and the end face shape at the 0° position, and the combination of the end face shape at the 180° position and the end face shape at the 135° position, the root mean square (RMS) was calculated according to the steps of the present invention shown in Fig. 1. The results are shown in Table 1.

[0041]

[0042] From the results shown in Table 1, it can be evaluated that the end face shape at the 180° position and the end face shape at the 135° position have a high similarity, while the end face shape at the 180° position and the end face shape at the 0° position have a low similarity.

[0043] [Example 2] For a short bevel-shaped silicon wafer, the end face shape was measured with an edge profiler at three locations shown in Fig. 4 (taking the notch position as 0°, the positions of 0°, 135°, and 180°). Fig. 6 shows the end face shape (edge profile) on the XY orthogonal coordinate plane.

[0044] For the combination of the end face shape at the 180° position and the end face shape at the 0° position, and the combination of the end face shape at the 180° position and the end face shape at the 135° position, the root mean square (RMS) was calculated according to the steps of the present invention shown in Fig. 1. The results are shown in Table 2.

[0045]

[0046] From the results shown in Table 2, it can be evaluated that the end face shape at the 180° position and the end face shape at the 135° position have a high similarity, while the end face shape at the 180° position and the end face shape at the 0° position have a low similarity.

[0047] The method for evaluating the end face shape of a wafer according to the present invention can be applied to the manufacture of various wafers such as silicon wafers.

[0048] Furthermore, the wafer edge shape evaluation method according to the present invention can improve the yield of semiconductor devices by suppressing evaluation variability. Improved yield enhances the manufacturing efficiency of semiconductor products, enabling the production of more high-quality products, contributing to the promotion of technological innovation and the sustainable development of the industry. Improved yield also contributes to the efficient use of resources by reducing material waste in the semiconductor product manufacturing process. Moreover, improved yield reduces energy waste in the semiconductor product manufacturing process, consequently contributing to the reduction of greenhouse gas emissions.

[0049] In other words, the present invention can contribute, for example, to Sustainable Development Goals (SDGs) "Goal 9: Build industry, innovation and infrastructure," "Goal 12: Ensure sustainable consumption and production," and "Goal 13: Address climate change."

Claims

1. A step of obtaining first end face shape data by measuring the end face shape of the first wafer at a first position on the outer periphery of the first wafer; a step of obtaining second end face shape data by measuring the end face shape of the second wafer at a second position on the outer periphery of the second wafer; a step of obtaining the XY coordinates of the first end face shape data and the second end face shape data, with the thickness centerlines of the first and second wafers as the X axis and the thickness direction of the first and second wafers as the Y axis; a step of converting the obtained XY coordinates of the first end face shape data and the second end face shape data into Rθ polar coordinates, with the origin of the XY Cartesian coordinate plane as the pole and the X axis as the starting line; a step of displaying the Rθ polar coordinates of the first end face shape data and the second end face shape data superimposed on an Rθ Cartesian coordinate plane with the horizontal axis as θ and the vertical axis as R, to obtain a first end face shape graph and a second end face shape graph, respectively. A method for evaluating the edge shape of a wafer, comprising: a step of obtaining a first edge shape correction graph and a second edge shape correction graph, respectively, by subtracting the average value of R in each graph from the R values ​​of each data point included in the first edge shape graph and the second edge shape graph on the Rθ orthogonal coordinate plane; a step of obtaining a difference graph with the horizontal axis as θ and the vertical axis as the difference of R R' by taking the difference of R at the same θ on the Rθ orthogonal coordinate plane with respect to the first edge shape correction graph and the second edge shape correction graph; a calculation step of calculating the arithmetic mean of the absolute values ​​of R', or the 2nth root of the arithmetic mean of the values ​​obtained by raising R' to the power of 2n (where n is a natural number) from the difference graph; and a step of evaluating the degree of similarity between the edge shape of the first wafer at the first position and the edge shape of the second wafer at the second position based on the calculated value.

2. The method for evaluating the end face shape of a wafer according to claim 1, wherein the first wafer and the second wafer are the same wafer, and the first position and the second position are different circumferential positions.

3. The method for evaluating the edge shape of a wafer according to claim 2, wherein the first position is the position of a notch, and the second position is a position other than a notch.

4. The method for evaluating the end face shape of a wafer according to claim 1, wherein the first wafer and the second wafer are different wafers.

5. The method for evaluating the edge shape of a wafer according to claim 4, wherein both the first position and the second position are positions other than a notch.

6. The method for evaluating the end face shape of a wafer according to claim 4, wherein the first wafer and the second wafer have different thicknesses.

7. The method for evaluating the edge shape of a wafer according to any one of claims 1 to 6, wherein in the calculation step, n = 1 and the root mean square of R' is calculated.

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