Film substrate stress detection method and system based on piezoelectric cantilever beam impact excitation

Abstract

The invention discloses a thin film substrate stress detection method and system based on piezoelectric cantilever beam impact excitation, and belongs to the field of detection and metering. According to the method, an elastic wave excitation method based on piezoelectric cantilever beam impact excitation and a substrate elastic wave excitation and longitudinal wave velocity calculation method are provided, an acoustic elastic model of substrate global average stress and longitudinal wave velocity is established, and the substrate global average stress is obtained through inversion calculation according to the longitudinal wave velocity propagated on the surface of the substrate. Performing stress detection on the substrate; on the basis, a corresponding detection system is provided, and compared with other substrate stress detection methods, the method has higher test efficiency, can perform stress detection on a large batch of substrates in a short time, and provides a guarantee for subsequent substrate processing steps. The method is suitable for carrying out stress detection on the substrate before thin film deposition and evaluating the surface stress state of the substrate.

Description

Technical Field

[0001] This invention belongs to the field of testing and measurement, and specifically relates to a method and system for detecting stress in thin film substrates based on piezoelectric cantilever beam impact excitation. Background Technology

[0002] Thin film technology, as a key technology in the field of microelectronics, plays an indispensable role in many high-tech fields. By generating surface thin films with thicknesses in the micrometers or even nanometers on the substrate surface, composite systems composed of thin films and substrates can possess physical properties that traditional systems do not have. For example, in the semiconductor field, chemical vapor deposition (CVD) technology is used to generate surface thin films by chemically reacting gaseous precursors on the surface of silicon wafers. Combined with photolithography, etching, and other technologies, chips can be fabricated. In the field of military engineering, physical vapor deposition (PVD) technology is used to coat metal / alloy thin films on the surface of devices or equipment, which can greatly improve their surface hardness, thereby extending their service life and preventing damage.

[0003] For thin film technology, besides the technology itself, another crucial factor in improving the quality and efficiency of thin film formation is the substrate. Thin films are never formed in isolation; they are always deposited on a substrate. The substrate's characteristics, such as residual stress, thermal expansion, surface roughness, and chemical composition, directly affect the adhesion and structural integrity of the film deposited on its surface, determining the usability of the composite system composed of the film and substrate. Before thin film deposition, the substrate typically undergoes mechanical processing such as cutting, grinding, and polishing. These processes usually cause plastic deformation on the substrate surface, while the substrate interior remains in an elastic state. This mutual constraint between the plastic deformation and elastic regions leads to residual stress on the substrate surface. During thin film deposition, if the internal stress of the film is unbalanced with the residual stress on the substrate surface, problems such as warping between the film and substrate, decreased adhesion, and failure of the physical functions of the composite system can occur. Therefore, detecting the residual stress on the substrate surface before thin film deposition is of great significance for improving the quality and efficiency of thin film formation.

[0004] Currently, residual stress detection on substrate surfaces typically employs X-ray diffraction (XRD). This method has been widely studied and applied in practice, demonstrating its feasibility. However, it suffers from drawbacks such as cumbersome operation, expensive equipment, and low efficiency, making it unsuitable for efficient stress detection on large quantities of substrate specimens. Therefore, it is essential to propose a testing method and system capable of efficiently detecting substrate stress. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a method and system for detecting the stress of a thin film substrate based on piezoelectric cantilever beam impact excitation.

[0006] This invention performs stress detection on isotropic substrates used for thin film deposition.

[0007] One objective of this invention is to propose a method for detecting the stress on a thin film substrate based on the impact excitation of a piezoelectric cantilever beam.

[0008] The present invention provides a method for detecting the stress of a thin film substrate based on piezoelectric cantilever beam impact excitation, comprising the following steps:

[0009] 1) A pressure head is fixedly installed on the lower surface of the free end of the piezoelectric cantilever beam, and the fixed end of the piezoelectric cantilever beam is supported on the displacement stage through the base; the substrate to be tested is set on the operating table; an impact point and multiple measurement points are set on the surface of the substrate, and corresponding optical sensors are set on each measurement point, with different distances between each measurement point and the impact point;

[0010] 2) The computer controls the position of the pressure head through the displacement stage. The horizontal position of the pressure head is directly above the impact point and at the height of the pressure head for a single transient point impact.

[0011] 3) Apply a pulse voltage of the target voltage value to the piezoelectric cantilever beam. The piezoelectric cantilever beam will generate a step response and perform a single transient point impact on the impact point on the substrate surface to complete one impact.

[0012] 4) A single transient point impact generates a broadband elastic wave at the impact point on the substrate surface and propagates outward. The longitudinal wave in the broadband elastic wave propagates outward from the impact point along the substrate surface at the fastest speed.

[0013] 5) Each optical sensor measures the time it takes for the longitudinal wave to arrive at its corresponding measurement point and transmits the data to the computer;

[0014] 6) The computer establishes a set of equations for solving the longitudinal wave velocity of a single impact, and solves the set of equations to obtain the longitudinal wave velocity of a single impact.

[0015] 7) Repeat steps 3) to 6) to perform multiple impacts to obtain multiple longitudinal wave velocities of a single impact. Average the longitudinal wave velocities of multiple single impacts to obtain the longitudinal wave velocity propagating on the substrate surface. Based on the longitudinal wave velocity propagating on the substrate surface, calculate the global average stress of the substrate to complete the stress detection of the substrate.

[0016] In step 1), the piezoelectric cantilever beam comprises a cantilever beam and a piezoelectric sheet adhered to its lower surface. The cantilever beam is made of stainless steel, and the piezoelectric sheet is polarized along its thickness direction. The indenter is made of stainless steel and is spherical in shape. The displacement stage is a high-precision three-dimensional displacement stage. The optical sensor is a non-contact optical sensor, and the optical path of the optical sensor and the line connecting the laser probe to the corresponding measurement point are perpendicular to the substrate surface. The distances between each measurement point and the impact point vary significantly. Arranging the distances between each measurement point and the impact point in ascending order, the difference between two adjacent distances is 70-130% of the shortest distance.

[0017] In step 2), the displacement stage controls the horizontal position of the piezoelectric cantilever beam so that the indenter is directly above the impact point. Before testing the substrate, a pulse voltage is applied to the piezoelectric cantilever beam to the target voltage value, and the step response of the piezoelectric cantilever beam is measured under the pulse voltage of the target voltage value. Based on the pulse voltage and the step response curve of the piezoelectric cantilever beam, the height of the first minimum point and the height of the second minimum point corresponding to the free end of the piezoelectric cantilever beam in the step response are obtained. The displacement stage controls the height of the indenter, that is, adjusts the initial distance between the indenter and the substrate surface so that the substrate surface is located between the height of the first minimum point and the height of the second minimum point corresponding to the free end of the piezoelectric cantilever beam in the step response.

[0018] In step 3), considering the step response characteristics of the piezoelectric cantilever beam under pulsed voltage, the substrate surface is located between the first and second lowest points corresponding to the free end of the piezoelectric cantilever beam in the step response. After the indenter impacts the substrate surface for the first time, it will not impact the substrate a second time, thus achieving a single transient point impact on the substrate surface. By adjusting the target voltage value of the pulsed voltage and the initial distance between the indenter and the substrate surface, the impact effect of the piezoelectric cantilever beam on the substrate surface is controlled, thereby actively controlling the excited elastic wave.

[0019] In step 4), a single transient point impact is performed on the substrate surface, which actively excites broadband elastic waves on the substrate and propagates outward from the impact point. Among the elastic waves, the longitudinal wave has the fastest wave velocity. Therefore, in the elastic waves propagating on the isotropic substrate surface, the longitudinal wave will propagate outward from the impact point along the substrate surface at the fastest speed.

[0020] In step 5), when the signal measured by the optical sensor first reaches the peak, it is considered that the longitudinal wave has propagated from the impact point to the measurement point. The time when the pulse signal is applied is taken as the time origin for the optical sensor to collect the signal, and the optical sensor takes the time when the signal first reaches the peak as the time when the longitudinal wave arrives at the measurement point.

[0021] In step 6), the propagation time of the longitudinal wave to the corresponding measurement point is obtained by subtracting the response time of the piezoelectric cantilever beam under a single impact from the time it takes for the longitudinal wave to reach the corresponding measurement point. There are at least two measurement points. Based on the distance between the impact point and each measurement point, and the propagation time of the longitudinal wave to the corresponding measurement point, a nonlinear equation is established for each measurement point, resulting in a set of equations for solving the longitudinal wave velocity. The set of equations contains at least two nonlinear equations, containing two unknowns: the response time of the piezoelectric cantilever beam under a single impact and the longitudinal wave velocity. These equations are solved using Newton's iteration method to minimize the sum of squared errors, thus obtaining the longitudinal wave velocity under a single impact.

[0022] Further measurement points are set to more than three. The equation set for solving the longitudinal wave velocity established by a single impact has more than three nonlinear equations. Two unknowns are solved. The method of minimizing the sum of squared errors is used to solve the unknowns, thereby reducing the impact of measurement errors on the calculation and improving the accuracy of the results.

[0023] In step 7), an acoustoelastic model is established based on the global average stress and P-wave velocity of the substrate. The acoustoelastic relationship is calibrated using a substrate with known surface residual stress. The global average stress of the substrate is calculated from the surface residual stress, yielding the acoustoelastic relationship between the global average stress and the P-wave velocity. For substrates with unknown surface residual stress, the global average stress is calculated by inversion based on the calculated P-wave velocity propagating on the substrate surface. The operating table sequentially delivers the substrates to be tested to the testing position. Each substrate can undergo stress testing once within a short time. Based on the obtained global average stress result, it is determined whether the substrate is suitable for subsequent thin film deposition. For substrates that meet the conditions, the operating table delivers the substrate to the next system for subsequent operations. For substrates that do not meet the conditions, the operating table filters and removes the substrate.

[0024] The calculation of the global average stress of the substrate by means of surface residual stress includes: calculating the average stress by averaging the normal stress in the x-direction and the normal stress in the y-direction of the surface residual stress, and then integrating the average stress on the substrate surface and then averaging the area to obtain the global average stress of the substrate.

[0025] Furthermore, the number of impact points is two or more. After impacting one impact point, the displacement stage controls the pressure head to move to the next impact point, and steps 3) to 6) are repeated to detect the stress of the next impact. Impacting from different impact points allows for the measurement and calculation of the longitudinal wave velocity of the isotropic substrate from different directions and paths, resulting in more accurate calculation results that can reflect the global characteristics of the substrate.

[0026] Another objective of this invention is to propose a thin film substrate stress detection system based on piezoelectric cantilever beam impact excitation.

[0027] The thin-film substrate stress detection system based on piezoelectric cantilever beam impact excitation of the present invention includes: a base, a displacement stage, a piezoelectric cantilever beam, an indenter, an optical sensor, an operating table, a signal generator, a power amplifier, a data acquisition card, and a computer; wherein, the piezoelectric cantilever beam includes a cantilever beam and a piezoelectric sheet attached to its lower surface, the piezoelectric sheet being polarized along the thickness direction; an indenter, which is a spherical indenter, is fixed to the lower surface of the free end of the cantilever beam; the fixed end of the cantilever beam is fixed to the base, and the base is mounted on the displacement stage; the substrate to be tested is placed on the operating table, and impact points and multiple measurement points are set on the substrate surface, with different distances between each measurement point and the impact point; a corresponding optical sensor is set on each measurement point, the optical sensor being a non-contact optical sensor, the laser path of the optical sensor and the line connecting the laser probe to the corresponding measurement point being perpendicular to the substrate surface; the optical sensor is connected to the data acquisition card; the signal generator is connected to the power amplifier, and the power amplifier is connected to the piezoelectric sheet; the signal generator, operating table, and displacement stage are respectively connected to the computer; the optical sensor and the data acquisition card are interconnected with the computer.

[0028] Advantages of this invention:

[0029] This invention proposes an elastic wave excitation method based on piezoelectric cantilever beam impact excitation, and a method for calculating substrate elastic wave excitation and longitudinal wave velocity. An acoustoelastic model of the global average stress and longitudinal wave velocity of the substrate is established. The global average stress of the substrate is calculated by inversion based on the longitudinal wave velocity propagating on the substrate surface, thereby enabling stress detection of the substrate. Based on this, a corresponding detection system is proposed, which has higher testing efficiency compared to other substrate stress detection methods, enabling stress detection of a large number of substrates in a short time, thus providing a guarantee for subsequent substrate processing steps. This invention is applicable to stress detection of substrates before thin film deposition, assessing their surface stress state, and determining whether they are suitable for subsequent thin film deposition or other tests. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of one embodiment of the piezoelectric cantilever beam of the present invention;

[0031] Figure 2 This is a schematic diagram of the step response generated by the piezoelectric cantilever beam of the present invention, wherein (a) is a schematic diagram of the pulse voltage applied to the piezoelectric cantilever beam, and (b) is a graph of the step response generated by the piezoelectric cantilever beam;

[0032] Figure 3 This is a schematic diagram of an elastic wave excitation of a substrate by a piezoelectric cantilever beam; where (a) is the front view and (b) is the left view.

[0033] Figure 4 A schematic diagram showing the number and location distribution of impact points and measurement points;

[0034] Figure 5 This is a schematic diagram of an embodiment of the thin film substrate stress detection system based on piezoelectric cantilever beam impact excitation of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0036] As a traditional piezoelectric actuator, the piezoelectric cantilever beam has many advantages, such as large stroke, high precision, and fast response. Its principle is to attach piezoelectric sheets to the upper and / or lower surfaces of the cantilever beam. The piezoelectric sheets are polarized along the thickness direction. A voltage is applied through the electrodes on the surface of the piezoelectric sheets to form an electric field. Under the action of the electric field, deformation occurs due to the inverse piezoelectric effect. Since the length of the piezoelectric sheet is much greater than its thickness and width, it mainly undergoes expansion and contraction deformation under the action of the external electric field. This causes the cantilever beam to bend and deform, and the displacement is output outward through the free end. Thus, the expansion and contraction motion mode of the piezoelectric sheet can induce the bending motion mode of the cantilever beam, and the output displacement can be amplified to tens or even hundreds of micrometers. Considering that piezoelectric elements have extremely fast response speed and can quickly respond to an applied electric field, this characteristic is also very evident in piezoelectric cantilever beams. When the voltage applied to the piezoelectric cantilever beam is a pulse voltage, that is, when the voltage acting on the piezoelectric element changes abruptly from 0V to the target voltage value U, the piezoelectric cantilever beam will produce a step response, rapidly actuating within a short time. The free end outputs a corresponding displacement and continuously vibrates near the equilibrium position. The vibration amplitude decays continuously over time and eventually tends to stabilize.

[0037] Based on the above analysis, this invention proposes an elastic wave excitation method using a piezoelectric cantilever beam impact excitation. This method achieves a single transient point impact on a substrate through the step response of the piezoelectric cantilever beam, thereby actively exciting a broadband elastic wave on the substrate, which is isotropic. A schematic diagram of the piezoelectric cantilever beam is shown below. Figure 1 As shown, the structure includes a stainless steel cantilever beam and a piezoelectric sheet adhered to its lower surface, with the piezoelectric sheet polarized along its thickness. An indenter is fixed to the lower surface of the free end of the stainless steel cantilever beam. The indenter is typically made of stainless steel. To avoid excessive plastic deformation on the substrate surface during a single transient point impact, a spherical indenter is chosen. Its advantage is that at lower contact depths, the contact stress between the indenter and the contact surface is relatively small, resulting only in elastic deformation. As the contact depth increases, it gradually transitions to smooth plastic deformation. The fixed end of the stainless steel cantilever beam is fixed to a base, which is mounted on a high-precision three-dimensional displacement stage. The high-precision three-dimensional displacement stage controls the overall spatial position of the piezoelectric cantilever beam, thereby controlling the spatial position of the indenter at the free end.

[0038] The pulse voltage applied to the piezoelectric cantilever beam and the step response of the piezoelectric cantilever beam under its action, such as Figure 2 As shown. In Figure 2 In (a) of the diagram, the horizontal axis represents time, and the vertical axis represents the voltage applied to the piezoelectric element of the piezoelectric cantilever beam. The moment when the pulse voltage is applied, and U is the target voltage value of the pulse voltage, at time... When a pulse voltage is applied to the piezoelectric plate of a piezoelectric cantilever beam, the voltage and electric field build-up speed is much higher than the step response speed of the piezoelectric cantilever beam. Therefore, the effect of the pulse voltage can be considered as a step, i.e., at time t. The voltage applied to the piezoelectric element of the piezoelectric cantilever beam abruptly changes from 0V to the target voltage value U. Under the action of the pulsed voltage, the piezoelectric cantilever beam produces a step response, such as... Figure 2 As shown in (b), the horizontal axis represents time, and the vertical axis represents the height of the free end of the piezoelectric cantilever beam, where the moment the pulse voltage is applied is... The piezoelectric cantilever beam begins to produce a step response. The moment when the free vibration of the piezoelectric cantilever beam completely stops and it reaches its equilibrium height. Let be the initial height of the free end of the piezoelectric cantilever beam, h be the equilibrium height of the free end of the piezoelectric cantilever beam, A be the position where the free end of the piezoelectric cantilever beam first reaches its lowest point, and B be the position where the free end of the piezoelectric cantilever beam reaches its lowest point for the second time after vibration. The heights of the first and second lowest points corresponding to the free end of the piezoelectric cantilever beam in the step response are denoted as h0 and h1, respectively. A and h B At that moment When a pulsed voltage is applied to the piezoelectric element of a piezoelectric cantilever beam, the beam produces a step response. Its free end outputs displacement within a short time. However, due to the beam's low stiffness and the effects of inertia and damping, it will continuously vibrate around its equilibrium height, with the vibration amplitude constantly decaying, exhibiting the characteristics of free vibration decay. As the vibration amplitude gradually decreases until it stops vibrating, the free end will... It remains stable at the equilibrium height. Since the vibration amplitude continuously decays, as shown in the diagram, the initial lowest point height h corresponding to the free end... A Compared to the height h of the second minimum point B To achieve a lower value, the output displacement at the free end needs to be larger. This is because energy is dissipated by factors such as damping during vibration.

[0039] Based on the step response characteristics of a piezoelectric cantilever beam under pulsed voltage, this invention proposes the following method to achieve a single transient point impact on the substrate: placing the substrate surface at the height h corresponding to the first lowest point of the piezoelectric cantilever beam at its free end during the step response. A With the height h of the second lowest pointB Between these points, when the piezoelectric cantilever beam exhibits a step response, the free end of the piezoelectric cantilever beam will descend from its initial height h0 to its first lowest point height h. A During the process, the indenter comes into contact with the substrate surface and impacts the impact point on the substrate surface. After the impact, it will rebound. However, the energy output by the piezoelectric cantilever beam is dissipated by its own vibration and also consumed by the impact of the indenter on the substrate surface. When the free end of the piezoelectric cantilever beam is at its lowest point again after rebound, its output displacement is smaller than that under free conditions. Therefore, after the first impact on the substrate surface, there will be no secondary impact on the substrate. This achieves a single transient point impact on the substrate surface.

[0040] A single transient point impact on the substrate surface is achieved by using the step response of a piezoelectric cantilever beam, which in turn generates a broadband elastic wave at the impact point on the substrate surface and propagates outward. By adjusting the target voltage value of the pulse voltage and the initial distance between the indenter and the substrate surface, the impact effect of the piezoelectric cantilever beam on the substrate surface can be controlled, thereby actively controlling the excited elastic wave.

[0041] Compared to traditional methods that use the mass of a heavy object to excite elastic waves, the elastic wave excitation method based on piezoelectric cantilever beam impact excitation proposed in this invention can control the impact effect of a single transient point impact by adjusting the pulse voltage and the initial height between the indenter and the substrate surface, thereby actively controlling the elastic wave and exhibiting better controllability and repeatability. The impact is a single transient event, preventing secondary impacts due to subsequent vibrations or rebounds, which would affect the elastic wave generated by the initial impact excitation. The indenter fixed to the free end of the piezoelectric cantilever beam is a stainless steel spherical indenter, which produces minimal plastic deformation during the impact process, making it less likely to alter the mechanical properties of the substrate to the point of rendering it unusable.

[0042] like Figure 3As shown, a piezoelectric cantilever beam is mounted on a high-precision three-dimensional displacement stage. By controlling the overall spatial position of the piezoelectric cantilever beam, the impact position of the indenter on the substrate surface is controlled. When a pulse voltage is applied to the piezoelectric cantilever beam, it generates a step response, delivering a single transient point impact to the substrate surface. This actively excites a broadband elastic wave on the substrate, which propagates outward from the impact point. Considering that longitudinal waves have the fastest wave velocity in elastic waves, the longitudinal wave will propagate outward from the impact point along the substrate surface at the fastest speed. To measure the longitudinal wave on the substrate surface, this invention proposes using non-contact optical sensors. Each optical sensor corresponds to a measurement point. The line connecting the laser probe of the optical sensor to the measurement point and the optical path are all perpendicular to the substrate surface. When the longitudinal wave on the substrate surface propagates from the impact point to the measurement point of the optical sensor, the optical sensor performs real-time, high-precision measurement of the wave state at that point. This non-contact measurement method does not require extensive preprocessing of the substrate, enabling in-situ testing and significantly improving testing efficiency. Since the longitudinal wave has the fastest velocity, the optical sensor will first measure the longitudinal wave propagating from the impact point along the substrate surface. However, because the substrate is a thin plate structure, its boundary conditions will cause reflection and refraction of the elastic wave during propagation, making it difficult to distinguish the waveform components. Therefore, this study mainly measures the fastest propagating longitudinal wave on the substrate surface using the optical sensor. When the measured signal first reaches its peak, it is considered that the longitudinal wave has propagated from the impact point to the measurement point of the optical sensor. After this point, due to the reflection and refraction of the elastic wave, the measurement signal of the optical sensor will become chaotic due to waveform aliasing, making it difficult to distinguish the waveform components; therefore, this is not analyzed. Finally, the longitudinal wave velocity propagating on the substrate surface is calculated based on the distance between the impact point and the measurement point, as well as the measurement signal from the optical sensor.

[0043] The vertical projection of the laser probe of the optical sensor onto the substrate surface is located at the measurement point. This invention proposes a design for the number and location of impact points and measurement points, ensuring that the distances between the impact points and each measurement point are approximately arithmetically equal. This avoids measurement errors from having an excessive impact on the calculation of longitudinal wave velocity, thus improving calculation accuracy. The specific distribution is as follows: Figure 4 As shown in the diagram, the radius of the substrate is R. Three optical sensors simultaneously measure different positions on the substrate surface from three different measurement points. The first to third measurement points are S1, S2, and S3, with corresponding coordinates of (0, R), (0, -R), and (R, 0), respectively. The two impact points of the piezoelectric cantilever beam are the first and second impact points, E1 and E2, with corresponding coordinates of (0, R / 2) and (0, -R / 2), respectively. High-precision positioning of the indenter on the substrate surface can be achieved using a high-precision three-dimensional displacement stage mounted on the piezoelectric cantilever beam.

[0044] Since the substrate is isotropic, the longitudinal waves on the substrate surface propagate at the same speed in all directions. First, a high-precision three-dimensional displacement stage is used to position the indenter at the first impact point E1, preparing for impact excitation. Simultaneously, a pulse voltage is applied to the piezoelectric cantilever beam, and measurement signals from three optical sensors are acquired. After the impact excitation, the longitudinal waves on the substrate surface will propagate from the impact point along the substrate surface in all directions. When they reach the measurement point, the optical sensors measure the longitudinal waves, and the data acquisition card acquires the measurement signals from the optical sensors. When the measurement signal first reaches its peak, the corresponding time is the time when the longitudinal wave reaches the measurement point. The moment the pulse signal is applied is taken as the origin of the time for the optical sensors to acquire signals, and the origin of the time for the data acquisition card to acquire signals is also taken as the moment the pulse signal is applied. The computer controls the data acquisition card to activate when the signal generator emits a pulse voltage. Since the measurement signal is acquired as soon as the pulse voltage is applied to the piezoelectric cantilever beam, and the piezoelectric cantilever beam requires a certain response time before impacting the substrate surface under the pulse voltage, the response time of the piezoelectric cantilever beam needs to be subtracted from the arrival time of the longitudinal wave determined by the measurement signal to obtain the true propagation time of the longitudinal wave from the impact point to the measurement point. Based on the distance between the impact point and the three measurement points, as well as the measurement signal from the optical sensor, the longitudinal wave velocity on the substrate surface is calculated. The equation for the longitudinal wave velocity of a single impact is as follows:

[0045] (1)

[0046] Let this impact excitation be denoted as the first impact. The first equation is obtained by the longitudinal wave propagating from the first impact point E1 to the first measurement point S1. The second equation is obtained by the longitudinal wave propagating from the first impact point E1 to the second measurement point S2. The third equation is obtained by the longitudinal wave propagating from the first impact point E1 to the third measurement point S3. In the equation system, t1 1 t2 1 and t3 1 The times t0 represent the arrival times of the longitudinal wave at the first to third measurement points (S1, S2, and S3) measured by the three optical sensors during the first impact. 1 To represent the response time of the piezoelectric cantilever beam under the first impact, X1 and Y1, X2 and Y2, and X3 and Y3 are the planar coordinates of the first to third measurement points S1, S2, and S3, respectively, and x1 and y1 are the planar coordinates of the first impact point E1. This represents the P-wave velocity of the first impact. There are three nonlinear equations in total, containing... and t0 1 Given two unknowns, we can solve for the unknowns by minimizing the sum of squared errors using Newton's iteration method.

[0047] After the first impact excitation, a high-precision three-dimensional displacement stage was used to position the indenter at the second impact point E2, and this impact was recorded as the second impact. Then, the base was rotated 180° counterclockwise, and the indenter was again positioned at the first and second impact points E1 and E2 using the same high-precision three-dimensional displacement stage. These two impacts were recorded as the third and fourth impacts, respectively. The elastic wave excitation and wave velocity calculation for each impact were the same as for the first impact. Each impact yielded three nonlinear equations for solving the longitudinal wave velocity, written in the following form:

[0048] (2)

[0049] in For the optical sensor at the i-th measurement point S during the j-th impact... i The measured time of arrival of the longitudinal wave at the measurement point, Let X be the response time of the piezoelectric cantilever beam under the j-th impact. i and Y i For the i-th measurement point S i Planar coordinates, x i and y i Let J be the coordinates of the impact point of the j-th impact. Let be the longitudinal wave velocity of the j-th impact. Finally, the longitudinal wave velocities of the four impacts are averaged to obtain the longitudinal wave velocity v propagating on the substrate surface:

[0050] (3)

[0051] Based on the proposed elastic wave excitation method using piezoelectric cantilever beam impact excitation, a method for elastic wave excitation and wave velocity calculation of the substrate is proposed. A high-precision three-dimensional displacement stage is used to locate the impact points on the substrate surface, and an optical sensor is used to measure the propagation time of the elastic wave on the substrate surface. By designing the number and location of the impact points and measurement points, the longitudinal wave velocity propagating on the substrate surface is calculated. The advantages of this method are: using a non-contact optical sensor to measure the elastic wave on the substrate surface is an in-situ measurement method that does not require complicated preprocessing of the substrate surface, greatly improving testing efficiency; designing the number and distribution of impact points and measurement points so that the distance between the impact points and measurement points is approximately an arithmetic gradient prevents measurement errors from having an excessive impact on the wave velocity calculation, thus improving the accuracy of the longitudinal wave velocity calculation on the substrate surface.

[0052] Based on the above discussion, the longitudinal wave velocity propagating on the substrate surface was calculated. Considering the acoustoelastic effect in elastic wave theory, the presence of residual stress within the material affects its equivalent elastic stiffness, thus influencing the propagation speed of elastic waves within the material. This invention proposes an acoustoelastic model for the global average stress of the substrate and the longitudinal wave velocity. Using a substrate with known surface residual stress, the acoustoelastic relationship between the global average stress and the longitudinal wave velocity is calibrated, yielding the acoustoelastic relationship. For substrates with unknown surface residual stress, the global average stress of the substrate is calculated by inversion based on the calculated longitudinal wave velocity propagating on the substrate surface, thereby enabling stress detection of the substrate, as detailed below:

[0053] First, since substrate fabrication typically involves cutting, grinding, and polishing, these machining processes usually introduce plastic deformation into the substrate surface, while the substrate interior is generally in an elastic state. Due to the constraint between the plastic deformation and the elastic region, residual stress is generated on the substrate surface. This residual stress is mostly compressive or tensile stress; therefore, this study focuses primarily on the normal stress distribution on the substrate surface, neglecting shear stress and normal stress perpendicular to the substrate surface. To determine the residual stress distribution on the substrate surface, X-ray diffraction (XRD) is used to measure it. The theory and applications of these methods are well-established and will not be elaborated upon here. After obtaining the residual stress distribution on the substrate surface, the residual stress is processed to obtain the global average stress of the substrate.

[0054] (4)

[0055] in, and These represent the normal stress in the x-direction and the normal stress in the y-direction of the measured residual stress on the substrate surface. For the average stress, through and The average was calculated to obtain, The average stress on the substrate is denoted as S, and the surface area of ​​the substrate is denoted as S. It is obtained by integrating the average stress on the substrate surface and then averaging the area. It is a global index of the residual stress on the substrate surface.

[0056] The residual stress distribution on the substrate surface was determined using X-ray diffraction (XRD). For substrates without residual stress, the longitudinal wave velocity propagating on the substrate surface was calculated to obtain the longitudinal wave velocity propagating on the substrate surface without residual stress. For substrates with residual stress on the surface and a known distribution, the longitudinal wave velocity propagating on the substrate surface under the presence of residual stress is also calculated. Due to the acoustoelastic effect, the calculated longitudinal wave velocity at this time is lower than the longitudinal wave velocity propagating on the substrate surface without residual stress. There are differences, and to measure these differences, the following processing method is used:

[0057] (5)

[0058] in, This represents the difference in longitudinal wave velocities calculated. According to the acoustoelastic effect in elastic wave theory, when the residual stress is small, the relationship between the residual stress and the change in wave velocity is linear; therefore, we have:

[0059] (6)

[0060] Wherein, K is the acoustoelastic coefficient, used to illustrate the influence of the global average stress of the substrate on the longitudinal wave velocity propagating on the substrate surface. The longitudinal wave velocity propagating on the substrate surface is calculated for a series of substrates with known residual stress conditions, yielding a corresponding array of values. and The acoustic elastic coefficient K is obtained through linear fitting.

[0061] For a substrate with unknown residual stress distribution on the substrate surface, the longitudinal wave velocity propagating on the substrate surface is calculated. Based on the acoustoelastic relationship between the global average stress of the substrate and the longitudinal wave velocity obtained from formula (6), and the longitudinal wave velocity propagating on the substrate surface when there is no residual stress, the longitudinal wave velocity is calculated. The inversion calculation yielded the global average stress of the base. This allows for stress detection of the substrate.

[0062] Based on the acoustoelastic model of global average stress and longitudinal wave velocity proposed in this invention, when the residual stress distribution on the substrate surface is unknown, the global average stress is obtained by calculating the longitudinal wave velocity propagating on the substrate surface using the elastic wave excitation and wave velocity calculation method. When the global average stress exceeds the stress threshold, the residual stress on the substrate surface is considered too high, making it unsuitable for thin film deposition. If the global average stress is within the normal range, the substrate can be used for thin film deposition or for more refined testing. Compared to other substrate stress detection methods, the method proposed in this invention is more efficient, requires no complex pretreatment of the substrate, and can perform stress testing on a large number of substrates in a short time.

[0063] like Figure 5 As shown, the thin film substrate stress detection system based on piezoelectric cantilever beam impact excitation in this embodiment includes: a base, a displacement stage, a piezoelectric sheet, a cantilever beam, an indenter, an optical sensor, an operating table, a signal generator, a power amplifier, a data acquisition card, and a computer.

[0064] The piezoelectric cantilever beam is the loading component of the testing system, comprising the cantilever beam and a piezoelectric sheet adhered to its lower surface, bonded together with epoxy resin. The piezoelectric sheet is polarized along its thickness direction, and the cantilever beam is made of stainless steel. A spherical indenter is fixed to the lower surface of the free end of the cantilever beam. The fixed end of the cantilever beam is fixed to a base, which is mounted on a high-precision three-dimensional displacement stage. The spatial position of the piezoelectric cantilever beam is controlled by the displacement stage, thereby controlling the impact position of the indenter on the substrate surface.

[0065] The substrate is placed on the operating table, which controls the initial positioning, delivery, and rotation of the substrate. Optical sensors, which are non-contact optical sensors, are positioned above the substrate. The number and arrangement of the optical sensors are as follows: Figure 3 As shown; the laser probe and laser path of the optical sensor are perpendicular to the substrate surface, used to perform high-precision measurement of the propagation time of the longitudinal wave in the elastic wave on the substrate surface.

[0066] The entire system is controlled by a computer. The computer is connected to the displacement stage, which is then automatically controlled to precisely position the impact point of the indenter on the substrate surface. The computer is also connected to the operating console, which controls the initial positioning of the substrate and its automated delivery and rotation. A signal generator is connected to the computer to modulate and trigger pulse voltage signals. The signal generator is connected to a power amplifier to amplify the pulse voltage signals generated by the signal generator. The power amplifier is connected to the piezoelectric element of the piezoelectric cantilever beam to apply the pulse voltage to the piezoelectric element. A data acquisition card and optical sensors are interconnected with the computer. The computer sets the measurement parameters of the optical sensors, the data acquisition card acquires the measurement signals from the optical sensors, and the computer sets the acquisition parameters of the data acquisition card and saves and processes the acquired results for further analysis.

[0067] A typical substrate stress testing procedure for the testing system is as follows: The computer sets the parameters for the entire testing system, including the pulse voltage generated by the signal generator, the data acquisition parameters of the data acquisition card, and the measurement parameters of the optical sensor; the operating platform moves the substrate to be tested to the test position and performs initial positioning; the computer triggers the test, controlling the displacement stage to position the indenter at the first impact point on the substrate surface, performing the first piezoelectric cantilever beam impact excitation, and collecting and saving the measurement results; the operating platform controls the displacement stage to position the indenter at the second impact point on the substrate surface, performing the second piezoelectric cantilever beam impact excitation, and collecting and saving the measurement results; the operating platform rotates the substrate counterclockwise by 180°, and the displacement stage controls the indenter... The first impact point on the substrate surface is positioned, and a third piezoelectric cantilever beam impact excitation is performed. The measurement results are collected and saved. The displacement stage is controlled to position the indenter at the second impact point on the substrate surface, and a fourth piezoelectric cantilever beam impact excitation is performed. The measurement results are collected and saved. The results of the four impact excitations are processed by computer to calculate the longitudinal wave velocity propagating on the substrate surface. Based on the acoustoelastic relationship between the global average stress of the substrate and the longitudinal wave velocity obtained from calibration, the global average stress of the substrate is calculated by inversion, and it is determined whether the substrate is suitable for thin film deposition. The operating stage sends out the tested substrate and puts in the next substrate to be tested. The above process is repeated to complete the stress detection of the substrate to be tested.

[0068] Because the entire testing system is computer-controlled, it possesses a high degree of automation. After the overall parameters of the testing system are set by the computer, stress testing can be performed on a large number of substrates. The operating table sequentially delivers the substrates to be tested to the testing position. Each substrate can undergo a stress test within a short time. Based on the obtained global average stress result, it is determined whether the substrate is suitable for subsequent thin film deposition. For substrates that meet the conditions, the operating table delivers them to the next system for subsequent operations. For substrates that do not meet the conditions, the operating table filters and removes them. Therefore, the testing system proposed in this invention measures the global average stress of the substrate, which is a global indicator of the stress condition on the substrate surface. Although it cannot obtain the specific distribution of residual stress on the substrate surface, it has extremely high testing efficiency and can perform stress testing on a large number of substrates in a short time. This provides a guarantee for subsequent thin film deposition or more stringent substrate testing, preventing resource waste due to excessive residual stress on the substrate surface.

[0069] Finally, it should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. However, those skilled in the art will understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the claims.

Claims

1. A method for detecting stress in a thin film substrate based on piezoelectric cantilever beam impact excitation, characterized in that, The detection method includes the following steps: 1) A pressure head is fixedly installed on the lower surface of the free end of the piezoelectric cantilever beam, and the fixed end of the piezoelectric cantilever beam is supported on the displacement stage through the base; the substrate to be tested is set on the operating table; an impact point and multiple measurement points are set on the surface of the substrate, and corresponding optical sensors are set on each measurement point, with different distances between each measurement point and the impact point; 2) The computer controls the position of the pressure head through the displacement stage. The horizontal position of the pressure head is directly above the impact point and at the height of the pressure head for a single transient point impact. 3) Apply a pulse voltage of the target voltage value to the piezoelectric cantilever beam, and the piezoelectric cantilever beam will generate a step response, performing a single transient point impact on the impact point on the substrate surface to complete one impact. 4) A single transient point impact generates a broadband elastic wave at the impact point on the substrate surface and propagates outward. The longitudinal wave in the broadband elastic wave propagates outward from the impact point along the substrate surface at the fastest speed. 5) Each optical sensor measures the time it takes for the longitudinal wave to arrive at its corresponding measurement point and transmits the data to the computer; 6) The computer establishes a set of equations for solving the longitudinal wave velocity of a single impact, and solves the set of equations to obtain the longitudinal wave velocity of a single impact. 7) Repeat steps 3) to 6) to perform multiple impacts to obtain multiple longitudinal wave velocities of a single impact. Average the longitudinal wave velocities of multiple single impacts to obtain the longitudinal wave velocity propagating on the substrate surface. Based on the longitudinal wave velocity propagating on the substrate surface, calculate the global average stress of the substrate to complete the stress detection of the substrate.

2. The detection method according to claim 1, characterized in that, In step 1), the distances between each measurement point and the impact point are arranged in order of least to greatest, and the difference between two adjacent distances is 70 to 130% of the shortest distance.

3. The detection method according to claim 1, characterized in that, Before testing the substrate, a pulse voltage is applied to the piezoelectric cantilever beam to the target voltage value. The step response of the piezoelectric cantilever beam under the pulse voltage of the target voltage value is measured. Based on the pulse voltage and the step response curve of the piezoelectric cantilever beam, the height of the first minimum point and the height of the second minimum point corresponding to the free end of the piezoelectric cantilever beam in the step response are obtained. The height of the indenter is controlled by the displacement stage, that is, the initial distance between the indenter and the substrate surface is adjusted so that the substrate surface is located between the height of the first minimum point and the height of the second minimum point corresponding to the free end of the piezoelectric cantilever beam in the step response.

4. The detection method according to claim 3, characterized in that, In step 3), by combining the step response of the piezoelectric cantilever beam under pulse voltage, the piezoelectric cantilever beam is controlled to perform a single transient point impact on the substrate surface by adjusting the target voltage value of the pulse voltage and the initial distance between the indenter and the substrate surface.

5. The detection method according to claim 1, characterized in that, In step 5), the moment when the pulse signal is applied is taken as the time origin for the optical sensor to acquire the signal, and the optical sensor takes the moment when the signal first reaches the peak as the time when the longitudinal wave arrives at the measurement point.

6. The detection method according to claim 1, characterized in that, In step 6), the propagation time of the longitudinal wave to the corresponding measurement point is obtained by subtracting the response time of the piezoelectric cantilever beam under a single impact from the time it takes for the longitudinal wave to reach the corresponding measurement point. There are at least two measurement points. Based on the distance between the impact point and each measurement point and the propagation time of the longitudinal wave to the corresponding measurement point, a nonlinear equation is established for each measurement point to obtain a set of equations for solving the longitudinal wave velocity. The set of equations has at least two nonlinear equations containing two unknowns: the response time of the piezoelectric cantilever beam under a single impact and the longitudinal wave velocity. The longitudinal wave velocity under a single impact is obtained by minimizing the sum of squared errors using the Newton-Raphson iteration method.

7. The detection method according to claim 6, characterized in that, Further measurement points are set to more than three, and the equation set for solving the longitudinal wave velocity established by a single impact has more than three nonlinear equations.

8. The detection method according to claim 1, characterized in that, In step 7), an acoustoelastic model is established based on the global average stress of the substrate and the longitudinal wave velocity. The acoustoelastic relationship is calibrated using a substrate with known surface residual stress. The global average stress of the substrate is calculated from the surface residual stress, and the acoustoelastic relationship between the global average stress of the substrate and the longitudinal wave velocity is obtained. For a substrate to be tested with unknown surface residual stress, the global average stress of the substrate is obtained by inversion calculation based on the longitudinal wave velocity propagating on the substrate surface.

9. A detection system for a thin film substrate stress detection method based on piezoelectric cantilever beam impact excitation according to any one of claims 1 to 8, characterized in that, The detection system includes: a base, a displacement stage, a piezoelectric cantilever beam, an indenter, an optical sensor, an operating table, a signal generator, a power amplifier, a data acquisition card, and a computer. The piezoelectric cantilever beam comprises a cantilever beam and a piezoelectric sheet adhered to its lower surface. An indenter is fixed to the lower surface of the free end of the cantilever beam. The fixed end of the cantilever beam is fixed to the base, which is mounted on the displacement stage. The substrate to be tested is placed on the operating table, and impact points and multiple measurement points are set on the substrate surface, with different distances between each measurement point and the impact point. A corresponding optical sensor is set above each measurement point. The optical sensor is connected to the data acquisition card. The signal generator is connected to the power amplifier, which is connected to the piezoelectric sheet. The signal generator, operating table, and displacement stage are all connected to the computer. The optical sensor and data acquisition card are interconnected with the computer.

10. The detection system according to claim 9, characterized in that, The piezoelectric sheet is polarized along the thickness direction; the indenter is spherical; the optical sensor is a non-contact optical sensor, and the laser path of the optical sensor and the line connecting the laser probe and the corresponding measurement point are perpendicular to the substrate surface.

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