Method, system and silicon wafer for detecting residual stress of silicon wafer

Abstract

The presently disclosed embodiments disclose a method, a system, and a silicon wafer for detecting residual stress of a silicon wafer. The method comprises: when the silicon wafer to be tested is in a first physical state, emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, respectively, and obtaining a first optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction; when the silicon wafer to be tested is in a second physical state, emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, respectively, and obtaining a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction; obtaining a photoelastic coefficient based on the first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be tested, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient; and obtaining the residual stress of the silicon wafer to be tested based on the photoelastic coefficient and the first proportional relationship.

Description

Technical Field

[0001] The embodiments of the present disclosure relate to the field of semiconductor manufacturing technology, and more particularly to a method and system for detecting residual stress of a silicon wafer, and a silicon wafer. Background Art

[0002] With the rapid development of the semiconductor industry, the detection and control of residual stress of silicon wafers, as the basic material for integrated circuit manufacturing, has become particularly critical. This is mainly because the residual stress of silicon wafers can directly affect the performance, reliability and yield of semiconductor devices manufactured from the silicon wafers.

[0003] At present, the detection methods for residual stress of silicon wafers in related technologies include X-ray diffraction, laser Raman scattering, and optical polarization measurement. Although these detection methods can obtain the residual stress of silicon wafers to a certain extent, these detection methods often have inaccurate detection results. For example, due to the influence of the crystal orientation and lattice parameters of the silicon wafer, the X-ray diffraction method may not accurately reflect the distribution of local residual stress inside the silicon wafer. The laser Raman scattering method may cause the incident laser to scatter due to the limitations of the surface conditions of the silicon wafer, resulting in signal attenuation or distortion, thereby causing inaccurate residual stress detection results. Optical polarization measurement technology is limited by the accuracy of the detection equipment and the operating level of the process personnel, and is prone to detection errors, thereby affecting the accuracy of the detection results.

[0004] Therefore, there is an urgent need for a method for detecting the residual stress of a silicon wafer to accurately obtain the residual stress of the silicon wafer. Summary of the invention

[0005] In view of this, the embodiments of the present disclosure are intended to provide a method, system and silicon wafer for detecting residual stress of a silicon wafer, which can improve the accuracy of the detection results of the residual stress of the silicon wafer.

[0006] The technical solution of the embodiment of the present disclosure is implemented as follows:

[0007] In a first aspect, an embodiment of the present disclosure provides a method for detecting residual stress of a silicon wafer, the method comprising:

[0008] When the silicon wafer to be tested is in a first physical state, emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, respectively, and obtaining a first optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction;

[0009] When the silicon wafer to be tested is in a second physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, respectively, and a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained; wherein the angular velocity corresponding to the silicon wafer to be tested in the first physical state is less than the angular velocity corresponding to the silicon wafer to be tested in the second physical state;

[0010] Obtaining the photoelastic coefficient based on the first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient;

[0011] Based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained.

[0012] In some examples, when the first physical state of the silicon wafer to be tested is that the silicon wafer to be tested is in a stationary state, the second physical state of the silicon wafer to be tested is that the silicon wafer to be tested is rotating at a first angular velocity.

[0013] In some examples, when the silicon wafer to be tested is in a stationary state, the first proportional relationship is expressed as a ratio of an absolute value of the first optical path difference to the photoelastic coefficient, which is the residual stress of the silicon wafer to be tested.

[0014] In some examples, when the silicon wafer to be tested rotates at the first angular velocity, the second proportional relationship is expressed as a ratio of the absolute value of the second optical path difference to the photoelastic coefficient equals the sum of the absolute value of the difference between the first radial stress component and the first circumferential stress component and the residual stress;

[0015] Among them, the first radial stress component is the radial stress component of the internal stress in the set crystal direction generated when the silicon wafer to be tested rotates at the first angular velocity, and the first circumferential stress component is the circumferential stress component of the internal stress in the set crystal direction generated when the silicon wafer to be tested rotates at the first angular velocity.

[0016] In some examples, when the first physical state of the silicon wafer to be tested is that the silicon wafer to be tested rotates at a second angular velocity, the second physical state of the silicon wafer to be tested is that the silicon wafer to be tested rotates at a third angular velocity; wherein the third angular velocity is greater than the second angular velocity.

[0017] In some examples, when the silicon wafer to be tested rotates at the second angular velocity, the first proportional relationship is expressed as a ratio of an absolute value of the first optical path difference to the photoelastic coefficient to a sum of an absolute value of a difference between a second radial stress component and a second circumferential stress component and the residual stress;

[0018] Among them, the second radial stress component is the radial stress component of the internal stress in the set crystal direction generated when the silicon wafer to be tested rotates at the second angular velocity, and the second circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the second angular velocity.

[0019] In some examples, when the silicon wafer to be tested rotates at the third angular velocity, the second proportional relationship is expressed as a ratio of the absolute value of the second optical path difference to the photoelastic coefficient equals the sum of the absolute value of the difference between the third radial stress component and the third circumferential stress component and the residual stress;

[0020] Among them, the third radial stress component is the radial stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the third angular velocity, and the third circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the third angular velocity.

[0021] In some examples, obtaining the photoelastic coefficient based on the first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient includes:

[0022] Based on the first proportional relationship and the second proportional relationship, obtaining a corresponding relationship among the photoelastic coefficient, the first optical path difference, and the second optical path difference;

[0023] The photoelastic coefficient is obtained based on the first optical path difference, the second optical path difference, and the corresponding relationship.

[0024] In a second aspect, an embodiment of the present disclosure provides a system for detecting residual stress of a silicon wafer, the system comprising:

[0025] A driving device, the driving device is used to control the silicon wafer to be tested to be in a first physical state or a second physical state; wherein the angular velocity corresponding to the silicon wafer to be tested in the first physical state is less than the angular velocity corresponding to the silicon wafer to be tested in the second physical state;

[0026] A laser emitter, used for emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested respectively when the silicon wafer to be tested is in the first physical state or the second physical state;

[0027] A laser receiver, used for receiving a polarized light beam after passing through the silicon wafer to be tested;

[0028] The processor is configured as:

[0029] When the silicon wafer to be tested is in a first physical state, obtaining a first optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction;

[0030] When the silicon wafer to be tested is in a second physical state, obtaining a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction;

[0031] Obtaining the photoelastic coefficient based on the first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient;

[0032] Based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained.

[0033] In a third aspect, an embodiment of the present disclosure provides a silicon wafer, wherein the residual stress of the silicon wafer calculated according to a first optical path difference in a first physical state and a second optical path difference in a second physical state, a first proportional relationship between the first optical path difference and a photoelastic coefficient of the silicon wafer, and a second proportional relationship between the second optical path difference and the photoelastic coefficient is in a range of 0.1 KPa to 10 KPa;

[0034] Among them, the first optical path difference is that when the silicon wafer is in the first physical state, a polarized light beam is emitted toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer, and the optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained; the second optical path difference is that when the silicon wafer is in the second physical state, a polarized light beam is emitted toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer, and the optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained.

[0035] The embodiment of the present disclosure provides a method, system and silicon wafer for detecting the residual stress of a silicon wafer; when the silicon wafer to be tested is in a first physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, and a first optical path difference between the polarized light beams in the radial direction and the circumferential direction is obtained; when the silicon wafer to be tested is in a second physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, and a second optical path difference between the polarized light beams in the radial direction and the circumferential direction is obtained; based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be tested, the second optical path difference and the second proportional relationship between the second optical path difference and the photoelastic coefficient, the photoelastic coefficient is obtained. Finally, based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained. The residual stress detection method provided by the present disclosure obtains the residual stress of the silicon wafer to be tested by obtaining the photoelastic coefficient corresponding to the silicon wafer to be tested, thereby improving the accuracy of the detection result of the residual stress of the silicon wafer to be tested. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A schematic diagram of a scanning infrared depolarization measurement system for detecting residual stress of a silicon wafer in the related art;

[0037] Figure 2 A testing system for photoelastic coefficient in related technology;

[0038] Figure 3 A schematic flow chart of a method for detecting residual stress of a silicon wafer provided in an embodiment of the present disclosure;

[0039] Figure 4 A schematic diagram of the relationship between the Poisson's ratio and the crystal orientation of the silicon wafer to be tested on the (100) crystal plane of the silicon wafer to be tested provided in an embodiment of the present disclosure;

[0040] Figure 5 A schematic diagram of the system composition for detecting residual stress of silicon wafers;

[0041] Figure 6 A schematic diagram of the residual stress detection result of a silicon wafer obtained by the related art;

[0042] Figure 7 Schematic diagram of residual stress detection results of silicon wafers obtained according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure.

[0044] See also Figure 1, which shows a schematic diagram of a scanning infrared depolarization measurement (SIRD) system for detecting residual stress of a silicon wafer 1 in the related art. The SIRD system 100 includes a laser transmitter 101, a laser receiver 102, and a processor 103. The laser transmitter 101 can emit polarized light beams ( Figure 1 ). It can be understood that when residual stress exists inside the silicon wafer 1, it will cause stress birefringence effect. This stress birefringence effect will cause the polarized light beam to depolarize after passing through the silicon wafer 1. The laser receiver 102 is used to receive the polarized light beam after passing through the silicon wafer 1. The processor 103 is used to obtain the residual stress of the silicon wafer 1 according to the light intensity between the polarized light beams in different directions.

[0045] It should be noted that, in the specific implementation process, the light intensity between polarized light beams in different directions can be characterized by the optical path difference between the polarized light beams in different directions. Therefore, the residual stress of the silicon wafer 1 can be obtained according to the optical path difference between the polarized light beams in different directions and the photoelastic coefficient of the silicon wafer 1, which can be specifically expressed by the following formula:

[0046]

[0047] in, It represents the optical path difference between polarized light beams in different directions. represents the residual stress of silicon wafer, Represents the photoelastic coefficient of silicon wafer.

[0048] It should be noted that, in the process of detecting the residual stress of the silicon wafer, the laser emitter 101 emits a polarized light beam toward the surface of the silicon wafer 1 along the radial and circumferential directions of the silicon wafer 1 to obtain the optical path difference between the polarized light beams in the radial and circumferential directions. In the specific implementation process, the optical path difference between the polarized light beams in the radial and circumferential directions of the silicon wafer 1 can be measured and obtained by a six-step phase shift method, an interference method, etc., and the present disclosure does not make specific limitations on this.

[0049] Based on the above formula, when the photoelastic coefficient of silicon wafer 1 is known, the residual stress of silicon wafer 1 can be obtained. At present, in the related art, the photoelastic coefficient of silicon wafer 1 is set as a fixed value. However, for different silicon wafers, due to the different types and contents of dopants, the lattice structure of the silicon wafer will also be different, which in turn affects the degree of induction of the stress birefringence effect by the residual stress inside the silicon wafer, resulting in different photoelastic coefficients corresponding to different silicon wafers. Therefore, if only a fixed value is set as the photoelastic coefficient of the silicon wafer and the residual stress of the silicon wafer is calculated based on the above formula, the calculated residual stress of the silicon wafer may be inaccurate, so that it is not possible to timely discover the phenomenon of cracks in the silicon wafer, and the continuous residual stress will shorten the performance and service life of the semiconductor device corresponding to the silicon wafer.

[0050] Based on the above description, the present disclosure hopes to obtain the residual stress of silicon wafer by accurately obtaining the photoelastic coefficient of silicon wafer, thereby improving the accuracy of residual stress detection results. However, it is found in the specific implementation that, for example Figure 2 The feasibility of the photoelastic coefficient testing system 200 in the related art shown in FIG. 2 for testing the photoelastic coefficient of a silicon wafer is low. Specifically, the photoelastic coefficient testing system 200 mainly includes:

[0051] A light source transmitter 201, used for transmitting a non-polarized light beam A;

[0052] An adjuster 202 having a light-transmitting hole 2021 at the center thereof, and the amount of the non-polarized light beam passing through the adjuster 202 is controlled by adjusting the aperture of the light-transmitting hole 2021;

[0053] A polarizer 203, used to convert the non-polarized light beam passing through the regulator 202 into a polarized light beam having a specific polarization direction;

[0054] The loading device 204 is used to fix the workpiece 2 to be tested and apply a bending load to the workpiece 2 to be tested ( Figure 2 As shown by the dotted arrow in the figure) to generate internal stress inside the workpiece 2 to be tested; wherein the loading device 204 includes an upper loading device 2041 and a lower loading device 2042, and the upper loading device 2041 and the lower loading device 2042 are used to fix the workpiece 2 to be tested;

[0055] A Babinet compensator 205 is used to compensate for the phase delay caused by the internal stress inside the workpiece 2 to be measured;

[0056] The analyzer 206 is used to observe the interference fringes generated by the stress birefringence effect after the polarized light beam passes through the workpiece 2 to be measured, and the interference fringes are used to characterize the change of the polarization state of the polarized light beam after passing through the workpiece 2 to be measured; wherein the polarization direction of the analyzer 206 is perpendicular to the polarization direction of the polarizer 203;

[0057] The measuring device 207 is used to determine the phase delay corresponding to the polarized light beam after passing through the workpiece 2 to be measured by analyzing the above-mentioned interference fringes.

[0058] In some examples, after obtaining the phase delay corresponding to the polarized light beam after passing through the workpiece 2 to be measured, the phase delay can be calculated based on To obtain the photoelastic coefficient of the workpiece 2 to be tested, where: represents the photoelastic coefficient of the workpiece 2 to be tested; represents the phase delay mentioned above; Indicates the thickness of the workpiece 2 to be measured; represents the wavelength corresponding to the unpolarized light beam A; Indicates the internal stress inside the workpiece 2 to be measured.

[0059] Despite the use Figure 2 The test system 200 shown can test and calculate the photoelastic coefficient of the workpiece 2 to be tested, but it is worth pointing out that Figure 2 The test system 200 shown in FIG. 1 is not suitable for testing the photoelastic coefficient of silicon wafers. This is because Figure 2 The workpiece 2 to be tested in the embodiment is thicker and rectangular, while the silicon wafer 1 in the present disclosure is thinner and circular. Since the workpiece 2 to be tested and the silicon wafer 1 in the present disclosure have a large difference in shape and size, Figure 2 The test system 200 shown in the figure may not be able to provide enough contact points or supports to stabilize the silicon wafer 1 for accurate measurement during the specific implementation process, resulting in the inability to accurately obtain the stress state inside the silicon wafer. Therefore, the photoelastic coefficient of the silicon wafer to be tested obtained by the test system 200 is not accurate.

[0060] Based on the above description, the present disclosure expects Figure 1 The SIRD system 100 shown, when the silicon wafer 1 is in different motion conditions, emits polarized light beams along the radial and circumferential directions of the silicon wafer 1 toward the surface of the silicon wafer 1, and then obtains the stress distribution of the silicon wafer 1 under different motion conditions according to the optical path difference between the polarized light beams in the radial and circumferential directions of the silicon wafer 1, and finally obtains the photoelastic coefficient of the silicon wafer 1 according to the stress distribution of the silicon wafer 1 under different motion conditions, and then calculates the residual stress of the silicon wafer 1 according to the photoelastic coefficient obtained by the test, thereby improving the accuracy of the residual stress detection result of the silicon wafer 1. Specifically, Figure 3As shown, the embodiment of the present disclosure provides a method for detecting residual stress of a silicon wafer, the method specifically comprising:

[0061] In step S301, when the silicon wafer to be tested is in a first physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, and a first optical path difference between the radial polarized light beam and the circumferential polarized light beam is obtained.

[0062] In step S302, when the silicon wafer to be tested is in a second physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial and circumferential directions of the silicon wafer to be tested, and a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained; wherein the angular velocity corresponding to the silicon wafer to be tested in the first physical state is less than the angular velocity corresponding to the silicon wafer to be tested in the second physical state.

[0063] In some examples, the first physical state and the second physical state of the silicon wafer to be tested respectively represent different motion conditions of the silicon wafer to be tested, that is, the silicon wafer to be tested is in a rotating state or a stationary state. For example, the first physical state and the second physical state of the silicon wafer to be tested can both be set as the silicon wafer to be tested is in a rotating state. Of course, in the specific implementation process, the first physical state can be set as the silicon wafer to be tested is in a stationary state, and the corresponding second physical state can be set as the silicon wafer to be tested is in a rotating state. It can be understood that when the angular velocity corresponding to the silicon wafer to be tested in the first physical state is zero, the silicon wafer to be tested is in a stationary state.

[0064] It should be noted that the above-mentioned rotation state of the silicon wafer to be tested refers to the rotation of the silicon wafer to be tested around its central axis ( Figure 1 The dotted line X in the figure rotates clockwise or counterclockwise.

[0065] In step S303, the photoelastic coefficient is obtained based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient.

[0066] According to the above formula It can be seen that when the silicon wafer to be tested is in a stationary state, after emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial and circumferential directions of the silicon wafer to be tested respectively, the optical path difference between the polarized light beams in the radial and circumferential directions of the silicon wafer to be tested is directly proportional to the photoelastic coefficient of the silicon wafer to be tested.

[0067] In addition, the stress distribution inside the silicon wafer to be tested is different between the first physical state and the second physical state. In the present disclosure, the photoelastic coefficient corresponding to the silicon wafer to be tested is obtained by measuring different optical path differences under different physical states, and different proportional relationships between different optical path differences and photoelastic coefficients. On the one hand, it is possible to identify and eliminate common system errors or environmental factors that exist when testing under different physical states, thereby improving the test accuracy of the photoelastic coefficient, and further improving the accuracy of the residual stress detection results of the silicon wafer to be tested. On the other hand, obtaining the photoelastic coefficient based on the change in the optical path difference caused by the different physical states of the silicon wafer to be tested can improve the detection sensitivity of small residual stress changes, and further improve the accuracy of the residual stress detection results of the silicon wafer to be tested.

[0068] In step S304, the residual stress of the silicon wafer to be tested is obtained based on the photoelastic coefficient and the first proportional relationship.

[0069] In the present disclosure, after the photoelastic coefficient of the silicon wafer to be tested is obtained, the residual stress of the silicon wafer to be tested can be obtained based on the photoelastic coefficient and the first proportional relationship.

[0070] for Figure 3 The technical solution shown, when the silicon wafer to be tested is in a first physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, and a first optical path difference between the polarized light beams in the radial direction and the circumferential direction is obtained; when the silicon wafer to be tested is in a second physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, and a second optical path difference between the polarized light beams in the radial direction and the circumferential direction is obtained; based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be tested, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient, the photoelastic coefficient is obtained. Finally, based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained. The residual stress detection method provided by the present disclosure obtains the residual stress of the silicon wafer to be tested by obtaining the photoelastic coefficient corresponding to the silicon wafer to be tested, thereby improving the accuracy of the residual stress detection result of the silicon wafer to be tested.

[0071] for Figure 3 In the technical solution shown, in some possible implementations, when the first physical state of the silicon wafer to be tested is that the silicon wafer to be tested is in a stationary state, the second physical state of the silicon wafer to be tested is that the silicon wafer to be tested is rotating at a first angular velocity.

[0072] Since the silicon wafer to be tested will show different stress distributions in the static state and the rotating state, the corresponding optical path difference is obtained by using the stress distribution of the silicon wafer to be tested in the static state and the rotating state. This can eliminate the test errors caused by system equipment errors or environmental factors under different physical states, so as to obtain a more accurate photoelastic coefficient of the silicon wafer to be tested.

[0073] In addition, when the optical path difference is obtained when the silicon wafer to be tested is in a rotating state, it is ensured that the residual stress calculated using the photoelastic coefficient obtained by the optical path difference can characterize the stress distribution on the entire circumference of the silicon wafer to be tested or the stress distribution of the entire silicon wafer to be tested.

[0074] For the above implementations, in some examples, when the silicon wafer to be tested is in a stationary state, the first proportional relationship is expressed as the ratio of the absolute value of the first optical path difference to the photoelastic coefficient, which is the residual stress of the silicon wafer to be tested.

[0075] It can be understood that when the silicon wafer to be tested is in a stationary state, after emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, according to the first optical path difference between the polarized light beams in the radial direction and the circumferential direction of the silicon wafer to be tested, , we can get the first proportional relationship as: .

[0076] Optionally, when the silicon wafer to be tested rotates at a first angular velocity, the second proportional relationship is expressed as a ratio of an absolute value of the second optical path difference to a photoelastic coefficient equal to a sum of an absolute value of a difference between a first radial stress component and a first circumferential stress component and a residual stress;

[0077] Among them, the first radial stress component is the radial stress component corresponding to the internal stress generated when the silicon wafer to be tested rotates at a first angular velocity in the set crystal direction, and the first circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer to be tested rotates at the first angular velocity in the crystal direction.

[0078] Specifically, for a rotating disk, the centrifugal force generated during the rotation process will cause internal stress inside the disk. According to the theory of elastic mechanics, the radial stress component and circumferential stress component corresponding to the internal stress at any point inside the disk can be calculated using the following formula:

[0079]

[0080]

[0081] in, Represents the radial stress component corresponding to the internal stress at any point inside the disk; It represents the circumferential stress component corresponding to the internal stress at any point inside the disk; represents the Poisson's ratio of the disk; represents the material density of the disk; represents the angular velocity of the disk; represents the radius of the disk; It represents the distance between any point and the center of the disk in the direction parallel to the surface of the disk.

[0082] Due to the anisotropy of the silicon wafer to be tested, the calculation formulas for the radial stress component and the circumferential stress component corresponding to the internal stress at any point inside the above disk are applicable to the silicon wafer to be tested. Therefore, during the rotation of the silicon wafer to be tested, the first radial stress component and the first circumferential stress component corresponding to the internal stress of the silicon wafer to be tested in different crystal directions can be expressed according to the following formulas:

[0083]

[0084]

[0085] in, Represents a first radial stress component corresponding to the internal stress in any crystal direction of the silicon wafer to be tested; It represents the first circumferential stress component corresponding to the internal stress on any crystal direction of the silicon wafer to be tested.

[0086] It should be noted that the above angle It means the angle between any position on the silicon wafer to be tested and the polar axis when the polar coordinates are established with the center of the silicon wafer to be tested as the origin and the horizontal radius of the silicon wafer to be tested as the polar axis. It can be understood that at different angles of the silicon wafer to be tested, Indicates different crystal orientations in the silicon wafer to be tested. In the specific implementation process, the Poisson's ratio and density on different crystal orientations of the silicon wafer to be tested are different, for example Figure 4 FIG. 1 is a schematic diagram showing the variation of the Poisson's ratio of the silicon wafer to be tested with the crystal orientation on the (100) crystal plane of the silicon wafer to be tested. It can be understood that if it is necessary to know the (100) crystal plane of the silicon wafer to be tested, = Poisson's ratio at 45° , that is <110> Poisson's ratio in the crystal direction When Figure 4 In addition, on the (100) crystal plane of the silicon wafer to be tested, Figure 4 In µ α Representation and Crystalline angle α Poisson's ratio in the crystal direction.

[0087] When the silicon wafer to be tested is at a first angular velocity ωWhen rotating, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, and a second optical path difference between the polarized light beams in the radial direction and the circumferential direction of the silicon wafer to be tested is obtained. , the second proportional relationship can be obtained as: It should be noted that when there is no residual stress inside the silicon wafer to be tested, the internal stress caused by the silicon wafer to be tested during the rotation process is based on and When there is residual stress inside the silicon wafer to be tested, the overall stress distribution of the silicon wafer to be tested is obtained according to the residual stress when the silicon wafer to be tested rotates. And the internal stress caused by the silicon wafer to be tested during the rotation process is obtained.

[0088] for Figure 3 In the technical solution shown, in some possible implementations, when the first physical state of the silicon wafer to be tested is that the silicon wafer to be tested rotates at a second angular velocity, the second physical state of the silicon wafer to be tested is that the silicon wafer to be tested rotates at a third angular velocity; wherein the third angular velocity is greater than the second angular velocity.

[0089] Since the silicon wafer to be tested will show different stress distributions in different rotational states, the corresponding optical path difference can be obtained by using the stress distribution of the silicon wafer to be tested in different rotational states. This can eliminate the test errors caused by system equipment errors or environmental factors in different rotational states, so as to obtain a more accurate photoelastic coefficient of the silicon wafer to be tested.

[0090] In addition, by performing measurements under different rotation states, the consistency of the photoelastic coefficient finally obtained can be ensured, the reliability of the measurement results of the photoelastic coefficient can be improved, and the detection accuracy of the residual stress of the silicon wafer to be measured can be improved.

[0091] It should be noted that when the angular velocity of the silicon wafer to be tested rotates too high, the optical signal corresponding to the polarized light beam received by the laser receiver 102 after passing through the silicon wafer to be tested will drift. Therefore, in the specific implementation process, the laser transmitter 101 and the laser receiver 102 are rotated simultaneously to reduce the angular velocity difference between the laser transmitter 101 and the laser receiver 102, thereby eliminating or alleviating the drift of the optical signal received by the laser receiver 102. The rotation direction of the laser transmitter 101 and the laser receiver 102 is the same as the rotation direction of the silicon wafer to be tested.

[0092] For the above-mentioned embodiments, in some examples, when the silicon wafer to be tested rotates at a second angular velocity, the first proportional relationship is expressed as a ratio of the absolute value of the first optical path difference to the photoelastic coefficient to the sum of the absolute value of the difference between the second radial stress component and the second circumferential stress component and the residual stress;

[0093] Among them, the second radial stress component is the radial stress component of the internal stress in the set crystal direction generated when the silicon wafer to be tested rotates at the second angular velocity, and the second circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the second angular velocity.

[0094] It can be understood that when the silicon wafer to be tested is at the second angular velocity ω 2, after emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, according to the first optical path difference between the polarized light beams in the radial direction and the circumferential direction of the silicon wafer to be tested, , we can get the first proportional relationship as: .

[0095] Optionally, when the silicon wafer to be tested rotates at a third angular velocity, the second proportional relationship is expressed as a ratio of the absolute value of the second optical path difference to the photoelastic coefficient to the sum of the absolute value of the difference between the third radial stress component and the third circumferential stress component and the residual stress;

[0096] Among them, the third radial stress component is the radial stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at a third angular velocity, and the third circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at a third angular velocity.

[0097] It can be understood that when the silicon wafer to be tested is at the third angular velocity ω 3, after emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, according to the second optical path difference between the polarized light beams in the radial direction and the circumferential direction of the silicon wafer to be tested, , the second proportional relationship can be obtained as: .

[0098] for Figure 3 In some possible implementations of the technical solution shown, the photoelastic coefficient is obtained based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient, including:

[0099] Based on the first proportional relationship and the second proportional relationship, obtaining a corresponding relationship among the photoelastic coefficient, the first optical path difference, and the second optical path difference;

[0100] Based on the first optical path difference, the second optical path difference and the corresponding relationship, a photoelastic coefficient is obtained.

[0101] In some examples, when the silicon wafer to be tested is in a stationary state and rotates at a first angular velocity, according to a first proportional relationship And the second proportional relationship , we can get: From this, the photoelastic coefficient can be obtained When the photoelastic coefficient is obtained Then, the photoelastic coefficient Substitute into the first proportional relationship Or the second proportional relationship , the residual stress of the silicon wafer to be tested can be obtained .

[0102] In other examples, when the silicon wafer to be tested rotates at the second angular velocity and the third angular velocity respectively, according to the first proportional relationship And the second proportional relationship , we can get: From this, the photoelastic coefficient can be obtained When the photoelastic coefficient is obtained Then, the photoelastic coefficient Substitute into the first proportional relationship Or the second proportional relationship , the residual stress of the silicon wafer to be tested can be obtained .

[0103] It can be understood that after the photoelastic coefficient of the silicon wafer to be tested is obtained, the residual stress of the silicon wafer to be tested can be obtained. In the present disclosure, the residual stress of the silicon wafer to be tested is preferably calculated using the photoelastic coefficient and the first proportional relationship. This is mainly because the silicon wafer to be tested corresponding to the first proportional relationship is in a stationary state or rotates at a relatively small angular velocity. When the silicon wafer to be tested is in a stationary state or rotates at a relatively small angular velocity, the internal stress generated by the silicon wafer to be tested during the rotation process is very small, and it is even considered that the internal stress can be ignored, thereby having a smaller impact on the residual stress detection result.

[0104] Based on the same inventive concept as the above technical solution, see Figure 5 The embodiment of the present disclosure provides a system 500 for detecting residual stress of a silicon wafer, the system 500 comprising:

[0105] A driving device 501, the driving device 501 is used to control the silicon wafer to be tested to be in a first physical state or a second physical state; wherein the angular velocity corresponding to the silicon wafer to be tested in the first physical state is less than the angular velocity corresponding to the silicon wafer to be tested in the second physical state;

[0106] The laser emitter 101 is used to emit a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested respectively when the silicon wafer to be tested is in the first physical state or the second physical state;

[0107] A laser receiver 102, used to receive a polarized light beam after passing through the silicon wafer to be tested;

[0108] The processor 103 is configured to:

[0109] When the silicon wafer to be tested is in a first physical state, obtaining a first optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction;

[0110] When the silicon wafer to be tested is in a second physical state, a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained;

[0111] Obtaining a photoelastic coefficient based on the first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient;

[0112] Based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained.

[0113] See also Figure 6 and Figure 7 , which respectively show the residual stress test results of the silicon wafer obtained by using the relevant technology and the residual stress test results of the silicon wafer obtained by using the embodiment of the present disclosure. Specifically, a uniform thin film layer is formed on the surface of the silicon wafer by using a vapor deposition method to simulate the uniform stress applied to the silicon wafer. When the relevant technology is used for detection, the photoelastic coefficient of the silicon wafer is set. Afterwards, based on Figure 1 The SIRD system 100 shown in the figure emits a polarized light beam toward the surface of the silicon wafer along the radial direction and the circumferential direction of the silicon wafer, and obtains an optical path difference between the polarized light beams in the radial direction and the circumferential direction. Afterwards, using the formula The residual stress corresponding to the silicon wafer is obtained, and the final stress distribution of the entire silicon wafer is as follows Figure 6 As shown. Figure 6 It can be seen that the stress distribution in the silicon wafer detected by the relevant technology is uneven. Figure 5 The system 500 for detecting residual stress of a silicon wafer as shown in the figure emits a polarized light beam toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer 1 when the silicon wafer is in a stationary device, and obtains a first optical path difference between the polarized light beams in the radial and circumferential directions. When the silicon wafer moves at the first angular velocity ω When the silicon wafer 1 rotates, a polarized light beam is emitted toward the surface of the silicon wafer along the radial direction and the circumferential direction of the silicon wafer 1, and a second optical path difference between the polarized light beams in the radial direction and the circumferential direction is obtained. , which can accurately obtain the photoelastic coefficient corresponding to the silicon wafer , and then use the photoelastic coefficient The calculated residual stress of the silicon wafer corresponds to the stress distribution of the entire silicon wafer. Figure 7 As shown. Figure 7 It can be seen that the stress distribution in the silicon wafer is uniform, and the result is closer to the actual situation of the stress distribution, which shows that the technical solution provided by the embodiment of the present disclosure can improve the accuracy of the detection results of the residual stress of the silicon wafer.

[0114] Finally, the embodiment of the present disclosure provides a silicon wafer, wherein the residual stress of the silicon wafer calculated according to a first optical path difference in a first physical state and a second optical path difference in a second physical state, a first proportional relationship between the first optical path difference and a photoelastic coefficient of the silicon wafer, and a second proportional relationship between the second optical path difference and the photoelastic coefficient is in a range of 0.1 KPa to 10 KPa;

[0115] Among them, the first optical path difference is that when the silicon wafer is in the first physical state, a polarized light beam is emitted toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer, and the optical path difference between the radial polarized light beam and the circumferential polarized light beam is obtained; the second optical path difference is that when the silicon wafer is in the second physical state, a polarized light beam is emitted toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer, and the optical path difference between the radial polarized light beam and the circumferential polarized light beam is obtained.

[0116] It should be noted that the technical solutions described in the embodiments of the present disclosure can be combined arbitrarily without conflict.

[0117] The above is only a specific embodiment of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present disclosure, which should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. A method for detecting residual stress of a silicon wafer, characterized in that: The method comprises: When the silicon wafer to be tested is in a first physical state, emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, respectively, and obtaining a first optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction; When the silicon wafer to be tested is in a second physical state, a polarized light beam is emitted toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested, respectively, and a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained; wherein the angular velocity corresponding to the silicon wafer to be tested in the first physical state is less than the angular velocity corresponding to the silicon wafer to be tested in the second physical state; The photoelastic coefficient is obtained based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient; wherein, the photoelastic coefficient is obtained based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient, including: Based on the first proportional relationship and the second proportional relationship, obtaining a corresponding relationship among the photoelastic coefficient, the first optical path difference, and the second optical path difference; obtaining the photoelastic coefficient based on the first optical path difference, the second optical path difference and the corresponding relationship; Based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained.

2. The method according to claim 1, characterized in that When the first physical state of the silicon wafer to be tested is that the silicon wafer to be tested is in a stationary state, the second physical state of the silicon wafer to be tested is that the silicon wafer to be tested is rotating at a first angular velocity.

3. The method according to claim 2, characterized in that When the silicon wafer to be tested is in a stationary state, the first proportional relationship is expressed as the ratio of the absolute value of the first optical path difference to the photoelastic coefficient, which is the residual stress of the silicon wafer to be tested.

4. The method according to claim 2, characterized in that: When the silicon wafer to be tested rotates at the first angular velocity, the second proportional relationship is expressed as a ratio of the absolute value of the second optical path difference to the photoelastic coefficient equal to the sum of the absolute value of the difference between the first radial stress component and the first circumferential stress component and the residual stress; Among them, the first radial stress component is the radial stress component of the internal stress in the set crystal direction generated when the silicon wafer to be tested rotates at the first angular velocity, and the first circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the first angular velocity.

5. The method according to claim 1, characterized in that When the first physical state of the silicon wafer to be tested is that the silicon wafer to be tested rotates at a second angular velocity, the second physical state of the silicon wafer to be tested is that the silicon wafer to be tested rotates at a third angular velocity; wherein the third angular velocity is greater than the second angular velocity.

6. The method according to claim 5, characterized in that When the silicon wafer to be tested rotates at the second angular velocity, the first proportional relationship is expressed as the ratio of the absolute value of the first optical path difference to the photoelastic coefficient to the sum of the absolute value of the difference between the second radial stress component and the second circumferential stress component and the residual stress; Among them, the second radial stress component is the radial stress component of the internal stress in the set crystal direction generated when the silicon wafer to be tested rotates at the second angular velocity, and the second circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the second angular velocity.

7. The method according to claim 6, characterized in that When the silicon wafer to be tested rotates at the third angular velocity, the second proportional relationship is expressed as a ratio of the absolute value of the second optical path difference to the photoelastic coefficient equals the sum of the absolute value of the difference between the third radial stress component and the third circumferential stress component and the residual stress; Among them, the third radial stress component is the radial stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the third angular velocity, and the third circumferential stress component is the circumferential stress component of the internal stress in the crystal direction generated when the silicon wafer to be tested rotates at the third angular velocity.

8. A system for detecting residual stress of a silicon wafer, characterized in that: The system comprises: A driving device, the driving device is used to control the silicon wafer to be tested to be in a first physical state or a second physical state; wherein the angular velocity corresponding to the silicon wafer to be tested in the first physical state is less than the angular velocity corresponding to the silicon wafer to be tested in the second physical state; A laser emitter, used for emitting a polarized light beam toward the surface of the silicon wafer to be tested along the radial direction and the circumferential direction of the silicon wafer to be tested respectively when the silicon wafer to be tested is in the first physical state or the second physical state; A laser receiver, used for receiving a polarized light beam after passing through the silicon wafer to be tested; The processor is configured as: When the silicon wafer to be tested is in a first physical state, obtaining a first optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction; When the silicon wafer to be tested is in a second physical state, obtaining a second optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction; The photoelastic coefficient is obtained based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient; wherein, the photoelastic coefficient is obtained based on the first optical path difference, the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer to be measured, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient, including: Based on the first proportional relationship and the second proportional relationship, obtaining a corresponding relationship among the photoelastic coefficient, the first optical path difference, and the second optical path difference; obtaining the photoelastic coefficient based on the first optical path difference, the second optical path difference and the corresponding relationship; Based on the photoelastic coefficient and the first proportional relationship, the residual stress of the silicon wafer to be tested is obtained.

9. A silicon wafer, characterized in that: The silicon wafer is detected according to the method for detecting residual stress of a silicon wafer according to any one of claims 1 to 7; the residual stress of the silicon wafer calculated according to a first optical path difference in a first physical state and a second optical path difference in a second physical state, a first proportional relationship between the first optical path difference and a photoelastic coefficient of the silicon wafer, and a second proportional relationship between the second optical path difference and the photoelastic coefficient is in a range of 0.1 KPa to 10 KPa; Among them, the first optical path difference is that when the silicon wafer is in the first physical state, a polarized light beam is emitted toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer, and the optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained; the second optical path difference is that when the silicon wafer is in the second physical state, a polarized light beam is emitted toward the surface of the silicon wafer along the radial and circumferential directions of the silicon wafer, and the optical path difference between the polarized light beam in the radial direction and the polarized light beam in the circumferential direction is obtained.

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