On-line testing method for simultaneously measuring multiple MEMS material characteristic parameters

Abstract

This invention discloses an online testing method for simultaneously measuring multiple MEMS material property parameters. The invention includes the design and application of an online MEMS testing structure. The required testing structure consists of a V-shaped thermal actuator and two comb-shaped electrostatic actuators at its front and rear ends. Analysis of the behavior of these actuators allows for the calculation of the Young's modulus, residual stress, and coefficient of thermal expansion of the silicon material layer. To achieve this, a physical model is first established to design the geometric parameters of the two comb-shaped electrostatic actuators and the V-shaped thermal actuator, ensuring that the actuators are sufficiently sensitive to the properties of the material layer and relatively easy to drive. This invention completes the measurement process by applying electrical excitation, analyzing the electrical signal feedback, and subsequent data processing. It does not rely on other complex testing equipment or harsh testing environments and is applicable to different MEMS processes without requiring additional processing steps. This has practical significance for improving MEMS testing efficiency and the degree of automation in the testing process.

Description

Technical Field

[0001] This invention belongs to the field of microelectromechanical systems (MEMS) testing, specifically relating to an online testing method that can simultaneously measure multiple characteristic parameters of MEMS silicon materials. Background Technology

[0002] The performance of MEMS devices is highly dependent on the physical and mechanical properties of the constituent materials, such as Young's modulus, thermal conductivity, coefficient of thermal expansion, residual stress, and resistivity. Since MEMS devices are extremely sensitive to changes in the external environment, even minute fluctuations in material parameters can cause performance drift, structural failure, or fatigue damage. Therefore, accurately obtaining material property parameters is crucial for the design optimization, performance evaluation, quality inspection, and reliability assurance of MEMS devices.

[0003] Existing methods for testing material properties mainly include physical tests such as nanoindentation, resonant frequency analysis, and tensile testing, as well as various optical measurement techniques. While these methods each have their advantages, they generally suffer from problems such as cumbersome testing processes, high costs, the need for complex testing systems or special testing environments, and potential destructiveness, which limit their widespread adoption in the large-scale manufacturing of MEMS devices. To address this, researchers have proposed in-circuit testing methods for MEMS. These methods acquire material parameters under actual operating conditions through microstructures designed within the device, enabling non-destructive testing and real-time monitoring, while also possessing good integration and scalability. However, most current research still focuses on designing separate test structures for each material property parameter or using a set of test structures to measure multiple parameters. While this approach improves the accuracy of individual tests, it leads to cumbersome procedures, low testing efficiency, and hinders automation and system-level integration. In contrast, in-circuit testing methods that can simultaneously measure multiple material property parameters within the same test structure help simplify system design, improve testing efficiency and automation, and drive MEMS testing towards higher integration and intelligence. Therefore, designing an online testing method for MEMS with multi-parameter synchronous testing capability is of great theoretical significance and application value for realizing rapid detection, state sensing and performance regulation of MEMS devices. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of existing online testing methods, this invention provides an online testing method that can simultaneously measure multiple characteristic parameters of MEMS silicon materials. Using this method, the Young's modulus, residual stress and coefficient of thermal expansion of the material can be efficiently measured online using the same set of test structures.

[0005] Technical Solution: To achieve the above objectives, this invention provides an online testing method capable of simultaneously measuring multiple characteristic parameters of MEMS silicon materials, comprising the following steps:

[0006] S1: Based on the approximate range of the material properties parameters to be tested in the MEMS process line, establish a relevant physical model to design the MEMS test structure. This structure includes a V-shaped thermal actuator and two comb-shaped electrostatic actuators with different geometric parameters connected at its two ends, ensuring that the actuators are sufficiently sensitive to the parameters to be tested and relatively easy to drive.

[0007] S2: Perform finite element simulation on the designed test structure, fit the simulation results, and then correct the calculation results of the physical model to obtain a new analytical expression that is easier to solve in subsequent steps.

[0008] S3: Build a test circuit and connect it to the test structure. Without energizing the V-shaped thermal actuator, measure the pull-in voltage of the two comb-shaped electrostatic actuators respectively. Based on the fitted analytical expression obtained in step S2, establish a set of equations and solve for the Young's modulus of the material and the initial displacement caused by the residual stress, and calculate the residual stress of the material accordingly.

[0009] S4: Measure the resistance of the V-shaped thermal actuator in the unpowered state, then power on the thermal actuator until its displacement is limited. Calculate the temperature rise caused by Joule heating based on the voltage, current and the temperature coefficient of resistance of the material at this time, and finally calculate the thermal expansion coefficient of the material by combining the initial displacement obtained in step S3, thus completing the test.

[0010] Based on the above steps, the online testing method proposed in this invention, which can simultaneously measure multiple characteristic parameters of MEMS silicon materials, has the following main innovative features:

[0011] 1. The test is completed entirely by applying electrical excitation to the test structure and analyzing the feedback of electrical signals. The test process mainly uses electrical instruments, is simple to operate, does not require complex test equipment or harsh test environment, and has high compatibility with MEMS process lines.

[0012] Second, the fabrication of the test structure used is applicable to different MEMS processes, including epitaxial thick material layer processes for which there is currently little research on online testing issues, thus filling a research gap in this field.

[0013] Compared with existing methods, the online testing method proposed in this invention helps simplify system design, improve testing efficiency and automation, and promote the development of MEMS testing towards high integration and high intelligence. The all-electric approach proposed in this invention not only simplifies the test system structure and improves controllability and stability, but also makes MEMS online testing easier to integrate with existing electronic testing platforms, possessing good compatibility and engineering application prospects. Especially under the premise of compatibility with integrated circuit manufacturing processes, this method is expected to be directly integrated with mainstream integrated circuit process control monitoring (PCM) technology, realizing online verification and process tracking of key material parameters of MEMS devices, thereby significantly improving the closed-loop control capability and product consistency of the MEMS manufacturing process. Therefore, the multi-parameter electrical online testing method proposed in this study not only has theoretical innovation, but also possesses engineering application value and industrialization potential for the MEMS-IC convergence development trend. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the V-shaped thermal actuator structure used in online testing;

[0015] Figure 2 This is a schematic diagram of the comb-shaped electrostatic actuator used in online testing;

[0016] Figure 3 It shows the complete test structure and the circuit diagram used in the test.

[0017] Figure 1 In the middle: 101 is the anchor zone; 102 is the V-shaped actuator beam; 103 is the slider;

[0018] Figure 2 In the middle: 201 is the anchor area; 202 is the fixed electrode; 203 is the fixed comb tooth; 204 is the central mass block; 205 is the movable comb tooth; 206 is the spring. Detailed Implementation

[0019] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0020] Example: The test structure used in the test method proposed in this invention is as follows Figure 1 The V-shaped thermal actuator shown and such Figure 2 The comb-shaped electrostatic actuator shown is complete with the following test structure and test circuit: Figure 3 As shown, the specific steps of the test are as follows:

[0021] 1) Design such as Figure 1 The V-shaped thermal actuator shown has a spring constant k. V The expression is:

[0022] (1)

[0023] Where E is the Young's modulus of silicon; L and W are the length and width of the V-shaped beam (102), respectively; h is the thickness of the silicon material layer; and θ is the inclination angle of the V-shaped beam. When residual stress σ exists in the V-shaped beam... R The force caused by time is

[0024] (2)

[0025] Therefore, the initial forward displacement of the slider (103) caused by residual stress is

[0026] (3)

[0027] If the V-shaped thermal actuator experiences an average temperature increase after being powered on and heated compared to before heating... The force generated by thermal expansion is

[0028] (4)

[0029] Where α is the coefficient of thermal expansion of the material, and the displacement caused by thermal expansion is...

[0030] (5)

[0031] 2) Design such as Figure 2 The comb-shaped electrostatic actuator shown is an example. Figure 2 If the displacement of the movable comb tooth (205) towards the closer fixed comb tooth (203) is x, then according to the parallel plate capacitor model, the capacitance C on both sides of the movable comb tooth is... near (x) and C far (x) are respectively

[0032] (6)

[0033] (7)

[0034] Where ε0, ε r Here, l represents the vacuum permittivity and the relative permittivity of air, respectively; l is the comb tooth length; and g is the relative permittivity of air. T To determine the length of the non-overlapping portion of the fixed comb teeth and the movable comb teeth, g near and g far These refer to the distances between the movable comb teeth and the adjacent, closer and farther fixed comb teeth, respectively, and g is ensured during the design process. near Significantly smaller than g far When the applied voltage is V, the electrostatic force F on both sides of the movable comb teeth is... E, near (x) and F E, far (x) are respectively

[0035] (8)

[0036] (9)

[0037] A comb-shaped electrostatic actuator consists of multiple parallel-plate capacitor-like structures connected in parallel. If the parallel-plate capacitor structures generating power and resistance have n values ​​respectively... near and n far If there are 1, then due to the symmetry of the structure, the total electrostatic force on the central mass block (204) is:

[0038] (10)

[0039] like Figure 2 The movable comb teeth (205) shown are located at the center mass block (204), which is connected at both ends to the anchor area (201) fixed to the substrate by springs (206). The springs are composed of folded cantilever arms, and their spring constants are expressed as follows:

[0040] (11)

[0041] Where w s The width of the cantilever; l p and l o These are the lengths of the folding cantilever along the spring's extension and retraction direction, and perpendicular to the spring's extension and retraction direction, respectively. When the movable comb tooth displaces by x towards the closer fixed comb tooth, its total mechanical restoring force is F. res (x) = –2k x x, in equilibrium state F E (x) + F res (x) = 0, therefore, combining equation (10), we can obtain the relationship between the applied voltage V and the displacement x as follows:

[0042] (12)

[0043] When the electrostatic actuator engages, at the engagement point x pull-in In addition to the above expression, it also satisfies the relation |∂F E (x) / ∂x| = |∂F res (x) / ∂x|, that is,

[0044] (13)

[0045] Combining (12) and (13), the displacement at the attraction point satisfies

[0046] (14)

[0047] Solve the above equation using an iterative method for x. pull-inValue: Take the initial value x0 = 0 and iterate according to the form of equation (12) until convergence.

[0048] (15)

[0049] Substituting the calculated pull-in point into equation (13) yields the pull-in voltage.

[0050] (16)

[0051] 3) Step 2) The estimation process of electrostatic force is based only on a simple parallel plate capacitor model and does not consider the influence of factors such as the edge effect of the electrostatic field. These factors are difficult to estimate analytically. In addition, the estimation process partially relies on iterative solution, which is not conducive to subsequent parameter decoupling. Therefore, it is necessary to perform finite element simulation on the designed electrostatic actuator and fit the simulation results to solve the above problems. An anchor area for limiting is designed at the front end of the slider (103) of the V-shaped thermal actuator so that the feedback of the test structure can appear in the form of electrical contact. The limiting is set so that the maximum forward displacement is d. max This assumes that this maximum value can be ensured to be greater than the maximum displacement that can be caused by the residual stress of the MEMS process line, and that g is ensured to be greater than the maximum displacement that can be caused by the residual stress of the MEMS process line. near >d max Then, the displacement x mentioned in step 2) can take values ​​within the range of –d. max ≤ x ≤ d max Within this range, a set of pull-in voltage vectors V can be calculated by parametrically scanning the displacement x. p Furthermore, theoretically, when the forward displacement of the V-shaped thermal actuator tip reaches g... near At this time, the fixed comb teeth (203) will directly contact the movable comb teeth (205), which is equivalent to V. pull-in = 0, therefore, to ensure that the fitting results conform to physical laws, it is necessary to adjust the simulation results x and V. p Add data point V to the base pull-in (g near After E) = 0, a third polynomial fitting is performed. From the principle described in claim 5, the spring constant k of the folding cantilever is known. x ∝ E and the mechanical restoring force of the folding cantilever is not directly affected by edge effects, therefore V pull-in ∝ k x The rule still holds, that is, V pull-in ∝ In the simulation, the Young's modulus of the material is set to E0. The analytical expression obtained after fitting is:

[0052] (17)

[0053] Where a0, a1, a2, and a3 are fitting coefficients.

[0054] Due to such Figure 3 The fixed comb teeth of the electrostatic actuator shown are connected to the slider (103) of the V-shaped thermal actuator. When the test structure is released, both will generate an initial displacement Δd0 of the magnitude calculated by step 1) due to residual stress. As shown in equations (16) and (17), in order to calculate the Young's modulus E of silicon Si The two unknowns, the initial displacement Δd0 and the initial displacement Δd0, require at least two equations, indicating that the test structure needs to include two g... near , g far , n near , n far By connecting comb-shaped electrostatic actuators with different geometric parameters and fixing the comb teeth to the front and rear ends of the slider of a V-shaped thermal actuator, and measuring the pull-in voltages V1 and V2 of the two actuators when the V-shaped thermal actuator is not energized, the following set of equations can be obtained.

[0055] (18)

[0056] like Figure 3 The process shown involves disconnecting switch S and slowly increasing the voltages of power supplies U2 and U3 until the ammeter reading is no longer zero; this voltage is the pull-in voltage. The Davidenko method can be used to iteratively solve equation (16).

[0057] (19)

[0058] In the i-th iteration, y i = [x i E i ] T ,f(y i ) – V p = [f1(x i E i ) – V1, f2(x i E i ) –V2] T γ is a coefficient controlling the convergence rate, and J is the Jacobian matrix.

[0059] (20)

[0060] After calculating the Young's modulus E of silicon Si After determining the initial displacement Δd0, the residual stress σ can be calculated using equations (1), (2), and (3). R .

[0061] 4) Let the maximum forward displacement of the top of the V-shaped thermal actuator be d. maxTime (e.g.) Figure 3 (This can be achieved by using anchor zone E for limiting). If the actuator generates an initial displacement Δd0 under residual stress, then the distance it can still move forward before being limited is d. max – Δd0. After completing step 3), measure the resistance R0 between anchor areas A and B, then close switch S and slowly increase the voltage of power supply U1 until the reading of voltmeter V1 is not zero and the thermal actuator is limited. If the thermal actuator has an average temperature rise compared to before heating... Combining equations (1), (4), and (5), we can obtain the following relation:

[0062] (twenty one)

[0063] By recording the value of voltage U1 and the reading of ammeter A1 at this moment, the resistance R can be calculated. T The temperature rise caused by heating can be calculated by the change in resistance.

[0064] (twenty two)

[0065] in Let be the temperature coefficient of resistance of the material. The coefficient of thermal expansion of the material can be calculated from equations (1), (4), (21) and (22) to complete the online testing process.

[0066] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.

Claims

1. An online testing method for simultaneously measuring multiple MEMS material property parameters, characterized in that, Includes the following steps: S1: Design a MEMS test structure based on the relevant physical model. The test structure includes a V-shaped thermal actuator and two comb-shaped electrostatic actuators with different geometric parameters connected at its two ends. S2: Perform finite element analysis on the electrostatic actuator designed in step S1, and fit the finite element simulation results to obtain a new analytical expression based on the physical model for subsequent calculations and data processing. S3: Apply electrical excitation to the test structure designed in step S1 and analyze the electrical signal response to calculate the Young's modulus, residual stress, and coefficient of thermal expansion of the silicon material layer. The calculation and analysis of the response of the V-shaped thermal actuator directly adopts the physical model of step S1, while the analysis of the comb-shaped electrostatic actuator adopts the fitting expression of step S2.

2. The online testing method for simultaneously measuring multiple MEMS material characteristic parameters according to claim 1, characterized in that, The spring constant k of the V-shaped thermal actuator designed in step S1 V is expressed by the following equation. (1) where E is the Young's modulus of silicon; L and W are the length and width of the V-shaped actuator beam, respectively; h is the thickness of the silicon material layer; θ is the tilt angle of the V-shaped beam, and the resulting force when there is a residual stress σ R in the V-shaped beam is (2) Therefore, the initial forward displacement of the top of the V-beam caused by residual stress is (3)。 3. The online testing method for simultaneously measuring multiple MEMS material characteristic parameters according to claim 1, characterized in that, The comb-shaped electrostatic actuator designed in step S1 includes two parts: a fixed comb and a movable comb. The fixed comb is connected to the slider of the V-shaped thermal actuator and its relative position to the movable comb is adjusted by energizing the thermal actuator. The movable comb is connected at both ends to the anchor area fixed to the substrate by springs. The electrostatic actuator has fixed and movable comb teeth arranged alternately. The distances between the movable comb teeth and the fixed comb teeth on both sides are unequal. Assume that the length of all comb teeth is l, and the length of the non-overlapping portion of the fixed and movable comb teeth is g. T The distances between the movable comb teeth and the adjacent, closer and farther fixed comb teeth are g, respectively. near and g far And ensure g during the design process near Significantly smaller than g far If the displacement of the movable comb tooth towards the closer fixed comb tooth is x, then according to the parallel plate capacitor model, the capacitance C on both sides of the movable comb tooth at this time is... near (x) and C far (x) are respectively (4) (5) Where ε0, ε r Let V be the permittivity of vacuum and the relative permittivity of air, respectively. When the applied voltage is V, the electrostatic force F on both sides of the movable comb teeth is... E, near (x) and F E, far (x) are respectively (6) (7) A comb-shaped electrostatic actuator consists of multiple parallel-plate capacitor-like structures connected in parallel. If the parallel-plate capacitor structures generating power and resistance have n values ​​respectively... near and n far If there are , then the total electrostatic force on the central mass block is (8)。 4. The online testing method for simultaneously measuring multiple MEMS material characteristic parameters according to claim 3, characterized in that, The two ends of the movable comb teeth are connected by springs to anchor areas fixed to the substrate. The springs are composed of folded cantilever arms, and their spring constants are expressed as follows: (9) Where w s The width of the cantilever; l p and l o These are the lengths of the folding cantilever along the spring's extension and retraction direction, and the lengths perpendicular to the spring's extension and retraction direction, respectively. When the movable comb tooth's displacement towards the closer fixed comb tooth is x, the total mechanical restoring force it experiences is F. res (x) = –2k x x, in equilibrium state F E (x) + F res (x) = 0, therefore, combining with (8), we can obtain the relationship between the applied voltage V and the displacement x as follows: (10) When the electrostatic actuator engages, at the engagement point x pull-in In addition to satisfying the above equation, the condition should also satisfy the relation |∂F E (x) / ∂x| = |∂F res (x) / ∂x|, that is, (11) Combining (10) and (11), the displacement at the attraction point satisfies (12) For x pull-in The value is solved using an iterative method: take the initial value x0 = 0 and iterate according to the form of equation (12) until convergence. (13) Where i is the number of iterations performed, the pull-in voltage can be calculated by substituting the calculated pull-in point position into equation (11). (14)。 5. The online testing method for simultaneously measuring multiple MEMS material property parameters according to claim 4, characterized in that, If the maximum forward displacement of the V-shaped thermal actuator tip is d, then by designing a limiting anchor zone... max Furthermore, this maximum value is greater than the maximum displacement that can be caused by residual stress in the MEMS process line, and the displacement x will not exceed –d. max ≤ x ≤ d max Within this range, a set of pull-in voltage vectors V is calculated by parametrically scanning the displacement x. p In the simulation results x and V p Add data point V to the base pull-in (g near After setting E) = 0, a cubic polynomial fit is performed. If the Young's modulus of the material is set to E0 during simulation, the analytical expression obtained after fitting is: (15) Where a0, a1, a2, and a3 are fitting coefficients.

6. The online testing method for simultaneously measuring multiple MEMS material property parameters according to claim 5, characterized in that, After the test structure is released, both will experience residual stress, resulting in a displacement of magnitude Δd0 calculated from the initial displacement. Two geometric parameters g are then designed and manufactured. near , g far , n near , n far Different comb-shaped electrostatic actuators are used, with their fixed comb teeth connected to the front and rear ends of the slider of a V-shaped thermal actuator, respectively. Measuring the pull-in voltages V1 and V2 when the V-shaped thermal actuator is not energized yields the following set of equations. Solving this set of equations calculates the Young's modulus E of silicon. Si and initial displacement Δd0 (16) The above system of equations can be solved iteratively using the Davidenko method. (17) In the i-th iteration, y i = [x i E i ] T ,f(y i ) – V p = [f1(x i E i ) – V1, f2(x i E i ) –V2] T γ is a coefficient controlling the convergence rate, and J is the Jacobian matrix. (18) After calculating the Young's modulus E of silicon Si After determining the initial displacement Δd0, the residual stress σ can be calculated using equations (1), (2), and (3). R .

7. The online testing method for simultaneously measuring multiple MEMS material property parameters according to claim 6, characterized in that, When the maximum forward displacement of the V-shaped thermal actuator tip is d max If the actuator generates an initial displacement Δd0 under residual stress, then the distance it can still move forward before being limited is d. max – Δd0, after energizing and heating, if the V-shaped thermal actuator experiences an average temperature increase compared to before heating. The force generated by thermal expansion is (19) Where α is the coefficient of thermal expansion of the material, combined with the spring constant k of the V-shaped thermal actuator calculated by equation (1) V The following relationship was obtained and the coefficient of thermal expansion α was calculated. (20)。 8. The online testing method for simultaneously measuring multiple MEMS material property parameters according to claim 7, characterized in that, Step S3, applying electrical excitation to the test structure and analyzing the electrical signal response, includes the following process: First, without energizing the V-shaped thermal actuator, apply voltage to the two electrostatic actuators until they engage. Record this voltage as the engagement voltage and calculate the Young's modulus and residual stress of the material, as well as the initial displacement of the V-shaped thermal actuator under residual stress. Then, de-energize the electrostatic actuators and measure the resistance of the V-shaped thermal actuators when they are not energized. Next, energize the thermal actuators until their forward displacement reaches its maximum value and is limited. Record the voltage and current at this point to calculate the resistance under the energized heating state. Based on the resistance change, calculate the average temperature rise when the maximum displacement is generated. (21) Where R0 and R T These are the resistances before and after heating with electricity, respectively. The temperature coefficient of resistance of the material is given by equations (19), (20) and (21), and the coefficient of thermal expansion of the material is calculated to complete the online testing process.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the online testing method for simultaneously measuring multiple MEMS material property parameters as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, the computer instructions implement an online testing method for simultaneously measuring multiple MEMS material property parameters as described in any one of claims 1-7.

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