Metallization method for trimming after assembly of micro-hemispherical harmonic oscillator

Abstract

The invention relates to the technical field of manufacturing of micro electro mechanical systems, in particular to a metallization method of a micro-hemispherical harmonic oscillator for trimming after assembly, which comprises the following steps of: establishing a micro-hemispherical harmonic oscillator structure model, simulating and calculating modal parameters of the harmonic oscillator; calculating an influence rule of the trimming width and the trimming depth on frequency splitting of the micro-hemispherical harmonic oscillator model by adopting finite element software to obtain a relation curve of trimming quality and frequency splitting change; measuring the resonant frequency f and the frequency cracking f of the working mode of the harmonic oscillator to be processed, estimating the removal mass required by the corresponding frequency cracking according to the calculated relation curve, carrying out mass trimming to obtain a relation curve of the actual removal mass and the frequency cracking, and confirming the minimum width wmin required by the actual trimming; and removing the film layer with the ring width of wmin by adopting laser. According to the invention, quality trimming is carried out on the premise of not influencing the capacitance value of the harmonic oscillator, and driving and detection gain errors caused by quality trimming are reduced.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems (MEMS) manufacturing technology, and more specifically to a method for metallizing a micro-hemispherical resonator for post-assembly adjustment. Background Technology

[0002] A Coriolis gyroscope is a type of gyroscope based on the Coriolis effect, measuring external angular motion by detecting the displacement of a mass element during rotation. Most commonly seen miniature gyroscopes are Coriolis gyroscopes, their core advantages stemming from their miniaturized structure and high-performance design. The micro-hemispherical gyroscope is a novel type of Coriolis gyroscope. Based on the high-precision working principle of the traditional hemispherical resonant gyroscope, it is manufactured using special micromachining techniques, possessing characteristics such as high sensitivity, small size, and low cost. Furthermore, thanks to its solid-state design without moving mechanical parts, it also boasts advantages such as long service life and high reliability, making it one of the current research hotspots in miniature gyroscopes.

[0003] Microspherical gyroscopes induce standing wave vibrations (such as four-antinode vibrations) in a resonator through electrostatic excitation. As the gyroscope rotates, Coriolis forces cause the standing wave nodes to shift, and the external angular motion information can be calculated by detecting the shift. Ideally, the driving mode and the detection mode of the resonator have the same frequency, resulting in optimal gyroscope performance. However, manufacturing errors and structural defects (such as uneven wall thickness and material density) cause the driving mode and the detection mode to have inconsistent frequencies, resulting in frequency fragmentation and significantly affecting the standing wave characteristics. Simultaneously, manufacturing errors and structural defects also disrupt the symmetry of the vibration modes, leading to unbalanced resonator vibrations, increased anchor point loss, and a significant reduction in gyroscope accuracy. Mass trimming is a technique to eliminate the asymmetric mass distribution of the resonator, typically using local material addition or subtraction (such as laser ablation, ion beam etching, or metal deposition) to eliminate frequency fragmentation and reduce energy loss.

[0004] To improve tuning accuracy and efficiency, micro-hemispherical gyroscopes typically employ femtosecond lasers for mass tuning after the resonator and electrodes are assembled. Under these conditions, the resonator is already metallized. When the femtosecond laser acts on the resonator structure, the damage threshold of the metal film is much lower than that of fused silica glass. Even without completely removing some mass, the metal film adhering to the resonator surface will be ablated. Since mass tuning only targets a localized area on the resonator lip, the area where the film is removed will be randomly distributed. This results in individual differences in capacitance values ​​at each electrode due to mass tuning, leading to errors in drive and detection gain, and consequently affecting the gyroscope's performance. Therefore, there is an urgent need to propose a new method for resonator metallization that can achieve post-assembly tuning without affecting capacitance values. Summary of the Invention

[0005] To address the problems existing in the prior art and reduce the driving and detection gain errors introduced by quality adjustment, this invention proposes a metallization method for micro-hemispherical resonators used for post-assembly adjustment, specifically including the following steps:

[0006] A micro-hemispherical harmonic oscillator structural model was established using finite element software. The modal parameters of the model were simulated and obtained, and the equivalent mass of the harmonic oscillator was calculated.

[0007] By keeping the adjustment length l equal to the adjustment width w, and changing the adjustment width w and adjustment depth d respectively, the influence of width w and depth d on the frequency fragmentation of the micro-hemispherical harmonic oscillator model is calculated using finite element software, and the relationship curve between adjustment quality and frequency fragmentation is obtained.

[0008] The resonant frequency f and frequency split Δf of the operating mode of the resonator to be processed are measured. Based on the calculated relationship curve, the mass to be removed for the corresponding frequency split is estimated, and mass adjustment is performed to obtain the relationship curve between the actual removed mass and the frequency split, thus confirming the minimum width w required for actual adjustment. min ;

[0009] The harmonic oscillator is metallized using magnetron sputtering.

[0010] Adjust the femtosecond laser parameters, determine the damage threshold of the resonator material, draw the processing area, and use laser removal to remove a ring of width w. min The film layer enables precise patterning of metal films.

[0011] Furthermore, the process of simulating and calculating the relationship curve between the tuning mass and the frequency splitting change includes: setting the tuning depth d equal to the thickness of the harmonic oscillator lip, keeping the tuning length l equal to the tuning width w, changing the tuning width w, and calculating the relationship curve between mass removal and frequency splitting change.

[0012] Furthermore, the process of simulating and calculating the relationship curve between the tuning quality and the frequency splitting change includes: keeping the tuning length l equal to the tuning width w, changing the tuning width w and the tuning depth d respectively, and calculating the relationship curve between the quality surface removal and the frequency splitting change.

[0013] Preferably, when estimating the required mass removal for the corresponding frequency split based on the calculated relationship curve, if both mass volume removal (i.e., the relationship curve between mass volume removal and frequency split change, where d equals the harmonic oscillator thickness) and surface removal (i.e., the relationship curve between mass surface removal and frequency split change, where d is less than the harmonic oscillator thickness) can achieve mass adjustment, then the minimum width w is preferentially determined based on the relationship curve between mass volume removal and frequency split. min .

[0014] Furthermore, in the curve showing the relationship between mass surface removal and frequency fragmentation, the horizontal axis is Δm.i / M eff The vertical coordinate is △f i / f 1i , where △m i The mass removed during the i-th adjustment is represented as: Δm i =ρd i l i w i ρ is the density of the harmonic oscillator, d i For the depth of the i-th adjustment, l i w is the length of the i-th adjustment. i M represents the width adjusted for the i-th time; eff Let Δf be the equivalent mass of the harmonic oscillator in its operating mode. i For the frequency splitting after the i-th tuning, f 1i is the low-frequency resonant frequency after the i-th adjustment.

[0015] Furthermore, the tuning position is located on the low-frequency axis of the resonator, and a four-point tuning is adopted, with the azimuth angle of each tuning point being 90° apart.

[0016] Furthermore, the resonator is actually mass-adjusted to confirm the minimum width w required for adjustment. min The process includes: using mass removal to reduce the frequency fragmentation Δf of the resonator to Δf / 10, the width to be removed is the minimum width w. min .

[0017] Furthermore, when using a laser for metal layer stripping and trimming point thinning, the laser pulse width is less than 300 fs.

[0018] Furthermore, the laser overlap rate of the laser is 96%, and the laser overlap rate is calculated as follows:

[0019]

[0020] Where OL is the laser overlap ratio; v is the laser scanning speed; and f c Where is the repetition frequency and D is the spot diameter.

[0021] Furthermore, when the laser performs metal layer stripping, the processing trajectory is a set of concentric circles, with a line overlap rate of 10%. The line overlap rate of each concentric circle is calculated as follows:

[0022]

[0023] Where D is the diameter of the light spot, and ΔD is the radial offset of each concentric circle.

[0024] Furthermore, when using a laser to peel off the metal layer, the process of determining the laser's single-pulse energy includes: placing a flat piece of fused silica glass made of the same material as the micro-hemispherical resonator in the laser processing area, drawing a cross-shaped processing trajectory, setting single-pulse lasers of different energy densities to process the flat piece, and using a laser confocal microscope to observe and measure the maximum diameter of the micro-holes formed during processing until the cross-shaped pattern is no longer observable on the flat piece. Based on the curve fitting of the single-pulse energy and micro-hole diameter data, the damage threshold of the laser on the fused silica glass flat piece and the corresponding single-pulse energy are obtained.

[0025] Compared with the prior art, the advantages of the present invention are as follows:

[0026] 1. By combining numerical simulation and experiment, a region for removing the metal film layer along the lip of the resonator was designed. When performing quality adjustment in this region, the capacitance value at that location will not be affected, ensuring the consistency of the driving and detection gain of each electrode. This provides a new technical approach for the manufacture of high-performance micro-hemispherical gyroscopes.

[0027] 2. Precise patterning of the metal film layer of the resonator can be achieved using femtosecond laser without damaging the surface of the resonator, eliminating the need for mask fabrication and simplifying the operation. Attached Figure Description

[0028] Figure 1 This is the overall flowchart of the present invention;

[0029] Figure 2 This is a simulation model diagram of the quality adjustment in step 2 of the present invention;

[0030] Figure 3 This is a simulation model diagram of mass removal in step 2 of the present invention;

[0031] Figure 4 This is a simulation model diagram of mass surface removal in step 2 of the present invention;

[0032] Figure 5 The cross-shaped pattern formed after processing along the cross trajectory in step 5 of this invention;

[0033] Figure 6 This refers to the circular machining trajectory in step 5 of the present invention;

[0034] Figure 7 This is a schematic diagram of the metallization of the harmonic oscillator in step 5 of the present invention.

[0035] The labels in the figure represent the following: 1. Micro-hemispherical harmonic oscillator; 101. Metallization film layer; 102. Annular peel-off region. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] This invention proposes a method for metallizing a micro-hemispherical resonator for post-assembly adjustment, specifically including the following steps:

[0038] A micro-hemispherical harmonic oscillator structural model was established using finite element software. The modal parameters of the model were simulated and obtained, and the equivalent mass of the harmonic oscillator was calculated.

[0039] By keeping the adjustment length l equal to the adjustment width w, and changing the adjustment width w and adjustment depth d respectively, the influence of width w and depth d on the frequency fragmentation of the micro-hemispherical harmonic oscillator model is calculated using finite element software, and the relationship curve between adjustment quality and frequency fragmentation is obtained.

[0040] The resonant frequency f and frequency split Δf of the operating mode of the resonator to be processed are measured. Based on the calculated relationship curve, the mass to be removed for the corresponding frequency split is estimated, and mass adjustment is performed to obtain the relationship curve between the actual removed mass and the frequency split, thus confirming the minimum width w required for actual adjustment. min ;

[0041] The harmonic oscillator is metallized using magnetron sputtering.

[0042] Adjust the femtosecond laser parameters, determine the damage threshold of the resonator material, draw the processing area, and use laser removal to remove a ring of width w. min The film layer enables precise patterning of metal films.

[0043] This invention is particularly applicable to the internal surface metallization of the micro-hemispherical gyroscope structure described in Chinese patent application CN202211517923.5, such as... Figure 2 As shown, the final harmonic oscillator structure is as follows: Figure 7 As shown, the inner surface of the resonator is metallized, and then a ring with a width of w is peeled off from the outermost edge of the lip inward. min The membrane layer provides a reserved area for quality adjustment.

[0044] Example 1

[0045] In this application, a quality adjustment region without a metal film is prepared on the lip of the resonator, the size of which meets the size requirements required to reduce the initial frequency of the resonator to the design value (theoretical value is zero).

[0046] This invention is applicable to micro-hemispherical gyroscopes employing planar electrode structures. It is simple to operate, allows for the design of mass adjustment regions, and enables precise patterning of the metal film layer of the micro-hemispherical resonator using femtosecond lasers. This reduces driving and detection gain errors introduced by adjustment. The adjustment process of this invention includes:

[0047] Step 1: Establish a micro-hemispherical harmonic oscillator structural model using the finite element software COMSOL Multiphysics, simulate the modal parameters of the model, obtain the mode shape φ and modal frequency f, and calculate the equivalent mass M of the harmonic oscillator. eff ;

[0048] Step 2: Let the adjustment length l always be equal to the adjustment width w. Change the adjustment width w and adjustment depth d respectively. Use finite element software to calculate the influence of adjustment width w and adjustment depth d on the frequency splitting of the micro-hemispherical harmonic oscillator model and obtain the relationship curve between adjustment quality and frequency splitting.

[0049] Step 3: Take a resonator, measure its operating mode resonant frequency f and frequency split Δf, and estimate the mass to be removed based on the relationship curve. Perform mass adjustment on the resonator to obtain the actual relationship curve between the adjusted mass and the frequency split change. Based on the relationship curve, determine the minimum adjustment width w. min ;

[0050] Step 4: Metallize the micro-hemispherical resonator 1 by magnetron sputtering to obtain a metallized film 101;

[0051] Step 5: Adjust the femtosecond laser parameters to determine the damage threshold of the resonator material; draw the processing area and use laser to remove the ring with a width of w. min The film layer enables precise patterning of metal films.

[0052] As an optional implementation, the equivalent mass M of the harmonic oscillator is obtained. eff The process includes:

[0053]

[0054] Among them, M eff Let ρ be the equivalent mass of the resonator in its operating mode, ρ be the density of the resonator material, and φ be the mass of the resonator. xi φ yi φ zi (i = 1, 2) represent the components of the mode shape function of the i-th mode on the x, y, and z axes in the three-dimensional coordinate system; V is the volume of the harmonic oscillator.

[0055] As an optional implementation, the process of obtaining the relationship curve between tuning quality and frequency splitting includes the following steps:

[0056] Step 201, let the adjustment depth d be equal to the thickness of the lip of the micro-hemispherical harmonic oscillator, i.e. Figure 3 Mass removal is performed at the position corresponding to the low-frequency axis on the lip of the resonator using a volume adjustment method, forming a corresponding notch. The adjustment length l is always equal to the adjustment width w. By changing the adjustment width w, the relationship curve between mass volume removal and frequency splitting is calculated.

[0057] Step 202: Let the adjustment length l always equal to the adjustment width w. Change the adjustment width w and adjustment depth d respectively, and calculate the relationship curve between the quality surface removal and the frequency fragmentation change. The obtained relationship curve between the adjustment quality and the frequency fragmentation change is expressed as the function f(Δm). i / M eff , △f i / f 1i That is, in the curve showing the relationship between mass surface removal and frequency fragmentation, the horizontal axis is Δm. i / M eff The vertical coordinate is △f i / f 1i , where △m i The mass removed during the i-th adjustment is represented as: Δm i =ρdl i w i ρ is the density of the harmonic oscillator, d is the thickness of the lip of the micro-hemispherical harmonic oscillator, and l i w is the length of the i-th adjustment. i The width is adjusted for the i-th time; △f i For the frequency splitting after the i-th tuning, f 1i is the low-frequency resonant frequency after the i-th adjustment.

[0058] Preferably, in this embodiment, the adjustment position is located on the low-frequency axis of the resonator, and four-point adjustment is adopted, with the azimuth angle of each adjustment point being 90° apart.

[0059] In steps 1 to 2 of this embodiment, software simulation is used to obtain the optimal theoretical values. During the simulation, parameters such as adjustment width w and adjustment depth d need to be set according to the laser processing accuracy when increasing or decreasing, so that they can be realized in the actual processing scenario.

[0060] In one embodiment, the pulse width of the laser described in steps 3 and 5 is 210 fs.

[0061] In one embodiment, the micro-hemispherical resonator of the present invention is made of fused silica glass; in step 3, if both mass removal and surface removal can achieve mass adjustment, the minimum width w is preferentially determined based on the relationship curve between mass removal and frequency splitting. minAs an optimal implementation method, when the frequency split Δf of the resonator is reduced to Δf / 10 by removing the mass body, the width to be removed is the minimum width w. min Under the minimum width condition, the convergence of quality tuning can be ensured (i.e., the frequency fragmentation can be reduced to the design value through multiple tunings), and the capacitance value change caused by film removal can be avoided.

[0062] In one embodiment, the specific process of step 5, which achieves precise patterning of the metal film layer, includes:

[0063] Step 501: Take a flat sheet of fused silica glass of the same material and place it in the laser processing area, then draw as shown. Figure 5 The "+" pattern processing trajectory shown was used to process the flat sheet with single-pulse lasers of different energy densities. The maximum diameter of the micropores formed by the processing was observed and measured using a laser confocal microscope until the "+" pattern could no longer be observed on the flat sheet. Based on the fitting curve of single-pulse energy and micropore diameter data, the damage threshold of the laser on the fused silica glass flat sheet and the corresponding single-pulse energy were obtained.

[0064] Step 502: Place the metallized micro-hemispherical resonator 1 in the laser processing area and draw a ring with a width of w. min The circular machining trajectory, such as Figure 6 Using the outer contour of the harmonic oscillator as a reference circle, the circular machining trajectory of the machining center is determined as a set of concentric circles with a line overlap rate of 10%. Based on the single pulse energy determined in step 501, the machining is carried out according to the predetermined trajectory to remove the metallized film layer of the annular peeling area 102, thereby achieving precise patterning of the metal film layer.

[0065] As an optional embodiment, the overlap rate of the lines of each concentric circle is calculated as follows:

[0066]

[0067] Where D is the diameter of the light spot, and ΔD is the radial offset of each concentric circle.

[0068] Example 2

[0069] Example 1 presents a technical solution employing a mass removal scheme, primarily used for mass adjustment of resonators with significant initial frequency fragmentation. Its key feature is the achievement of large-volume mass removal through ablation penetrating the adjustment region. This invention uses a simulation model to predict w... min During the manufacturing process of resonators, when the process consistency requirements are met, the frequency splitting values ​​of each resonator in the same batch are basically similar. Therefore, the frequency splitting value determined by a single resonator is not significant. min It can meet the adjustment requirements of this batch of harmonic oscillators. Even if there are out-of-tolerance issues, the adjustment length l can be increased without changing the width w.min To meet the tuning requirements of higher frequency splitting.

[0070] In another embodiment of the invention, Figure 1 This is a flowchart illustrating the metallization design and fabrication method for a micro-hemispherical resonator used for post-assembly adjustment according to an embodiment of the present invention. The method includes:

[0071] Step 1: Establish a micro-hemispherical harmonic oscillator structural model using the finite element software COMSOL Multiphysics, simulate the modal parameters of the model, obtain parameters such as mode shape φ and modal frequency f, and calculate the equivalent mass M of the harmonic oscillator. eff ;

[0072] Step 2: Apply four-point tuning on the low-frequency axis of the harmonic oscillator model, ensuring the tuning length l is always equal to the tuning width w. Then, change the width w and depth d respectively, as follows: Figure 4 In this embodiment, the depth d is less than the thickness of the micro-hemispherical resonator lip. Mass removal is performed at the position corresponding to the low-frequency axis of the resonator lip using a volume adjustment method, thinning the lip. Finite element software is used to calculate the influence of width w and depth d on the frequency fragmentation of the micro-hemispherical resonator model, obtaining the relationship curve between adjustment surface removal and frequency fragmentation. This relationship curve is expressed as a function f(Δm). i / M eff , △f i / f 1i ), where: △m i =ρd i l i w i Let d be the mass of the i-th removal. i l i w i These represent the depth, length, and width of the i-th adjustment; △f i For the frequency splitting of the i-th tuning, f 1i The low frequency after the i-th adjustment;

[0073] Step 3: Take a resonator, measure its resonant frequency f and frequency split Δf of its working mode, and estimate the removal quality according to the relationship curve. Set the pulse width of the laser to 210fs and the overlap rate to 96%. Perform quality adjustment on the resonator to obtain the actual relationship curve between the removal of the adjustment surface and the change of frequency split.

[0074] Step 4: Metallize the micro-hemispherical resonator 1 by magnetron sputtering to obtain a metallized film 101;

[0075] Step 5: Adjust the femtosecond laser parameters to determine the damage threshold of the resonator material. Draw the processing area and use laser to remove a ring of width w. minThe method for achieving precise patterning of the metal film layer 102 is as follows:

[0076] Step 501: Place a flat sheet of fused silica glass of the same material in the laser processing area, draw a cross-shaped processing trajectory, and process the flat sheet with single-pulse lasers of different energy densities. Observe and measure the maximum diameter of the micropores formed during processing using a laser confocal microscope until the cross-shaped pattern is no longer visible on the flat sheet. Based on the fitting curve of single-pulse energy and micropore diameter data, obtain the damage threshold of the laser on the fused silica glass flat sheet and the corresponding single-pulse energy.

[0077] Step 502: Place the micro-hemispherical resonator 1 with its inner surface metallized into the laser processing area and draw a ring with a width of w. min The circular processing trajectory is a set of concentric circles with a line overlap rate of 10%. The processing center is determined by taking the outer contour of the micro-hemispherical resonator 1 as the reference circle. According to the single pulse energy determined in step 501, the processing is carried out according to the predetermined trajectory to remove the metallized film layer in the annular peeling area 102 and realize the precise patterning of the metal film layer.

[0078] As another embodiment of the present invention, the difference between Embodiment 2 and Embodiment 1 is that Embodiment 2 adopts the technical solution of the trimming surface removal scheme, which is mainly used for mass trimming of the resonator with a small initial frequency split. Its feature is that the trimming region does not need to be ablated through. Therefore, in step 2, the trimming depth d is a variable.

[0079] Finally, it should be noted that: although this embodiment Figure 1 The steps are shown sequentially as indicated by the arrows, but they are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are performed; they can be executed in other orders. Figure 1 At least some steps in the process may include multiple sub-steps. These sub-steps are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps is not necessarily sequential, but can be executed in turn or alternately with at least some of the sub-steps of other steps.

[0080] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for metallizing a micro-hemispherical resonator for post-assembly adjustment, characterized in that, Includes the following steps: A micro-hemispherical harmonic oscillator structural model was established using finite element software. The modal parameters of the model were simulated and obtained, and the equivalent mass of the harmonic oscillator was calculated. By keeping the adjustment length l equal to the adjustment width w, and changing the adjustment width w and adjustment depth d respectively, the influence of width w and depth d on the frequency fragmentation of the micro-hemispherical harmonic oscillator model is calculated using finite element software, and the relationship curve between adjustment quality and frequency fragmentation is obtained. The resonant frequency f and frequency split Δf of the operating mode of the resonator to be processed are measured. Based on the calculated relationship curve, the mass to be removed for the corresponding frequency split is estimated, and mass adjustment is performed to obtain the relationship curve between the actual removed mass and the frequency split, thus confirming the minimum width w required for actual adjustment. min ; The harmonic oscillator is metallized using magnetron sputtering. Adjust the femtosecond laser parameters, determine the damage threshold of the resonator material, draw the processing area, and use laser removal to remove a ring of width w. min The film layer enables precise patterning of metal films.

2. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 1, characterized in that, The process of simulating the relationship curve between the adjustment mass and the frequency splitting change includes: setting the adjustment depth d equal to the thickness of the resonator lip, keeping the adjustment length l equal to the adjustment width w, changing the adjustment width w, and calculating the relationship curve between mass removal and frequency splitting change.

3. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 1, characterized in that, The process of simulating the relationship curve between tuning quality and frequency splitting includes: keeping the tuning length l equal to the tuning width w, changing the tuning width w and tuning depth d respectively, and calculating the relationship curve between quality surface removal and frequency splitting.

4. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to any one of claims 1 to 3, characterized in that, In the curve showing the relationship between tuning quality and frequency splitting, the horizontal axis is Δm. i / M eff The vertical coordinate is △f i / f 1i , where △m i The mass removed during the i-th adjustment is represented as: Δm i =ρd i l i w i ρ is the density of the harmonic oscillator, d i For the depth of the i-th adjustment, l i w is the length of the i-th adjustment. i M represents the width adjusted for the i-th time; eff Let Δf be the equivalent mass of the harmonic oscillator in its operating mode. i For the frequency splitting after the i-th tuning, f 1i is the low-frequency resonant frequency after the i-th adjustment.

5. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to any one of claims 2 to 3, characterized in that, The tuning position is located on the low-frequency axis of the resonator, and four-point tuning is used, with each tuning point spaced 90° apart.

6. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 1, characterized in that, Perform actual mass adjustment on the resonator to confirm the minimum width w required for adjustment. min The process includes: using mass removal to reduce the frequency fragmentation Δf of the resonator to Δf / 10, the width to be removed is the minimum width w. min .

7. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 5 or 6, characterized in that, When using a laser for quality adjustment and removal of metal films, the laser pulse width is less than 300 fs.

8. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 7, characterized in that, The laser overlap ratio of the laser is 96%. The laser overlap ratio is calculated as follows: Where OL is the laser overlap ratio; v is the laser scanning speed; and f c Where is the repetition frequency and D is the spot diameter.

9. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 1, characterized in that, When using lasers to remove metal films, the processing trajectory consists of a set of concentric circles with a 10% overlap rate. The calculation method for the overlap rate of each concentric circle is as follows: Where D is the diameter of the light spot, and ΔD is the radial offset of each concentric circle.

10. The method for metallizing a micro-hemispherical resonator for post-assembly adjustment according to claim 1, characterized in that, When using a laser to remove a metal layer, the process of determining the laser's single-pulse energy includes: placing a flat piece of fused silica glass made of the same material as the micro-hemispherical resonator in the laser processing area, drawing a cross-shaped processing trajectory, setting single-pulse lasers of different energy densities to process the flat piece, and using a laser confocal microscope to observe and measure the maximum diameter of the micro-holes formed during processing until the cross pattern is no longer observable on the flat piece. Based on the single-pulse energy and micro-hole diameter data, a curve is fitted to obtain the damage threshold of the laser on the fused silica glass flat piece and the corresponding single-pulse energy.

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