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

Abstract

A method for measuring residual stress of a silicon wafer (1), comprising: when a silicon wafer (1) undergoing measurement is in a first physical state, separately emitting polarized light beams (A) in the radial direction and the circumferential direction of said silicon wafer towards the surface of said silicon wafer, 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 said silicon wafer (1) is in a second physical state, separately emitting polarized light beams (A) in the radial direction and the circumferential direction of said silicon wafer (1) towards the surface of said silicon wafer (1), 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; on the basis of the first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of said silicon wafer (1), the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient, obtaining the photoelastic coefficient; and on the basis of the photoelastic coefficient and the first proportional relationship, obtaining the residual stress of said silicon wafer (1). Further provided are a system for measuring residual stress of a silicon wafer (1) and a corresponding silicon wafer (1).

Description

Methods, systems, and silicon wafers for detecting residual stress in silicon wafers

[0001] Cross-reference to related applications

[0002] This disclosure claims priority to Chinese Patent Application No. 202411437904.0, filed in China on October 15, 2024, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates to the field of semiconductor manufacturing technology, and more particularly to a method, system, and silicon wafer for detecting residual stress in silicon wafers. Background Technology

[0004] With the rapid development of the semiconductor industry, the detection and control of residual stress in 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 them.

[0005] Currently, methods for detecting residual stress in silicon wafers include X-ray diffraction, laser Raman scattering, and optical polarization measurement. While these methods can obtain residual stress to some extent, they often yield inaccurate results. For example, due to the influence of the crystal orientation and lattice parameters of the silicon wafer, X-ray diffraction may not accurately reflect the distribution of localized residual stress within the wafer. Laser Raman scattering may cause scattering of the incident laser light due to surface conditions, leading to signal attenuation or distortion and thus inaccurate results. Optical polarization measurement is limited by the precision of the testing equipment and the skill level of the operators, making it prone to errors that affect the accuracy of the results.

[0006] Therefore, there is an urgent need for a method to detect the residual stress of silicon wafers in order to accurately obtain the residual stress of silicon wafers. Summary of the Invention

[0007] In view of this, the present disclosure aims to provide a method, system, and silicon wafer for detecting residual stress in silicon wafers, thereby improving the accuracy of the detection results of residual stress in silicon wafers.

[0008] The technical solution of this disclosure embodiment is implemented as follows:

[0009] In a first aspect, embodiments of this disclosure provide a method for detecting residual stress in a silicon wafer, the method comprising:

[0010] When the silicon wafer under test is in the first physical state, polarized beams are emitted toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, and a first optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam.

[0011] When the silicon wafer under test is in the second physical state, polarized beams are emitted toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, and a second optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam; wherein, the angular velocity corresponding to the silicon wafer under test in the first physical state is less than the angular velocity corresponding to the silicon wafer under test in the second physical state.

[0012] 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 under test, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient.

[0013] The residual stress of the silicon wafer under test is obtained based on the photoelastic coefficient and the first proportional relationship.

[0014] In some examples, when the first physical state of the silicon wafer under test is that the silicon wafer under test is stationary, the second physical state of the silicon wafer under test is that the silicon wafer under test is rotating at a first angular velocity.

[0015] In some examples, when the silicon wafer under test is in a static state, the first proportional relationship is expressed as the ratio of the absolute value of the first optical path difference to the photoelastic coefficient as the residual stress of the silicon wafer under test.

[0016] In some examples, when the silicon wafer under test rotates at the first angular velocity, the second proportional relationship is expressed as the ratio of the absolute value of the second optical path difference to the photoelastic coefficient being 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.

[0017] Wherein, the first radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the 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 under test rotates at the first angular velocity in the set crystal direction.

[0018] In some examples, when the first physical state of the silicon wafer under test is that the silicon wafer under test is rotating at a second angular velocity, the second physical state of the silicon wafer under test is that the silicon wafer under test is rotating at a third angular velocity; wherein the third angular velocity is greater than the second angular velocity.

[0019] In some examples, when the silicon wafer under test 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 being 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.

[0020] Wherein, the second radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the second angular velocity in the set crystal direction, and the second circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer under test rotates at the second angular velocity in the crystal direction.

[0021] In some examples, when the silicon wafer under test rotates at the third angular velocity, the second proportional relationship is expressed as the ratio of the absolute value of the second optical path difference to the photoelastic coefficient being 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.

[0022] Wherein, the third radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the third angular velocity in the crystal direction, and the third circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer under test rotates at the third angular velocity in the crystal direction.

[0023] 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 under test, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient includes:

[0024] Based on the first proportional relationship and the second proportional relationship, the correspondence between the photoelastic coefficient, the first optical path difference, and the second optical path difference is obtained;

[0025] The photoelastic coefficient is obtained based on the first optical path difference, the second optical path difference, and the corresponding relationship.

[0026] Secondly, embodiments of this disclosure provide a system for detecting residual stress in silicon wafers, the system comprising:

[0027] A driving device is used to control the silicon wafer under test to be in a first physical state or a second physical state; wherein the angular velocity of the silicon wafer under test in the first physical state is less than the angular velocity of the silicon wafer under test in the second physical state.

[0028] A laser emitter is used to emit polarized beams toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, when the silicon wafer under test is in a first physical state or a second physical state.

[0029] A laser receiver for receiving a polarized light beam after it has passed through the silicon wafer under test;

[0030] The processor is configured as follows:

[0031] When the silicon wafer under test is in a first physical state, a first optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam.

[0032] When the silicon wafer under test is in the second physical state, a second optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam.

[0033] 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 under test, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient.

[0034] The residual stress of the silicon wafer under test is obtained based on the photoelastic coefficient and the first proportional relationship.

[0035] Thirdly, embodiments of this disclosure provide a silicon wafer in which the residual stress of the silicon wafer, calculated based on a first optical path difference in a first physical state and a second optical path difference in a second physical state, is in the range of 0.1 kPa to 10 kPa.

[0036] Wherein, the first optical path difference is obtained by emitting polarized light beams toward the surface of the silicon wafer along both the radial and circumferential directions when the silicon wafer is in the first physical state, and obtaining the optical path difference between the radially polarized light beam and the circumferentially polarized light beam; the second optical path difference is obtained by emitting polarized light beams toward the surface of the silicon wafer along both the radial and circumferential directions when the silicon wafer is in the second physical state, and obtaining the optical path difference between the radially polarized light beam and the circumferentially polarized light beam.

[0037] This disclosure provides a method, system, and silicon wafer for detecting residual stress in a silicon wafer. When the silicon wafer under test is in a first physical state, polarized light beams are emitted radially and circumferentially towards the surface of the silicon wafer, respectively, and a first optical path difference is obtained between the radially and circumferentially polarized beams. When the silicon wafer under test is in a second physical state, polarized light beams are emitted radially and circumferentially towards the surface of the silicon wafer, respectively, and a second optical path difference is obtained between the radially and circumferentially polarized beams. 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 under test, the second optical path difference, and a 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 under test is obtained. The residual stress detection method provided by this disclosure improves the accuracy of the residual stress detection results by obtaining the photoelastic coefficient corresponding to the silicon wafer under test. Attached Figure Description

[0038] Figure 1 is a schematic diagram of a scanning infrared depolarization measurement system used to detect residual stress in silicon wafers in related technologies.

[0039] Figure 2 shows the testing system for the photoelastic coefficient in related technologies;

[0040] Figure 3 is a schematic flowchart of a method for detecting residual stress in a silicon wafer according to an embodiment of this disclosure;

[0041] Figure 4 is a schematic diagram showing the relationship between Poisson's ratio and crystal orientation on the (100) crystal plane of the silicon wafer under test, according to an embodiment of this disclosure.

[0042] Figure 5 is a schematic diagram of the system composition used to detect residual stress in silicon wafers;

[0043] Figure 6 is a schematic diagram of the detection results of residual stress in silicon wafers obtained by related technologies;

[0044] Figure 7 is a schematic diagram of the detection results of residual stress in silicon wafers obtained in the embodiments of this disclosure. Detailed Implementation

[0045] The technical solutions in the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings.

[0046] Referring to Figure 1, a schematic diagram of a scanning infrared depolarization measurement (SIRD) system for detecting residual stress in a silicon wafer 1 is shown in the related art. The SIRD system 100 includes a laser emitter 101, a laser receiver 102, and a processor 103. The laser emitter 101 emits polarized beams in different directions toward the surface of the silicon wafer 1 (indicated by the dotted-dash arrows in Figure 1). Understandably, the presence of residual stress within the silicon wafer 1 causes stress birefringence. This stress birefringence effect causes the polarized beam to depolarize after passing through the silicon wafer 1. The laser receiver 102 receives the polarized beam after it has passed through the silicon wafer 1. The processor 103 determines the residual stress in the silicon wafer 1 based on the intensity of the beams polarized in different directions.

[0047] It should be noted that, in the specific implementation process, the light intensity between polarized beams in different directions can be characterized by the optical path difference between them. Therefore, the residual stress of silicon wafer 1 can be obtained based on the optical path difference between polarized beams in different directions and the photoelastic coefficient of silicon wafer 1, which can be expressed by the following formula:

[0048] |Δn|=C σ Δσ

[0049] Where |Δn| represents the optical path difference between polarized beams in different directions, Δσ represents the residual stress of the silicon wafer, and C σ This represents the photoelastic coefficient of a silicon wafer.

[0050] It should be noted that during the detection of residual stress in the silicon wafer, the laser emitter 101 emits polarized beams toward the surface of the silicon wafer 1 along both the radial and circumferential directions to obtain the optical path difference between the radial and circumferential polarized beams. In specific implementations, the optical path difference between the radial and circumferential polarized beams of the silicon wafer 1 can be obtained by measurement using methods such as the six-step phase-shifting method or interferometry; this disclosure does not impose specific limitations on this method.

[0051] Based on the above formula, the residual stress of silicon wafer 1 can be obtained when its photoelastic coefficient is known. Currently, the photoelastic coefficient of silicon wafer 1 is set to a fixed value in related technologies. However, for different silicon wafers, the type and content of dopants vary, resulting in differences in the lattice structure of the silicon wafer. This affects the degree to which the residual stress inside the silicon wafer induces the stress birefringence effect, thus causing different photoelastic coefficients for different silicon wafers. Therefore, if only a fixed value is used as the photoelastic coefficient of the silicon wafer and the residual stress is calculated based on the above formula, the calculated residual stress may be inaccurate, failing to detect cracks and other phenomena in the silicon wafer in a timely manner. Furthermore, the continuous residual stress will shorten the performance and lifespan of the semiconductor devices corresponding to the silicon wafer.

[0052] Based on the above description, this disclosure aims to improve the accuracy of residual stress detection results by accurately obtaining the photoelastic coefficient of the silicon wafer to determine the magnitude of residual stress. However, in practice, it has been found that the feasibility of using the photoelastic coefficient testing system 200 shown in Figure 2 for testing the photoelastic coefficient of silicon wafers is low. Specifically, the photoelastic coefficient testing system 200 mainly includes:

[0053] Light source emitter 201 is used to emit an unpolarized beam A;

[0054] A regulator 202 with a light-transmitting aperture 2021 at the center is provided, and the amount of light passing through the regulator 202 is controlled by adjusting the aperture of the light-transmitting aperture 2021.

[0055] Polarizer 203 is used to convert an unpolarized beam passing through the modulator 202 into a polarized beam with a specific polarization direction;

[0056] The loading device 204 is used to fix the workpiece 2 to be tested and to apply a bending load (shown by the dashed arrow in Figure 2) to the workpiece 2 to generate internal stress inside the workpiece 2; wherein, the loading device 204 includes an upper loading device 2041 and a lower loading device 2042, which are used to fix the workpiece 2 to be tested.

[0057] Babinet compensator 205 is used to compensate for phase delay caused by internal stress within the workpiece 2 under test;

[0058] The analyzer 206 is used to observe the interference fringes generated by the stress birefringence effect after the polarized beam passes through the workpiece 2 under test. The interference fringes are used to characterize the change in the polarization state of the polarized beam after passing through the workpiece 2 under test. The polarization direction of the analyzer 206 is perpendicular to the polarization direction of the polarizer 203.

[0059] The measuring device 207 is used to determine the phase delay of the polarized beam after passing through the workpiece 2 by analyzing the interference fringes described above.

[0060] In some examples, once the phase delay of the polarized beam after passing through the workpiece 2 can be obtained, it can be determined according to... The photoelastic coefficient of the workpiece 2 under test is obtained, where C represents the photoelastic coefficient of the workpiece 2 under test; δ represents the phase delay mentioned above; t represents the thickness of the workpiece 2 under test; λ represents the wavelength corresponding to the unpolarized beam A; and Δσ1 represents the internal stress inside the workpiece 2 under test.

[0061] Although the photoelastic coefficient of the workpiece 2 under test can be tested and calculated using the test system 200 shown in Figure 2, it is worth noting that the test system 200 shown in Figure 2 is not suitable for testing the photoelastic coefficient of silicon wafers. This is because the workpiece 2 under test in Figure 2 is relatively thick and rectangular, while the silicon wafer 1 in this disclosure is relatively thin and circular. Due to the significant difference in shape and size between the workpiece 2 under test and the silicon wafer 1 in this disclosure, the test system 200 shown in Figure 2 may not be able to provide sufficient contact points or support to stabilize the silicon wafer 1 for accurate measurement during implementation. This results in the inability to accurately obtain the internal stress state of the silicon wafer, and therefore the photoelastic coefficient of the silicon wafer under test obtained by the test system 200 is inaccurate.

[0062] Based on the above description, this disclosure aims to utilize the SIRD system 100 shown in Figure 1 to emit polarized light beams towards the surface of the silicon wafer 1 along both the radial and circumferential directions under different motion conditions. Then, based on the optical path difference between the radial and circumferential polarized light beams, the stress distribution of the silicon wafer 1 under different motion conditions is obtained. Finally, the photoelastic coefficient of the silicon wafer 1 is obtained based on the stress distribution under different motion conditions, and the residual stress of the silicon wafer 1 is calculated based on the measured photoelastic coefficient, thereby improving the accuracy of the residual stress detection results of the silicon wafer 1. Specifically, as shown in Figure 3, an embodiment of this disclosure provides a method for detecting the residual stress of a silicon wafer, which specifically includes:

[0063] In step S301, when the silicon wafer under test is in the first physical state, polarized beams are emitted toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, and a first optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam.

[0064] In step S302, when the silicon wafer under test is in the second physical state, polarized beams are emitted toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, and a second optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam; wherein, the angular velocity corresponding to the silicon wafer under test in the first physical state is less than the angular velocity corresponding to the silicon wafer under test in the second physical state.

[0065] In some examples, the first and second physical states of the silicon wafer under test (SUT) represent different motion states of the SUT, i.e., the SUT is either rotating or stationary. For example, both the first and second physical states of the SUT can be set to the SUT being rotating. However, in practice, the first physical state can be set to the SUT being stationary, and the corresponding second physical state can be set to the SUT being rotating. Understandably, when the angular velocity of the SUT in the first physical state is zero, the SUT is stationary.

[0066] It should be noted that the above-mentioned silicon wafer under test being in a rotating state refers to the silicon wafer under test rotating clockwise or counterclockwise around its central axis (the dotted line X in Figure 1).

[0067] 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 tested, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient.

[0068] From the aforementioned formula |Δn|=C σ Δσ indicates that when the silicon wafer under test is in a static state, after polarized beams are emitted toward the surface of the silicon wafer in both the radial and circumferential directions, the optical path difference between the polarized beams in the radial and circumferential directions is directly proportional to the photoelastic coefficient of the silicon wafer under test.

[0069] Furthermore, the stress distribution within the silicon wafer under test differs between the first and second physical states. This disclosure obtains the photoelastic coefficient of the silicon wafer under test by measuring different optical path differences under different physical states and by analyzing the different proportional relationships between these optical path differences and the photoelastic coefficient. This approach can, on the one hand, identify and eliminate common systematic errors or environmental influencing factors present when testing under different physical states, thereby improving the accuracy of the photoelastic coefficient test and consequently improving the accuracy of the residual stress detection results for the silicon wafer under test. On the other hand, obtaining the photoelastic coefficient based on the changes in optical path difference caused by the different physical states of the silicon wafer under test can improve the detection sensitivity to minute residual stress changes, thereby improving the accuracy of the residual stress detection results for the silicon wafer under test.

[0070] In step S304, the residual stress of the silicon wafer under test is obtained based on the photoelastic coefficient and the first proportional relationship.

[0071] In this disclosure, after obtaining the photoelastic coefficient of the silicon wafer under test, the residual stress of the silicon wafer under test can be obtained based on the photoelastic coefficient and the first proportional relationship.

[0072] For the technical solution shown in Figure 3, when the silicon wafer under test is in a first physical state, polarized light beams are emitted towards the surface of the silicon wafer along both the radial and circumferential directions, respectively, and a first optical path difference is obtained between the radial and circumferential polarized light beams. When the silicon wafer under test is in a second physical state, polarized light beams are emitted towards the surface of the silicon wafer along both the radial and circumferential directions, respectively, and a second optical path difference is obtained between the radial and circumferential polarized light beams. 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 under test, the second optical path difference, and a 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 under test is obtained. The residual stress detection method provided in this disclosure improves the accuracy of the residual stress detection results by obtaining the photoelastic coefficient corresponding to the silicon wafer under test.

[0073] For the technical solution shown in Figure 3, in some possible implementations, when the first physical state of the silicon wafer under test is that the silicon wafer under test is in a stationary state, the second physical state of the silicon wafer under test is that the silicon wafer under test rotates at a first angular velocity.

[0074] Since the silicon wafer under test exhibits different stress distributions in static and rotating states, obtaining the corresponding optical path difference by measuring the stress distribution of the silicon wafer under test in static and rotating states can eliminate test errors caused by system equipment errors or environmental factors under different physical states, thereby obtaining a more accurate photoelastic coefficient of the silicon wafer under test.

[0075] Furthermore, based on the optical path difference obtained when the silicon wafer under test is in a rotating state, it is ensured that the residual stress calculated using the photoelastic coefficient obtained from the optical path difference can characterize the stress distribution on the entire circumference of the silicon wafer under test or the stress distribution of the entire silicon wafer under test.

[0076] In some examples of the above implementation methods, when the silicon wafer under test is in a static state, the first proportional relationship is expressed as the ratio of the absolute value of the first optical path difference to the photoelastic coefficient as the residual stress of the silicon wafer under test.

[0077] Understandably, when the silicon wafer under test is in a stationary state, after emitting polarized light beams towards the surface of the silicon wafer along both the radial and circumferential directions, respectively, based on the first optical path difference |Δn1| between the radial and circumferential polarized light beams, a first proportional relationship can be obtained as: |Δn1|=C σ Δσ.

[0078] Optionally, when the silicon wafer under test rotates at the first angular velocity, the second proportional relationship is expressed as the ratio of the absolute value of the second optical path difference to the photoelastic coefficient being 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.

[0079] Wherein, the first radial stress component is the radial stress component corresponding to the internal stress generated when the silicon wafer under test rotates at the 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 under test rotates at the first angular velocity in the crystal direction.

[0080] Specifically, for a rotating disk, the centrifugal force generated during rotation causes internal stress to form inside the disk. According to the theory of elasticity, the radial and circumferential stress components corresponding to the internal stress at any point inside the disk can be calculated using the following formulas:

[0081] Where, σ r σ represents the radial stress component corresponding to the internal stress at any point inside the disk; θ denoted by ω, representing the circumferential stress component corresponding to the internal stress at any point inside the disk; μ represents the Poisson's ratio of the disk; ρ represents the material density of the disk; ω represents the angular velocity of the disk's rotation; b represents the radius of the disk; and r represents the distance between that point and the center of the disk in a direction parallel to the surface of the disk.

[0082] Due to the anisotropy of the silicon wafer under test, the formulas for calculating the radial and circumferential stress components corresponding to the internal stress at any point inside the disk described above are applicable to the silicon wafer under test. Therefore, during the rotation of the silicon wafer under test, the first radial stress component and the first circumferential stress component corresponding to the internal stress in different crystal orientations of the silicon wafer under test can be expressed by the following formulas:

[0083] Where, σ r (φ) represents the first radial stress component corresponding to the internal stress in any crystal orientation of the silicon wafer under test; σ θ (φ) represents the first circumferential stress component corresponding to the internal stress in any crystal direction of the silicon wafer under test.

[0084] It should be noted that the angle φ mentioned above represents the angle between any position on the silicon wafer under test and the polar axis when establishing polar coordinates with the center of the silicon wafer under test as the origin and the radius of the horizontal direction of the silicon wafer under test as the polar axis. Understandably, different angles φ on the silicon wafer under test represent different crystal orientations. In specific implementation, the Poisson's ratio and density are different in different crystal orientations of the silicon wafer under test. For example, Figure 4 shows a schematic diagram of the Poisson's ratio of the silicon wafer under test changing with crystal orientation on the (100) crystal plane. Understandably, if it is necessary to know the Poisson's ratio μ(φ) at the position φ = 45° on the (100) crystal plane of the silicon wafer under test, that is... <110> When the Poisson's ratio μ(φ) is in the crystal orientation, it can be found in Figure 4. Furthermore, on the (100) crystal plane of the silicon wafer under test, μα in Figure 4 represents the... Poisson's ratio for crystal orientations at an angle α.

[0085] When the silicon wafer under test rotates at a first angular velocity ω1, polarized light beams are emitted toward the surface of the silicon wafer along both the radial and circumferential directions, respectively. Based on the second optical path difference |Δn2| between the radial and circumferential polarized light beams, the second proportional relationship can be obtained as: |Δn2|=C σ (Δσ+|σ r (φ,ω1)-σ θ (φ,ω1)|). It should be noted that when there is no residual stress inside the silicon wafer under test, the internal stress caused by the rotation of the silicon wafer under test is determined by σ. r (φ,ω1) and σ θ The difference between (φ, ω1) is obtained. When residual stress exists inside the silicon wafer under test, the overall stress distribution of the silicon wafer under test is obtained based on the residual stress Δσ and the internal stress caused by the rotation of the silicon wafer under test.

[0086] For the technical solution shown in Figure 3, in some possible implementations, when the first physical state of the silicon wafer under test is that the silicon wafer under test rotates at a second angular velocity, the second physical state of the silicon wafer under test is that the silicon wafer under test rotates at a third angular velocity; wherein, the third angular velocity is greater than the second angular velocity.

[0087] Since the silicon wafer under test exhibits different stress distributions under different rotational states, obtaining the corresponding optical path difference by measuring the stress distribution of the silicon wafer under test under different rotational states can eliminate the test errors caused by system equipment errors or environmental factors under different rotational states, thereby obtaining a more accurate photoelastic coefficient of the silicon wafer under test.

[0088] Furthermore, by performing measurements under different rotational states, the consistency of the final obtained photoelastic coefficient can be ensured, the reliability of the photoelastic coefficient measurement results can be improved, and thus the accuracy of residual stress detection in the silicon wafer under test can be improved.

[0089] It should be noted that when the angular velocity of the silicon wafer under test is too high, the optical signal corresponding to the polarized beam received by the laser receiver 102 after passing through the silicon wafer will drift. Therefore, in the specific implementation, the laser transmitter 101 and the laser receiver 102 are rotated simultaneously to reduce the angular velocity difference between them, thereby eliminating or mitigating the drift phenomenon 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 under test.

[0090] In some examples of the above implementation methods, when the silicon wafer under test rotates at a 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 being 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.

[0091] The second radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the second angular velocity in the set crystal direction, and the second circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer under test rotates at the second angular velocity in the crystal direction.

[0092] Understandably, when the silicon wafer under test rotates at a second angular velocity ω2, polarized light beams are emitted towards the surface of the silicon wafer along both the radial and circumferential directions, respectively. Based on the first optical path difference |Δn1| between the radial and circumferential polarized light beams of the silicon wafer under test, the first proportional relationship can be obtained as: |Δn1|=C σ (Δσ+|σ r (φ,ω2)-σ θ (φ,ω2)|).

[0093] Optionally, when the silicon wafer under test rotates at the third angular velocity, the second proportional relationship is expressed as the ratio of the absolute value of the second optical path difference to the photoelastic coefficient, which is 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.

[0094] Among them, the third radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the third angular velocity in the crystal direction, and the third circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer under test rotates at the third angular velocity in the crystal direction.

[0095] Understandably, when the silicon wafer under test rotates at a third angular velocity ω3, polarized light beams are emitted towards the surface of the silicon wafer along both the radial and circumferential directions, respectively. Based on the second optical path difference |Δn2| between the radial and circumferential polarized light beams of the silicon wafer under test, the second proportional relationship can be obtained as: |Δn2|=C σ (Δσ+|σ r (φ,ω3)-σ θ (φ,ω3)|).

[0096] For the technical solution shown in Figure 3, in some possible implementations, the photoelastic coefficient is obtained based on a first optical path difference, a first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer under test, a second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient, including:

[0097] Based on the first proportional relationship and the second proportional relationship, the corresponding relationship between the photoelastic coefficient, the first optical path difference and the second optical path difference is obtained;

[0098] The photoelastic coefficient is obtained based on the first optical path difference, the second optical path difference, and their corresponding relationships.

[0099] In some examples, when the silicon wafer under test is at rest and rotating at a first angular velocity, respectively, according to the first proportional relationship |Δn1|=C σ Δσ and the second proportional relationship |Δn2|=C σ (Δσ+|σ r (φ,ω1)-σ θ From (φ,ω1)|), we can obtain: |Δn2|-|Δn1|=C σ (|σ r (φ,ω1)-σ θ (φ,ω1)|). Therefore, the photoelastic coefficient can be obtained. When the photoelasticity coefficient C was obtained σ Then, the photoelastic coefficient Substituting into the first proportional relationship |Δn1|=C σ Δσ or the second proportional relationship |Δn2|=C σ (Δσ+|σ r (φ,ω1)-σ θ The residual stress of the silicon wafer under test can be obtained by using (φ,ω1)|).

[0100] In other examples, when the silicon wafer under test rotates at a second angular velocity and a third angular velocity respectively, according to the first proportional relationship |Δn1|=C σ (Δσ+|σ r (φ,ω2)-σ θ(φ,ω2)|) and the second proportional relationship |Δn2|=C σ (Δσ+|σ r (φ,ω3)-σ θ (φ,ω3)|), we can obtain: |Δn2|-|Δn1|=C σ (|σ r (φ,ω3)-σ θ (φ,ω3)|-|σ r (φ,ω2)-σ θ (φ,ω2)|). Therefore, the photoelastic coefficient can be obtained. When the photoelasticity coefficient C was obtained σ Then, the photoelastic coefficient Substituting into the first proportional relationship |Δn1|=C σ (Δσ+|σ r (φ,ω2)-σ θ (φ,ω2)|) or the second proportional relationship |Δn2|=C σ (Δσ+|σ r (φ,ω3)-σ θ The residual stress of the silicon wafer under test can be obtained by using (φ,ω3)|).

[0101] Understandably, once the photoelastic coefficient of the silicon wafer under test is obtained, the residual stress of the silicon wafer under test can be obtained. In this disclosure, the residual stress of the silicon wafer under test is preferably calculated using the photoelastic coefficient and a first proportional relationship. This is mainly because the silicon wafer under test corresponding to the first proportional relationship is in a stationary state or rotating at a relatively small angular velocity. When the silicon wafer under test is in a stationary state or rotating at a relatively small angular velocity, the internal stress generated by the silicon wafer under test during rotation is very small, or even negligible, and thus has less impact on the residual stress detection results.

[0102] Based on the same inventive concept as the above-described technical solution, and referring to Figure 5, this disclosure provides a system 500 for detecting residual stress in silicon wafers. The system 500 includes:

[0103] The driving device 501 is used to control the silicon wafer under test to be in a first physical state or a second physical state; wherein the angular velocity of the silicon wafer under test in the first physical state is less than the angular velocity of the silicon wafer under test in the second physical state.

[0104] The laser emitter 101 is used to emit polarized beams toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, when the silicon wafer under test is in a first physical state or a second physical state.

[0105] Laser receiver 102 is used to receive a polarized beam of light after it passes through the silicon wafer under test;

[0106] Processor 103 is configured as follows:

[0107] When the silicon wafer under test is in the first physical state, the first optical path difference between the radially polarized beam and the circumferentially polarized beam is obtained;

[0108] When the silicon wafer under test is in the second physical state, the second optical path difference between the radially polarized beam and the circumferentially polarized beam is obtained;

[0109] 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 under test, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient.

[0110] The residual stress of the silicon wafer under test is obtained based on the photoelastic coefficient and the first proportional relationship.

[0111] Referring to Figures 6 and 7, which respectively show the detection results of residual stress on a silicon wafer obtained using related techniques and the detection results of residual stress on a silicon wafer obtained using embodiments of this disclosure. Specifically, a uniform thin film layer is formed on the surface of the silicon wafer using a vapor deposition method to simulate uniform stress applied to the silicon wafer. When using related techniques for detection, the photoelastic coefficient C of the silicon wafer is set... σ Then, based on the SIRD system 100 shown in Figure 1, polarized beams are emitted toward the surface of the silicon wafer along the radial and circumferential directions, and the optical path difference |Δn| between the polarized beams in the radial and circumferential directions is obtained. Then, the formula |Δn|=C is used. σ The residual stress corresponding to the silicon wafer obtained by Δσ is shown in Figure 6, and the final stress distribution of the entire silicon wafer is as follows. As can be seen from Figure 6, the stress distribution in the silicon wafer detected using related technologies is not uniform. When using the technical solution provided in this disclosure for detection, based on the system 500 for detecting the residual stress of the silicon wafer shown in Figure 5, when the silicon wafer is in a stationary state, polarized light beams are emitted radially and circumferentially toward the surface of the silicon wafer 1, and a first optical path difference |Δn1| is obtained between the radially and circumferentially polarized light beams. When the silicon wafer rotates at a first angular velocity ω1, polarized light beams are emitted radially and circumferentially toward the surface of the silicon wafer 1, and a second optical path difference |Δn2| is obtained between the radially and circumferentially polarized light beams. This allows for the accurate acquisition of the photoelastic coefficient C corresponding to the silicon wafer. σ Furthermore, by utilizing the photoelastic coefficient C σThe calculated residual stress of the silicon wafer and the final stress distribution of the entire silicon wafer are shown in Figure 7. As can be seen from Figure 7, the stress distribution in the silicon wafer is uniform, and the result is closer to the actual stress distribution, indicating that the technical solution provided in this embodiment can improve the accuracy of the residual stress detection results of the silicon wafer.

[0112] Finally, this disclosure provides a silicon wafer in which the residual stress of the silicon wafer, calculated based on a first optical path difference in a first physical state and a second optical path difference in a second physical state, is in the range of 0.1 kPa to 10 kPa.

[0113] The first optical path difference is the optical path difference between the radially polarized beam and the circumferentially polarized beam obtained when the silicon wafer is in a first physical state, by emitting polarized beams toward the surface of the silicon wafer along both the radial and circumferential directions; the second optical path difference is the optical path difference between the radially polarized beam and the circumferentially polarized beam obtained when the silicon wafer is in a second physical state, by emitting polarized beams toward the surface of the silicon wafer along both the radial and circumferential directions.

[0114] It should be noted that the technical solutions described in the embodiments of this disclosure can be combined arbitrarily without conflict.

[0115] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for detecting residual stress in a silicon wafer, the method comprising: When the silicon wafer under test is in the first physical state, polarized beams are emitted toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, and a first optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam. When the silicon wafer under test is in the second physical state, polarized beams are emitted toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, and a second optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam; wherein, the angular velocity corresponding to the silicon wafer under test in the first physical state is less than the angular velocity corresponding to the silicon wafer under test 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 under test, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient. The residual stress of the silicon wafer under test is obtained based on the photoelastic coefficient and the first proportional relationship.

2. The method of claim 1, wherein, When the first physical state of the silicon wafer under test is that the silicon wafer under test is stationary, the second physical state of the silicon wafer under test is that the silicon wafer under test is rotating at a first angular velocity.

3. The method of claim 2, wherein, When the silicon wafer under test is in a static 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 under test.

4. The method of claim 2, wherein, When the silicon wafer under test rotates at the first angular velocity, the second proportional relationship is expressed as the ratio of the absolute value of the second optical path difference to the photoelastic coefficient, which is 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. Wherein, the first radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the 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 under test rotates at the first angular velocity in the crystal direction.

5. The method of claim 1, wherein, When the first physical state of the silicon wafer under test is that the silicon wafer under test rotates at a second angular velocity, the second physical state of the silicon wafer under test is that the silicon wafer under test rotates at a third angular velocity; wherein the third angular velocity is greater than the second angular velocity.

6. The method of claim 5, wherein, When the silicon wafer under test 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, which is 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. Wherein, the second radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the second angular velocity in the set crystal direction, and the second circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer under test rotates at the second angular velocity in the crystal direction.

7. The method of claim 6, wherein, When the silicon wafer under test rotates at the third angular velocity, the second proportional relationship is expressed as the ratio of the absolute value of the second optical path difference to the photoelastic coefficient, which is 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. Wherein, the third radial stress component is the radial stress component of the internal stress generated when the silicon wafer under test rotates at the third angular velocity in the crystal direction, and the third circumferential stress component is the circumferential stress component of the internal stress generated when the silicon wafer under test rotates at the third angular velocity in the crystal direction.

8. The method of claim 1, wherein, The process of 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 under test, the second optical path difference, and a second proportional relationship between the second optical path difference and the photoelastic coefficient includes: Based on the first proportional relationship and the second proportional relationship, the correspondence between the photoelastic coefficient, the first optical path difference, and the second optical path difference is obtained; The photoelastic coefficient is obtained based on the first optical path difference, the second optical path difference, and the corresponding relationship.

9. A system for detecting residual stress in a silicon wafer, the system comprising: A driving device is used to control the silicon wafer under test to be in a first physical state or a second physical state; wherein the angular velocity of the silicon wafer under test in the first physical state is less than the angular velocity of the silicon wafer under test in the second physical state. A laser emitter is used to emit polarized beams toward the surface of the silicon wafer under test along the radial and circumferential directions, respectively, when the silicon wafer under test is in a first physical state or a second physical state. A laser receiver for receiving a polarized light beam after it has passed through the silicon wafer under test; The processor is configured as follows: When the silicon wafer under test is in a first physical state, a first optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam. When the silicon wafer under test is in the second physical state, a second optical path difference is obtained between the radially polarized beam and the circumferentially polarized beam. 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 under test, the second optical path difference, and the second proportional relationship between the second optical path difference and the photoelastic coefficient. The residual stress of the silicon wafer under test is obtained based on the photoelastic coefficient and the first proportional relationship.

10. A silicon wafer, wherein the residual stress of the silicon wafer, calculated based on a first optical path difference in a first physical state and a second optical path difference in a second physical state, is in the range of 0.1 kPa to 10 kPa, and the first proportional relationship between the first optical path difference and the photoelastic coefficient of the silicon wafer and the second proportional relationship between the second optical path difference and the photoelastic coefficient are used. wherein The first optical path difference is obtained when the silicon wafer is in the first physical state, by emitting polarized light beams along the radial and circumferential directions toward the surface of the silicon wafer, respectively, and obtaining the optical path difference between the radially polarized light beam and the circumferentially polarized light beam; the second optical path difference is obtained when the silicon wafer is in the second physical state, by emitting polarized light beams along the radial and circumferential directions toward the surface of the silicon wafer, respectively, and obtaining the optical path difference between the radially polarized light beam and the circumferentially polarized light beam.

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