Method for measuring thermal expansion coefficient of low-expansion ultra-thin substrate

Abstract

This invention belongs to the field of thermal expansion coefficient measurement technology, specifically relating to a method for measuring the thermal expansion coefficient of a low-expansion ultrathin substrate. The testing method includes the following steps: S1, Sample preparation: A planar low-expansion ultrathin substrate is rolled into a helical cylindrical sample with equal gaps using a shaping fixture, without any supporting material; S2, Sample fixing: A ring-shaped fixing element is used to fit around the helical cylindrical sample; S3, Parameter testing: The fixed sample is placed in a thermomechanical analyzer and tested under a preset temperature program and constant micro-load conditions to obtain thermal expansion coefficient data at different temperatures; S4, Data processing: The arithmetic mean of the multiple sets of thermal expansion coefficient data obtained in step S3 is taken to obtain the thermal expansion coefficient of the low-expansion ultrathin substrate. This invention can achieve sample without compression damage, and the testing error can be controlled within ±0.1×10⁻⁶. ‑6 / ℃ or less.

Description

Technical Field

[0001] This invention belongs to the field of thermal expansion coefficient measurement technology, specifically relating to a method for measuring the thermal expansion coefficient of a low-expansion ultrathin substrate. Background Technology

[0002] Low-expansion ultrathin substrates are widely used in high-end manufacturing fields such as microelectronics, optoelectronics, and precision instruments. Their coefficient of thermal expansion is a key performance parameter that determines the dimensional stability and reliability of products. Due to the characteristics of these substrates, such as extremely thin thickness (usually in the micrometer range), poor rigidity, and low coefficient of thermal expansion, traditional measurement methods have many limitations.

[0003] Existing methods for determining the coefficient of thermal expansion are mostly designed for samples of conventional thickness and high rigidity, employing direct flat-laying or clamping methods. Commonly used methods include laser interferometry and push-rod thermomechanical analysis. While laser interferometry offers high accuracy, it requires extremely high sample surface flatness. Low-expansion ultrathin substrates, due to their inherent low rigidity, are prone to microscopic wrinkles after flat-laying, leading to disordered laser reflection signals and large data dispersion. Push-rod thermomechanical analysis uses clamping to fix the sample, but for ultrathin substrates with thicknesses of only 10μm-100μm, precise clamping force is difficult to control. Too little force causes the sample to slip, while too much force causes plastic deformation of the substrate, damaging the original structure of the sample and resulting in systematic deviations in the coefficient of thermal expansion test results.

[0004] Meanwhile, the coefficient of thermal expansion of low-expansion ultrathin substrates is typically around 10. -6 The temperature is on the order of / ℃, far lower than that of conventional metal substrates (whose coefficient of thermal expansion is typically 10). -5 Its deformation is on the order of / ℃, and within the conventional test temperature range (25℃-300℃), it is extremely small. The detection accuracy of conventional testing equipment is insufficient to meet the requirements, often failing to capture minute changes in thermal expansion, resulting in large deviations in test results, with errors typically exceeding ±0.1×10. -6 / ℃. In addition, the existing fixing method does not take into account the curling characteristics of ultra-thin substrates and lacks a suitable fixing structure. During the test, the sample is easily affected by factors such as airflow disturbance in the furnace cavity and uneven thermal stress during the heating process, resulting in morphological changes and further aggravating the test error.

[0005] Patent CN117805173A discloses a method for determining the coefficient of thermal expansion of low-expansion ultrathin metal strips, including: embedding the sample to be tested in a support material; then placing the support material containing the sample to be tested and a standard sample in a thermal expansion meter to obtain multiple sets of thermal expansion coefficients of the sample to be tested at different temperatures; averaging the multiple sets of thermal expansion coefficient test values ​​of the sample to be tested at different temperatures, performing correction value fitting, and finally obtaining the thermal expansion coefficient of the sample to be tested. However, this method is only designed for metal strip systems, relying on the nesting of support materials and correction fitting to achieve the test. Its clamping and data processing methods cannot be applied to non-metal-based ultrathin substrates with poorer rigidity. During the clamping and heating process, the support nesting structure is prone to extrusion, deformation, or even damage to the ultrathin non-metallic substrate with weak mechanical properties; at the same time, metal strips and non-metallic substrates have fundamental differences in key properties such as thermal expansion behavior, modulus, and flexibility. Directly applying this test procedure will introduce systematic bias and cannot truly reflect the low thermal expansion characteristics. In addition, this method relies on synchronous comparative testing of standard samples, which is cumbersome and lacks versatility, making it difficult to meet the high-efficiency and accurate testing requirements of non-metal-based low-expansion ultrathin substrates.

[0006] Therefore, existing testing methods have significant limitations when dealing with non-metallic, low-expansion ultrathin substrates: sample fixing methods are prone to wrinkling, deformation, slippage, or compression damage, resulting in insufficient test stability; measurement accuracy is limited, making it difficult to accurately characterize 10. -6 The substrate exhibits a low coefficient of thermal expansion on the order of / ℃; however, the overall design does not match the structural characteristics, mechanical properties, and thermal behavior of this type of substrate, resulting in insufficient reliability of test results and inaccurate characterization of key performance aspects. This limits its application in high-end scenarios such as microelectronic packaging and precision optical devices. Therefore, there is an urgent need in this field for a method to determine the coefficient of thermal expansion of non-metal-based low-expansion ultrathin substrates, which can balance test stability, measurement accuracy, and process simplicity, filling the gap in existing technologies. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art by providing a method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate.

[0008] The objective of this invention can be achieved through the following technical solutions: A method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate includes the following steps: S1. Sample preparation: The planar low-expansion ultrathin substrate to be tested is rolled into a spiral cylindrical sample with equal gaps using a shaping tool, without any supporting material nesting. S2. Sample Fixation: A ring-shaped fixing element is used to fit around the spiral cylindrical sample to achieve compression-free shaping and gap-preserving fixation. S3. Parameter test: Place the fixed sample to be tested in the thermomechanical analyzer and test it under the preset temperature program and constant micro-load conditions to obtain the thermal expansion coefficient data at different temperatures. S4. Data processing: Take the arithmetic mean of the multiple sets of thermal expansion coefficient data obtained in step S3 to obtain the thermal expansion coefficient of the low expansion ultrathin substrate to be tested.

[0009] Furthermore, in step S1, the shaping fixture is a cylindrical core mold with equidistant spiral grooves. The groove width matches the thickness of the low-expansion ultrathin substrate to be tested, and the groove width is slightly larger than the substrate thickness. The total gap on both sides is 0.01~0.06 mm. The groove spacing is 1~2 times the substrate thickness to ensure that after the ultrathin substrate is rolled and embedded in the groove, a uniform gap is formed between the spiral turns, avoiding the turns from sticking together or being squeezed.

[0010] The structural parameters of the spiral sample have a significant impact on the test results, with the inter-coil gap being the core control parameter. If the gap is too small or non-existent, adjacent coils will squeeze each other and create constraints when the substrate expands due to heat, resulting in a smaller measured deformation. If the gap is too large, it will reduce the overall structural stiffness of the sample, making the sample susceptible to shaking due to airflow and probe pressure interference, causing fluctuations in the test data.

[0011] Furthermore, in step S1, the thickness of the low-expansion ultrathin substrate to be tested is 20~120μm, and the outer diameter of the spiral sample formed after rolling is 5~10mm, with ≥3 spiral turns.

[0012] Furthermore, in step S1, after the spiral sample is rolled and formed, the gap deviation between the spirals is ≤0.03mm, and the gap deviation during the test is ≤0.05mm.

[0013] The multi-turn spiral structure not only improves the overall structural stability of the sample and addresses the problem of uneven stress distribution in single-turn or few-turn structures, but also expands the effective testing area and testing dimensions, magnifies the micro-deformation of the substrate, facilitates the detection of thermal expansion deformation, and significantly improves testing accuracy.

[0014] Furthermore, insufficient spiral turns will result in an insufficient effective test size, making it impossible to accurately detect minute thermal expansion. When the sample has concentricity deviations or uneven distribution of gaps between turns, asymmetrical stress will occur during thermal expansion, leading to local deformation or positional shift. Inconsistent substrate curling tightness will also leave residual initial internal stress. When the sample is heated, the stress is released, resulting in additional deformation not caused by thermal expansion, further increasing the test error.

[0015] Furthermore, in step S2, the annular fixing component is an aluminum or copper ring with anti-slip micro-textures on the inner wall, and its inner diameter matches the outer diameter of the rolled sample, that is, the inner diameter is 5~10mm, and the fitting gap between the inner wall of the annular fixing component and the outer wall of the rolled sample is ≤0.1mm. This fitting method can perform secondary shaping of the spiral structure to prevent the substrate from springing back and deforming, and at the same time avoid displacement of the sample during the test due to excessive gap. Under the premise of ensuring the reliability of fixation, the sample is prevented from being squeezed and damaged.

[0016] This invention uses aluminum and copper rings to make the annular fixing parts because the coefficients of thermal expansion of these two materials are similar to those of the low-expansion ultrathin substrate. They exhibit excellent synergy in thermal deformation under high-temperature conditions, preventing compression of the sample due to differences in expansion. Furthermore, aluminum and copper materials have uniform thermal conductivity, moderate density, and are easy to precision machine, allowing for precise fit with curled samples, stable constraint of sample shape, prevention of slippage, and no damage to the ultrathin substrate. They also exhibit chemical stability within the testing temperature range. If materials such as stainless steel, plastic, or ceramics are used, defects such as thermal expansion mismatch, uneven thermal conductivity, insufficient rigidity, or brittle cracking are likely to occur, making it impossible to achieve non-destructive and stable sample clamping.

[0017] The ring structure provides uniform circumferential constraint on the cylindrical spiral sample, exhibiting strong adaptability to the sample's shape. It reliably fixes the sample without obstructing the probe's testing area. Compared to square clamps, clamp-type clamps, and semi-open clamps, it offers more uniform constraint, simplifies clamping operations, and effectively maintains uniform gaps between sample rings, ensuring testing accuracy.

[0018] Limiting the fit gap between the inner wall and the outer wall of the sample to ≤0.1 mm can achieve circumferential positioning and shape fixation of the sample on the one hand, and avoid radial extrusion force caused by interference fit on the other hand, preventing sample extrusion deformation, inter-ring gap displacement and structural damage, so that the sample can remain in a free expansion state during the test and improve the accuracy of thermal expansion coefficient test.

[0019] Preferably, the fitting gap between the inner wall of the annular fastener and the outer wall of the rolled sample is greater than 0 and not greater than 0.1 mm. If the gap is zero, on the one hand, the processing precision requirements are too high, which is not conducive to industrial production; on the other hand, when the sample expands due to heat, it will make rigid contact with the fastener, generating additional constraint stress, inhibiting normal thermal expansion, and causing the test results to be distorted. At the same time, the assembly process is prone to scratching and squeezing the ultra-thin substrate. By adopting the above-mentioned gap range, the sample can be stably positioned and slipped, while also ensuring the sample can expand freely, thus balancing assembly processability and testing accuracy.

[0020] Furthermore, in step S2, the anti-slip grooves on the inner wall of the annular fastener have a depth of 0.02~0.05mm and a width of 0.05~0.1mm, which are used to increase the contact friction with the outer wall of the sample, further prevent the spiral structure from slipping during the test, and avoid the gap between the rings from changing due to slippage.

[0021] Furthermore, in step S3, the constant micro-loading force is 0.05~0.2N. This loading force is only used to ensure stable contact between the thermomechanical analyzer probe and the sample surface, ensuring accurate deformation measurement. Moreover, the loading force is much less than the deformation resistance threshold of the non-gold-based ultrathin substrate, so it will not cause damage to the sample structure, nor will it cause changes in the gap between the spiral coils.

[0022] Furthermore, in step S3, the preset temperature program has a heating / cooling rate of 3~5℃ / min, and 4~5 key temperature points are selected for fixed-point testing. The slow heating / cooling rate avoids deformation of the spiral structure due to uneven thermal stress. The test temperature range is set according to the material properties of the substrate under test and the application requirements.

[0023] Furthermore, the maximum diameter of the rolled sample is less than or equal to the diameter of the thermomechanical analyzer probe, which is 10-12 mm in diameter. This ensures that the probe can make vertical and precise contact with the sample surface, avoiding test errors caused by contact deviation. The test length of the sample is 10-30 mm, and the original length of the sample is less than the maximum allowable length of the thermomechanical analyzer furnace cavity (35 mm). This ensures that the sample can be completely placed in the furnace cavity for uniform heating, and also avoids the overlapping of the rolled structure due to excessive length, which would affect the test.

[0024] Further, the low-expansion ultrathin substrate to be tested is a low-expansion polymer substrate, a ceramic substrate, a glass substrate, or a composite material substrate. The composite material substrate has low thermal expansion characteristics and includes, but is not limited to, glass fiber reinforced epoxy resin substrates, silica-filled polyimide substrates, silicon carbide particle reinforced aluminum substrates, or other similar composite structures with low thermal expansion characteristics. Preferably, the low-expansion ultrathin substrate to be tested is a ceramic substrate or a glass substrate.

[0025] Compared with the prior art, the present invention has the following beneficial effects: (1) Excellent test stability: The method of rolling the ultrathin substrate into a cylindrical (spiral) shape and fixing it with aluminum / copper rings effectively solves the technical pain points of poor rigidity and easy deformation of the ultrathin substrate, avoids displacement, bending or stress damage to the sample during the test, and ensures that the test process is stable and controllable.

[0026] (2) Significantly improved test accuracy: The spiral curling structure and multi-turn design increase the effective test dimension of the sample, which can accurately capture the small thermal expansion deformation of the low expansion substrate; combined with multi-temperature point testing and arithmetic mean processing, the error of a single test is effectively reduced, and the accuracy of the test results is greatly improved.

[0027] (3) Strong adaptability and wide range of applications: By matching the sample size, curling structure, fastener specifications and thermomechanical analyzer parameters, it can accurately adapt to the structure and mechanical properties of low expansion ultrathin substrates, making up for the limitations of traditional testing methods for this type of sample.

[0028] (4) Simple operation and easy to promote: The test process of this invention is simple, the sample preparation and fixation method is simple and easy to implement, no complex pretreatment equipment is required, and the test can be completed directly on a conventional thermomechanical analyzer, which is convenient for industrial application.

[0029] (5) This invention breaks through the existing technical design concept, abandons the traditional nested structure of support materials, and innovatively adopts a clamping scheme of direct rolling without support and non-extrusion fitting of aluminum / copper rings. Combined with constant micro-load force control and arithmetic mean data processing, it is highly adaptable to the mechanical properties of non-metallic low-expansion ultrathin substrates, simultaneously improving test stability and accuracy. This invention can achieve sample without extrusion damage, obtain accurate results without complex data correction and fitting, and control the test error within ±0.1×10⁻⁶. -6 Within / ℃. The effect of this technology is beyond what a person skilled in the art could have predicted based on existing technology. It effectively fills the technical gap in high-precision thermal expansion testing of non-metal-based low-expansion ultrathin substrates, and is especially suitable for various ultrathin substrates with thicknesses of 20~120 μm, such as low-expansion polymer-based, ceramic-based, and glass-based substrates. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the appearance of the spiral sample in Embodiment 1 of the present invention; In the figure: 1-Low expansion ultrathin substrate, 2-Annular fastener. Detailed Implementation

[0031] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0032] Unless otherwise specified, all raw materials and equipment used in this invention are commercially available products.

[0033] This invention provides a method for determining the coefficient of thermal expansion of low-expansion ultrathin substrates, comprising four main steps: sample preparation, sample fixation, parameter testing, and data processing. The entire process does not require nesting with supporting materials, enabling high-precision, compression-free measurement of the coefficient of thermal expansion of ultrathin substrates. It is applicable to low-expansion polymer substrates, ceramic substrates, glass substrates, and composite material substrates with thicknesses ranging from 20 to 120 μm. The specific testing method is as follows: S1, Sample Preparation A fixed tooling was used to roll up the planar low-expansion ultrathin substrate to be tested, and a spiral cylindrical sample with equal gaps was prepared. No supporting material was used in the entire preparation process.

[0034] The shaping fixture is a cylindrical core mold with equidistant spiral grooves on its outer wall. The width of the spiral grooves is precisely matched to the thickness of the low-expansion ultrathin substrate to be tested, and the groove spacing is set to 1 to 2 times the substrate thickness. In specific operation, one end of the low-expansion ultrathin substrate to be tested is inserted into the starting end of the spiral groove of the cylindrical core mold, and slowly rolled up to the preset number of turns along the extension direction of the groove. The spiral structure is initially shaped by the limiting effect of the spiral groove. The groove spacing can directly limit the distance between the spiral turns, so that a uniform gap is formed between the layers of the sample after rolling, effectively preventing the layers from sticking together and being squeezed.

[0035] The thickness of the low-expansion ultrathin substrate to be tested is controlled between 20 and 120 μm; after rolling, the outer diameter of the spiral sample is 5 to 10 mm, and the number of spiral turns is no less than 3. After rolling, the gap between the spirals is measured to ensure that the deviation of the gap between the spirals is no greater than 0.03 mm.

[0036] The test length of the sample is controlled to be 10~30 mm. The original length of the sample is less than the maximum allowable length of the furnace cavity of the thermomechanical analyzer to ensure that the sample is heated uniformly in the test area and there is no structural overlap.

[0037] S2, Sample Fixation After being rolled and shaped by the cylindrical mandrel, the evenly spaced spiral cylindrical sample is removed from the fixture and immediately fitted onto the outside of the sample using a ring-shaped fastener. This completes the secondary shaping and gap retention of the sample, achieving compression-free fixation and preventing springback deformation and inter-ring gap shift. The fixed sample is as follows: Figure 1 As shown.

[0038] The annular fastener is made of aluminum or copper with anti-slip micro-textures machined on its inner wall, and its inner diameter matches the outer diameter of the spiral sample. The depth of the anti-slip micro-textures on the inner wall of the annular fastener is 0.02~0.05 mm, and the width is 0.05~0.1 mm, which can improve the stability of the assembly fit. The fit gap between the inner wall of the annular fastener and the outer wall of the spiral sample is no more than 0.1 mm. This gap fit will not generate radial compressive force on the sample, and at the same time can limit the radial displacement of the sample.

[0039] The principle of maintaining the gap in this step is as follows: First, the spiral groove of the cylindrical core mold is used to achieve precise forming of the sample rings with equal gaps. Then, the overall structure is formed by using the non-extrusion gap of the annular fixing part. The position of the spiral rings is constrained without compressing the sample, which ensures that the gap between the rings remains uniform throughout the entire testing process and avoids interference with thermal expansion deformation caused by the rings sticking together and being squeezed.

[0040] S3, Parameter Testing The fixed sample to be tested is placed in a thermomechanical analyzer (TA Instruments TMA Q450 model) for testing. The maximum diameter of the rolled sample does not exceed the probe diameter of the thermomechanical analyzer, which is set to 10~12 mm. The test process does not require simultaneous detection with a standard sample; data is collected directly according to the preset temperature program and constant micro-load conditions.

[0041] A constant micro-load force of 0.05~0.2 N is applied during the test to avoid changes in the inter-coil gap caused by external disturbances, thus ensuring data acquisition accuracy. The temperature program's heating and cooling rates are controlled at 3~5 ℃ / min, and 4~5 key temperature points are selected for fixed-point testing, collecting the raw data of the thermal expansion coefficient of the sample at each temperature point. The sample status is monitored in real time during the testing phase to ensure that the deviation of the inter-coil gap of the spiral sample does not exceed 0.05 mm during the test.

[0042] S4, Data Processing Multiple sets of raw thermal expansion coefficient data corresponding to several key temperature points in step S3 are collected. The arithmetic mean of all valid data is calculated, and the result is used as the final thermal expansion coefficient of the low-expansion ultrathin substrate under test. This data processing method can effectively reduce the random error caused by a single test and further improve the accuracy of the test results.

[0043] Example 1 In this embodiment, the low-expansion ultrathin substrate to be tested is a ceramic-based ultrathin substrate with a test thickness of 50 μm. Its coefficient of thermal expansion is determined according to the following steps: S1. Sample Preparation: Cut a 20mm long section of the substrate to be tested, roll it into a spiral structure with an outer diameter of 8mm and 3 turns. Figure 1 As shown; S2. Sample fixation: Select an aluminum ring with an inner diameter of 8mm, and put the coiled spiral sample into the aluminum ring so that the inner wall of the aluminum ring fits tightly against the outer wall of the sample to achieve stable sample fixation. S3. Parameter test: Place the aluminum ring with the sample in the thermomechanical analyzer, set the test temperature range to 25~300℃, the heating rate to 5℃ / min, and test and record the coefficient of thermal expansion at 5 key temperature points (50℃, 100℃, 150℃, 200℃, 250℃) within this temperature range. S4. Data Processing: The arithmetic mean of the thermal expansion coefficient test results at the above 5 temperature points was taken, and the final thermal expansion coefficient of the ceramic-based ultrathin substrate was found to be 1.2 × 10⁻⁶. -6 / ℃.

[0044] Example 2 In this embodiment, the low-expansion ultrathin substrate to be tested is a glass-based ultrathin substrate with a test thickness of 30 μm. Its coefficient of thermal expansion is determined according to the following steps: S1. Sample preparation: Cut a 15mm long substrate to be tested and roll it into a spiral structure with an outer diameter of 6mm and 4 turns of the spiral. S2. Sample fixation: Select a copper ring with an inner diameter of 6mm, and put the coiled spiral sample into the copper ring so that the inner wall of the copper ring fits tightly against the outer wall of the sample to achieve stable sample fixation. S3. Parameter test: Place the copper ring with the sample in the thermomechanical analyzer, set the test temperature range to 25~250℃, the heating rate to 3℃ / min, and test and record the coefficient of thermal expansion at 4 key temperature points (80℃, 120℃, 180℃, 220℃) within this temperature range. S4. Data Processing: The arithmetic mean of the thermal expansion coefficient test results at the above four temperature points was taken, and the final thermal expansion coefficient of the glass-based ultrathin substrate was found to be 0.9 × 10⁻⁶. -6 / ℃.

[0045] In all the above embodiments, the maximum diameter of the rolled-up sample was smaller than the probe diameter of the thermomechanical analyzer (10 mm), and the original length of the sample was smaller than the maximum allowable length of the furnace cavity (35 mm). During the test, no abnormal phenomena such as deformation or displacement were observed in the sample, and the test results showed good repeatability with an error controllable within ±0.1 × 10⁻⁶ mm. -6 / ℃ or less.

[0046] The present invention was compared with typical existing technologies such as the push-rod dilatometer method (contact method) and laser interferometry method (optical method), and the results are shown in Table 1. As can be seen from Table 1, existing typical methods are either unable to accurately test low-expansion ultrathin substrates due to deformation of ultrathin samples caused by probe contact force or due to excessively high requirements for surface finish. In contrast, the present invention is superior to existing technologies in terms of sample applicability and testing accuracy, and can meet the needs of high-end manufacturing fields for accurate testing of the thermal expansion coefficient of low-expansion ultrathin substrates.

[0047] Table 1. Comparison of accuracy between the present invention and existing technologies The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate, characterized in that, Includes the following steps: S1. Sample preparation: The planar low-expansion ultrathin substrate to be tested is rolled into a spiral cylindrical sample with equal gaps using a shaping tool, without any supporting material nesting. S2. Sample fixation: A ring-shaped fixing element is used to be fitted around the spiral cylindrical sample to be tested. S3. Parameter test: Place the fixed sample to be tested in the thermomechanical analyzer and test it under the preset temperature program and constant micro-load conditions to obtain the thermal expansion coefficient data at different temperatures. S4. Data processing: Take the arithmetic mean of the thermal expansion coefficient data obtained in step S3 to obtain the thermal expansion coefficient of the low expansion ultrathin substrate to be tested.

2. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, In step S1, the shaping fixture is a cylindrical core mold with equidistant spiral grooves. The groove width matches the thickness of the low-expansion ultrathin substrate to be tested, and the groove spacing is 1 to 2 times the substrate thickness.

3. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, In step S1, the thickness of the low-expansion ultrathin substrate to be tested is 20~120μm, and the outer diameter of the spiral sample formed after rolling is 5~10mm, with ≥3 spiral turns.

4. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, In step S1, after the spiral sample is rolled and formed, the gap deviation between the spirals is ≤0.03mm, and the gap deviation during the test is ≤0.05mm.

5. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, In step S2, the annular fastener is an aluminum or copper ring with anti-slip micro-textures on its inner wall. Its inner diameter matches the outer diameter of the rolled sample, and the fitting gap between the inner wall of the annular fastener and the outer wall of the rolled sample is ≤0.1mm.

6. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 5, characterized in that, In step S2, the anti-slip grooves on the inner wall of the annular fastener have a depth of 0.02~0.05mm and a width of 0.05~0.1mm.

7. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, In step S3, the constant micro-loading force is 0.05~0.2N.

8. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, In step S3, the heating / cooling rate of the preset temperature program is 3~5℃ / min, and 4~5 temperature points are selected for fixed-point testing.

9. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, The maximum diameter of the curled sample is less than or equal to the diameter of the thermomechanical analyzer probe, which is 10-12 mm in diameter; the test length of the sample is 10-30 mm.

10. The method for determining the coefficient of thermal expansion of a low-expansion ultrathin substrate according to claim 1, characterized in that, The low-expansion ultrathin substrate to be tested is a low-expansion polymer substrate, ceramic substrate, glass substrate, or composite material substrate.

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