I-shaped silicon micromechanical gyroscope comb tooth gap size identification method

Abstract

The application discloses a kind of I-shaped silicon micromechanical gyroscope comb teeth gap size identification method, for I-shaped MEMS gyroscope in MEMS processing technology caused by comb teeth gap processing error, utilize the influence of comb teeth capacitance electrostatic negative stiffness to detection mode and detection in-phase mode, by adjusting the DC voltage of the comb teeth to be measured, the rate of change of frequency with voltage square is used to characterize comb teeth gap.The test method provided by the application can measure the gap size of drive comb teeth, drive-detection comb teeth and detection comb teeth respectively, and it is an in-situ test method, which can be applied to wafer-level comb teeth gap size identification.

Description

Technical Field

[0001] This invention belongs to the field of silicon micromechanical gyroscope technology, specifically a method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope. Background Technology

[0002] Silicon micromechanical gyroscopes are MEMS inertial sensors that use the Coriolis effect to sense the angular velocity of an object's rotation. They are characterized by small size, light weight, low cost, and high precision. They are the core sensing components of inertial measurement units (IMUs) and have broad application prospects in military, civilian, and aerospace fields.

[0003] Electrostatic actuation and detection in silicon micromechanical gyroscopes are achieved through comb-tooth capacitance. MEMS processes inevitably introduce comb-tooth shape and position errors, including etching losses and relative displacement between moving and fixed comb teeth, resulting in uneven comb-tooth gap distribution. For MEMS devices packaged using low-stress technology, the process errors mainly originate from the wafer stage. Unequal gaps between the upper and lower comb teeth prevent the electrostatic forces on the teeth from balancing, and the asymmetry in the fabrication of the left and right structures of the gyroscope prevents the electrostatic forces on the left and right sides from canceling each other out, thus creating interfering torques, causing orthogonal errors, and deteriorating gyroscope performance such as zero-bias stability. Therefore, it is necessary to identify the comb-tooth gaps of MEMS gyroscopes at the wafer stage. Commonly used methods for three-dimensional topography identification of MEMS devices include optical methods such as microscopy, grating methods, interferometry, and wafer process control and monitoring (PCM).

[0004] In 2018, Ma Suodong et al. disclosed a microstructure morphology measurement device based on dispersive spectral coding (201821425530.0). With the help of a spatial light modulator, an axial dispersive microscope objective, and a snapshot-type multi / hyperspectral imaging detector, they achieved rapid acquisition of full-field non-contact measurement data of microstructures.

[0005] In 2020, Li Jing et al. disclosed a sample morphology measurement device and method (202010464683.1). When the projection grating and imaging grating use low diffraction order and the measurement signal has large nonlinearity, the aperture is used to select the signal of the required diffraction order for measurement, thereby improving the measurement accuracy while ensuring the measurement range.

[0006] In 2020, Qiao Yu'e et al. disclosed a wafer-level capacitor standard sample and its preparation method (202011578776.3), which is used for the overall calibration of on-chip capacitor parameters of PCM equipment to ensure the process stability and product quality of semiconductor devices.

[0007] However, optical methods typically require damaging the package and can only measure the surface dimensions of a single comb tooth gap; while PCM methods measure the electrical parameters of the structure under test and cannot directly obtain the comb tooth gap dimensions. Summary of the Invention

[0008] The purpose of this invention is to provide a method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope, which is used to identify the gap size of the gyroscope driving comb teeth, driving detection comb teeth and detection comb teeth at the wafer level.

[0009] The technical solution to achieve the purpose of this invention is as follows:

[0010] A method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope includes the following steps:

[0011] S1: Set the DC voltage on the common terminal electrode, the drive comb electrode, and the drive detection comb electrode to zero;

[0012] S2: Adjust the DC voltage on the detection comb electrode to obtain the monotonic relationship curve L1 of the detection in-phase mode frequency as a function of the square of the detection voltage, and the monotonic relationship curve L2 of the detection mode frequency as a function of the square of the detection voltage. Use the least squares method to perform linear fitting on L1 and L2 to obtain the mechanical frequency of the detection in-phase mode and the mechanical frequency of the detection mode; calculate the gap g1 of the detection comb teeth and the stiffness k of the detection beam. sy With torsion bar and multi-fold beam rotational stiffness k bθ ;

[0013] S3: Set the drive detection voltage to zero, adjust the DC voltage on the drive electrode, and use the detection voltage adjustment to eliminate the influence of the negative stiffness of the detection comb teeth. Obtain the monotonic relationship curve L3 of the detection mode frequency changing with the square of the drive voltage. Use the least squares method to perform linear fitting on L3 and calculate the drive comb tooth gap d. d ;

[0014] S4: Set the driving voltage to zero and adjust the DC voltage on the driving detection electrode. During this process, the influence of the negative stiffness of the detection comb teeth is eliminated by adjusting the detection voltage. Obtain the monotonic relationship curve L4 of the detection mode frequency changing with the square of the driving detection voltage. Use the least squares method to perform linear fitting on L4 and calculate the gap d between the driving detection comb teeth. ds .

[0015] The significant advantages of this invention compared to existing technologies are:

[0016] (1) The present invention can identify the gap between the driving comb teeth, driving detection comb teeth and detection comb teeth of the I-shaped silicon micro gyroscope.

[0017] (2) The comb tooth gap identified by the present invention is the size equivalent value of the comb tooth gap within a single chip, and has statistical characteristics;

[0018] (3) This invention is an in-situ testing method that does not require damaging the packaging and can be applied to wafer-level identification. Attached Figure Description

[0019] Figure 1 This is a flowchart of the identification method of the present invention.

[0020] Figure 2 This is a schematic diagram of the experimental I-shaped gyroscope structure of the present invention.

[0021] Figure 3 This is a schematic diagram of the gyroscope detection modal spring mass model considering the negative stiffness of the comb teeth in this invention.

[0022] Figure 4 This is a schematic diagram of the in-phase mode spring mass model for gyroscope detection considering the negative stiffness of the comb teeth in this invention.

[0023] Figure 5 This is a schematic diagram illustrating the relationship between frequency and voltage squared, which is of interest in this invention. (a) shows the linear relationship between the detection in-phase frequency and the square of the detection voltage; (b) shows the linear relationship between the detection frequency and the square of the detection voltage when the driving voltage and the driving detection voltage are both zero; (c) shows the linear relationship between the detection frequency and the square of the driving voltage after removing the negative stiffness effect of the detection comb teeth when the driving detection voltage is zero; (d) shows the linear relationship between the detection frequency and the square of the driving detection voltage after removing the negative stiffness effect of the detection comb teeth when the driving voltage is zero. Detailed Implementation

[0024] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0025] Combined with appendix Figure 1 This embodiment describes a method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope, specifically addressing the following: Figure 2 The I-shaped silicon micromechanical gyroscope shown utilizes an attached... Figure 4 The electrostatic negative stiffness effect of the comb-tooth capacitor on the detection mode and attachment Figure 5 The effect of the electrostatic negative stiffness of the comb teeth capacitance on the detected in-phase mode frequency was investigated. By adjusting the DC voltage across the comb teeth, the rate of change of the detected frequency and the detected in-phase frequency with respect to the voltage was measured, which was used to characterize the comb tooth gap. (See attached diagram.) Figure 1 The method mainly includes: (1) calculating the bending stiffness of the detection beam and the rotational stiffness of the torsion bar and multi-fold beam by detecting the mechanical frequencies of the detection modes and the detection in-phase modes; (2) adjusting the DC voltage on the comb teeth, measuring the rate of change of the detection frequency and the detection in-phase frequency with the square of the voltage, and using this to characterize the comb tooth gap. (See attached...) Figure 2The structure of the I-beam silicon micromechanical gyroscope in this embodiment includes: a common terminal electrode 101, an isolation structure 102, an I-beam 2, a driving structure 3, a detection structure 4, a driving beam 501, a detection beam 502, a torsion bar 503, and a multi-fold beam 504. The driving structure 3 includes a driving electrode 301, driving comb teeth 302, a driving detection electrode 303, and driving detection comb teeth 304; the detection structure 4 includes a detection electrode 401 and detection comb teeth 402.

[0026] The specific implementation steps are as follows:

[0027] S1: Set the DC voltage on the common terminal electrode 101, the driving electrode 301, and the driving detection electrode 303 to zero;

[0028] S2: Adjust the DC voltage on the detection electrode 401 to obtain the monotonic relationship curve L1 of the frequency of the detected in-phase mode as a function of the square of the detection voltage, and the monotonic relationship curve L2 of the frequency of the detected in-phase mode as a function of the square of the detection voltage. Perform linear fitting on L1 and L2 using the least squares method. The slope of the linear fitting of L1 is denoted as K1, and the intercept is the mechanical frequency of the detected in-phase mode, denoted as f. Y0 The linear fitting intercept of L2 is the mechanical frequency of the detected mode, denoted as f. s0 Calculate the gap g1 of the detection comb 402 and the stiffness k of the detection beam 502. sy Rotational stiffness k of torsion bar 503 and multi-fold beam 504 bθ The relationship curves L1 and L2 are shown in the attached figure. Figure 5 As shown in (a) and (b);

[0029] S2.1: Mark s voltage points in [2,10]V as the detection voltage values;

[0030] S2.2: At each detection voltage point, the gyroscope mode is excited by electrostatic excitation, and the detection frequency f in the frequency domain is obtained by Fast Fourier Transform (FFT). s The detection in-phase frequency f Y ;

[0031] S2.3: Using the least squares method to analyze f s A linear fit is performed with the square of the detected voltage to obtain the linear fit intercept f. s0 ;

[0032] S2.4: Using the least squares method to analyze f Y A linear fit is performed with the square of the detected voltage to obtain the linear fit coefficient K1 and the intercept f. Y0 Calculate the mechanical bending stiffness of beam 502. Calculate the rotational stiffness of torsion bar 503 and folded beam Calculate the gap of the detection comb teeth 402 In equations (1), (2), and (3), E is Young's modulus, h is the structural thickness, and L is the elastic modulus. sb To detect the length of beam 502, w s,simu To test the design value of beam width for beam 502, f Y,simu To substitute the design value of beam width 502 into the simulation results of the in-phase frequency detection in the structural modal simulation, A1 and B1 are structurally relevant parameters, m s For the mass of mass block 403, n s The number of teeth in a set of detection combs 402, where the distance from the single-sided gyroscope to the center of the structure is equal, ε is the vacuum permittivity, and g 10 With g 20 These are the design values ​​for the large and small gaps of the 402 comb teeth, respectively. s0 To detect the overlap length of comb teeth 402.

[0033] S3: Set the driving detection voltage to zero, adjust the DC voltage on the driving electrode 301, and use the detection voltage adjustment to remove the influence of the negative stiffness on the detection comb teeth 402. Obtain the monotonic relationship curve L3 of the detection mode frequency changing with the square of the driving voltage. Use the least squares method to perform linear fitting on L3, and denot the slope of the linear fitting as K3. Calculate the gap d of the driving comb teeth 302. d The relationship curve L3 is shown in the attached figure. Figure 5 As shown in (c);

[0034] S3.1: Mark t voltage points in [2,10]V as driving voltages V DCd The possible values ​​of ;

[0035] S3.2: At each driving voltage point, repeat steps S2.1, S2.2, and S2.3, and label the linear fitting intercept obtained in S2.3 as f. s_d ;

[0036] S3.3: Using the least squares method to apply f s_d The linear fitting coefficient K3 is obtained by fitting the equation to the square of the driving voltage, and the gap of the driving comb teeth 302 is calculated. In equation (4), A2 and B2 are structural parameters, and n d L represents the number of teeth in a set of drive combs 302 that are equidistant from the center of the structure of a single-sided gyroscope. di L is the distance in the x-direction from the i-th group of comb teeth to the center of the structure. d0 The overlap length of the drive comb teeth 302.

[0037] S4: Set the driving voltage to zero and adjust the DC voltage on the driving detection electrode 303. During this process, the influence of the negative stiffness on the detection comb 402 is eliminated by adjusting the detection voltage. Obtain the monotonic relationship curve L4 of the detection mode frequency changing with the square of the driving detection voltage. Perform linear fitting on L4 using the least squares method, and denote the slope of the linear fitting as K4. Calculate the gap d of the driving detection comb 304. ds The relationship curve L4 is shown in the attached figure. Figure 5 As shown in (d).

[0038] S4.1: Mark t voltage points in [2,10]V as driving detection voltages V DCds The possible values ​​of ;

[0039] S4.2: At each driving voltage point, repeat steps S2.1, S2.2, and S2.3, and label the linear fitting intercept obtained in S2.3 as f. s_ds ;

[0040] S4.3: Using the least squares method to analyze f s_ds The linear fitting coefficient K4 is obtained by fitting the signal to the square of the drive detection voltage, and the gap of the drive detection comb teeth 304 is calculated. In equation (5), n ds L represents the number of teeth in a set of drive detection combs 304 that are equidistant from the center of the structure on a single-sided gyroscope. dsi L is the distance in the x-direction from the i-th group of comb teeth to the center of the structure. ds0 To drive the detection of the overlap length of comb teeth 304.

[0041] The above description is merely a preferred embodiment of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made to the method without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope, characterized in that, Includes the following steps: S1: Set the DC voltage on the common terminal electrode, the drive detection electrode, and the detection electrode to zero; S2: Adjust the DC voltage on the detection electrode to obtain the monotonic relationship curve L1 of the frequency of the detected in-phase mode as a function of the square of the detection voltage, and the monotonic relationship curve L2 of the frequency of the detected mode as a function of the square of the detection voltage. Use the least squares method to perform linear fitting on L1 and L2 to obtain the mechanical frequency of the detected in-phase mode and the mechanical frequency of the detected mode; calculate the gap g1 of the detection comb teeth and the stiffness k of the detection beam. sy With torsion bar and multi-fold beam rotational stiffness k bθ ; Specifically, the steps include the following: S2.1: Mark multiple voltage points as the detection voltage values; S2.2: At each voltage point where the detection voltage is taken, the gyroscope mode is excited by electrostatic excitation, and the detection frequency f in the frequency domain is obtained by FFT. s The detection in-phase frequency f Y ; S2.3: Using the least squares method to analyze f s A linear fit is performed with the square of the detected voltage to obtain the linear fit intercept f. s0 ; S2.4: Using the least squares method to analyze f Y A linear fit is performed with the square of the detected voltage to obtain the linear fit coefficient K1 and the intercept f. Y0 Calculate the mechanical bending stiffness of the test beam Calculate the rotational stiffness of torsion bars and multi-fold beams. Calculate the gap between the detection comb teeth ; Where E is Young's elastic modulus, h is the structural thickness, and L is... sb To detect the beam length, w s,simu To detect the design value of the beam width, f Y,simu To substitute the simulation results of the in-phase frequency detection in the structural modal simulation when the design value of the beam width is detected, A1 and B1 are structurally relevant parameters, m s Let n be the mass of the mass block. s Let ε be the number of teeth in a set of detection combs that are equidistant from the center of the structure of a single-sided gyroscope, and g be the vacuum permittivity. 10 With g 20 These are the design values ​​for the largest and smallest gaps between the comb teeth, respectively. s0 To detect the overlap length of the comb teeth; S3: Set the drive detection voltage to zero, adjust the DC voltage on the drive electrode, and use the detection voltage adjustment to eliminate the influence of the negative stiffness of the detection comb teeth. Obtain the monotonic relationship curve L3 of the detection mode frequency changing with the square of the drive voltage. Use the least squares method to perform linear fitting on L3 and calculate the drive comb tooth gap d. d ; S4: Set the driving voltage to zero and adjust the DC voltage on the driving detection electrode. During this process, the influence of the negative stiffness of the detection comb teeth is eliminated by adjusting the detection voltage. Obtain the monotonic relationship curve L4 of the detection mode frequency changing with the square of the driving detection voltage. Use the least squares method to perform linear fitting on L4 and calculate the gap d between the driving detection comb teeth. ds .

2. The method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope according to claim 1, characterized in that, Step S3 specifically includes the following steps: S3.1: Mark multiple voltage points as driving voltage V DCd The value of ; S3.2: At each voltage point where the driving voltage is taken, repeat steps S2.1, S2.2, and S2.3, and obtain the linear fitting intercept as f. s_d ; S3.3: Using the least squares method to apply f s_d The linear fitting coefficient K3 is obtained by fitting the equation to the square of the driving voltage, and the gap of the driving comb teeth is calculated. ; Where A2 and B2 are structurally relevant parameters, n d L is the number of teeth in a set of driving combs that are equidistant from the center of the structure in a single-sided gyroscope. di L is the distance in the x-direction from the i-th group of comb teeth to the center of the structure. d0 The overlap length of the drive comb teeth.

3. The method for identifying the gap size of the comb teeth in an I-shaped silicon micromechanical gyroscope according to claim 1, characterized in that, Step S4 specifically includes the following steps: S4.1: Mark multiple voltage points as driving detection voltage V DCds The value of ; S4.2: At each voltage point where the drive detection voltage is taken, repeat steps S2.1, S2.2, and S2.3, and obtain the linear fitting intercept as f. s_ds ; S4.3: Using the least squares method to analyze f s_ds The linear fitting coefficient K4 is obtained by fitting the signal to the square of the drive detection voltage, and the gap of the drive detection comb teeth is calculated. ; Where, n ds L represents the number of teeth in a set of drive detection combs that are equidistant from the center of the structure for a single-sided gyroscope. dsi L is the distance in the x-direction from the i-th group of comb teeth to the center of the structure. ds0 To drive the detection of comb tooth overlap length.

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