Method of manufacturing a mechanical resonator

Abstract

One aspect of the invention relates to a method for manufacturing a set of mechanical resonators (2a) whose average value of a structure characteristic is within a predetermined numerical range, the method comprising the steps of: forming (21) mechanical resonators (2b, 2c) and oscillating members (10a, 10b, 10c) in a substrate (1); calculating, on the basis of values determined for said structure characteristic, size correction values to be applied to the formed resonators (2b, 2c); and then modifying (28) the size of the formed resonators (2b, 2c) on the basis of the calculated size correction values, in order to obtain a set of resonators (2a) whose structure characteristic values are within the predetermined numerical range.

Description

Technical Field

[0001] This invention relates to the field of manufacturing mechanical resonators, particularly in the field of watchmaking. More specifically, this invention relates to a method for manufacturing a set of mechanical resonators, wherein structural characteristics common to these resonators, such as stiffness, are within a predetermined numerical range. Background Technology

[0002] In the prior art, methods commonly used to manufacture mechanical resonators such as clock hairsprings in substrates involve etching techniques such as laser etching, plasma etching, deep reactive ion etching (DRIE), or wet etching.

[0003] However, it has been found that using this method often results in geometric discrepancies between all clock springs formed on the same substrate with the same pattern.

[0004] To overcome these shortcomings, solutions have been proposed in the prior art, particularly patents EP 3181938 and EP3181939, which describe methods for manufacturing hairsprings.

[0005] In patent EP3181938, the manufacturing method includes the following steps: a) forming a hairspring with a size larger than that required to obtain a hairspring with a predetermined stiffness; b) determining the stiffness of the hairspring formed in step a) by measuring the frequency of the hairspring connected to a balance wheel with a predetermined inertia; c) calculating the thickness of material to be removed to obtain a hairspring with a predetermined stiffness; and d) removing the calculated thickness of material from the hairspring formed in step a), wherein steps b), c), and d) can be repeated to further improve dimensional accuracy.

[0006] In patent EP 3181939, the manufacturing method includes the following steps: a) forming a hairspring with a size smaller than that required to obtain a hairspring with a predetermined stiffness; b) determining the stiffness of the hairspring formed in step a) by measuring the frequency of the hairspring connected to a balance wheel with a predetermined inertia; c) calculating the missing material thickness for obtaining a hairspring with a predetermined stiffness; d) modifying the hairspring formed in step a) to compensate for the missing material thickness, wherein steps b), c), and d) can be repeated to further improve dimensional accuracy.

[0007] Such methods can be improved, especially to limit substrate contamination that may occur during the measurement steps.

[0008] In this situation, it is clear that a solution is needed that can bring about such an improvement. Summary of the Invention

[0009] The present invention aims to provide a method for manufacturing a set of mechanical resonators that meet the above requirements.

[0010] The present invention also aims to improve the manufacturing precision of multiple sets of mechanical resonators, wherein the average value of structural characteristics such as stiffness of the multiple sets of mechanical resonators is within a predetermined range.

[0011] This invention relates to a method for manufacturing a set of mechanical resonators, wherein the average value of the structural characteristics of the set of mechanical resonators is within a predetermined numerical range, said structural characteristics being common to each mechanical resonator in the set, the method comprising the following steps:

[0012] a) The step of forming a mechanical resonator in a substrate, wherein the size of the mechanical resonator is different from the size required to obtain the set of mechanical resonators with structural characteristics within the predetermined numerical range;

[0013] (b) The step of forming at least one oscillating member in the substrate, the at least one oscillating member being formed in an opening of the substrate, the oscillating member being composed of a main body and two flexible arms, the main body being connected at a first end to a fixing portion of the outer peripheral wall of the opening, the two flexible arms being connected to a second end of the main body via a connecting portion, the two flexible arms being parallel to the axis of symmetry of the main body and extending toward the fixing portion, the axial section of the second end being smaller than the axial section of the first end and larger than the axial section of each of the flexible arms;

[0014] c) A determination step, in which a value related to the structural characteristics of the at least one oscillating member formed is determined;

[0015] d) Calculation step, in which the size correction value to be applied to the formed mechanical resonator is calculated based on the value determined for the structural characteristics;

[0016] e) Modification step, in which the dimensions of the formed mechanical resonator are modified based on the calculated dimension correction value to obtain the set of mechanical resonators with structural characteristic values ​​within a predetermined range.

[0017] In other embodiments:

[0018] - In the step of forming the oscillating member, each of the flexible arms is given a length that can be adjusted according to a resonance measurement tolerance factor, which is defined by at least one dimension of the flexible portion of the mechanical resonator associated with the at least one oscillating member;

[0019] - In the step of forming the oscillating member, each flexible arm is respectively placed at a first distance and a second distance from the body of the main body and the fixing part of the outer peripheral wall of the opening, wherein the first distance is greater than the second distance;

[0020] - In the step of forming the oscillating component, the thickness of each of the flexible arms is made equal to or substantially equal to the thickness of the flexible portion of each mechanical resonator formed in the substrate;

[0021] - In the step of forming the oscillating member, the free end of each of the flexible arms is integrally formed with an end member, the mass of which is greater than the mass of the rest of the body of the flexible arm;

[0022] - The end member has a circular or polygonal cross-section;

[0023] - In the step of forming the oscillating member, the axial section of the second end of the main body is 1 / 3 to 1 / 5 of the axial section of the first end;

[0024] - The steps of forming the mechanical resonator and forming at least one oscillating element are carried out by etching, particularly by deep reactive ion etching;

[0025] - The step of forming each oscillating element is carried out in the substrate for at least one of the mechanical resonators in the group of mechanical resonators;

[0026] - The step of forming oscillating components is used to form a plurality of oscillating components around at least one mechanical resonator in the substrate;

[0027] - The determining step includes an estimation sub-step in which at least one resonant frequency is estimated for each oscillating element associated with at least one mechanical resonator in the group of mechanical resonators;

[0028] - The determining step includes a definition sub-step in which a structural characteristic is defined for each oscillating element, the structural characteristic being the same as the structural characteristic common to each of the formed mechanical resonators. The definition sub-step is executed by a processing unit connected to a device for modifying the formed mechanical resonators. The processing unit executes an algorithm to calculate the structural characteristic of each oscillating element based on the estimated resonant frequency.

[0029] - The calculation step includes a material thickness determination sub-step, in which the thickness of material to be added to or removed from at least one dimension of each mechanical resonator associated with the oscillating member is determined based on structural characteristic values ​​determined for each oscillating member;

[0030] - The oscillating component is in the shape of a tuning fork;

[0031] - The structural characteristic mentioned is the stiffness characteristic. Attached Figure Description

[0032] Other features and advantages of the invention will become apparent from the description of specific embodiments of the invention provided with reference to the accompanying drawings, which are illustrative and not restrictive examples only, wherein:

[0033] Figure 1 This is a schematic diagram of a substrate according to an embodiment of the present invention, the substrate including a set of mechanical resonators, all of which have been simultaneously formed in the substrate, particularly by etching.

[0034] Figure 2A This is an enlarged view of an oscillating component in the form of a tuning fork according to an embodiment of the present invention. This oscillating component is capable of determining characteristic values ​​common to mechanical resonators. The oscillating component and its resonator are included in... Figure 1 In the substrate shown;

[0035] Figure 2B and Figure 2C According to an embodiment of the present invention Figure 2A A variation of the oscillating component, wherein the free end of the flexible arm of the oscillating component includes an end member, the mass of which is greater than the mass of the rest of the flexible arm;

[0036] Figure 3 This is a schematic cross-sectional view of the flexible portion of a resonator manufactured using the method according to an embodiment of the present invention. The dimensions of this cross-section are necessary to ensure that the average value of the structural characteristics of a group of mechanical resonators is within a predetermined range.

[0037] Figure 4 This is a schematic cross-sectional view of a flexible portion of a resonator formed in a substrate using a method according to an embodiment of the present invention. The dimension of this cross-section is greater than... Figure 3 The dimensions of the cross-section of the fabricated resonator are shown.

[0038] Figure 5 This is a schematic cross-sectional view of a flexible portion of a resonator formed in a substrate using a method according to an embodiment of the present invention. The dimension of this cross-section is smaller than... Figure 3 The dimensions of the cross-section of the fabricated resonator are shown.

[0039] Figure 6 This is a flowchart relating to a method for manufacturing a set of mechanical resonators according to an embodiment of the present invention, wherein the average value of the structural characteristics of the set of mechanical resonators is within a predetermined numerical range. Detailed Implementation

[0040] Figure 6A schematic diagram is shown of a method for fabricating a set of mechanical resonators 2a on a substrate 1 (referred to as a "wafer") formed of one material. The substrate 1 can be a monocrystalline silicon substrate, but it can also be a substrate made of other materials, such as polycrystalline silicon, amorphous silicon, other semiconductor materials, glass, ceramics, carbon, quartz, metals, alloys, or composite materials containing these materials. However, monocrystalline silicon is relatively insensitive to magnetic fields and is a cubic crystal with an isotropic coefficient of thermal expansion (α).

[0041] In this method, the mechanical resonators 2a, 2b, and 2c are elastically deformable components capable of being driven by oscillating motion. In other words, the mechanical resonators 2a, 2b, and 2c include a body composed of a flexible portion 3 and a rigid connecting portion relative to the flexible portion 3, the connecting portion allowing the mechanical resonators 2a, 2b, and 2c to be fixed to an axis or spindle. Such mechanical resonators 2a, 2b, and 2c can be used in watches, particularly in the mechanical regulators of mechanical watch movements. In watches, the oscillation of these mechanical resonators determines the timekeeping error of the movement. For example, many watches include a regulator comprising a hairspring acting as a mechanical resonator, mounted on the balance wheel axis and oscillating via an escapement mechanism. The natural frequency of the hairspring and balance wheel mechanism regulates the watch's speed. The watch hairspring includes a flexible strip connected at one end to an inner stud and wound in a spiral to form multiple consecutive turns, with the last turn extending into an attachment section for attachment, for example, to a fixed balance plate via an outer stud. The inner stud is designed to be fixed to a pivoting shaft. Other known types of resonators include those based on an oscillating rod or other mechanical components.

[0042] Therefore, this method can manufacture a set of mechanical resonators 2a whose average structural characteristics are within a predetermined range. In this method, the structural characteristics are common to all mechanical resonators 2a in the set. In other words, these mechanical resonators have the same structural characteristics. These structural characteristics can be the stiffness characteristics of the mechanical resonator 2a, particularly the stiffness characteristics of its flexible portion 3. In this case, the method enables the selection of the specific set of mechanical resonators 2a from a plurality of mechanical resonators formed in the substrate 1. To this end, the method helps to generate a mapping diagram indicating the geometrical dispersion among the dimensions of the plurality of mechanical resonators formed in the substrate, thereby indicating the dispersion among their common structural characteristics, and by correcting the selected set of mechanical resonators, ensuring that the average value of their structural characteristics is within a predetermined range. This method aims to ensure that the manufactured mechanical resonators 2a have extremely high dimensional accuracy while simultaneously guaranteeing that these mechanical resonators 2a have more precise structural characteristics.

[0043] It should be noted that, in a preferred embodiment of the method, the mechanical resonators 2a, 2b, and 2c can be watch hairsprings, and their structural characteristics can be the stiffness of the hairspring, particularly the stiffness of its strips. In this case, the method can then be a method for manufacturing a set of watch hairsprings 2a or a component of watch hairsprings 2a in a substrate 1, wherein the average stiffness of each hairspring is within a predetermined range.

[0044] refer to Figure 1 A set of mechanical resonators 2a are formed in the substrate 1. Each mechanical resonator 2a in the set includes a flexible part 3 and a rigid connecting part for fixing the mechanical resonator to a shaft or spindle.

[0045] In the case where the mechanical resonator is a hairspring, the hairspring includes an inner stud for securing it to the pivot mandrel.

[0046] This method is used in a system for fabricating a set of mechanical resonators 2a, 2b, 2c in a substrate 1. The system includes, but is not exhaustive or limited to, a processing unit (e.g., a computer), means for forming mechanical resonators 2b, 2c and at least one oscillating member 10a, 10b, 10c in the substrate 1, and means for modifying the mechanical resonators 2b, 2c formed in the substrate 1.

[0047] The apparatus for forming the mechanical resonators 2b and 2c and the oscillating components 10a, 10b, and 10c can be used to implement microfabrication techniques, such as photolithography, machining, and etching methods, in the substrate 1. In particular, methods such as deep reactive ion etching, laser etching, chemical etching, or etching using a focused ion beam can be employed.

[0048] The apparatus for modifying mechanical resonators 2b and 2c includes a module for determining the structural characteristics of mechanical resonators 2b and 2c and a module for correcting the dimensions of mechanical resonators 2b and 2c. The module for determining the structural characteristics includes:

[0049] - A drive submodule for driving / releasing the mechanical oscillating motion of the bodies of oscillating components 10a, 10b, and 10c about their stable equilibrium positions;

[0050] - Measurement submodule for measuring the resonant frequency of oscillating components 10a, 10b, and 10c during mechanical oscillation motion.

[0051] Regarding the dimension correction module for mechanical resonators 2b and 2c, it includes a calculation submodule for calculating the corrections required for mechanical resonators 2b and 2c, and a correction submodule for correcting these mechanical resonators 2b and 2c using techniques that oxidize and then deoxidize these mechanical resonators, including thermal oxidation, electroplating growth, physical vapor deposition, chemical vapor deposition, atomic layer deposition, or any other additive process.

[0052] In this system, a processing unit is connected to means for forming mechanical resonators 2b, 2c and at least one oscillating member 10a, 10b, 10c in the substrate 1, and means for modifying the formed mechanical resonators 2b, 2c. This processing unit includes at least a processor and a storage element. The processing unit is capable of executing computer program instructions, for example, designed to guide / control these two means. Specifically, the processing unit ensures guidance / control of the drive submodule and the measurement submodule, and ensures computational / processing operations, in which at least one algorithm stored in the storage element is executed. The algorithm may include machine learning algorithms and / or mathematical formulas. The algorithm is capable of using predictive or simulation models to determine the structural characteristics, particularly the stiffness, of at least one oscillating member 10a, 10b, 10c, and to determine dimensional correction values ​​for the mechanical resonators 2b, 2c formed in the substrate 1.

[0053] The method includes a step 20 of forming mechanical resonators 2b and 2c, in which mechanical resonators 2b and 2c are formed in substrate 1 according to dimensions E2, E3, H2, H3, which are different from the dimensions E1 and H1 required for a set of mechanical resonators 2a to obtain an average value of structural characteristics within a predetermined range.

[0054] In step 20, mechanical resonators 2b and 2c are formed in the substrate 1. Preferably, these mechanical resonators 2b and 2c are formed simultaneously in the substrate 1. The formation of these mechanical resonators 2b and 2c in the substrate 1 is performed by a forming apparatus controlled by the processing unit of the system. It should be noted that these mechanical resonators 2b and 2c preferably have similar geometries or form similar structures.

[0055] Reference Figure 1 , Figure 4 and Figure 5The mechanical resonators 2b and 2c formed in the substrate 1 have flexible portions 3 with cross sections 4b and 4c, respectively, having dimensions E2, H2 and E3, H3. The cross sections 4b and 4c of the flexible portions 3 preferably have a polygonal shape similar to a hairspring strip, and are characterized in that the heights H2 and H3 and the thicknesses E2 and E3 of the cross sections 4b and 4c are different from the dimensions E1 and H1 required for a group of mechanical resonators 2a to achieve an average structural characteristic within a predetermined range. In other words, the dimensions E2, H2, E3, H3 of the cross sections 4b and 4c of the flexible portions 3 of each mechanical resonator 2b and 2c can be greater than or less than the dimensions E1 and H1 required for the cross sections 4a of the flexible portions of the manufactured mechanical resonators 2a to achieve an average structural characteristic within a predetermined range.

[0056] As described above, the substrate 1 is preferably made of doped or undoped silicon. The silicon can be monocrystalline silicon, polycrystalline silicon, or amorphous silicon. Furthermore, the silicon can have orientations {1,1,1}, {-1,1,1}, {1,-1,1}, and {-1,-1,1}, where orientation is the most important factor for the Young's modulus of silicon.

[0057] It should be noted that during step 20, the mechanical resonators 2b and 2c formed may have:

[0058] - Dimensions E2 and H2 are greater than the dimensions E1 and H1 required for a set of mechanical resonators 2a to obtain structural characteristics such as stiffness within a predetermined range. That is, the height H2 and / or the thickness E2 of the flexible part 3 are greater than the height H1 and / or the thickness E1 of the flexible part 3 of the mechanical resonator 2a to obtain structural characteristics such as stiffness within a predetermined range.

[0059] - Dimensions E3 and H3 are smaller than the dimensions E1 and H1 required for a set of mechanical resonators 2a to obtain structural characteristics such as stiffness within a predetermined range. That is, the height H3 and / or the thickness E3 of the flexible part 3 are smaller than the height H1 and / or the thickness E1 of the flexible part 3 of the mechanical resonator 2a to obtain structural characteristics such as stiffness within a predetermined range.

[0060] The method further includes a step 21 of forming at least one oscillating member 10a, 10b, 10c, in which at least one oscillating member 10a, 10b, 10c is formed in a substrate 1, the oscillating member including a main body 6 and flexible arms / branches 7, 8, the flexible arms / branches 7, 8 being parallel to the axis of symmetry A of the main body 6.

[0061] Step 21 is performed on the same substrate 1 including the formed mechanical resonators 2b and 2c, preferably simultaneously with step 20, which forms the mechanical resonators 2b and 2c.

[0062] In step 21, at least one oscillation element 10a, 10b, 10c is fabricated in the substrate 1 for at least one of the mechanical resonators 2b, 2c in the group of mechanical resonators 2b, 2c. For example, oscillation elements 10a, 10b, 10c can be fabricated for multiple mechanical resonators 2b, 2c arranged adjacent to each other or for each mechanical resonator 2b, 2c. Alternatively, multiple oscillation elements 10a, 10b, 10c can be arranged in the substrate 1 around a single mechanical resonator 2b, 2c, particularly in the adjacent region of the mechanical resonator 2b, 2c.

[0063] In step 21, the oscillating members 10a, 10b, and 10c are constructed in the opening 9 of the substrate 1. The opening 9 is a through-hole formed within the thickness of the substrate 1, and the opening 9 includes an outer peripheral wall 13. The opening 9 defines a space in which the oscillating members 10a, 10b, and 10c can freely perform guided / controlled mechanical oscillating motion.

[0064] As described above, the oscillating components 10a, 10b, and 10c include a main body / shaft portion 6, which comprises a preferably straight body. A first end 5a (also called an attachment end 5a) of this body is connected to the outer peripheral wall 13 of the opening 9, particularly to a fixing portion 15 connected to the outer peripheral wall 13. The body of the main body 6 also includes a second end 5d, the axial section S1 of which is smaller than the axial section S2 of the first end 5a. The body of the main body 6 comprises an axial section S4 between the first end 5a and the second end 5d, which is substantially constant. It should be noted that the axial section S1 of the second end 5d is preferably 1 / 3 to 1 / 5 of the axial section S2 of the first end 5a. The difference in axial cross-section can reduce the stiffness of the main body 6 at the second end 5d, and when measuring the structural characteristics of the oscillating members 10a, 10b, and 10c, it produces differences between the in-phase and out-of-phase modes of the flexible arms 7 and 8, which are used to determine the relative values ​​of this structural characteristic in step 22 described below. It should be noted that the in-phase mode corresponds to the mode in which the flexible arms oscillate simultaneously in the same direction. In the out-of-phase mode, the oscillation phase difference of the flexible arms is 180 degrees. Both flexible arms move simultaneously inward and outward.

[0065] In addition, it should be noted that the difference in axial cross sections increases the stiffness of the main body 6 at the first end 5a, so as to decouple the oscillating motion of the flexible arms 7, 8 of the substrate 1 during this measurement.

[0066] The main body 6 is preferably rigid relative to the flexible arms 7 and 8. More specifically, the main body 6 is connected to the flexible arms 7 and 8 at its second end 5d by means of a connecting portion 14. The two flexible arms 7 and 8 extend in a straight line within the opening 9 parallel to the axis of symmetry A and toward the fixing portion 15. It should be noted that the thickness of these flexible arms 7 and 8 may be equal to or substantially equal to the thickness of the flexible portion 3 of the mechanical resonators 2a and 2b.

[0067] The axial sections S3 of the two flexible arms 7 and 8 are similar. Each axial section S3 is defined relative to the axis of symmetry B of its respective flexible arm 7 or 8, which is parallel to the axis of symmetry A of the main body 6. In this configuration, the axial sections S1 and S2 of the main body 6 are larger than the axial sections S3 of each flexible arm 7 or 8.

[0068] Reference Figure 6 and Figures 2A to 2B In step 21, these flexible arms 7 and 8 are designed as follows:

[0069] - The main body 6 of the oscillating components 10a, 10b, and 10c is separated from the body by a first distance D1, which is preferably greater than or significantly greater than or substantially equal to the inter-turn distance of the mechanical resonators 2b and 2c (when the mechanical resonators 2b and 2c are springs or more specifically, hairsprings).

[0070] - The fixing part 15 is at a first distance D2 from the outer peripheral wall 13 of the opening 9.

[0071] In this configuration, the first distance D1 is greater than the second distance D2.

[0072] It should be noted that the thickness Er of these flexible arms 7, 8 is preferably designed to be equal to or substantially equal to the thickness E2, E3 of the flexible portion 3 of each mechanical resonator 2b, 2c formed in the substrate 1. In other words, when the flexible portion 3 is a strip of a hairspring, the thickness Er of each flexible arm 7, 8 is equal to or substantially equal to the thickness E2, E3 of the flexible portion 3. For example, the thickness Er of these flexible arms 7, 8 can be between 10µm and 60µm, preferably 30µm.

[0073] In step 21, the flexible arms 7 and 8 are given a length L, which can be adjusted according to the required resonance measurement tolerance. This tolerance is defined based on at least one deviation of the dimensions E2, E3, H2, H3 of the flexible portion 3 of the mechanical resonators 2b and 2c associated with the oscillating components 10a, 10b, and 10c. The value of this tolerance is equal to a frequency range in which the dimensional changes E2, E3, H2, H3 measured on the mechanical resonators 2b and 2c no longer require correction for stiffness differences. This value thus defines a measurement range in which it is no longer necessary to determine the fine / sensitive dimensional changes of the flexible portion 3 of the formed mechanical resonators 2b and 2c. In other words, no adjustment is required below this tolerance. This value is specifically adapted to the dimensions of the flexible portion 3 of the mechanical resonators 2b and 2c to improve measurement sensitivity and the sensitivity to detection of etching thickness variations. For example, the length is calculated as follows: when the frequency of the oscillating component changes by 10 Hz, the 10 nm size change E2 and E3 of the mechanical resonator can be measured.

[0074] In this step, the process of calculating the lengths of the oscillating components 10a, 10b, and 10c includes:

[0075] - Define dimension Er, which is preferably equal to or substantially equal to the thickness E2, E3, H2, H3 of the flexible portion 3 of each mechanical resonator 2b, 2c formed in the substrate 1;

[0076] - Defines the frequency variation that can be measured by the measurement system, thereby allowing for precise measurement of frequencies, where the frequency variation is 2 to 10 times the standard deviation of the measurement;

[0077] - Define the minimum dimensional variations of E2, E3, H2, and H3 for the mechanical resonators 2b and 2c to be measured;

[0078] - Calculate the length L of flexible arms 7 and 8, which is between 1 mm and 2 mm, so that the measurement of frequency change can lead to conclusions about the dimensional changes of E2, E3, H2, and H3 of mechanical resonators 2b and 2c.

[0079] It should be noted that the shorter the length L of the flexible arms 7 and 8, the higher the measured resonant frequency will be, and the more sensitive the ratio between the addition or removal of uniformly thick material on the oscillating components 10a, 10b, and 10c and its resonant frequency will be.

[0080] In step 21, it should be noted that the oscillating components 10a, 10b, and 10c are preferably arranged in the substrate 1 such that the positions of their flexible arms 7 and 8 allow the Young's modulus to reach its maximum or minimum value, especially when the substrate 1 is made of silicon. In fact, due to the anisotropy of silicon, this arrangement avoids significant changes in the Young's modulus caused by angles used to determine structural characteristics such as stiffness. Furthermore, the maximum Young's modulus should be prioritized to improve the accuracy of the correlation between stiffness and the measured frequency.

[0081] exist Figure 2B and 2C In the variant shown, step 21, which forms the oscillating members 10a, 10b, and 10c, causes the free ends 5b and 5c of each flexible arm 7 and 8 to be integrally formed with the end member 11, the mass of which is greater than the mass of the rest of the flexible arm 7 or 8. Figure 2B In the middle, the end member 11 has a polygonal cross-section; while in... Figure 2C In this configuration, the end member 12 has a circular cross-section. These end members 11 and 12 allow for a reduction in the resonant frequency of the flexible arms 7 and 8 while maintaining good sensitivity between the etching thickness Er and this frequency. In this case, the process of calculating the lengths of the oscillating members 10a, 10b, and 10c includes:

[0082] - Define dimension Er, which is preferably equal to or substantially equal to the thickness E2, E3, H2, H3 of the flexible portion 3 of each mechanical resonator 2b, 2c formed in the substrate 1;

[0083] - Defines the frequency change that can be measured by the measurement system, thereby allowing for precise measurement of the frequency, with the frequency change being between 2 and 10 times the standard deviation of the measurement; for example, the frequency change could be 10 Hz;

[0084] - Define the minimum size variation of E2, E3, H2, H3 of the mechanical resonators 2b and 2c to be measured; for example, for a measurable frequency variation of 10 Hz, the minimum size variation can be 10 nm.

[0085] - Calculate the length L of flexible arms 7 and 8, which is between 1 mm and 2 mm, so that the measurement of frequency change can lead to conclusions about the dimensional changes of E2, E3, H2, and H3 of mechanical resonators 2b and 2c;

[0086] - Calculate the dimensions of the flexible arm end to reduce the measurement frequency to a reasonable range for the measurement system.

[0087] Advantageously, the end members 11, 12 provide a larger surface area than the flexible arms 7, 8, which makes it easier to measure the resonant frequency of the oscillating members 10b, 10c.

[0088] It should be understood that the oscillating components 10a, 10b, and 10c designed during step 21 have the general shape of a tuning fork or are tuning forks themselves.

[0089] The oscillating components 10a, 10b, and 10c achieve optimal decoupling of the fixed-end effect from the resonant frequency. In fact, the fixed end has a significant impact on the resonant frequency during harmonic excitation. For oscillating components 10a, 10b, and 10c, there is a clear decoupling between the fixed end and the resonant frequencies of the flexible arms 7 and 8. The correlation between the resonant frequency and structural characteristics such as stiffness is no longer related to the etching quality of the fixed end.

[0090] Furthermore, these oscillating components 10a, 10b, and 10c are configured such that their structural characteristics can be easily determined by the structural characteristic determination module in the mechanical resonator modification device. It should be noted that these oscillating components 10a, 10b, and 10c are configured to vibrate at a stable frequency, even if certain parameters change, particularly those related to the fixed end and manufacturing process. This stable frequency change depends only on one or more parameters / structural characteristics of the oscillating components 10a, 10b, and 10c. In this embodiment, the structural characteristic of the oscillating components 10a, 10b, and 10c that can significantly change the resonant frequency is preferably the thickness Er of the flexible arm. Besides the thickness Er of the flexible arm, other characteristics, such as stiffness and the height h of the flexible arm, can also be used. In actual operation, the frequency is first measured, and then the dimension under the etched mask is derived (arm thickness = arm dimension on the DRIE mask - etched dimension). The stiffness of the tuning fork cannot be obtained directly. Therefore, after inferring this thickness (the dimension under the etched mask), the stiffness of the hairspring can be calculated so that necessary adjustments can be made.

[0091] The method then includes a determination step 22, in which the structural characteristics of at least one oscillating member 10a, 10b, 10c associated with at least one mechanical resonator 2b, 2c formed in the substrate 1 are determined. This determination step 22 includes an estimation sub-step 23, in which at least one resonant frequency of the at least one oscillating member 10a, 10b, 10c is estimated. In this estimation sub-step 23, the at least one oscillating member 10a, 10b, 10c is subjected to mechanical oscillating motion about its stable equilibrium position. During this motion, in a measurement phase 24, the resonant frequency of the oscillating member 10a, 10b, 10c is determined.

[0092] This measurement stage 24 is implemented by the measurement submodule of the structural characteristic determination module in the modification device of the mechanical resonators 2b and 2c. In a variant of the oscillating members 10b and 10c having flexible arms 7 and 8 (each flexible arm including end members 11 and 12), the measurement submodule includes a velocity meter that can be focused on the end members 11 and 12 of the flexible arms 7 and 8 that are oscillating. In this configuration, measurements can be performed out of plane, with the velocity meter axis perpendicular to the wafer plane.

[0093] It should be noted that when multiple oscillating elements 10a, 10b, 10c are associated with a single mechanical resonator 2a, 2c, the resonant frequencies of all these oscillating elements 10a, 10b, 10c are measured, and then the average of these frequencies is calculated to correspond to the resonant frequency associated with the combination of oscillating elements 10a, 10b, 10c. Alternatively, the measured resonant frequency of the combination can be the resonant frequency of only one of its oscillating elements 10a, 10b, 10c, or it can be the resonant frequency of a sample of its oscillating elements 10a, 10b, 10c.

[0094] Once the resonant frequency has been estimated, step 22 includes a definition sub-step 25, in which the structural characteristics, such as stiffness, of the at least one oscillating element 10a, 10b, 10c are defined. In this definition sub-step 25, the processing unit executes an algorithm for calculating the structural characteristics based on the estimated resonant frequency of the at least one oscillating element 10a, 10b, 10c.

[0095] The method then includes a calculation step 26, in which a dimensional correction value is calculated for each mechanical resonator 2b, 2c in the group of mechanical resonators, based on the structural characteristics determined for the relevant system 3. In calculation step 26, the dimensional correction amount to be applied to the mechanical resonators 2b, 2c is determined.

[0096] To this end, the calculation step 26 includes a material thickness determination sub-step 27, in which, based on the determined structural characteristics, the thickness e of the material to be added to or removed from at least one dimension of the mechanical resonators 2b, 2c formed in step 20 is determined to obtain a set of mechanical resonators 2a whose average structural characteristics are within a predetermined numerical range.

[0097] This dimensional correction actually corresponds to the thickness e of the material removed from or added to the mechanical resonators 2b and 2c, in order to change at least one of their dimensions E2, H2, E3, and H3, namely:

[0098] - Only the heights H2 and H3 of the flexible part 3, or

[0099] - Only the thicknesses E2 and E3 of the flexible part 3, or

[0100] - Both the heights H2 and H3 and the thicknesses E2 and E3.

[0101] The dimensional correction can be performed on one or more individual segments of the flexible portion 3 of the mechanical resonators 2b and 2c, or on the entire length of the flexible portion 3.

[0102] Therefore, by determining the size correction value, the material thickness determination sub-step 27 can participate in forming the geometry of the mechanical resonators 2b and 2c, so that their structural characteristic values ​​are within a predetermined range.

[0103] Then, the method includes a modification step 28, in which the dimensions E2, E3, H2, H3 of the mechanical resonators 2b and 2c are modified based on the calculated dimension correction values ​​to obtain a set of mechanical resonators 2a whose average structural characteristics are within a predetermined value range.

[0104] In this case, if the dimensions E2 and H2 of the mechanical resonator 2b are greater than the dimensions E1 and H1 required to bring the average structural characteristics of the group of mechanical resonators 2a within a predetermined range, then the modification step 28 includes a sub-step 29 in which material is removed based on the calculated thickness e of the material to be removed. Material removal can be performed using a process known in the art of oxidation followed by deoxidation for these mechanical resonators 2b. The purpose of this sub-step 29 is to reduce the dimension of the cross-section 4b of the flexible portion 3 of the mechanical resonator 2b over a given length or the entire length of the flexible portion 3.

[0105] If the dimensions E3 and H3 of the mechanical resonator 2c are smaller than the dimensions E1 and H1 required to bring the average structural characteristics of the set of mechanical resonators 2a within a predetermined range, then modification step 28 includes sub-step 30, in which material is added according to the calculated thickness e of the material to be added. The material can be added using methods known in the art, such as thermal oxidation, electroplating growth, physical vapor deposition, chemical vapor deposition, atomic layer deposition, or any other additive process. The purpose of this sub-step 30 is to increase the dimensions E3 and H3 of the cross-section 4c of the flexible portion 3 of the mechanical resonator 2c over a given length or the entire length of the flexible portion 3.

[0106] Therefore, this method can utilize the high precision provided by the reference stiffness indication system to correct dimensional errors in resonators manufactured using methods such as photolithography and / or DRIE technology.

[0107] the term

[0108] 1. A substrate including at least one mechanical resonator

[0109] 2a. A manufactured mechanical resonator

[0110] 2b. A mechanical resonator formed in a substrate and having a cross-sectional dimension larger than that of a manufactured mechanical resonator.

[0111] 2c. A mechanical resonator formed in a substrate and having a cross-sectional dimension smaller than that of a manufactured mechanical resonator.

[0112] 3. Flexible part of mechanical resonator

[0113] 4a. Cross-section of a manufactured mechanical resonator

[0114] 4b. The cross-sectional area of ​​the mechanical resonator is larger than the cross-sectional area of ​​the manufactured mechanical resonator.

[0115] 4c. The cross-sectional area of ​​a mechanical resonator whose dimensions are smaller than the cross-sectional dimensions of the manufactured mechanical resonator.

[0116] 5a. Attachment end of the oscillating component

[0117] 5b, 5c. Free ends of the oscillating component

[0118] 6. Main body / shaft of the oscillating component

[0119] 7. The first flexible arm of the oscillating component

[0120] 8. The second flexible arm of the oscillating component

[0121] 9. An opening therein in which the oscillating component is arranged.

[0122] 10. Oscillating component

[0123] 11. End members of polygonal cross sections

[0124] 12. End members with circular cross-sections

[0125] 13. The outer peripheral wall of the opening

[0126] 14. Connect the flexible arm to the connecting part of the main body of the oscillating component.

[0127] 15. A fixing part on the outer peripheral wall of the opening of the oscillating component.

Claims

1. A method for manufacturing a set of mechanical resonators (2a) having an average structural characteristic within a predetermined range, said structural characteristic being common to each of the mechanical resonators (2a) in the set, said method comprising the following steps: a) Step (20) of forming mechanical resonators (2b, 2c) in substrate (1), wherein the size of the mechanical resonators (2b, 2c) is different from the size required to obtain the set of mechanical resonators (2a) with structural characteristics within the predetermined numerical range; (b) Step (21) forming at least one oscillating member (10a, 10b, 10c) in the substrate (1), the at least one oscillating member (10a, 10b, 10c) being formed in the opening (9) of the substrate (1), the oscillating member (10a, 10b, 10c) being composed of a main body (6) and two flexible arms (7, 8), the body of the main body (6) being connected at the first end (5a) to the fixing part (15) of the outer peripheral wall (13) of the opening (9), the two flexible arms being connected to the second end (5d) of the main body (6) through the connecting part (14), the two flexible arms (7, 8) being parallel to the axis of symmetry (A) of the main body (6) and extending toward the fixing part (15), the axial section (S1) of the second end (5d) being smaller than the axial section (S2) of the first end (5a) and larger than the axial section (S3) of each of the flexible arms (7, 8); c) Determine step (22), in which a value related to the structural characteristics of the formed at least one oscillating member (10a, 10b, 10c) is determined; d) Calculation step (26), in which the size correction values ​​to be applied to the formed mechanical resonators (2b, 2c) are calculated based on the values ​​determined for the structural characteristics; e) Modification step (28), in which the dimensions of the formed mechanical resonators (2b, 2c) are modified based on the calculated dimension correction values ​​to obtain the set of mechanical resonators (2a) with structural characteristic values ​​within a predetermined range.

2. The method according to claim 1, characterized in that, In step (21) of forming the oscillating components (10a, 10b, 10c), each of the flexible arms (7, 8) is given a length (L) that can be adjusted according to a resonance measurement tolerance factor defined by at least one dimension (E2, E3, H2, H3) of the flexible portion (3) of the mechanical resonator (2b, 2c) associated with the at least one oscillating component (10a, 10b, 10c).

3. The method according to any one of the preceding claims, characterized in that, In step (21) of forming the oscillating components (10a, 10b, 10c), each flexible arm is positioned at a first distance (D1) and a second distance (D2) from the body of the main body (6) and the fixing part (15) of the outer peripheral wall (13) of the opening (9), respectively. The first distance (D1) is greater than the second distance (D2).

4. The method according to any one of the preceding claims, characterized in that, In step (21) of forming the oscillating components (10a, 10b, 10c), the thickness (Er) of each of the flexible arms (7, 8) is made equal to or substantially equal to the thickness of the flexible portion (3) of each mechanical resonator (2b, 2c) formed in the substrate (1).

5. The method according to any one of the preceding claims, characterized in that, In step (21) of forming the oscillating components (10a, 10b, 10c), the free end (5b, 5c) of each of the flexible arms (7, 8) is integrally formed with the end member (11, 12), the mass of which is greater than the mass of the rest of the body of the flexible arm (7, 8).

6. The method according to claim 6, characterized in that, The end members (11, 12) have a circular or polygonal cross-section.

7. The method according to any one of the preceding claims, characterized in that, In step (21) of forming the oscillating member (10a, 10b, 10c), the axial section (S1) of the second end (5d) of the body of the main stem (6) is 1 / 3 to 1 / 5 of the axial section (S2) of the first end (5a).

8. The method according to any one of the preceding claims, characterized in that, The steps (20) of forming the mechanical resonator (2b, 2c) and (21) of forming at least one oscillating element (10a, 10b, 10c) are carried out by etching, particularly by deep reactive ion etching.

9. The method according to any one of the preceding claims, characterized in that, Step (21) of forming each oscillating element (10a, 10b, 10c) is carried out in the substrate (1) for at least one of the mechanical resonators (2b, 2c) in the group of mechanical resonators (2b, 2c).

10. The method according to any one of claims 1 to 8, characterized in that, Step (21) of forming oscillating members (10a, 10b, 10c) is used to form a plurality of oscillating members (10a, 10b, 10c) around at least one mechanical resonator (2b, 2c) in the substrate (1).

11. The method according to any one of the preceding claims, characterized in that, The determining step (22) includes an estimation sub-step (23), in which at least one resonant frequency is estimated for each oscillating element (10a, 10b, 10c) associated with at least one mechanical resonator (2b, 2c) in the group of mechanical resonators (2b, 2c).

12. The method according to any one of the preceding claims, characterized in that, The determining step (22) includes a defining sub-step (25) in which a structural characteristic is defined for each oscillating element (10a, 10b, 10c) that is the same as the structural characteristic shared by each of the formed mechanical resonators (2b, 2c). The defining sub-step (25) is performed by a processing unit connected to a device for modifying the formed mechanical resonators (2b, 2c). The processing unit executes an algorithm to calculate the structural characteristic of each oscillating element (10a, 10b, 10c) based on the estimated resonant frequency.

13. The method according to any one of the preceding claims, characterized in that, The calculation step (26) includes a material thickness determination sub-step (27), in which the thickness (e) of the material to be added to or removed from at least one dimension of each mechanical resonator (2b, 2c) associated with each oscillating member (10a, 10b, 10c) is determined based on the structural characteristic values ​​determined for each oscillating member (10a, 10b, 10c).

14. The method according to any one of the preceding claims, characterized in that, The oscillating component (10) is in the shape of a tuning fork.

15. The method according to any one of the preceding claims, characterized in that, The structural characteristic mentioned is stiffness characteristic.

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