Material analysis method

Abstract

The present invention provides a material analysis method. Multiple wafers processed from multiple ingots are measured by a measuring instrument to obtain the average bow value of the wafers after processing of each ingot and the multiple full width at half maximum (FWHM) values of each wafer. Key factors corresponding to each ingot are calculated based on the FWHM values of each wafer. A regression equation is obtained by using these key factors and the average bow value.

Description

Technical Field

[0001] The present invention relates to an evaluation and detection method, and particularly to a material analysis method that can be used to predict the bow of a wafer after an ingot is processed into the wafer. Background Art

[0002] Ingot verification has always been a very important issue, especially the stress of the ingot has a great impact on subsequent processing processes. Among them, the bow of the wafer is directly related to the quality of the wafer.

[0003] Currently, if an operator wants to know the bow of a wafer, it is necessary to wait until the ingot is purchased and processed before measuring the bow of the wafer. If the quality of the wafer does not meet the requirements, this ingot will be wasted. Accordingly, how to evaluate the quality of the ingot in advance and estimate the bow of its wafer, so as to predict the quality of the wafer after processing before the ingot is processed and reduce unnecessary waste is one of the current issues. Summary of the Invention

[0004] The present invention is directed to a material analysis method that can be used to predict the bow of a wafer after an ingot is processed into the wafer.

[0005] The material analysis method of the present invention includes: measuring, by a measuring instrument, a plurality of wafers processed from a plurality of ingots to obtain the average bow of these wafers after each ingot is processed and the plurality of full widths at half maximum of each wafer; calculating a key factor corresponding to each ingot based on the full width at half maximum of each wafer; and obtaining a regression equation by using the plurality of key factors corresponding to these ingots and the plurality of average bows.

[0006] In an embodiment of the present invention, the step of measuring, by the measuring instrument, the wafers processed from the ingots includes: respectively measuring the bows of a plurality of wafers of the same ingot, and calculating an average bow based on the bows; and respectively measuring the full widths at half maximum of a plurality of specified positions of a first wafer and a second wafer of the same ingot.

[0007] In an embodiment of the present invention, the first wafer and the second wafer are respectively wafers at the head and tail ends of the same ingot.

[0008] In an embodiment of the present invention, the step of calculating a key factor corresponding to each ingot based on the full width at half maximum of each wafer includes: calculating a first coefficient of variation of the first wafer and a second coefficient of variation of the second wafer based on the full width at half maximum of each of the first wafer and the second wafer of the same ingot; and calculating the key factor corresponding to the ingot based on the first coefficient of variation and the second coefficient of variation.

[0009] In an embodiment of the present invention, the step of calculating a key factor based on a first coefficient of variation and a second coefficient of variation includes: calculating a difference between the first coefficient of variation and the second coefficient of variation, and taking the absolute value of the difference as the key factor.

[0010] In an embodiment of the present invention, the designated positions include the center point positions of each of the first wafer and the second wafer and four representative positions respectively located in four quadrants.

[0011] In an embodiment of the present invention, the center point position of each of the first wafer and the second wafer is set as the origin, and each of the first wafer and the second wafer is divided into four quadrants.

[0012] In an embodiment of the present invention, after obtaining the regression equation, it further includes: measuring the full width at half maximum of a test wafer corresponding to a test ingot, and calculating the key factor accordingly; and inputting the key factor into the regression equation to obtain the predicted curvature of the wafer processed from the test ingot.

[0013] Based on the above, the present disclosure can obtain the predicted curvature of the wafer after the ingot is processed into a wafer by using the regression equation before processing the ingot, so as to predict the geometric quality of the wafer after the ingot is processed. Accordingly, unnecessary waste can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a block diagram of an analysis system according to an embodiment of the present invention;

[0015] Figure 2 is a flowchart of a material analysis method according to an embodiment of the present invention;

[0016] Figure 3 is a schematic diagram of an ingot according to an embodiment of the present invention;

[0017] Figure 4 is a schematic diagram of designated positions according to an embodiment of the present invention;

[0018] Figure 5 is a curve graph of a regression equation according to an embodiment of the present invention.

[0019] DESCRIPTION OF REFERENCE NUMERALS

[0020] 2: Ingot

[0021] 21: First wafer

[0022] 22: Second wafer

[0023] 110: Measuring instrument

[0024] 120: Analysis device

[0025] S205 - S215: Each step of the material analysis method

[0026] 300: Slicing

[0027] P0 - P4: Designated positions Detailed implementation manners

[0028] Reference will now be made in detail to exemplary embodiments of the present invention. Examples of the exemplary embodiments are illustrated in the accompanying drawings. Whenever possible, the same component symbols are used in the drawings and the description to represent the same or similar parts.

[0029] Figure 1 is a block diagram of an analysis system according to an embodiment of the present invention. Please refer to Figure 1 , the analysis system includes a measuring instrument 110 and an analysis device 120. Data transmission between the measuring instrument 110 and the analysis device 120 can be carried out, for example, by wired or wireless communication means.

[0030] The measuring instrument 110 includes a diffractometer, such as an X - ray diffractometer (XRD) or an optical instrument, such as FRT or Tropel, which are respectively used to measure wafers to obtain the full width at half maximum (FWHM) and curvature at different positions in each wafer. The measuring instrument 110 can be implemented by any device to measure the FWHM and curvature of the wafer, and the present invention is not limited thereto. The X - ray diffractometer uses accelerated electrons to strike a metal target to generate X - rays, and then irradiates the X - rays onto the wafer to obtain the crystal structure. When the X - rays are emitted at an incident angle θ to a plane of the lattice, diffraction peaks are generated when meeting the Bragg condition nλ = 2dsinθ, where n is an integer, λ is the wavelength of the incident wave, d is the plane spacing within the atomic lattice, and θ is the angle between the incident wave and the scattering plane. The FWHM is obtained from half of the width at the highest point of the diffraction peak. The FWHM can represent the crystallization quality, so the FWHM is measured here as the basis for judgment.

[0031] The analysis device 120 is an electronic device with computing functions, which can be implemented by a personal computer, a notebook computer, a tablet computer, a smart phone, etc. or any device with computing functions, and the present invention is not limited thereto. The analysis device 120 receives measurement data of a plurality of known wafers from the measuring instrument 110, and thereby conducts training to obtain a prediction model (regression equation) for subsequent use of the measurement data of the wafers to be measured to obtain the predicted curvature of the wafer after an ingot is processed into a wafer.

[0032] Figure 2 is a flowchart of a material analysis method according to an embodiment of the present invention. Please refer to Figure 2, in step S205, a measuring instrument 110 measures a plurality of wafers processed from a plurality of ingots to obtain the average bow of the wafers after processing of each ingot and the plurality of full widths at half maximum (FWHM) of each wafer. Here, each ingot undergoes one or more processing processes, such as cutting, grinding, polishing, etc. to form wafers, and the measuring instrument 110 measures each of the plurality of wafers processed from each ingot one by one to obtain the bow of each wafer. Furthermore, the analysis device 120 uses the bows of these wafers to obtain the average bow of the wafers.

[0033] Moreover, the measuring instrument 110 separately measures the FWHM of these wafers at a plurality of specified positions. In one embodiment, it may be only for the wafers at the head and tail ends of the same wafer, that is, the FWHM of both the first wafer and the second wafer at a plurality of specified positions. Figure 3 is a schematic diagram of an ingot according to an embodiment of the present invention. Please refer to Figure 3 , and the wafers at the head and tail ends of the ingot 2 are used as the first wafer 21 and the second wafer 22.

[0034] The measuring instrument 110 separately measures the FWHM of both the first wafer 21 and the second wafer 22 at a plurality of specified positions. Here, it is set to sample (measure) at 5 specified positions. The 5 positions are: the center point position and 4 representative positions respectively located in 4 quadrants.

[0035] Figure 4 is a schematic diagram of the specified positions according to an embodiment of the present invention. As Figure 4 shown, the wafer 300 includes the specified positions P0 - P4. In this embodiment, the wafer 300 is, for example, one of the wafers at the head and tail ends processed from the ingot 2, such as the first wafer 21 or the second wafer 22. Taking the center point position (specified position P0) of the wafer 300 as the origin (0,0), it is divided into four quadrants, and representative positions P1 - P4 are respectively taken in the four quadrants. Among them, for example, the coordinates of the representative position P1 are (45, 45), the coordinates of the representative position P2 are (45, -45), the coordinates of the representative position P3 are (-45, 45), and the coordinates of the representative position P4 are (-45, -45). For example, Table 1 shows the FWHM measured at the representative positions of the wafers (the first wafer 21, the second wafer 22) at the head and tail ends processed from the same ingot.

[0036] In step S210, based on the FWHM of each wafer, the key factor corresponding to each ingot is calculated. Specifically, based on the FWHM of the first wafer and the second wafer of the same ingot respectively, the first coefficient of variation of the first wafer and the second coefficient of variation of the second wafer are calculated. And based on the first coefficient of variation and the second coefficient of variation, the key factor is calculated.

[0037] The following presents an embodiment to illustrate the detailed steps of calculating the key factors. Table 1 exemplifies the full width at half maximum (FWHM) of the first wafer 21 and the second wafer 22 at the head and tail ends of a known ingot (such as the ingot 2 of Figure 3 ) after processing, at the designated positions P0 to P4 respectively.

[0038] Table 1

[0039] Coordinates representing positions Full width at half maximum of the first wafer 21 Full width at half maximum of the second wafer 22 P0(0,0) 97.8 124.1 P1(45,45) 89.4 105.1 P2(45,-45) 92.4 107.8 P3(-45,45) 90.6 105.1 P4(-45,-45) 101.9 114.4

[0040] First, calculate the average value and standard deviation of the FWHM of the first wafer 21, and calculate the average value and standard deviation of the FWHM of the second wafer 22. Then, calculate the first coefficient of variation of the first wafer 21 based on the average value and standard deviation of its FWHM, and calculate the second coefficient of variation of the second wafer 22 based on the average value and standard deviation of its FWHM.

[0041] The calculation method of the standard deviation is as follows:

[0042]

[0043] where N is the number of FWHM values, x i is the i-th FWHM value, and x is the average value of the FWHM.

[0044] The calculation method of the coefficient of variation is as follows:

[0045]

[0046] After obtaining the first coefficient of variation of the first wafer 21 and the second coefficient of variation of the second wafer 22, calculate the difference between the first coefficient of variation and the second coefficient of variation, and take the absolute value of the difference as the key factor corresponding to the ingot 2, that is, the key factor of the wafers processed from the ingot 2. Table 2 shows the key factor corresponding to the ingot number 001 (the ingot 2 shown in Figure 3 ).

[0047] Table 2

[0048]

[0049] Based on the above method, calculate the key factors corresponding to multiple ingots and the average value of the curvature of multiple wafers after processing each ingot, as shown in Table 3.

[0050] Table 3

[0051] Ingot number Key factor Average curvature 001 0.016942 15.96 002 0.025422 60.48 003 0.037921 70.13 004 0.029729 98.84 … … …

[0052] After that, in step S215, use the multiple key factors and the multiple average curvature values to obtain the regression equation.Figure 5 is a graph of a regression equation according to an embodiment of the present invention. Please refer to Figure 5 , in this embodiment, the regression equation is, for example, y = α + βx. Taking the multiple average camber values and multiple key factors shown in Table 3 obtained as the y-value and x-value respectively, thereby finding α and β. After calculation, it is obtained that: α = -2.3671, β = 2322.6, and the correlation coefficient R is obtained, where R2 = 0.869, and the regression equation is y = -2.3671 + 2322.6x. Specifically, the regression equation of the embodiment of the present invention is only for illustration, and the present invention is not limited thereto.

[0053] After obtaining the regression equation, when obtaining a to-be-tested ingot, by measuring the full width at half maximum of a to-be-tested wafer corresponding to the to-be-tested ingot, the corresponding key factor can be calculated, and the key factor is input into the regression equation, then the predicted camber of the to-be-tested ingot processed into a wafer can be obtained.

[0054] In summary, the present disclosure utilizes the measurement data of known wafers to perform training to obtain a regression equation as a prediction model. And, the predicted camber of the to-be-tested ingot processed into a wafer can be obtained only by using the wafers at the head and tail ends of the to-be-tested ingot. Accordingly, before processing the ingot, the predicted camber of the corresponding wafer can be obtained by using the regression equation to predict the geometric quality of the ingot after processing, thereby reducing unnecessary waste.

[0055] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A material analysis method, characterized in that, comprising: measuring, via a measuring instrument, a plurality of wafers processed from a plurality of ingots to obtain an average bow value of the plurality of wafers after processing of each of the ingots and a plurality of full widths at half maximum (FWHM) of each of the wafers; calculating a first coefficient of variation of the first wafer and a second coefficient of variation of the second wafer based on the plurality of FWHM of each of the first wafer and the second wafer among the plurality of wafers of the same ingot of each of the ingots, calculating a difference between the first coefficient of variation and the second coefficient of variation, and taking an absolute value of the difference as a key factor corresponding to each of the ingots; and obtaining a regression equation by using the plurality of key factors corresponding to the plurality of ingots and the plurality of average bow values.

2. The material analysis method according to claim 1, characterized in that, the step of measuring, via the measuring instrument, the plurality of wafers processed from the plurality of ingots comprises: respectively measuring a plurality of bow values of the plurality of wafers of the same ingot of each of the ingots, and calculating the average bow value based on the plurality of bow values; and respectively measuring the FWHM of a plurality of designated positions of each of the first wafer and the second wafer among the plurality of wafers of the same ingot of each of the ingots.

3. The material analysis method according to claim 2, characterized in that, the first wafer and the second wafer are respectively wafers located at the head and tail ends of the same ingot.

4. The material analysis method according to claim 2, characterized in that, the plurality of designated positions include a center point position of each of the first wafer and the second wafer and 4 representative positions respectively located in 4 quadrants.

5. The material analysis method according to claim 4, characterized in that, setting the center point position of each of the first wafer and the second wafer as the origin, and dividing each of the first wafer and the second wafer into 4 quadrants.

6. The material analysis method according to claim 1, characterized in that, after obtaining the regression equation, further comprising: measuring the plurality of FWHM of a test wafer corresponding to a test ingot, and calculating the key factor accordingly; and inputting the key factor into the regression equation to obtain a predicted bow value of a wafer processed from the test ingot.

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