A Quasi-convex Quartz Resonator Achieving High Quality Factor and Its Design Method

Abstract

This invention relates to a quasi-convex quartz resonator achieving a high quality factor and its design method. The quasi-convex quartz resonator includes: a quartz wafer plate region and a plurality of rectangular protrusions arranged in parallel at intervals thereon, the plurality of rectangular protrusions forming a square wave region; the width of the rectangular protrusions is W. H The distance between two adjacent rectangular protrusions is W. L The distance between the same side of two adjacent rectangular protrusions (W) H +W L All are equal; the duty cycle of each of the rectangular protrusions [W] is equal. H / (W H +W L The thickness is calculated based on the integral thickness of the sub-intervals divided into corresponding regions of the plano-convex quartz resonator. This invention reproduces the shape of the plano-convex quartz resonator by arranging fine protrusions on the surface of the resonator; this shape is called "quasi-convex." The shape of the protrusions gradually changes according to a rule. Simultaneously, by optimizing the thickness H and length L of the rectangular protrusions to simulate the vibration displacement characteristics of the plano-convex quartz resonator, the excellent quality factor Q and sufficiently high productivity of the plano-convex resonator are achieved.

Description

Technical Field

[0001] This invention belongs to the field of sensors, specifically relating to a quasi-convex quartz resonator with a high quality factor and its design method. Background Technology

[0002] AT-cut quartz resonators are electronic components that utilize the piezoelectric effect of quartz crystals to generate high-precision oscillation frequencies. They are widely used as timing devices in computers, mobile information and communication tools, etc. When quartz resonators are applied to high-sensitivity devices, AT-cut quartz resonators must possess excellent temperature characteristics and a high quality factor Q to improve frequency stability.

[0003] The factors affecting the quality factor Q of a quartz resonator mainly include the energy trapping effect and parasitic mode coupling, both of which are determined by the resonator shape. Therefore, the most important parameter in quartz resonator design is the shape of the quartz blank's cross-section; the simplest and most common shape is a plane containing rectangles or circles. Furthermore, bevel polishing has been widely used to reduce parasitic modes caused by the edges of the quartz blank. To more effectively reduce parasitic modes, a mesa resonator with stepped regions designed on the surface of a planar blank has been developed.

[0004] Recently, plano-convex and biconvex shapes with curved projections on their surfaces have attracted attention as the most effective shapes for reducing parasitic modes, and some methods for processing convex portions have been reported. Analytical and experimental results have demonstrated that plano-convex resonators have a higher quality factor Q due to their superior vibrational characteristics. However, the curved surface structure of plano-convex resonators requires very fine machining, and due to limitations in processing technology, manufacturing convex shapes on the surface of quartz wafers presents certain technical difficulties, resulting in significant defects in mass production. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a quasi-convex quartz resonator with a high quality factor and its design method. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a quasi-convex quartz resonator that achieves a high quality factor, comprising: a quartz wafer plate region and a plurality of rectangular protrusions arranged in parallel intervals thereon, the plurality of rectangular protrusions forming a square wave region;

[0007] The width of the rectangular protrusion is W. H The distance between two adjacent rectangular protrusions is W. L The distance W between the same side of two adjacent rectangular protrusions H +W L All are equal; the duty cycle of each of the rectangular protrusions [W]H / (W H +W L The thickness is calculated based on the integral thickness of the sub-intervals divided into corresponding regions of the plano-convex quartz resonator.

[0008] In one embodiment of the present invention, the width of the rectangular protrusion is not less than 1 μm.

[0009] In one embodiment of the present invention, the distance between two adjacent rectangular protrusions is not less than 1 μm.

[0010] In one embodiment of the present invention, the thickness of the rectangular protrusion is 10 μm.

[0011] In one embodiment of the present invention, the length of the rectangular region ranges from 1000 to 1250 μm.

[0012] This invention also provides a design method for a quasi-convex quartz resonator achieving a high quality factor, comprising:

[0013] Step 1: Verify through simulation whether square wave resonators and mesa resonators have similar vibration characteristics;

[0014] Step 2: Obtain the functional relationship between the resonant frequency of the square wave resonator and the duty cycle of its rectangular protrusion through simulation calculation;

[0015] Step 3: Adjust the duty cycle of the rectangular protrusion of the square wave resonator to simulate the vibration characteristics of the plano-convex resonator and obtain the initial surface profile of the quasi-convex resonator.

[0016] Step 4: Verify through simulation whether the quasi-convex resonator can reproduce the vibration characteristics of the plano-convex resonator in terms of thickness shear vibration;

[0017] Step 5: Optimize the initial surface profile of the convex resonator through simulation and calculation to reduce the influence of parasitic coupling and determine the values ​​of the thickness of the rectangular protrusion and the length of the rectangular region.

[0018] In one embodiment of the present invention, step 3 includes:

[0019] The cross-sectional shape of the plano-convex resonator is divided into several continuous sub-intervals, and the cross-sectional shape of the sub-intervals is transformed into a stepped shape by integration;

[0020] By using the functional relationship between the thickness of the rectangular protrusion and the duty cycle, the integral thickness of the sub-interval is converted into the duty cycle of the rectangular protrusion in each sub-interval, thus obtaining the initial surface profile of the quasi-convex resonator.

[0021] In one embodiment of the present invention, step 5 includes:

[0022] The length range of the rectangular region is determined based on the simulation results of the thickness shear vibration displacement of the quasi-convex resonator.

[0023] Within the length of the rectangular region, the thickness of the rectangular protrusion is determined based on the simulation results of the parasitic coupling strength and vibration characteristics, so as to minimize the parasitic coupling strength of the quasi-convex resonator and maximize the stability of its vibration characteristics.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] This invention relates to a quasi-convex quartz resonator and its design method for achieving a high quality factor. By arranging fine protrusions on the surface of the quartz resonator, the shape of a plano-convex quartz resonator is reproduced. This shape is called "quasi-convex." The shape of the protrusions gradually changes according to a rule. Simultaneously, by optimizing the thickness H of the rectangular protrusion portion and the length L of the rectangular region, the vibration displacement characteristics of the plano-convex quartz resonator are simulated. This shape achieves the excellent vibration characteristics and sufficiently high productivity of the plano-convex resonator, effectively reducing parasitic mode coupling of the quartz resonator and thus realizing the high quality factor Q of the quasi-convex quartz resonator. Simulation results also confirm that the vibration displacement characteristics of the quasi-convex quartz resonator are completely consistent with those of the plano-convex quartz resonator. This shape can also be easily realized using microelectromechanical systems (MEMS) fabrication techniques such as reactive ion etching.

[0026] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0027] Figure 1 It is a simulation model of a square wave quartz resonator;

[0028] Figure 2 These are vibration displacement distribution curves of a square wave resonator and a mesa resonator.

[0029] Figure 3 This is a graph showing the relationship between the resonant frequency and duty cycle of a square wave resonator.

[0030] Figure 4 This is a schematic diagram illustrating the design process of the surface profile of the quartz resonator provided in this embodiment of the invention, from plano-convex to quasi-convex.

[0031] Figure 5(a) is a numerical simulation of the right half surface profile of the plano-convex and quasi-convex resonators provided in the embodiments of the present invention;

[0032] Figure 5(b) is a duty cycle distribution diagram of the right half surface of the quasi-convex resonator provided in the embodiment of the present invention;

[0033] Figure 6(a) is a vibration displacement distribution diagram of the upper surface of the quartz blank for the plano-convex and quasi-convex resonators provided in the embodiments of the present invention;

[0034] Figure 6(b) is a vibration displacement distribution diagram of the lower surface of the quartz blank for the plano-convex and quasi-convex resonators provided in the embodiments of the present invention;

[0035] Figure 7 This is a diagram showing the relationship between the parasitic coupling of the quasi-convex resonator and the length of the rectangular region in an embodiment of the present invention.

[0036] Figure 8 This is a diagram showing the relationship between the parasitic coupling and the thickness of the rectangular protrusion in a quasi-convex resonator according to an embodiment of the present invention.

[0037] Figure 9(a) is a simulation diagram of the optimized design results of a quasi-convex resonator provided in an embodiment of the present invention;

[0038] Figure 9(b) is a simulation diagram of the optimized design result of another quasi-convex resonator provided in the embodiment of the present invention. Detailed Implementation

[0039] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following, in conjunction with the accompanying drawings and specific embodiments, provides a detailed description of a quasi-convex quartz resonator and its design method for achieving a high quality factor according to the present invention.

[0040] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0041] Example 1

[0042] To achieve excellent vibration characteristics and a high quality factor in plano-convex resonators, and to solve the manufacturing challenges of the convex shape, this embodiment provides a design method for a quasi-convex quartz resonator that achieves a high quality factor, including:

[0043] Step 1: Verify through simulation whether square wave resonators and mesa resonators have similar vibration characteristics.

[0044] Please see Figure 1 , Figure 1 It is a simulation model of a square wave quartz resonator.

[0045] As shown in the figure, the square wave quartz resonator blank of this embodiment has a total length of 2000 μm and a total thickness of 100 μm. Fifty rectangular protrusions are arranged in parallel at intervals on the quartz wafer plate area. These rectangular protrusions form a square wave region, with a length L of 1000 μm and a width W of [missing information]. H The diameter is 10 μm, and the distance between two adjacent rectangular protrusions is W. L The thickness H of the rectangular protrusion is 3μm, and the distance (W) between the same side of two adjacent rectangular protrusions is... H +W L All are equal, and the duty cycle of the rectangular protrusion [W] is [...]. H / (W H +W L The thickness of the quartz crystal plate region of the mesa resonator is 97 μm, and the thickness of the step set on the quartz crystal plate region is 1.5 μm.

[0046] The vibration displacement characteristics of the table resonator and the square wave resonator are simulated and compared. A left-right symmetrical Cartesian coordinate system is established with the center of the resonator as the origin.

[0047] The vibration displacement distribution curves of the mesa resonator and the square wave resonator are shown in the figure. Figure 2 As shown in Figure 1, the vibration characteristics of the square wave resonator and the mesa resonator are shown in the figure, where f0 is the resonant frequency and max(U) is the resonant frequency. X ) represents the maximum displacement in the X direction, max(U Y ′) represents the maximum displacement in the Y direction. Simulation verification shows that the square wave resonator and the mesa resonator have similar vibration characteristics.

[0048] Table 1 Vibration characteristics of square wave resonators and mesa resonators

[0049]

[0050] Step 2: Obtain the functional relationship between the resonant frequency of the square wave resonator and the duty cycle of its rectangular protrusion through simulation calculation.

[0051] To extend the vibration characteristics of the square wave resonator in this embodiment and verify that the square wave resonator in this embodiment can equivalently simulate the vibration characteristics of a resonator with any cross-section, simulation was performed.

[0052] Please see Figure 3 , Figure 3 This is a graph showing the relationship between the resonant frequency and duty cycle of a square wave resonator.

[0053]

[0054] Where T0 is the total thickness of the square wave resonator, which is converted from the average thickness of the mesa resonator using an empirical formula, and C' 66 C1'1 is the elastic stiffness coefficient of the quartz blank cut by AT, L0 is the total length of the quartz blank of the square wave quartz resonator, and ρ is the density of the quartz blank.

[0055] The duty cycle [W] of the rectangular protrusion of the square wave resonator is calculated using formula (1). H / (W H +W L The theoretical resonant frequencies varied from 0 to 100% were compared with the simulation results.

[0056] like Figure 3 The diagram showing the relationship between the resonant frequency and duty cycle of the square wave resonator reveals that the theoretical resonant frequency is close to or even identical to the simulation result. This indicates a functional relationship between the resonant frequency of the square wave resonator and the duty cycle of its rectangular protrusion. Therefore, it can be inferred that since the microscopic effect of a small rectangle itself is very weak, the rectangular portion as a whole mainly affects the resonator's vibration macroscopically through the energy trapping effect. This design approximates an arched resonator (plano-convex resonator) by using small rectangles of different widths as a whole. Because the influence of the small rectangles themselves is very small, the energy trapping effect when approximating an arch with the entire rectangle is very close.

[0057] This means that by changing the duty cycle of the rectangle in each region, the shape of a square wave can be equivalently simulated to any cross section, and thus the vibration characteristics of a plano-convex resonator can be simulated by a square wave resonator.

[0058] Step 3: Adjust the duty cycle of the rectangular protrusion of the square wave resonator to simulate the vibration characteristics of the plano-convex resonator and obtain the initial surface profile of the quasi-convex resonator.

[0059] In an optional implementation, step 3 includes:

[0060] Step 3.1: Divide the cross-sectional shape of the plano-convex resonator into several continuous sub-intervals, and transform the cross-sectional shape of the sub-intervals into a stepped shape through integration;

[0061] Step 3.2: By using the functional relationship between the thickness of the rectangular protrusion and the duty cycle, the integral thickness of the sub-interval is converted into the duty cycle of the rectangular protrusion in each sub-interval, thus obtaining the initial surface profile of the quasi-convex resonator.

[0062] Please refer to the above. Figure 4 Figures 5(a) and 5(b) Figure 4Figure 5(a) is a schematic diagram of the design process of the surface profile of the quartz resonator from plano-convex to quasi-convex, provided in the embodiments of the present invention; Figure 5(b) is a numerical simulation of the right half surface profile of the plano-convex and quasi-convex resonators provided in the embodiments of the present invention; Figure 5(b) is a duty cycle distribution diagram of the right half surface of the quasi-convex resonator provided in the embodiments of the present invention. In this embodiment, the rectangular region length L = 1000 μm, the rectangular protrusion thickness H = 3 μm, and the distance between the same side of two adjacent rectangular protrusions (W) are selected. H +W L =20μm.

[0063] like Figure 4 As shown, the interface shape of the square wave resonator of the present invention is called "quasi-convex". The flat-convex region of the flat-convex resonator is divided into several continuous sub-intervals. By integration, the sub-intervals are approximated as stepped, and the thickness of the sub-intervals is obtained. Then, by using the empirical formula of thickness and duty cycle, the thickness is converted into the duty cycle of each sub-interval, and the initial surface profile of the quasi-convex resonator is obtained. In order to improve productivity, the average thickness of the sub-intervals is determined by simulation.

[0064] To illustrate that the quasi-convex resonator of this embodiment can achieve the vibration characteristics of a plano-convex resonator, the vibration characteristics of the plano-convex resonator and the quasi-convex resonator of this embodiment are simulated. To reduce the computational load of the simulation, only the vibration characteristics of the right half of the surface profile are simulated here, that is, the first quadrant of the coordinate system.

[0065] As shown in Figures 5(a) and 5(b), the right half of the surface profile in Figure 5(a) is a numerical profile obtained by dividing the cross-sectional shape of the plano-convex resonator into several continuous sub-intervals and then approximating the cross-sectional shape of the sub-intervals as a stepped shape through integration. Figure 5(a) has two vertical axes: the left axis represents the average height of the stepped shape approximated by integrating the arc surfaces of the plano-convex resonator sub-intervals; the right axis represents the duty cycle of the rectangular protrusions in the sub-intervals, converted from stepped protrusions of different heights using integral thickness quasi-convex equivalence. The right half of the surface profile in Figure 5(b) is the initial surface profile of the quasi-convex resonator obtained by converting the integral thickness of the sub-intervals into the duty cycle of the rectangular protrusions in each sub-interval through a functional relationship between the thickness of the rectangular protrusions and the duty cycle.

[0066] In this embodiment, the length of the rectangular region is temporarily set to L = 1000 μm, the thickness of the rectangular protrusions is set to H = 3 μm, and the distance between the same side of two adjacent rectangular protrusions is set to W. H +W L =20μm.

[0067] Step 4: Verify through simulation whether the quasi-convex resonator can reproduce the vibration characteristics of the plano-convex resonator in terms of thickness shear vibration.

[0068] The surface profiles in Figures 5(a) and 5(b) were simulated, and the simulation results are shown in Figures 6(a) and 6(b). Figure 6(a) is a vibration displacement distribution diagram of the upper surface of the quartz blank of the plano-convex and quasi-convex resonator provided in the embodiment of the present invention; Figure 6(b) is a vibration displacement distribution diagram of the lower surface of the quartz blank of the plano-convex and quasi-convex resonator provided in the embodiment of the present invention.

[0069] As shown in the figure, by combining the vibration displacement distribution of the upper and lower surfaces of the quartz blanks of the plano-convex resonator and the quasi-convex resonator, it is proved that the quasi-convex resonator can reproduce the vibration characteristics of the plano-convex resonator in terms of thickness shear vibration (X-direction vibration).

[0070] Step 5: Optimize the initial surface profile of the convex resonator through simulation and calculation to reduce the influence of parasitic coupling and determine the values ​​of the thickness of the rectangular protrusion and the length of the rectangular region.

[0071] In this embodiment, the initial surface profile of the convex resonator is optimized based on the functional relationship between parasitic coupling strength and thickness shear vibration displacement to reduce the influence of parasitic coupling.

[0072] In an optional implementation, step 5 includes:

[0073] Step 5.1: Determine the length range of the rectangular region based on the simulation results of the thickness shear vibration displacement of the quasi-convex resonator;

[0074] Step 5.2: Within the length of the rectangular region, determine the thickness of the rectangular protrusion based on the simulation results of the parasitic coupling strength and vibration characteristics, so as to minimize the parasitic coupling strength of the quasi-convex resonator and maximize the stability of its vibration characteristics.

[0075] Specifically, in order to further reduce the effects of parasitic coupling and determine the optimal design parameters of the quasi-convex resonator, the surface profile of the quasi-convex resonator is optimized.

[0076] First, determine the length L of the rectangular region.

[0077] To quantitatively assess parasitic coupling, the coupling strength is calculated using the following methods:

[0078]

[0079]

[0080] Where rms is the root mean square, U X (x) represents the TS vibration modal displacement in the X direction, and g(x) is the approximation of U through numerical analysis. X(x) is a Gaussian function, where A is the first variable used for numerical analysis, C is the second variable used for numerical analysis, σ is the third variable used for numerical analysis, x is the coordinate value in the X-axis direction, and exp is an exponential function with the natural constant e as its base.

[0081] As can be seen from formula (2), the strength of parasitic coupling is defined as the ratio of the RMS amplitude of the parasitic mode to the displacement of the TS (thickness shear) vibration mode.

[0082] like Figure 7 The diagram showing the relationship between parasitic coupling and the length of the rectangular region in the quasi-convex resonator of this embodiment of the invention illustrates a V-shaped curve for simulations of the rectangular region length L. Analysis confirms that strong LT (length-direction stretching vibration mode) coupling occurs at shorter L lengths, while strong TF (thickness bending mode) coupling occurs at longer L lengths. Therefore, 1000 to 1250 μm is the optimal rectangular region length L.

[0083] Then, determine the thickness H of the rectangular protrusion.

[0084] like Figure 8 The diagram shown illustrates the relationship between parasitic coupling and the thickness of the rectangular protrusion in the quasi-convex resonator of this invention, where the lengths L of the rectangular regions are 1000 μm and 1250 μm, respectively. For comparison, simulation results of the plano-convex resonator are also shown. Figure 8 In the simulation results for the plano-convex resonator, the parasitic coupling strength decreases as the thickness H of the rectangular protrusion increases. This trend implies that the larger the thickness H of the rectangular protrusion, the stronger the energy trapping effect. As shown in the figure, within the range of H = 0–3 μm, the relationship between the parasitic coupling strength of the quasi-convex resonator and the thickness H of the rectangular protrusion is almost the same as that of the plano-convex resonator. However, the parasitic coupling strength of the quasi-convex resonator (L = 1000 μm) increases rapidly in the range of H = 4 μm–8 μm. This is due to the strong coupling effect of the sixth overtone LT (length-stretching vibration mode) caused by the length L of the rectangular region.

[0085] Please refer to the simulation results of the optimized design of the quasi-convex resonator shown in Figures 9(a) and 9(b); in Figure 9(a), the rectangular region of the quasi-convex resonator has a length L = 1000 μm, and the thickness of the rectangular protrusion is H = 8 μm and H = 10 μm, respectively; in Figure 9(b), the rectangular region of the quasi-convex resonator has a length L = 1000 μm, and the thickness of the rectangular protrusion is H = 10 μm and H = 12 μm, respectively.

[0086] As can be seen from the figure, parasitic coupling is strongest at H = 8 μm, while H = 10 μm represents the optimal design thickness. The vibration displacement at the optimal design thickness is almost the ideal TS (thickness shear) vibration mode displacement with no parasitic coupling.

[0087] This embodiment also provides a quasi-convex quartz resonator that achieves a high quality factor. The quasi-convex quartz resonator, obtained through the above design method, includes: a quartz wafer plate region and a plurality of rectangular protrusions arranged in parallel intervals on the plate, wherein the plurality of rectangular protrusions form a square wave region.

[0088] The width of the rectangular protrusion is W. H The distance between two adjacent rectangular protrusions is W. L The distance between the same side of two adjacent rectangular protrusions (W) H +W L All are equal; the duty cycle of each rectangular protrusion [W] is equal. H / (W H +W L The thickness is calculated based on the integral thickness of the sub-intervals divided into corresponding regions of the plano-convex quartz resonator.

[0089] In one alternative implementation, considering manufacturing processes such as the resolution of the exposure equipment and the width W of the rectangular protrusion. H Not less than 1μm, the spacing W between two adjacent rectangular protrusions L Not less than 1μm.

[0090] In this embodiment, the length L of the rectangular region of the quasi-convex quartz resonator ranges from 1000 to 1250 μm, and the thickness H of the rectangular protrusion is 10 μm.

[0091] It should be noted that in this embodiment, the thickness H of the rectangular protrusion is considered to be fixed. However, considering actual processing, the aspect ratio needs to be taken into account for different equipment implementations, and a value near the optimal value can be used.

[0092] This invention discloses a quasi-convex quartz resonator and its design method for achieving a high quality factor. By arranging fine protrusions on the surface of the quartz resonator, the shape of a plano-convex quartz resonator is reproduced. This shape is called "quasi-convex." The shape of the protrusions gradually changes according to a rule. Simultaneously, by optimizing the thickness H of the rectangular protrusion portion and the length L of the rectangular region, the vibration displacement characteristics of the plano-convex quartz resonator are simulated. This shape achieves the excellent vibration characteristics and sufficiently high productivity of the plano-convex resonator, effectively reducing parasitic mode coupling of the quartz resonator and thus realizing the high quality factor Q of the quasi-convex quartz resonator. Simulation results also confirm that the vibration displacement characteristics of the quasi-convex quartz resonator are completely consistent with those of the plano-convex quartz resonator. This shape can also be easily realized using microelectromechanical systems (MEMS) fabrication techniques such as reactive ion etching.

[0093] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0094] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A quasi-convex quartz resonator achieving a high quality factor, characterized in that, include: A quartz wafer flat plate area and a plurality of rectangular protrusions arranged in parallel intervals thereon, the plurality of rectangular protrusions forming a square wave area, the square wave area having a rectangular area length; The width of the rectangular protrusion is The distance between two adjacent rectangular protrusions is The spacing between the same side of two adjacent rectangular protrusions All are equal; the duty cycle of each of the rectangular protrusions is equal. The thickness is calculated based on the integral thickness of the sub-intervals divided into corresponding regions of the plano-convex quartz resonator. The calculation process is as follows: the cross-sectional shape of the plano-convex quartz resonator is divided into several continuous sub-intervals, the cross-sectional shape of the sub-intervals is converted into a stepped thickness by integration, and then the integral thickness of the sub-intervals is converted into the duty cycle of the rectangular protrusion corresponding to each sub-interval by using the functional relationship between the thickness of the rectangular protrusion and the duty cycle.

2. The quasi-convex quartz resonator achieving a high quality factor according to claim 1, characterized in that, The width of the rectangular protrusion is not less than 1 μm.

3. The quasi-convex quartz resonator achieving a high quality factor according to claim 1, characterized in that, The distance between two adjacent rectangular protrusions is not less than 1 μm.

4. The quasi-convex quartz resonator achieving a high quality factor according to claim 1, characterized in that, The thickness of the rectangular protrusion is 10 μm.

5. The quasi-convex quartz resonator achieving a high quality factor according to claim 1, characterized in that, The length of the rectangular region ranges from 1000 to 1250 μm.

6. A design method for a quasi-convex quartz resonator achieving a high quality factor, used to design and implement the quasi-convex quartz resonator achieving a high quality factor as described in any one of claims 1 to 5, characterized in that, include: Step 1: Verify through simulation whether square wave resonators and mesa resonators have similar vibration characteristics; Step 2: Obtain the functional relationship between the resonant frequency of the square wave resonator and the duty cycle of the rectangular protrusion in the square wave region it forms through simulation calculation; Step 3: Adjust the duty cycle of the rectangular protrusion of the square wave resonator to simulate the vibration characteristics of the plano-convex resonator, and obtain the initial surface profile of the quasi-convex resonator; wherein, Step 3 specifically includes: dividing the cross-sectional shape of the plano-convex resonator into several continuous sub-intervals, and converting the cross-sectional shape of the sub-intervals into a stepped shape by integration; using the functional relationship between the thickness of the rectangular protrusion and the duty cycle, converting the integral thickness of the sub-intervals into the duty cycle of the rectangular protrusion corresponding to each sub-interval, and obtaining the initial surface profile of the quasi-convex resonator; Step 4: Verify through simulation whether the quasi-convex resonator can reproduce the vibration characteristics of the plano-convex resonator in terms of thickness shear vibration; Step 5: Optimize the initial surface profile of the quasi-convex resonator through simulation and calculation to reduce the influence of parasitic coupling, and determine the values ​​of the thickness of the rectangular protrusion and the length of the rectangular region.

7. The design method for a quasi-convex quartz resonator achieving a high quality factor according to claim 6, characterized in that, Step 5 includes: The length range of the rectangular region is determined based on the simulation results of the thickness shear vibration displacement of the quasi-convex resonator. Within the length of the rectangular region, the thickness of the rectangular protrusion is determined based on the simulation results of the parasitic coupling strength and vibration characteristics, so as to minimize the parasitic coupling strength of the quasi-convex resonator and maximize the stability of its vibration characteristics.

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