Wafer warpage detection system and wafer warpage detection method

Abstract

A wafer warping detection system and method, comprising: a support assembly composed of a plurality of support units arranged below the wafer, each support unit comprising a support member and a piezoelectric member, the piezoelectric member having sensing and driving functions; a force acquisition assembly connected to each piezoelectric member at the input end, acquiring force feedback information of each support unit and outputting to the control assembly; a control assembly with a pre-constructed flexibility matrix, setting a target support force according to the corresponding wafer local microelement area gravity of each support unit, and correcting the driving voltage of each piezoelectric member based on the flexibility matrix by executing a coordinated iterative algorithm until the error between the measured support force and the target support force of all support units meets the convergence condition; a warping measurement assembly for measuring the warping amount of the wafer after the support force of all support units converges. The present application realizes the warping measurement after the wafer is supported to an approximate zero gravity state, effectively eliminates the interference of gravity deformation on warping detection, and improves the measurement accuracy.

Description

Technical Field

[0001] This invention relates to the field of semiconductor testing, and more specifically to a wafer warpage detection method and a wafer warpage detection system. Background Technology

[0002] Wafer warpage is a core parameter characterizing wafer geometry in semiconductor manufacturing, originating from uneven stress distribution introduced by the manufacturing process. Accurate measurement of process-induced wafer warpage is crucial for optimizing process parameters, controlling wafer deformation, and improving device yield. In current conventional horizontal support measurement scenarios, the wafer's own weight causes significant sagging deformation. This deformation is typically on the same order of magnitude as process-induced warpage, resulting in directly measured warpage results containing substantial gravity errors. This fails to accurately reflect the deformation characteristics introduced by the process itself, becoming a core bottleneck restricting the improvement of wafer warpage measurement accuracy.

[0003] To address the issue of eliminating the influence of gravity in wafer warpage measurement, existing technologies mainly focus on support methods and post-measurement compensation, specifically including: Vertical measurement method: The wafer is placed vertically so that its plane is parallel to the direction of gravity, thus eliminating the vertical sag caused by gravity when placed horizontally. However, in the vertical clamping state, the wafer will still be subjected to in-plane bending moment caused by its own weight, and the in-plane component of gravity will still cause in-plane deformation, making it impossible to achieve a true "zero gravity" support state.

[0004] The flip compensation method measures the warpage on both the front and back sides of the wafer (flipped 180°) and separates the actual process warpage and gravity sagging components based on the difference between the two measurements. However, the flip operation requires additional wafer handling steps, increasing the risk of wafer surface scratches and particle contamination, which does not meet the cleanliness requirements of advanced processes for wafer handling. Furthermore, there is a repeatability error in the wafer placement between the two measurements, which directly affects the accuracy of the differential calculation.

[0005] Finite element model compensation method: By establishing a finite element model of the wafer's elastic thin plate, the theoretical gravitational sag field is calculated based on known support boundary conditions and wafer material parameters. This calculated value is then subtracted from the measured warpage data to reconstruct the actual process warpage. However, the compensation accuracy of this method is highly dependent on the accuracy of the support boundary conditions. In actual measurements, factors such as the contact stiffness of multi-point supports, contact position errors, and the microstructure of the wafer surface are difficult to model accurately, leading to deviations between the theoretical calculations and actual gravitational deformation.

[0006] In summary, current wafer warp measurement technologies cannot completely eliminate the influence of wafer gravity and introduce additional process errors, modeling errors, and limited accuracy. Therefore, there is an urgent need in this field to develop a novel wafer warp measurement technology that can actively counteract the influence of wafer weight and achieve near-zero gravity support. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides a wafer warpage detection system and a wafer warpage detection method. By actively supporting each local micro-element of the wafer with individualized control, the gravity on each local micro-element area of ​​the wafer is precisely offset, thereby reducing the net gravitational load on the wafer during the measurement process to near zero.

[0008] This invention provides a wafer warpage detection system, comprising: a support assembly, the support assembly being composed of multiple support units arranged below the wafer, each support unit including a support component and a piezoelectric component, the piezoelectric component having driving and sensing functions; a force acquisition assembly, the input end of the force acquisition assembly being connected to each piezoelectric component, acquiring force feedback information of the measured support force of each support unit and outputting it to a control assembly; a control assembly, the control assembly having a pre-constructed compliance matrix, the control assembly setting a target support force based on the gravity of the wafer's local micro-area corresponding to each support unit, and executing a coordinated iterative algorithm based on the compliance matrix to correct the driving voltage of each piezoelectric component until the error between the measured support force and the target support force of all support units meets the convergence condition; and a warpage measurement assembly, the warpage measurement assembly measuring the wafer warpage after the support forces of all support units converge.

[0009] Preferably, the support components are uniformly arranged in a grid pattern below the wafer. By establishing a quantitative relationship between the spacing between each support unit and the wafer deflection residue, and using the threshold value of the wafer deflection residue as a constraint, the boundary value of the spacing is determined.

[0010] Preferably, the piezoelectric component realizes the sensing function through the direct piezoelectric effect, the driving function through the inverse piezoelectric effect, and the driving function and the sensing function are realized through time-division multiplexing.

[0011] Preferably, the force acquisition component includes a charge amplifier, a low-pass filter, and an analog-to-digital converter; the input terminal of the charge amplifier is connected to the piezoelectric component; the input terminal of the low-pass filter is connected to the output terminal of the charge amplifier; the input terminal of the analog-to-digital converter is connected to the output terminal of the low-pass filter; the force acquisition component acquires the induced signals of each support unit through multi-channel time-division multiplexing.

[0012] Preferably, the method for constructing the compliance matrix includes: obtaining the initial parameters of each of the support units in a fabless state; placing a standard wafer on the support assembly; sequentially changing the support force of each of the support units to obtain the response parameters of all the support units; and calibrating the compliance matrix according to the response parameters.

[0013] Preferably, the control component is further configured to model the jitter noise source of the support component and suppress the jitter of the support component by adding low-pass filtering and active damping.

[0014] Preferably, during the execution of the coordinated iterative algorithm based on the compliance matrix, the waiting time between correcting the driving voltage of each piezoelectric driving component and receiving the force feedback information again in each iteration is set as a preset refresh cycle. By ensuring that the duration of the preset refresh cycle is sufficient for the elastic deformation of the wafer to fully propagate to a steady state after each driving update before proceeding to the next iteration, the stability of the iteration is enhanced.

[0015] Preferably, the warp measurement assembly includes at least one of a piezoelectric measurement unit, an optical measurement unit, and a capacitance measurement unit.

[0016] This invention provides a method for detecting wafer warpage, comprising: S1. Place the wafer to be tested on the support assembly; S2. Obtain the nominal parameters of the wafer to be tested, and calculate the initial value of the target support force of the support component based on the nominal parameters; S3. Drive the support component to support the wafer under test with the initial value of the target support force; S4. Collect the force feedback information of the support component, and calculate the measured support force of the support component based on the force feedback information; S5. Determine whether the difference between the measured support force and the target support force meets the threshold requirement; S6. If not satisfied, the target support force is corrected by executing a coordination iterative algorithm based on the flexibility matrix, the support component is controlled to support the wafer under test with the corrected target support force, and the process returns to step S4. S7. If satisfied, confirm the force control convergence and perform warpage measurement on the wafer under test.

[0017] The present invention provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the above-described wafer warpage detection method.

[0018] The beneficial effects of this invention are: 1. By using active force feedback control, the net gravitational bending moment on the wafer is reduced to a minimum at the physical level, fundamentally eliminating the source of gravitational deformation, rather than approximating it through mathematical means; 2. By using a global coordination iterative algorithm based on the compliance matrix, the fundamental problem of wafer elastomer deformation coordination constraint is specifically addressed. The compliance matrix can be pre-calibrated offline, and the iterative control converges quickly. 3. After force control convergence, an active damping mechanism is introduced to bring the warping measurement error caused by the positional jitter of the support unit into a quantifiable and controllable range, ensuring the overall accuracy of the measurement system; 4. Taking advantage of the fact that wafer warp detection does not require a fast response, the refresh rate of the control loop is intentionally reduced, allowing the elastic deformation to fully propagate before the next update, thereby fundamentally suppressing the risks of overshoot and oscillation. Attached Figure Description

[0019] The above description of the present invention and the following detailed embodiments will be better understood when read in conjunction with the accompanying drawings. It should be noted that the drawings are merely examples of the claimed invention. In the drawings, the same reference numerals represent the same or similar elements.

[0020] Figure 1 This is a structural block diagram of the wafer warpage detection system according to an embodiment of the present invention.

[0021] Figure 2 This is a flowchart of a wafer warpage detection method according to an embodiment of the present invention.

[0022] Figure 3 This is a flowchart of a wafer warpage detection method according to another embodiment of the present invention. Detailed Implementation

[0023] The following detailed description of the features and advantages of the present invention is sufficient to enable any person skilled in the art to understand the technical content of the present invention and implement it accordingly. Furthermore, based on the specification, claims and drawings disclosed herein, those skilled in the art can easily understand the related objects and advantages of the present invention.

[0024] like Figure 1 As shown, the present invention also provides a wafer warpage detection system, including a support component 101, a force acquisition component 105, a control component 106, and a warpage measurement component 107, wherein the support component 101 is composed of a plurality of support units 102, and the support unit 102 includes a piezoelectric component 103 and a support component 104.

[0025] Based on the above system architecture, the functional principles and collaborative relationships of each component are as follows: The support component 101 independently supports various local areas of the wafer below the wafer through multiple support units 102. The piezoelectric component 103 of each support unit 102 has both driving and sensing functions, and can independently output controllable support force and collect the measured support force at that location in real time; the force acquisition component 105 obtains the force feedback information of the measured support force from each piezoelectric component 103 and converts it into a digital force value before outputting it to the control component 106; the control component 106, based on the pre-stored compliance matrix reflecting the force coupling relationship between each support unit and the force feedback information, corrects the support force of each support unit through a coordinated iterative algorithm, so that the measured support force of each support unit gradually converges to the target support force, thereby offsetting the gravity of each local micro-element of the wafer; the warpage measurement component 107 is activated after the force control converges, and performs warpage measurement on the wafer in a near-zero gravity support state.

[0026] Each support unit 102 of the support assembly 101 converts electrical signals into mechanical displacement to output support force through the inverse piezoelectric effect of the piezoelectric component 103, and converts wafer pressure into electrical signals through the direct piezoelectric effect to achieve force sensing. The support assembly 101 adopts a horizontal support structure, with multiple support units 102 distributed in an array below the wafer, so that each local area of ​​the wafer can obtain independent force control, thereby achieving point-by-point cancellation of the gravity of each micro-element of the wafer.

[0027] The force acquisition component 105 is electrically connected to the piezoelectric components 103 of each support unit 102, and is used to acquire the charge signals generated by each support unit 102 in real time during sensing mode. The force acquisition component 105 sequentially processes the charge signals through charge amplification, filtering, and analog-to-digital conversion, converting them into digital force values ​​before outputting them to the control component 106. Due to the large number of support units, the force acquisition component 105 adopts a multi-channel acquisition method, which can simultaneously or time-divisionally acquire the force feedback information of all support units, ensuring the integrity and real-time performance of the force feedback data.

[0028] The control component 106 is the core of the system's algorithm and is electrically connected to both the force acquisition component 105 and the support component 101. The control component 106 pre-stores a wafer compliance matrix obtained through offline calibration or theoretical calculation. This compliance matrix reflects the force coupling relationship between the support units, i.e., the impact of a change in the support force of one support unit on the forces of the remaining support units. Based on the force feedback information output by the force acquisition component 105, the control component 106 calculates the force error of each support unit and corrects the driving voltage of each support unit using a coordinated iterative algorithm based on the compliance matrix, gradually converging the measured support force of each support unit to the target support force.

[0029] The warp measurement component 107 is activated after force-controlled convergence. At this point, the gravity acting on each local micro-element of the wafer has been canceled out by the corresponding support unit, and the wafer is in a near-zero gravity suspended support state. The warp measurement component 107 acquires wafer surface height information through multiple measurement modes, including at least one of piezoelectric self-feedback-based measurement, optical measurement, and capacitance measurement. These modes can be flexibly selected according to the wafer surface characteristics, serving as alternatives and cross-validations.

[0030] More specifically, the support assembly 101 is positioned below the wafer and employs a horizontal support architecture. It can directly connect to the horizontal wafer transport station on the production line, eliminating the need for wafer flipping or vertical clamping operations and avoiding the risks of scratches, particle contamination, and repetitive positioning errors caused by flipping and handling. The support assembly 101 is a piezoelectric ceramic pin array, composed of multiple independent support units arranged in a uniform grid. Preferably, a hexagonal grid can be used, which offers higher coverage and better isotropy at the same spacing compared to a rectangular grid. For a 300mm wafer under test, the total number of support units can be configured from 2000 to 4000 depending on the spacing requirements. Approximately 2000 units are configured when the spacing between support units is 8mm, and approximately 3600 units are configured when the spacing is 5mm. Each support unit consists of two parts: a fine-diameter support pin and a piezoelectric ceramic stack. The fine-diameter support pin has a diameter of 0.5–1 mm and is made of tungsten carbide or alumina ceramic. It is used to directly contact and support the wafer under test. The piezoelectric ceramic stack is made of PZT-5H or PZT-4 material and is composed of 100–200 layers of piezoelectric ceramic sheets with a single layer thickness of 50–100 μm, connected in mechanical series and electrical parallel. The typical stroke is 10–100 μm, which can meet the support adjustment requirements of wafers with a warpage range of 50–500 μm. The typical piezoelectric sensing sensitivity is 1–10 mN / mV.

[0031] Preferably, the piezoelectric ceramic stack uses time-division multiplexing to implement driving and sensing functions in a time-division manner, avoiding crosstalk between the driving signal and the sensing signal. That is, the driving voltage is updated first in each control cycle, and the force feedback signal is collected after the elastic deformation of the wafer stabilizes. For example, based on the piezoelectric constant of PZT-5H material, the initial driving voltage is set to 5V / mN of support force, corresponding to an initial target support force of 0.38mN. An initial driving voltage of 1.9V is applied to each support unit to complete the initial support action.

[0032] The force acquisition component 105 is electrically connected to the piezoelectric ceramic stack of the piezoelectric component 103 of each support unit 102. The signal processing link sequentially includes a charge amplifier, a 4th-order Butterworth anti-aliasing low-pass filter, a 24-bit Σ-Δ ADC, and an analog multiplexer. The charge amplifier uses a high input impedance operational amplifier with an input impedance ≥10^12Ω to form a charge-to-voltage converter. It is configured with a 1nF feedback capacitor and a 1GΩ feedback resistor, resulting in a low-frequency cutoff frequency of 0.16Hz, far below the control bandwidth, ensuring accurate acquisition of quasi-static force signals. The sensitivity calculated using these parameters is 1mV / mN, capable of detecting sub-mN level force changes. The 4th-order Butterworth anti-aliasing low-pass filter has a cutoff frequency set to 0.4 times the control sampling frequency to filter out high-frequency electrical noise and mechanical resonance signals, preventing signal aliasing. The 24-bit Σ-Δ ADC has a sampling rate of not less than 1kS / The refresh rate is much higher than the control refresh rate, allowing for the acquisition of multiple sets of data within the refresh cycle and averaging to reduce noise. The quantization noise is equivalent to approximately 0.01mN. An analog multiplexer is used to achieve multi-channel time-division multiplexing acquisition. Since the total number of support units is 2000–4000, the support unit array is divided into 64–128 support units / groups. Each group shares a high-precision ADC. The analog multiplexer sequentially switches the acquisition signals of each support unit within the group. The switching time for a single channel within a group is approximately 10μs, and the total acquisition time for the entire group is approximately 0.5–1ms. Multiple rounds of acquisition and averaging of all support units can be completed within a control refresh cycle of 50–200ms. For example, each group is configured with 64 support units sharing a 24-bit ADC, and the entire array is configured with 57 acquisition links. The single-round acquisition time for the entire array is approximately 0.8ms, and 125 rounds of acquisition and averaging can be completed within a 100ms refresh cycle, reducing the acquisition noise to below 0.005mN.

[0033] The control component 106 controls the support force of the support units to counteract the gravity of the wafer through a global coordinated iterative control algorithm. The control component 106 is electrically connected to the force acquisition component 105 and the piezoelectric component 103, and is the core of the system algorithm. It pre-stores the wafer compliance matrix C obtained by offline calibration or Green's function method. The matrix element Cij is defined as the displacement of the wafer at the position of the i-th support unit when a unit force (1N) is applied only at the j-th support unit position. The control component 106 first calculates the initial target support force of each support unit according to the nominal parameters of the wafer to ensure that the support force of each support unit counteracts the gravity of the corresponding local micro-element of the wafer. Then, based on the force signal fed back by the force acquisition component 105, the global coordinated iterative control law is used to iteratively correct the driving voltage until the error between the measured support force and the target support force of all support units is less than the convergence threshold, so that the wafer is in a near-zero gravity suspended support state. The control component 106 employs a slow refresh control strategy. Within each control cycle, the drive voltage is updated first, and the force feedback signal is acquired only after the wafer's elastic deformation stabilizes. The refresh cycle is set to 50–200 ms to ensure the iterative stability of the high-dimensional support array. For example, the control component 106 is implemented using an embedded industrial computer, pre-stored with a sparse compliance matrix (CSR format, approximately 37 non-zero elements per row) corresponding to a 300mm silicon wafer. With an iteration step size α = 0.5, a refresh cycle of 100 ms, and a convergence threshold of 0.05 mN, force control convergence can be achieved within approximately 3 seconds after 30 iterations, reducing the net gravitational bending moment on the wafer to near zero.

[0034] In some embodiments, the system further includes a warpage measurement component 107, which comprises at least one of a piezoelectric measurement unit, an optical measurement unit, and a capacitance measurement unit. The piezoelectric measurement unit, after force-controlled convergence, infers the displacement of the top of the support unit based on the driving voltage and the measured support force, thus obtaining a height map of the wafer's lower surface. No additional hardware is required, and the measurement accuracy is typically 0.5–1 μm. The optical measurement unit uses a white light interferometer or a confocal sensor, positioned above the wafer, to perform non-contact scanning of the wafer's upper surface. Its longitudinal resolution can reach the 10 nm level, making it suitable for sub-micron level high-precision measurements. The capacitance measurement unit uses a capacitance displacement sensor array, positioned below the wafer, with a resolution of approximately 10 nm (at a spacing of 100 μm), suitable for inspecting thin wafers or wafers with special coatings. The three measurement units can operate independently or be cross-validated, improving the system's applicability and measurement reliability.

[0035] The wafer warpage detection system described in this embodiment can achieve near-zero gravity support for the wafer at the physical level through the main dynamic feedback and global coordinated iterative control of the piezoelectric ceramic pin array, fundamentally eliminating the interference of gravity deformation on warpage measurement. Combined with multi-modal measurement components and a high-stability control strategy, it can achieve high-precision and high-reliability wafer warpage detection. Moreover, the architecture is adapted to the horizontal transmission station of the production line and can meet the cycle time requirements of online integrated measurement.

[0036] This embodiment also provides a flowchart of a wafer warpage detection method, the detection method including: By employing active force feedback control, the gravitational forces acting on each local micro-element of the wafer are gradually canceled out, achieving a near-zero-gravity support state. This allows for warpage measurement under conditions where gravitational interference is eliminated. Specifically, the method comprises four stages: initial support, force feedback and error assessment, coordinated iterative correction, and warpage measurement.

[0037] In the initial support phase, the wafer under test is placed on the support assembly, and its nominal parameters, including basic physical parameters such as material, diameter, and thickness, are obtained. Based on these nominal parameters, the initial target support force for each support unit is calculated. The calculation principle is to ensure that the sum of the support forces of all support units equals the total weight of the wafer, and the support force of each support unit is distributed according to the corresponding local micro-area of ​​the wafer. The support assembly is then driven to provide initial support to the wafer using these initial values.

[0038] In the force feedback and error judgment stage, after initial support, force feedback information of each support unit is collected, and the measured support force of each support unit is calculated. The measured support force is compared with the target support force one by one, the force error is calculated, and it is determined whether the force error of all support units meets the preset threshold value requirement.

[0039] In the coordinated iterative correction phase, when the force error does not meet the threshold requirement, a compliance matrix reflecting the coupling relationship between the support forces of each support unit is constructed. Based on the compliance matrix, the target support force of each support unit is corrected through a coordinated iterative algorithm. The support assembly is then controlled to support the wafer with the corrected target support force, and the process returns to the force feedback acquisition step for reassessment. Through multiple iterations, the elastic coupling relationship described by the compliance matrix is ​​used to decouple the force interactions between the support units, allowing the measured support force of each support unit to gradually approach the target support force.

[0040] During the warpage measurement stage, once the force control converges, the wafer is in a near-zero-gravity suspended support state. Warpage measurement is then performed on the wafer at this point to eliminate the interference of gravitational deformation on the measurement results. Warpage measurement can employ at least one of piezoelectric measurement, optical measurement, and capacitance measurement methods to obtain wafer surface height information to reconstruct the warpage map.

[0041] Specifically, such as Figure 2As shown, the specific steps of the wafer warpage detection method are as follows: S201. Place the wafer to be tested on the support assembly.

[0042] The support assembly is a piezoelectric ceramic pin array integrally arranged below the wafer under test, employing a horizontal support architecture. It can directly connect to the horizontal wafer transfer station on the production line, eliminating the need for wafer flipping or vertical clamping operations. The support assembly consists of multiple independent support units, each capable of independently outputting support force and collecting force feedback information at its corresponding location. The total support force applied to the wafer by the support assembly is the combination of the support forces output by all support units. The total force feedback information collected by the subsequent force acquisition component is the sum of the force signals fed back by all support units. The support units are uniformly arranged in a hexagonal grid, which offers higher coverage and better isotropy at the same spacing compared to rectangular grids. For example, for a 300mm wafer under test, the total number of support units can be configured to 2000-4000 depending on the spacing requirements. Approximately 2000 units are configured when the support unit spacing is 8mm, and approximately 3600 units are configured when the spacing is 5mm.

[0043] Each support unit consists of a thin-diameter support pin and a stack of piezoelectric ceramics. Preferably, the diameter of the thin-diameter support pin is 0.5-1 mm, and the material is tungsten carbide or alumina ceramic, used to directly contact and support the wafer under test; the piezoelectric ceramic stack is composed of multiple layers of lead zirconate titanate (PZT) sheets connected in series mechanically or in parallel electrically, using PZT-5H or PZT-4 material, with 100-200 layers of lead zirconate titanate (PZT) sheets, a single layer thickness of 50-100 μm, and a typical stroke of 10-100 μm, which can meet the support adjustment requirements of wafer warpage ranges of 50-500 μm, and the piezoelectric sensing sensitivity is typically 1-10 mN / mV. For example, for a 300mm thick silicon wafer with a thickness of 775μm, a hexagonal arrangement scheme with a 5mm pitch is selected, with a total of 3600 support units. The fine-diameter support pins of each support unit are made of tungsten carbide material with a diameter of 0.8mm. The piezoelectric ceramic stack is made of 150 layers of PZT-5H material with a single layer thickness of 70μm. The rated stroke is 50μm and the sensing sensitivity is 5mN / mV, which can stably cover the support adjustment and force feedback acquisition requirements of the wafer.

[0044] The constitutive relation of the piezoelectric ceramic can be described by a set of linear piezoelectric equations. For a stacked PZT operating along the polarization direction (z-axis), its direct piezoelectric effect (sensing mode) and inverse piezoelectric effect (driving mode) are uniformly described by the following coupled equations:

[0045] in: For axial strain; Axial stress (Pa); electric field strength ( ); , To apply voltage, This represents the total thickness of the PZT stack. electric displacement ( ); Elastic compliance under constant electric field ( When the PZT is PZT-5H, its typical value is approximately ; piezoelectric constant ( or When the PZT is PZT-5H, its typical value is approximately ; The dielectric constant under constant stress ( ).

[0046] When the support component is in driving mode, the piezoelectric ceramic is in the inverse piezoelectric effect state; when a driving voltage is applied... At that time, the free elongation of the PZT stack is:

[0047] When the support component is under load (i.e., pushing the wafer), its actual displacement is less than its free elongation due to elastic compression, and needs to be corrected in conjunction with the load conditions. Define the driving stiffness. The equivalent spring constant of the PZT stack ( , (where PZT is the cross-sectional area), then the relationship between the actual output force and displacement is:

[0048] in This represents the actual displacement of the pin tip (i.e., the deflection of the wafer at that pin).

[0049] When the support component is in sensing mode, the piezoelectric ceramic is in a positive piezoelectric effect state. When Pin is subjected to external force... At that time, the charge generated by the PZT stack is:

[0050] The charge is converted into a voltage signal by a charge amplifier, achieving a direct conversion between force and electrical signals. The output of the charge amplifier is:

[0051] in This is the feedback capacitor for the charge amplifier. , For example, the sensitivity is It can detect sub-mN level force changes.

[0052] The support component achieves driving output through the inverse piezoelectric effect of the piezoelectric ceramic stack. Applying a corresponding voltage can output a controllable supporting force. It also achieves force sensing function through the direct piezoelectric effect, generating a corresponding charge signal when force is applied to provide feedback on the magnitude of the force.

[0053] In some implementations, the boundary value of the spacing between support units is determined by establishing a quantitative relationship between the spacing between each support unit and the wafer deflection residual, with the threshold value of the wafer deflection residual as a constraint.

[0054] Specifically, the local section of the wafer between two adjacent support units is approximated as a simply supported beam with a uniform cross-section, wherein the span... Line load ,in For wafer material density ( For silicon, ; The acceleration due to gravity ( ),generally ; Let be the wafer thickness (m). Then, its maximum deflection at mid-span is:

[0055] in, The maximum deflection (m) of the support unit at the spacing L; D is the wafer bending stiffness ( E is the elastic modulus of the wafer ( ); Poisson's ratio (dimensionless, for silicon) ).

[0056] Design constraints ,in Given the actual warpage (m) caused by the process, the maximum allowable support unit spacing can be calculated from this:

[0057] When the support components are uniformly arranged in a hexagonal grid below the wafer under test, the spacing between adjacent support units is L, taking into account the geometric characteristics of the hexagonal arrangement. However, the equivalent support span of the triangular region enclosed by every three adjacent pins differs from that of the simply supported beam model. Accurate analysis requires the use of the triangular plate bending theory. For an equilateral triangular region (side length L), the maximum deflection at the center under uniformly distributed load is:

[0058] in, (Coefficient of a simply supported plate in an equilateral triangle), while the equivalent value given by the formula for a simply supported beam is... The ratio of the two is approximately 1.18, meaning that the actual deflection of a hexagonal arrangement is approximately 18% greater than that of a simply supported beam with a rectangular arrangement.

[0059] To address the issue of increased deflection caused by the free boundary at the wafer edge, the spacing between the 1-2 rows of support units at the wafer edge can be reduced to 0.7 times the spacing between the support units in the central region. This increases the support density by densifying the support units at the edge. Alternatively, a low-stiffness flexible auxiliary support ring with an L-shaped cross-section can be set at the wafer edge to provide only radial constraints without restricting the wafer's out-of-plane degrees of freedom, thus avoiding deformation introduced by additional constraints.

[0060] When the wafer is extremely thin or the spacing between support units is large, causing the deflection to enter the medium deformation region, a film force effect (mid-surface stretching) is introduced for correction, using von Kármán's large deflection plate theory:

[0061] in This is a geometric nonlinearity correction coefficient (approximately 0.4-0.5 for simply supported plates). The nonlinear effect causes the actual deflection to be less than the linear prediction, meaning the linear approximation is conservative and does not affect the control safety.

[0062] Based on the above theory, for example, for a 300mm silicon wafer with a warpage of 100μm, the elastic modulus of silicon material is E=170GPa, Poisson's ratio ν=0.28, and density ρ=2329kg / m³. The calculated maximum allowable spacing between support units is approximately 8mm. In engineering practice, a margin of s=5mm is chosen, corresponding to δmax≈0.5μm, which is approximately warp / 200. This is far superior to the design constraints and leaves sufficient margin for imperfect convergence of force control.

[0063] S202. Obtain the nominal parameters of the wafer to be tested.

[0064] The nominal parameters include at least the basic physical parameters of the wafer, such as material, nominal diameter, and thickness. For wafers in repetitive process batches with a known warp shape, the measured warp map of the previous batch can also be obtained as a feedforward parameter to optimize the initial value of the subsequent support force to accelerate convergence. Parameters can be automatically read from the equipment's preset process recipe, or obtained through manual input or data interface with the MES system of the upstream station, ensuring that the parameters match the actual specifications of the wafer under test. For example, for a standard 300mm bare silicon wafer, the nominal parameters are: material monocrystalline silicon, diameter 300mm, thickness 775μm, and density 2329kg / m³. For repetitive production wafers in the same process batch, the convergence force distribution data stored in the previous batch is additionally read as a feedforward parameter.

[0065] S203. Calculate the initial value of the target support force of the support component based on the nominal parameters.

[0066] The initial value of the target support force is the initial set of target support forces for each support unit. First, based on the nominal parameters of the wafer, the total gravity of the wafer under test is calculated. The total gravity is then distributed to each support unit according to the local micro-element area of ​​the wafer corresponding to each support unit, serving as the initial value of the target support force for round 0. The target support force of a single support unit satisfies the local gravity cancellation condition. The target support force of the kth support unit is: ; in The target support force (N) for the k-th pin; For wafer material density ( For silicon, ; The acceleration due to gravity ( ),generally ; Wafer thickness (m); For the first The local micro-element area of ​​the wafer corresponding to each pin ( ).

[0067] When all support units meet this condition, the net bending moment on the wafer under test is zero, effectively achieving gravity-free support in the horizontal direction. For repetitive batches of wafers with a known warp shape, the measured warp pattern of the previous batch is used as feedforward to optimize the initial value of the target force distribution to accelerate convergence. For example, for a 300mm silicon wafer with a thickness of 775μm, a single-crystal silicon density ρ=2329kg / m³, and a gravitational acceleration g of 9.8m / s², the local micro-element area Ak corresponding to each support unit is approximately 21.65mm² (the unit area corresponding to a 5mm pitch hexagonal grid). The initial target support force of a single support unit is calculated to be Fk^t≈0.38mN, and the set of initial target support forces of all support units is the first support force.

[0068] S204, drive the support component to support the wafer under test with the initial value of the target support force.

[0069] Each support unit's piezoelectric ceramic stack utilizes the inverse piezoelectric effect to achieve drive output. The global coordination controller generates a corresponding drive voltage based on the initial target support force and applies it to the piezoelectric ceramic stack of each support unit, causing each support unit to output a corresponding support force to push the wafer upwards to achieve initial support.

[0070] Preferably, the piezoelectric ceramic stack uses time-division multiplexing to implement driving and sensing functions in a time-division manner, avoiding crosstalk between the driving signal and the sensing signal. That is, the driving voltage is updated first in each control cycle, and the force feedback signal is collected after the elastic deformation of the wafer stabilizes. For example, based on the piezoelectric constant of PZT-5H material, the initial driving voltage is set to 5V / mN of support force, corresponding to an initial target support force of 0.38mN. An initial driving voltage of 1.9V is applied to each support unit to complete the initial support action.

[0071] S205. Collect force feedback information from the support components and calculate the measured support force of the support components.

[0072] Force feedback information is acquired by a force acquisition component, which is electrically connected to the piezoelectric ceramic stack of each support unit. The component acquires the induced charge / current signal of each support unit in real time and sends it to the control component as the force feedback quantity.

[0073] The signal processing link of the force acquisition component includes, in sequence, a charge amplifier, a low-pass filter, an A / D converter, and a multi-channel multiplexer.

[0074] Specifically, the charge amplifier uses input impedance A high input impedance operational amplifier is used to construct a charge-to-voltage converter, in which a feedback resistor... The range of values ​​is Feedback capacitor The range of values ​​is At this time, the cutoff frequency The range is Preferably, select , ,but Hz, far below the control bandwidth, ensures accurate acquisition of quasi-static force signals.

[0075] The low-pass filter is a fourth-order Butterworth anti-aliasing low-pass filter, based on the Nyquist sampling theorem. The cutoff frequency is set to 0.4 times the control sampling frequency to filter out high-frequency electrical noise and mechanical resonance signals and prevent signal aliasing.

[0076] The A / D converter uses a 24-bit Σ-Δ ADC with a sampling rate of no less than 1kS / s, which is much higher than the control refresh rate. It can collect multiple sets of data within the refresh cycle and average them to reduce noise. Its quantization noise is equivalent to about 0.01mN.

[0077] Since the total number of support units is 2000–4000, configuring an independent charge amplifier and A / D converter for each support unit would be too costly. Therefore, a grouped time-division multiplexing scheme is adopted, dividing the support unit array into 64–128 support units / groups. Each group shares a high-precision A / D converter, and the signals of each support unit within the group are acquired sequentially by analog multiplexers. The single-channel switching time within a group is configured to be approximately 10μs, and the total acquisition time for the entire group is approximately 0.5–1ms. Multiple rounds of acquisition and averaging of all support units can be completed within a control refresh cycle of 50–200ms.

[0078] The force acquisition component collects the actual force signal of each support unit through the positive piezoelectric effect. Each piezoelectric ceramic stack generates a corresponding charge when subjected to wafer pressure, which is converted into a digital force value through a signal processing link. The combined signal is used to obtain the measured support force vector of all support units, which is the current force feedback information. For example, in each control cycle, after the drive voltage is updated, a 100ms wait is waited until the wafer elastic deformation stabilizes. Then, the support units are grouped into groups of 64, and the analog multiplexer is switched sequentially to collect the force signal of each support unit. 16 sets of data are collected from each channel and averaged to finally obtain the measured support force values ​​of 3600 support units, which form the force feedback vector.

[0079] S206. Determine whether the difference between the measured support force and the target support force meets the threshold requirement.

[0080] Threshold value is the force control convergence threshold. The convergence condition is , That is, the force error of the kth support element. . Based on the target support force accuracy and measurement accuracy indicators, the target support force accuracy of a single support unit is determined to be on the sub-mN level. The measured support force of each support unit is compared with the corresponding target support force one by one, and the absolute value of the force error is calculated. If the force error of all support units is less than the convergence threshold... If the threshold requirement is met, proceed to step S208; if the force error of any support element is greater than or equal to... If the condition is not met, proceed to step S207. For example, set a convergence threshold. =0.05mN. If the absolute value of the error between the measured support force of all support units and the target value is less than 0.05mN, then the convergence requirement is met.

[0081] S207. If not satisfied, the target support force is corrected by a coordinated iterative algorithm, and the support component is controlled to support the wafer under test with the corrected target support force.

[0082] Specifically, a flexibility matrix is ​​constructed to reflect the mutual influence of the support forces of each support unit. Based on the force feedback information of each support unit, the support forces of each support unit are corrected through the flexibility matrix.

[0083] In the After rounds of iteration, the force error vector is: ,in For the target support force vector, This is the measured support force vector. Due to the deformation coordination of the wafer elastomer, when the... The supporting force of each supporting unit changes At that time, the first The wafer displacement at each support unit changes This leads to the first The force experienced by each support unit changes. Define the system flexibility response matrix. To support the linear force-displacement mapping of the element, under the assumption of small deformation, the driving voltage correction vector can be solved by the following system of linear equations:

[0084] in The driving voltage vector for the supporting unit; The iteration step size ( G is the drive gain matrix, used to describe the relationship between drive voltage and output force; It is the identity matrix. It is the inverse of the piezoelectric drive gain matrix. To account for the decoupling correction term after elastic coupling.

[0085] Therefore, the driving voltage is updated as follows: .

[0086] Specifically, the flexible matrix is ​​constructed as follows: Flexibility matrix elements Defined as: only in the first When a unit force (1N) is applied at each support unit position, the wafer is at the [missing value]. Displacement generated at the location of each support unit (unit: For an ideal elastic thin plate, this matrix is ​​symmetric (i.e., ...). ), positive definite, and a function of the positions of all support units.

[0087] For a uniform, isotropic, elastic thin plate (wafer), under concentrated force Acting on point At time, point The deflection at a point can be given by the Green function of Kirchhoff's thin-plate theory:

[0088] in The distance between the two pins. The constant is determined by the boundary conditions (free edge, simply supported edge, or fixed edge). Where is the wafer radius.

[0089] For free boundaries (wafers without external constraints), accurate calculations can be performed using Bessel function series expansions. In engineering practice, a more practical method is to use numerical approximations: when... At that time, the far-field behavior can be simplified to:

[0090] This approximation illustrates that the elements of the flexibility matrix increase with the square of the pin spacing (logarithmic correction), meaning that the coupling is strongest between adjacent pins and rapidly decreases between distant pins. This physical property makes... It has good sparsity

[0091] Optionally, the compliance matrix is ​​obtained using a high-precision offline calibration process. The specific steps are as follows: First, obtain the initial parameters of each support unit in the fabless state, and record the zero-point drive voltage and force sensing zero point of all support units; then, the flatness... A standard optical flat with the same thickness as the nominal wafer is placed on the support assembly as a "dummy wafer" with known stiffness; then the support force of each support unit is changed sequentially, that is, a small force increment is applied to each support unit j. (Achieved through incremental driving voltage), while simultaneously acquiring the response parameters of all support elements and recording the force response changes of all support elements j. Subsequently, the compliance matrix is ​​obtained based on the response parameters, and the matrix elements are calculated using the inverse relationship between stiffness and compliance. , The displacement can be determined by inverse piezoelectric relationship or directly measured using high-precision displacement sensors such as capacitive micrometers; finally, matrix C is symmetricized, and... To eliminate asymmetric noise during the calibration process, the above calibration steps were repeated using actual wafers from typical process batches to verify consistency. The relative calibration error of the compliance matrix needs to be... To ensure convergence of the iterative algorithm, the system can maintain corresponding compliance matrix parameters for each wafer type, or adopt adaptive correction during online control to adapt to the differences in boundary conditions of wafers with different processes.

[0092] Preferably, the flexibility matrix is ​​sparsified by setting a cutoff value. For systems with N=2000-4000, C is an N×N full matrix, and the computational cost of direct storage and inversion is enormous. Therefore, taking advantage of the physical characteristic of rapid attenuation of coupling between distant support units, a cutoff radius is set. The spacing between the two support units is 3-5 times the distance between the support units. season The sparsified matrix is ​​stored in CSR (Compressed Sparse Row) format, and the inversion operation is performed using sparse Cholesky decomposition or the preconditional conjugate gradient method, which reduces the computational complexity from... Reduce to , Given the number of non-zero elements in each row, a solution can be achieved in milliseconds on an embedded controller. For example, for a support element array with a 5mm pitch, the cutoff radius can be set. =20mm (4 times the spacing), after sparsification, each row retains only about 37 non-zero elements. Compared with a full matrix of 3600×3600, the storage requirement is reduced by about 97%, and the solution time for a single iteration can be controlled within 2ms.

[0093] Step S208: If satisfied, confirm the force control convergence and perform warpage measurement on the wafer to be tested.

[0094] When the force control converges, the supporting force applied by all the supporting units just cancels out the gravity of the corresponding local micro-element of the wafer, so that the wafer is in a near-zero gravity suspended support state.

[0095] In another embodiment of the invention, such as Figure 3 As shown, steps S301-S308 are not mentioned. Figure 2 The steps S201-S208 are the same or similar, and will not be repeated here.

[0096] In the iterative process of correcting the target support force through a coordinated iterative algorithm, a time-division multiplexing slow refresh control strategy can be adopted.

[0097] Refresh cycle The selection principle is as follows:

[0098] in It is the lowest-order natural frequency (dominant mode) in the elastic response of the wafer-support system. For a safety factor (typically 3–5), finite element modal analysis of a 300mm wafer and support unit array system shows that the lowest-order natural frequency is approximately in the range of 50–100Hz. ms; taken in project implementation It can achieve convergence within 5–10 seconds while ensuring stability.

[0099] Specifically, within each control cycle (refresh cycle Ts is 50–200ms), the driving voltage of each support unit is first updated, and then 50–200ms is waited for the wafer's elastic deformation to stabilize (the waiting time must be ≥3–5 times the lowest-order natural vibration period of the system; the lowest-order natural frequency of the 300mm wafer-support unit system is approximately 50–100Hz). Then, the force feedback signals of all support units are collected using a force acquisition component. By extending the time of each iteration (i.e., increasing the refresh cycle Ts), sufficient time is allowed for the wafer's elastic deformation to propagate to a steady state after each driving voltage update, preventing the high-dimensional coupled system from exciting elastic oscillation modes and enhancing the stability of the iteration process. The iteration process continues until the error between the measured support force and the target support force of all support units is less than the convergence threshold. For example, by setting the refresh cycle Ts=100ms and the iteration step size α=0.5, and collecting force feedback after waiting 100ms in each iteration, calculating the correction amount and updating the driving voltage, the total convergence time is about 3s after about 30 iterations. This can achieve the convergence of the force error of all support units to within 0.05mN, which is far less than the design upper limit of 10s, leaving sufficient stability margin for the system.

[0100] In another embodiment of the invention, such as Figure 3 As shown, after the force control convergence condition is met, step S309 is added to suppress the jitter of the support component by adding low-pass filtering and active damping.

[0101] Specifically, after the support unit contacts the wafer surface and completes force-controlled convergence, residual jitter may still exist in its position. This residual jitter will be directly transmitted to the warp measurement results, affecting the detection accuracy. By modeling and analyzing the jitter noise source, targeted suppression strategies can be designed to control the contribution of residual jitter to the warp measurement error within an acceptable range.

[0102] In one implementation, the vibration noise sources of the support assembly are modeled, and the following three main noise sources are identified: (1) Electrical noise of drive circuit The support assembly includes a piezoelectric drive unit (PZT), whose displacement output is controlled by the output voltage of a piezoelectric drive power supply. The output voltage of the piezoelectric drive power supply has inherent electrical noise, which, after being amplified by the piezoelectric drive unit, causes displacement jitter at the support unit's position. Specifically, the amount of displacement jitter caused by the electrical noise of the drive circuit is related to the piezoelectric coefficient of the piezoelectric material and the output voltage noise of the drive power supply, and can be expressed as:

[0103] in The piezoelectric coefficient of the piezoelectric material. This represents the RMS value of the output voltage noise of the drive power supply. The spectral characteristics of this noise source are broadband white noise, and its bandwidth depends on the circuit design of the drive power supply.

[0104] In one specific embodiment, the piezoelectric coefficient The typical value is approximately The typical output voltage noise of the drive power supply is about 1–5 mV RMS, and the displacement jitter caused by electrical noise is estimated to be on the order of 3 nm.

[0105] (2) Mechanical structure resonance

[0106] After the support unit contacts the wafer surface, a spring-mass system is formed at the contact point, which has a natural resonant frequency. This natural resonant frequency is determined by the contact equivalent stiffness and the effective mass of the support unit, and can be expressed as:

[0107] in PZT stiffness With contact stiffness The series equivalent stiffness, This represents the effective mass of the pin (including the PZT stack mass, typically approximately 0.1–0.5 g). Estimate. The frequency range is approximately 500 Hz to 2 kHz. This resonance amplifies external vibrations and driving noise, and is the main contributor to jitter.

[0108] (3) Environmental vibration coupling

[0109] Environmental vibration noise originates from ground vibration and acoustic noise. Ground vibration can be suppressed using a vibration isolation platform. In one embodiment, the vibration isolation platform is an active vibration isolation table, which can achieve a reduction of more than 40 dB for vibrations above 5 Hz. The residual contribution of environmental vibration is significantly reduced after vibration isolation treatment.

[0110] In one specific implementation, the typical vibration level of the ground vibration is about 1–10 μm / s, and the frequency range is 1–100 Hz; after being suppressed by the vibration isolation platform, the residual contribution of the environmental vibration is about 0.01–0.05 μm.

[0111] The above modeling can clarify the amplitude characteristics, spectral distribution, and contribution weight of various noise sources to pin position jitter, providing a basis for the subsequent design of low-pass filtering and active damping.

[0112] In one embodiment, the low-pass filter is used to suppress high-frequency jitter noise components. This design is based on the fact that the spatial frequency bandwidth of warp measurement is limited; that is, the effective warp spatial frequency on the wafer surface does not exceed a preset upper limit of the spatial bandwidth, and high-frequency jitter components exceeding this upper limit do not substantially contribute to the warp measurement results.

[0113] Specifically, let the effective spatial bandwidth for warp measurement be... (cycles / mm), optical scanning speed is (mm / s), then the equivalent bandwidth in the time domain is:

[0114] by cycles / mm (corresponding to 10 cycles / diameter) Taking mm / s as an example, Hz. The low-pass filter cutoff frequency is set to Hz. Hz, employing a 4th-order Butterworth characteristic, at the resonant frequency The attenuation at kHz is:

[0115] That is, the noise attenuation at the resonance point is >120dB, and its contribution to the warp measurement is negligible.

[0116] It should be noted that the aforementioned low-pass filtering can be implemented digitally, i.e., after the support unit position signal is converted from analog to digital, the filtering algorithm is executed by a digital signal processing device; or it can be implemented analogally, i.e., an analog low-pass filter circuit is set in the signal acquisition link. Those skilled in the art can choose the appropriate implementation method according to the system architecture and cost constraints.

[0117] For low-frequency (below 100Hz) jitter noise, the suppression effect of the low-pass filter is limited. Therefore, in one implementation, active damping is used to compensate for and suppress low-frequency jitter.

[0118] The working principle of the active damping is as follows: the vibration component in the position signal of each support unit is detected in real time, and a compensation signal that is opposite to the vibration component is superimposed on the driving signal, thereby introducing an additional velocity-related damping force to the support unit-wafer contact mode.

[0119] Let the first The vibration signal at the position of each pin is The active damping control law is:

[0120] in For damping gain ( This is equivalent to introducing an additional velocity-dependent damping force into the pin-wafer contact mode. In the frequency domain, this control law is equivalent to increasing the damping ratio at the resonant frequency, reducing the resonant peak value from... Compress to .

[0121] Damping gain selection: An excessively large delay may lead to system instability (due to the delay in the feedback loop), and the Nyquist stability criterion must be satisfied. Let the total delay of the feedback loop be... (Typically about 50–100 μs, including A / D sampling, calculation, and D / A output), then the stability condition is:

[0122] Substituting typical parameters, The stable upper limit is approximately The engineering value is approximately 1 / 3 to 1 / 2 of the upper limit to ensure robustness.

[0123] After dual suppression via low-pass filtering and active damping, the contribution of pin position jitter to the warp measurement error is:

[0124] Estimate using typical parameters: Electrical noise remains after low-pass filtering (cutoff 33Hz): nm The residual effect of mechanical resonance after active damping (damping ratio increased from 0.01 to 0.3): nm ( (Approximately 50 nm is the peak value of the undamped resonance) Environmental vibration: nm (unfiltered) Due to the spatial averaging effect (the independent jitter of multiple pins partially cancels out after interpolation, with an attenuation coefficient of approximately...), , )back:

[0125] It is far better than the target value of 0.1 μm, with a margin of about 17 times.

[0126] In another embodiment of the invention, such as Figure 3 As shown, after the jitter suppression of the support component is completed, step S310, measurement mode selection, is added. Different measurement modes are selected according to the different requirements of the wafer under test.

[0127] Furthermore, such as Figure 3As shown, in step S311, the warpage measurement of the wafer under test includes at least one of piezoelectric measurement, optical measurement, and capacitance measurement. These three modes can be flexibly selected based on the wafer surface characteristics, serving as alternatives and cross-validations to improve the system's applicability and measurement reliability. The piezoelectric measurement mode is a piezoelectric self-feedback direct measurement mode. After force control convergence, based on the relationship between the displacement of the top of the support unit and the driving voltage and support force, the displacement d of the top of the support unit is inferred from the known driving voltage U and the measured support force F. This is the height of the wafer's lower surface at the support unit. The d values ​​of all support units are collected into a wafer lower surface height map. After removing the reference plane, the warpage is obtained. This mode requires no additional sensors, resulting in the simplest system structure. The typical accuracy is 0.5–1 μm; the optical measurement mode is an optical sensing mode, which uses a white light interferometer or confocal sensor to perform non-contact scanning on the upper surface of the wafer to obtain the height map of the upper surface of the wafer. Combined with the wafer thickness uniformity data, the warp is calculated. This mode is suitable for submicron-level high-precision measurement scenarios. The longitudinal resolution of the confocal sensor can reach the order of 10 nm, and the lateral resolution is about 1 μm; the capacitance measurement mode is a capacitance sensing mode, which uses a capacitance displacement sensor array to measure the lower surface of the wafer. The capacitance sensor resolution is about 10 nm (when the spacing is 100 μm). The measurement range is small and suitable for thin wafers (small warp) detection, especially suitable for wafers with special requirements for optical reflectivity, such as those with photoresist coated on the front side.

[0128] In another embodiment of the invention, such as Figure 3 As shown, step S312, warp graph reconstruction, has also been added.

[0129] Specifically, after jitter suppression is completed, the height data of each measurement point is mapped to the wafer coordinate system. After removing systematic tilt, the global continuous warp map is reconstructed by Kriging interpolation or bicubic interpolation, and finally the Warpage value (the difference between the highest and lowest points) defined by the SEMI standard is output.

[0130] In another embodiment of the invention, such as Figure 3 As shown, step S313, error budget calculation, has also been added.

[0131] Specifically, the contribution of various errors, such as the residual deflection between support units, residual jitter, and calibration error of support unit position, is statistically analyzed. The error budget of the total warpage measurement error is output. Through design and simulation verification, the residual gravity error of the system can be controlled within ≤5μm, and the total measurement accuracy meets the target of σ_total≤0.1μm, realizing quantitative closed-loop control of accuracy.

[0132] Finally, step S314 is executed to output the warping detection result.

[0133] The terminology and expressions used herein are for descriptive purposes only, and the invention should not be limited to these terms and expressions. The use of these terms and expressions does not mean the exclusion of any illustrative and descriptive equivalents (or parts thereof), and it should be recognized that various modifications that may exist should also be included within the scope of the claims. Other modifications, variations, and substitutions may also exist. Accordingly, the claims should be considered to cover all such equivalents.

[0134] Similarly, it should be noted that although the present invention has been described with reference to the specific embodiments described above, those skilled in the art should recognize that the above embodiments are only used to illustrate the present invention, and various equivalent changes or substitutions can be made without departing from the spirit of the present invention. Therefore, any changes or modifications to the above embodiments within the scope of the essential spirit of the present invention will fall within the scope of the claims of this application.

Claims

1. A wafer warpage detection system, characterized in that, The system includes: a support assembly, which consists of multiple support units arranged below the wafer, each support unit containing a support component and a piezoelectric component, the piezoelectric component having driving and sensing functions; a force acquisition assembly, the input end of which is connected to each piezoelectric component, acquires the force feedback information of the measured support force of each support unit and outputs it to a control assembly; a control assembly, which has a pre-built compliance matrix built in, sets a target support force based on the gravity of the local micro-area of ​​the wafer corresponding to each support unit, and executes a coordinated iterative algorithm based on the compliance matrix to correct the driving voltage of each piezoelectric component until the error between the measured support force and the target support force of all support units meets the convergence condition; and a warpage measurement assembly, which measures the warpage of the wafer after the support forces of all support units converge.

2. The wafer warpage detection system according to claim 1, characterized in that, The support components are uniformly arranged in a grid pattern below the wafer. By establishing a quantitative relationship between the spacing between each support unit and the wafer deflection residue, and using the threshold value of the wafer deflection residue as a constraint, the boundary value of the spacing is determined.

3. The wafer warpage detection system according to claim 1, characterized in that, The piezoelectric component achieves the sensing function through the direct piezoelectric effect, the driving function through the inverse piezoelectric effect, and the driving function and the sensing function through time-division multiplexing.

4. The wafer warpage detection system according to claim 1, characterized in that, The force acquisition component includes a charge amplifier, a low-pass filter, and an analog-to-digital converter; the input terminal of the charge amplifier is connected to the piezoelectric component; the input terminal of the low-pass filter is connected to the output terminal of the charge amplifier; the input terminal of the analog-to-digital converter is connected to the output terminal of the low-pass filter; the force acquisition component acquires the induced signals of each support unit through multi-channel time-division multiplexing.

5. The wafer warpage detection system according to claim 1, characterized in that, The method for constructing the compliance matrix includes: obtaining the initial parameters of each support unit in a fabless state; placing a standard wafer on the support assembly; sequentially changing the support force of each support unit to obtain the response parameters of all support units; and calibrating the compliance matrix based on the response parameters.

6. The wafer warpage detection system according to claim 1, characterized in that, The control component is also used to model the jitter noise source of the support component and suppress the jitter of the support component by adding low-pass filtering and active damping.

7. The wafer warpage detection system according to claim 1, characterized in that, In the process of executing the coordinated iterative algorithm based on the compliance matrix, the waiting time between correcting the driving voltage of each piezoelectric driving component and receiving the force feedback information again in each iteration is set as a preset refresh cycle. By ensuring that the duration of the preset refresh cycle is sufficient for the elastic deformation of the wafer to fully propagate to a steady state after each driving update before proceeding to the next iteration, the stability of the iteration is enhanced.

8. The wafer warpage detection system according to claim 1, characterized in that, The warp measurement assembly includes at least one of a piezoelectric measurement unit, an optical measurement unit, and a capacitance measurement unit.

9. A method for detecting wafer warpage, characterized in that, include: S1. Place the wafer to be tested on the support assembly; S2. Obtain the nominal parameters of the wafer to be tested, and calculate the initial value of the target support force of the support component based on the nominal parameters; S3. Drive the support component to support the wafer under test with the initial value of the target support force; S4. Collect the force feedback information of the support component, and calculate the measured support force of the support component based on the force feedback information; S5. Determine whether the difference between the measured support force and the target support force meets the threshold requirement; S6. If not satisfied, the target support force is corrected by executing a coordination iterative algorithm based on the flexibility matrix, the support component is controlled to support the wafer under test with the corrected target support force, and the process returns to step S4. S7. If satisfied, confirm the force control convergence and perform warpage measurement on the wafer under test.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, the steps of the wafer warpage detection method as described in claim 9 are implemented.

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