A frequency-temperature curve regulating method of a micromechanical resonator and a micromechanical device

Abstract

The present application belongs to the field of microelectronic technology, and discloses a frequency-temperature curve regulation method of a micro-mechanical resonator and a micro-mechanical device. The frequency-temperature curve regulation method of the micro-mechanical resonator provided by the present application firstly determines a preliminary regulation target range of a second-order frequency-temperature coefficient according to a set target cubic frequency-temperature curve; then selects a doping type of the micro-mechanical resonator, compares a difference between the second-order frequency-temperature coefficient corresponding to different doping concentrations and the preliminary regulation target range of the second-order frequency-temperature coefficient, and selects a doping concentration based on the difference; then adjusts a design parameter of the micro-mechanical resonator to match and adjust a first-order frequency-temperature coefficient and to cooperatively correct the second-order frequency-temperature coefficient, so that a deviation of a formed cubic frequency-temperature curve from the target cubic frequency-temperature curve is within a preset tolerance range. The present application can improve the frequency-temperature stability of the micro-mechanical resonator.

Description

Technical Field

[0001] This invention belongs to the field of microelectronics technology, and more specifically, relates to a method for controlling the frequency-temperature curve of a micromechanical resonator and a micromechanical device. Background Technology

[0002] Micromechanical resonators are core frequency reference components in micromechanical oscillators, clock systems, and high-precision sensing systems. Their frequency stability directly affects the system's synchronization accuracy, phase noise level, and long-term reliability. For applications such as communication, navigation, data transmission, industrial control, and precision measurement, the stability of the frequency reference is one of the key factors determining system performance. Temperature-induced resonant frequency drift is a significant factor affecting the frequency stability of micromechanical resonators. The resonant frequency drift of a micromechanical resonator with temperature is mainly due to changes in the elastic modulus of the resonator's structural materials and the thermal expansion characteristics of the materials. The temperature stability of the frequency of a micromechanical resonator characterizes the sensitivity of the resonant frequency to temperature changes and is typically measured by the temperature coefficient of frequency (TCF). TCF n Indicates the first n Rank TCF It can be defined as

[0003] Therefore, the overall shape of the frequency-temperature curve is not determined solely by the first-order frequency-temperature coefficient, but rather by multiple order frequency-temperature coefficients. For wide-temperature applications, simply reducing the first-order frequency-temperature coefficient often fails to achieve a sufficiently low frequency drift across the entire temperature range. Uncompensated silicon-based micromechanical resonators have a negative TCF, approximately -30 ppm / ℃. Consequently, the frequency of silicon-based micromechanical resonators decreases with increasing temperature. Within the industrial temperature range, the frequency shift of silicon-based micromechanical resonators exceeds 3700 ppm, significantly greater than that of quartz crystal oscillators. Excessive frequency drift can lead to clock synchronization errors, abnormal signal transmission, data sampling deviations, and even system failures. Therefore, improving the frequency-temperature stability of resonators is one of the biggest challenges that needs to be overcome in replacing quartz crystal oscillators with silicon-based micromechanical resonators. However, the frequency-temperature curves of traditional micromechanical resonators typically exhibit linear or quadratic dominance characteristics, resulting in a high maximum frequency drift within the target temperature range and poor frequency-temperature stability. Summary of the Invention

[0004] This invention provides a method for controlling the frequency-temperature curve of a micromechanical resonator and a micromechanical device, thereby solving the problem of poor frequency-temperature stability of micromechanical resonators in the prior art.

[0005] This invention provides a method for controlling the frequency-temperature curve of a micromechanical resonator, comprising the following steps: Based on the set target third frequency-temperature curve, determine the initial control target range of the second-order frequency-temperature coefficient; select the doping type of the micromechanical resonator, compare the difference between the second-order frequency-temperature coefficient corresponding to different doping concentrations and the initial control target range of the second-order frequency-temperature coefficient, and select the doping concentration based on the difference; By adjusting the design parameters of the micromechanical resonator, the first-order frequency-temperature coefficient is matched and adjusted, and the second-order frequency-temperature coefficient is synergistically corrected, so that the deviation between the formed third-order frequency-temperature curve and the target third-order frequency-temperature curve is within a preset tolerance range.

[0006] Preferably, the target third frequency-temperature curve is set in the following manner: Determine the operating temperature range, frequency drift index, and operating frequency range of the micromechanical resonator; Set target control information; wherein, the target control information includes at least one of the target position of temperature inflection point and the target position of central symmetry point, wherein the temperature inflection point is the temperature point corresponding to the first derivative of the cubic frequency-temperature curve being equal to zero, and the central symmetry point is the temperature point corresponding to the second derivative of the cubic frequency-temperature curve being equal to zero. The target cubic frequency-temperature curve is determined based on the operating temperature range, the frequency drift index, the operating frequency range, and the target control information.

[0007] Preferably, the initial target range for the second-order frequency-temperature coefficient is a preset numerical range in which the absolute value approaches 0.

[0008] Preferably, a material parameter temperature model and a parameterized structure model corresponding to the micromechanical resonator are established; after selecting the doping type of the micromechanical resonator, the second-order frequency-temperature coefficient corresponding to different doping concentrations is calculated based on the material parameter temperature model and the parameterized structure model. The material parameter temperature model is a model of how the elastic constants of the structural material in the micromechanical resonator change with temperature and doping concentration. The structural material is N-type heavily doped silicon or P-type heavily doped silicon. The material parameter temperature model includes the first-order and second-order temperature dependence of the elastic constants of silicon material. The material parameter temperature model can be used to predict the changing trends of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient of the micromechanical resonator with doping concentration. The parameterized structural model includes mandatory parameters and optional parameters. The mandatory parameters include doping concentration and structural geometry parameters. The optional parameters include some or all of the structural material layer ratio parameters, crystal orientation angle parameters, and mechanical coupling structural parameters.

[0009] Preferably, adjusting the design parameters of the micromechanical resonator includes adjusting some or all of the structural geometric parameters, mechanical coupling structural parameters, crystal orientation angle parameters, and structural material layer ratio parameters of the micromechanical resonator.

[0010] Preferably, the resonator of the micromechanical resonator is a single continuous structure, and the resonator has a closed standard geometric profile or an irregular profile in the plane; the structural geometric parameters include the in-plane dimensions and thickness of the resonator; when the resonator has an irregular profile, the irregular profile exhibits a non-constant radial dimension distribution along the circumference, and the in-plane dimensions include the radial dimensions, local width, or local curvature of the resonator at different positions in the circumference. By adjusting the geometric parameters of the structure, the equivalent stiffness distribution of the resonant oscillator in different crystal orientations can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0011] Preferably, the micromechanical resonator is formed by connecting at least two resonant units through a coupling block; the mechanical coupling structure parameters include the structural form and operating mode of the resonant unit; the structural form is any one or a combination of rectangular plate, fixed beam, disk, and ring; and the operating mode is any one or a combination of volume mode, shear mode, and bending mode. By adjusting the parameters of the mechanical coupling structure, the participation ratio of different working modes can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0012] Preferably, the crystal orientation angle parameter is the orientation angle of the principal vibration direction of the micromechanical resonator relative to the crystal coordinate axis; By adjusting the crystal orientation angle parameter, the contribution weight of different elastic constants and their temperature dependence on the equivalent stiffness of the working mode is changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0013] Preferably, the micromechanical resonator is any one of the following structures: a combination structure of a heavily doped silicon structure layer and a compensation material layer, a combination structure of a heavily doped silicon structure layer, a piezoelectric layer and a top electrode layer, a combination structure of a bottom electrode layer, a heavily doped silicon structure layer, a piezoelectric layer and a top electrode layer, or a combination structure of a heavily doped silicon structure layer, a piezoelectric layer, a top electrode layer and a compensation material layer. The structural material layer ratio parameters include the thickness ratio of at least a portion of the material layers selected from the heavily doped silicon structural layer, the compensation material layer, the piezoelectric layer, the top electrode layer, and the bottom electrode layer. By adjusting the proportion parameters of the structural material layers, the contribution weight of different material layers to the frequency-temperature characteristics of the resonator can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0014] On the other hand, the present invention provides a micromechanical device, which is a micromechanical resonator or a micromechanical oscillator; the micromechanical oscillator includes the micromechanical resonator and an oscillation holding circuit connected to the micromechanical resonator; the micromechanical resonator has a cubic frequency-temperature curve formed using the frequency-temperature curve control method of the micromechanical resonator described above.

[0015] One or more technical solutions provided in this invention have at least the following technical effects or advantages: The frequency-temperature curve control method for micromechanical resonators provided by this invention first determines the initial target range for the second-order frequency-temperature coefficient based on a set target cubic frequency-temperature curve. Then, it selects the doping type of the micromechanical resonator, compares the difference between the second-order frequency-temperature coefficient corresponding to different doping concentrations and the initial target range, and selects the doping concentration based on this difference. Next, by adjusting the design parameters of the micromechanical resonator, it matches and adjusts the first-order frequency-temperature coefficient and coordinates the correction of the second-order frequency-temperature coefficient, ensuring that the deviation between the resulting cubic frequency-temperature curve and the target cubic frequency-temperature curve is within a preset tolerance range. This invention can transform the frequency-temperature curve of a micromechanical resonator from a traditional linear or quadratic dominant curve to a cubic frequency-temperature curve, thereby reducing the maximum frequency drift within the target temperature range and improving the frequency-temperature stability of the micromechanical resonator. Attached Figure Description

[0016] Figure 1 The flowchart illustrates the method for controlling the frequency-temperature curve of a micromechanical resonator based on Embodiment 1 of the present invention to obtain a micromechanical resonator that meets the target requirements.

[0017] Figure 2 This is a schematic diagram comparing the traditional frequency offset-temperature curve with the three-dimensional frequency offset-temperature curve formed by the present invention.

[0018] Figure 3 For doping concentration and second-order frequency-temperature coefficient TCF A schematic diagram of the mapping relationship in Figure 2.

[0019] Figures 4-a to 4-b The doping concentration and the crystal orientation angle of the resonator are respectively related to the first-order frequency-temperature coefficient. TCF 1. Second-order frequency-temperature coefficient TCF 2. Relationship diagram.

[0020] Figure 5 This is a schematic diagram showing the adjustment of the three frequency shift-temperature curves corresponding to different crystal orientation angles of the resonator.

[0021] Figures 6-a to 6-cThis is a comparative schematic diagram of the standard geometric contour and the irregular contour structure provided in Embodiment 2 of the present invention.

[0022] Figure 7 This is a schematic diagram showing the adjustment of the three-dimensional frequency offset-temperature curves corresponding to different profile parameters of the resonator.

[0023] Figures 8-a to 8-h This is a schematic diagram of a resonator with different mechanical coupling structures provided in Embodiment 3 of the present invention.

[0024] Figures 9-a to 9-d This is a schematic diagram of a resonator with different composite material layer structures provided in Embodiment 4 of the present invention.

[0025] Figures 10-a to 10-c These are schematic diagrams of micromechanical oscillators for different applications. Detailed Implementation

[0026] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0027] Example 1: Example 1 provides a method for controlling the frequency-temperature curve of a micromechanical resonator, which mainly includes the following steps: S1. Based on the set target third frequency-temperature curve, determine the initial control target range of the second-order frequency-temperature coefficient; select the doping type of the micromechanical resonator, compare the difference between the second-order frequency-temperature coefficient corresponding to different doping concentrations and the initial control target range of the second-order frequency-temperature coefficient, and select the doping concentration based on the difference. S2. By adjusting the design parameters of the micromechanical resonator, the first-order frequency-temperature coefficient is matched and adjusted, and the second-order frequency-temperature coefficient is synergistically corrected, so that the deviation between the formed third-order frequency-temperature curve and the target third-order frequency-temperature curve is within the preset tolerance range.

[0028] Example 1 aims to obtain a micromechanical resonator with small frequency drift within the target operating temperature range. To achieve this objective, Example 1 first sets a target third-order frequency-temperature curve according to application requirements. Then, by adjusting the doping concentration and design parameters, the frequency-temperature curve of the micromechanical resonator is gradually transformed from a curve dominated by low-order terms into a third-order frequency-temperature curve that satisfies the target matching relationship, and the actual curve is made as close as possible to the target curve.

[0029] Specifically, in Example 1, the target third frequency-temperature curve is set in the following manner: (1) Determine the operating temperature range, frequency drift index, and operating frequency range of the micromechanical resonator; (2) Set target control information; wherein, the target control information includes at least one of the target position of the temperature inflection point and the target position of the central symmetry point, the temperature inflection point is the temperature point corresponding to the first derivative of the cubic frequency-temperature curve being equal to zero, and the central symmetry point is the temperature point corresponding to the second derivative of the cubic frequency-temperature curve being equal to zero. (3) Determine the target cubic frequency-temperature curve based on the operating temperature range, the frequency drift index, the operating frequency range, and the target control information.

[0030] That is, the target cubic frequency-temperature curve has identifiable cubic frequency-temperature curve characteristics within the operating temperature range. If a cubic frequency-temperature curve with two temperature inflection points is constructed, it is preferable that the target positions of the two temperature inflection points are located at or near the operating temperature range.

[0031] The initial control target range of the second-order frequency-temperature coefficient is preferably a preset numerical range in which the absolute value approaches 0.

[0032] Specifically, in Example 1, a material parameter temperature model and a parameterized structural model corresponding to the micromechanical resonator are established; after selecting the doping type of the micromechanical resonator, the second-order frequency-temperature coefficient corresponding to different doping concentrations is calculated based on the material parameter temperature model and the parameterized structural model.

[0033] The material parameter temperature model is a model of how the elastic constants of the structural material in the micromechanical resonator change with temperature and doping concentration. The structural material is N-type heavily doped silicon or P-type heavily doped silicon. The material parameter temperature model includes the first-order and second-order temperature dependence of the elastic constants of silicon material. Using the material parameter temperature model, the variation trend of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient of the micromechanical resonator with doping concentration can be predicted.

[0034] The parameterized structural model includes mandatory parameters and optional parameters. The mandatory parameters include doping concentration and structural geometry parameters. The optional parameters include some or all of the structural material layer ratio parameters, crystal orientation angle parameters, and mechanical coupling structural parameters.

[0035] Based on the material parameter temperature model and the parameterized structural model, the resonant frequencies of the micromechanical resonator at multiple temperature points under different design parameter conditions can be calculated, and the corresponding frequency-temperature curves can be obtained. Specifically, in Example 1, under the condition of selecting the doping type of the micromechanical resonator, the frequency-temperature curves corresponding to different doping concentrations are calculated, and the corresponding first-order and second-order frequency-temperature coefficients are obtained through low-order polynomial fitting. A mapping relationship is established between the doping concentration and the first-order and second-order frequency-temperature coefficients. Based on the target third-order frequency-temperature curve, the initial target range for adjusting the second-order frequency-temperature coefficient is determined; by comparing the deviation between the second-order frequency-temperature coefficients corresponding to different doping concentrations and the initial target range for adjusting the second-order frequency-temperature coefficient, the doping concentration with the smaller deviation is preferentially selected.

[0036] Specifically, adjusting the design parameters of a micromechanical resonator includes adjusting some or all of the structural geometric parameters, mechanical coupling structural parameters, crystal orientation angle parameters, and structural material layer ratio parameters of the micromechanical resonator.

[0037] That is, by selecting the doping type and doping concentration, the present invention can adjust the temperature dependence of the elastic constant of the structural material, so that the second-order frequency-temperature coefficient can be adjusted to the initial control target range. Then, based on this, by adjusting the structural geometric parameters, crystal orientation angle parameters, mechanical coupling structural parameters, or structural material layer ratio parameters, the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient can be further controlled, thereby adjusting the temperature inflection point position and the position of the central symmetry point of the cubic frequency-temperature curve.

[0038] The following explains each adjustment parameter and its corresponding adjustment principle.

[0039] (a) Structural geometric parameters.

[0040] The resonant oscillator of the micromechanical resonator is a single continuous structure, and the resonant oscillator has a closed standard geometric profile or an irregular profile in the plane; the structural geometric parameters include the in-plane dimensions and thickness of the resonant oscillator.

[0041] When the resonant oscillator has a standard geometric profile (i.e., a common shape structure), the in-plane dimensions include the length, width, radius, inner diameter, or outer diameter of the resonant oscillator.

[0042] When the resonant oscillator has an irregular profile, the irregular profile exhibits a non-constant radial dimension distribution along the circumference, and the in-plane dimensions include the radial dimension, local width, or local curvature of the resonant oscillator at different positions in the circumference.

[0043] By adjusting the geometric parameters of the structure, the equivalent stiffness distribution of the resonant oscillator in different crystal orientations can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0044] (b) Mechanical coupling structural parameters.

[0045] The micromechanical resonator is formed by connecting at least two resonant units through a coupling block; the mechanical coupling structure parameters include the structural form and operating mode of the resonant unit. The structural form is any one or more combinations of rectangular plate, fixed beam, disk, and ring; the operating mode is any one or more combinations of volume mode, shear mode, and bending mode; the volume mode includes length extension, width extension, square plate extension, circular plate extension, or ring extension mode; the shear mode includes lame mode, surface shear, width shear, length shear, or goblet mode.

[0046] By adjusting the parameters of the mechanical coupling structure, the participation ratio of different working modes can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0047] (c) Crystal orientation angle parameters.

[0048] The crystal orientation angle parameter is the orientation angle of the main vibration direction of the micromechanical resonator relative to the crystal coordinate axis.

[0049] By adjusting the crystal orientation angle parameter, the contribution weight of different elastic constants and their temperature dependence on the equivalent stiffness of the working mode can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0050] (d) Structural material layer ratio parameters.

[0051] The micromechanical resonator is any one of the following structures: (1) a combination of a heavily doped silicon structure layer and a compensation material layer; (2) a combination of a heavily doped silicon structure layer, a piezoelectric layer and a top electrode layer; (3) a combination of a bottom electrode layer, a heavily doped silicon structure layer, a piezoelectric layer and a top electrode layer; and (4) a combination of a heavily doped silicon structure layer, a piezoelectric layer, a top electrode layer and a compensation material layer.

[0052] The structural material layer ratio parameters include the thickness ratio of at least a portion of the material layers among the heavily doped silicon structural layer, the compensation material layer, the piezoelectric layer, the top electrode layer, and the bottom electrode layer.

[0053] By adjusting the proportion parameters of the structural material layers, the contribution weight of different material layers to the frequency-temperature characteristics of the resonator can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0054] The frequency-temperature curve control method for the micromechanical resonator provided in Example 1 can yield a micromechanical resonator that meets the target requirements. (See also...) Figure 1 Micromechanical resonators can be obtained through the following methods: (1) Determine the operating temperature range, frequency drift index, operating frequency range, operating mode and geometric structure of the micromechanical resonator.

[0055] The geometric structure of the micromechanical resonator can be a plate structure, beam structure, disk structure, ring structure, or a composite structure formed by combining the above structures, and is not limited to the structural forms listed above.

[0056] Since different geometric structures correspond to different resonant modes, their equivalent stiffness and temperature dependence also contribute differently to the resonant frequency. Therefore, this invention does not limit the micromechanical resonator to adopt a specific geometric structure. Instead, it can select the appropriate geometric structure according to the target operating mode and the target frequency-temperature characteristics, and adjust the structural parameters to make the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient satisfy the target matching relationship.

[0057] (2) Establish a material parameter temperature model for the structural material in the micromechanical resonator, which varies with temperature and doping concentration as the elastic constants of the material change.

[0058] The structural material is N-type heavily doped silicon or P-type heavily doped silicon; the material parameter temperature model includes the first and second-order temperature dependence of the elastic constants of silicon material, and can be used to predict the variation trend of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient of the resonator under different doping concentrations.

[0059] (3) Establish a parameterized structural model of the micromechanical resonator. The parameterized structural model includes at least the doping concentration and structural geometric parameters, and further includes optional structural material layer ratio parameters, crystal orientation angle parameters and mechanical coupling structural parameters.

[0060] (4) Based on the material parameter temperature model and the parameterized structure model, calculate the resonant frequency of the resonator at different temperatures, and obtain the predicted first-order frequency-temperature coefficient and second-order frequency-temperature coefficient through polynomial fitting to determine the initial frequency-temperature curve characteristics of the resonator.

[0061] The initial frequency-temperature curve is usually an approximately linear curve or a quadratic term-dominant curve. Using the initial frequency-temperature curve as a benchmark for subsequent parameter control can determine the pre-control direction of the second-order frequency-temperature coefficient and the matching control direction of the first-order frequency-temperature coefficient. It also provides a reference for the subsequent extraction of the effective third-order frequency-temperature coefficient and for determining whether the target third-order frequency-temperature curve has been formed.

[0062] (5) Establish the mapping relationship between doping concentration and second-order frequency-temperature coefficient, and adjust the temperature dependence of the elastic constant of the structural material by selecting the doping type and doping concentration, so that the second-order frequency-temperature coefficient can be adjusted to the initial control target range.

[0063] The initial target range for adjusting the second-order frequency-temperature coefficient is determined inversely based on the target cubic frequency-temperature curve. The target cubic frequency-temperature curve is defined by the target operating temperature range, target frequency drift index, target operating frequency range, target temperature inflection point position, and target center symmetry point position. By comparing the deviations between the second-order frequency-temperature coefficient and the target range at different doping concentrations, the target doping concentration range that makes the second-order frequency-temperature coefficient approach zero, shift from negative to positive, or exceed zero is determined.

[0064] In Example 1, the initial target range for adjusting the second-order frequency-temperature coefficient is not necessarily close to zero. The target range for the second-order frequency-temperature coefficient should be determined based on the position of the central symmetry point of the target cubic frequency-temperature curve. When the target central symmetry point is set near the reference temperature point, the second-order frequency-temperature coefficient can be adjusted to a preset range close to zero. When the target central symmetry point shifts relative to the reference temperature point, the second-order frequency-temperature coefficient can be positive or negative.

[0065] (6) When the second-order frequency-temperature coefficient is close to or greater than zero, the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient are controlled by adjusting some or all of the design parameters of the micromechanical resonator (structural geometric parameters, mechanical coupling structural parameters, crystal orientation angle parameters, and structural material layer ratio parameters) so that the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient satisfy the target matching relationship.

[0066] (7) Based on the target matching relationship between the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient, the frequency-temperature curve of the micromechanical resonator is transformed into a third-order frequency-temperature curve, and the third-order frequency-temperature coefficient is obtained by fitting a third-order polynomial.

[0067] The target matching relationship includes ensuring that the three-frequency-temperature curve has at least one temperature inflection point or a central symmetry point located within or near the target operating temperature range.

[0068] In some preferred embodiments, the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient are adjusted to near zero or within a preset range, under which the frequency offset is minimized.

[0069] (8) Based on the operating temperature range and frequency drift index, the doping concentration, structural geometric parameters and optional design parameters are iteratively optimized to finally output a design scheme for a micromechanical resonator that meets the target requirements.

[0070] like Figure 2 As shown, the frequency shift-temperature curve of a traditional micromechanical resonator typically exhibits linear or quadratic dominance. However, Example 1, by adjusting the doping concentration and design parameters, achieves coordinated control of the first-order and second-order frequency-temperature coefficients. Furthermore, a third-order frequency-temperature coefficient can be obtained through third-order polynomial fitting, transforming the frequency shift-temperature curve from a quadratic dominance curve to a cubic frequency shift-temperature curve (i.e., a quartz-like cubic curve). A cubic frequency shift-temperature curve ensures that at least one temperature inflection point or the center symmetry point of the cubic curve lies within the target operating temperature range, thereby reducing frequency drift within the target temperature region. Example 1 can also be understood as providing a method for achieving target matching of the first-order and second-order frequency-temperature coefficients, and constructing a frequency-temperature curve with a distinct cubic characteristic within the operating temperature range.

[0071] The following is a further explanation of the three frequency-temperature curves.

[0072] For a micromechanical resonator, its normalized third frequency-temperature curve can be expressed as:

[0073] In the formula, The resonant frequency is a function of temperature, Δ T The change in temperature, ΔT = T - T 0, T Operating temperature T 0 is the reference temperature. TCF 1. TCF 2. TCF 3 represents the first-order, second-order, and third-order frequency-temperature coefficients, respectively.

[0074] when TCF When 3≠0, the temperature inflection point of the cubic frequency-temperature curve is the temperature point corresponding to the first derivative of the curve being equal to 0, and the temperature inflection point satisfies:

[0075] If the curve is required to have two temperature inflection points, then it should satisfy the following:

[0076] Two temperature inflection points relative to the reference temperature point T The temperature changes at 0°C are as follows:

[0077]

[0078] The two corresponding temperature inflection points are as follows:

[0079]

[0080] in, ΔT l and ΔT h These are two temperature inflection points relative to a reference temperature point. T The change in temperature is 0. T l and T h These are the actual temperatures corresponding to the two temperature inflection points.

[0081] Furthermore, by taking the second derivative of the cubic frequency-temperature curve and setting it to zero, we can obtain that the central symmetric point of the cubic frequency-temperature curve satisfies:

[0082] In the formula, This represents the temperature change relative to the reference temperature at the point symmetrical to the center of the third frequency-temperature curve.

[0083] The temperature point corresponding to the center-symmetric point is: .

[0084] In this invention, only the following conditions are met: TCF 3 ≠ 0 does not necessarily mean that the frequency-temperature curve will exhibit a distinct cubic curve characteristic within the target operating temperature range. When TCF When the amplitude of frequency 3 is small, or the target operating temperature range is narrow, the third-order frequency-temperature term may be masked by the first-order and second-order frequency-temperature terms, causing the frequency-temperature curve to still appear as an approximately linear or approximately quadratic curve. Therefore, to ensure that the frequency-temperature curve is within the target operating temperature range ( T min , T max The curve exhibits distinct cubic curve characteristics. Judgment and adjustment can be made based on the frequency shift contribution of the third-order frequency-temperature term within the target operating temperature range, the degree of improvement in the residual between the third-order and second-order fittings, and the position of the central symmetry point of the cubic curve. The maximum residual of the second-order fitting curve can be expressed as E² = max(|F(T) - F²(T)|), where T ∈ (…). T min , T maxF(T) is the normalized frequency shift of the micromechanical resonator at temperature T, which can be obtained by testing or simulation. F2(T) is the second-order fitting curve obtained by fitting F(T) with a second-order polynomial. The maximum residual of the third-order fitting curve can be expressed as E3 = max(|F(T) - F3(T)|), T∈( T min , T max F3(T) is the third-order fitting curve obtained by fitting F(T) with a third-order polynomial. The smaller the value of E3 / E2, the more significant the reduction in residual after fitting with a third-order polynomial, and the more significant the influence of the third-order frequency-temperature term on the shape of the frequency-temperature curve.

[0085] Furthermore, when it is necessary for the frequency-temperature curve to exhibit a significant change in curvature direction within the target operating temperature range, the central symmetry point of the cubic frequency-temperature curve should also be located within the target operating temperature range, i.e., satisfying the following:

[0086] Therefore, it can be adjusted TCF 2 and TCF The proportional relationship between the three frequencies ensures that the central symmetrical point of the three frequency-temperature curves falls within the target operating temperature range, thereby causing the curvature direction of the frequency-temperature curves to change within the target operating temperature range.

[0087] Furthermore, when it is necessary for the three-frequency-temperature curve to exhibit obvious dual-temperature inflection point characteristics within the target operating temperature range, the two temperature inflection points should be located at or near the target operating temperature range.

[0088] Furthermore, the center of the two temperature inflection points corresponds to the temperature of the center symmetry point of the cubic frequency temperature curve, and half the distance between the two temperature inflection points is: .

[0089] Therefore, TCF 1. TCF 2 and TCF The matching relationship between the three factors jointly determines the distance between the two temperature inflection points. When the reference temperature point... T When 0 is set near the center of the target operating temperature range, it can be achieved by... TCF 2. Adjust to a preset range close to zero, so that the center symmetry point of the three frequency-temperature curves and the center position of the two temperature inflection points are close to the center of the target operating temperature range.

[0090] Furthermore, through coordinated regulation TCF 1. TCF 2 and TCF3. This allows the two temperature inflection points to be located on or near the two sides of the target operating temperature range, thus making the frequency-temperature curve exhibit obvious cubic curve characteristics within the target operating temperature range.

[0091] Therefore, in this invention, the target location of the temperature inflection point, the target location of the center symmetry point of the cubic frequency-temperature curve, and the frequency drift index can be used to reverse-determine the frequency drift index. TCF 1. TCF 2 and TCF The matching relationship of 3. Furthermore, this can be achieved by controlling the doping concentration. TCF 2. Pre-regulation is performed, and adjustments are made through crystal orientation angles, irregular profiles, mechanical coupling structures, or composite material thickness ratios. TCF 1 and TCF 2. Perform coordinated adjustment to transform the frequency-temperature curve from a quadratic dominant curve to a cubic frequency-temperature curve that satisfies the target matching relationship, thereby reducing frequency drift within the target operating temperature range and improving the frequency-temperature stability of the micromechanical resonator.

[0092] In a preferred embodiment, the reference temperature point can be set as the center of the operating temperature range, and... TCF 1 and TCF 2. Adjust to a preset range close to or zero to suppress the contribution of the first-order frequency-temperature term and the second-order frequency-temperature term to the frequency drift, so that the resonator frequency drift within the target operating temperature range can approach zero.

[0093] Figure 4-a and Figure 4-b This illustrates, in one specific embodiment, the relationship between doping concentration and resonator crystal orientation angle and the first-order frequency-temperature coefficient. TCF First and second order frequency-temperature coefficient TCF The regulatory effect of 2, among which, Figure 4-a The doping concentration, resonator crystal orientation angle, and second-order frequency-temperature coefficient are considered. TCF A diagram illustrating the relationship between two points; Figure 4-b The doping concentration, resonator crystal orientation angle, and first-order frequency-temperature coefficient are considered. TCF A diagram illustrating the relationship between 1 and 2.

[0094] Depend on Figure 4-a and Figure 4-b It can be determined separately that the following conditions are met. TCF 2=0 and TCF The parameter combinations where 1=0 are represented as corresponding parameter relationship curves. When the condition is met... TCF The parameter relationship curve of 2=0 and satisfying TCF When the parameter relationship curves with 1=0 intersect, the doping concentration and crystal orientation angle corresponding to the intersection point can simultaneously suppress the contributions of the first-order frequency-temperature term and the second-order frequency-temperature term to the frequency drift.

[0095] Under the parameter conditions corresponding to the aforementioned intersection point, the normalized frequency shift of the micromechanical resonator is mainly determined by the third-order frequency-temperature term. Therefore, the aforementioned intersection point can be considered as a preferred parameter combination for obtaining lower frequency drift and for exhibiting the characteristics of the third-order frequency-temperature curve within the target operating temperature range.

[0096] Furthermore, when the amplitude of the effective third-order frequency-temperature term is also within the preset range, the maximum frequency drift within the target operating temperature range can be further reduced, thereby improving the frequency-temperature stability of the micromechanical resonator.

[0097] It should be noted that, Figure 4-a and Figure 4-b Only the doping concentration and crystal orientation angle are shown. TCF 1 and TCF 2. This is one specific implementation method for coordinated regulation and does not constitute a limitation on the regulation method of the present invention.

[0098] In other embodiments, the basic dimensional parameters, irregular profile parameters, mechanical coupling structure parameters, or structural material layer thickness ratio of the micromechanical resonator can also be adjusted to... TCF 1 and TCF 2. Conduct coordinated regulation.

[0099] Taking a square plate monocrystalline silicon resonator as an example, the operating mode of the square plate monocrystalline silicon resonator is the square plate extension mode, and its main vibration direction is along the monocrystalline silicon. <100> Crystal orientation arrangement. For example... Figure 3 As shown, by scanning the frequency shift-temperature curves at different N-type doping concentrations, a mapping relationship between doping concentration and the second-order frequency-temperature coefficient can be established. With increasing N-type doping concentration, the temperature dependence of the elastic constant of silicon changes, causing the second-order frequency-temperature coefficient of the slab monocrystalline silicon resonator to gradually approach zero, and to shift from negative to positive values ​​or be modulated to a target range greater than zero. This provides a basis for subsequently generating a third-order frequency shift-temperature curve.

[0100] like Figure 4-a As shown, by further introducing the crystal orientation angle parameter, a relationship can be established between the doping concentration, the resonator crystal orientation angle, and the second-order frequency-temperature coefficient. The crystal orientation angle is the orientation angle of the resonator's principal vibration direction relative to the coordinate axes of the single-crystal silicon crystal. By changing the crystal orientation angle, i.e., changing the resonator's principal vibration direction relative to the coordinate axes of the single-crystal silicon crystal, the relationship between the resonator's principal vibration direction and the resonator's orientation angle can be established. <100> The deflection angle of the crystal orientation can change the contribution weight of different elastic constants and their temperature dependence on the equivalent stiffness of the resonator, thereby adjusting the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0101] When the doping concentration of single-crystal silicon is greater than 1.7 × 10⁻⁶ 20 cm -3At this time, the second-order frequency-temperature coefficient of the square plate single-crystal silicon resonator can be adjusted to a range close to zero, shifting from negative to positive, or greater than zero. Based on this, by further adjusting the crystal orientation angle of the resonator, the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient can satisfy the target matching relationship, so that the frequency offset-temperature curve exhibits cubic curve characteristics under third-order polynomial fitting. Figure 5 The figure shows different cubic frequency shift-temperature curves corresponding to different crystal orientation angles. By selecting the target crystal orientation angle, the position of the temperature inflection point of the cubic frequency shift-temperature curve, the position of the center symmetry point of the cubic curve, and the frequency drift within the target operating temperature range can be adjusted.

[0102] In summary, Example 1 presents a clear design objective, a predictable control path, and a stable implementation method, which can actively construct or precisely control the third-order frequency-temperature curve.

[0103] Based on Example 1, the following examples illustrate several micromechanical resonators with different structures, namely Example 2, Example 3, and Example 4.

[0104] Example 2: Example 2 provides a method for controlling the frequency-temperature curve of a micromechanical resonator. Example 2 controls the frequency-temperature characteristics of the micromechanical resonator by adjusting the structural geometric parameters (specifically, irregular contour structure).

[0105] Figure 6-a A schematic diagram comparing the standard geometric profile and the irregular profile structure of a square plate resonator is shown. Figure 6-b A schematic diagram comparing the standard geometric profile and the irregular profile structure of a circular plate resonator is shown. Figure 6-c A schematic diagram comparing the standard geometric profile and the irregular profile structure of a circular ring resonator is shown.

[0106] In Example 2, the resonator is a single continuous structure with a closed irregular profile in a plane. The irregular profile exhibits a non-constant radial dimension distribution along the circumference. By adjusting the radial dimension, local width, or local curvature of the resonator at different circumferential positions, the equivalent stiffness distribution of different crystal orientations of the resonator can be changed, thereby altering the frequency-temperature characteristics of the operating mode, thus achieving the control of the first-order and second-order frequency-temperature coefficients of the micromechanical resonator.

[0107] The irregular profile can have periodic variation characteristics and can have at least fourfold rotational symmetry. The irregular profile can be used in square plate resonators, circular plate resonators, or circular ring resonators.

[0108] The irregular contour can be represented as an angular modulation function in polar coordinates, which satisfies the following relationship:

[0109] In the formula, For the resonant oscillator at an angle Radial dimension in the direction, The average radial dimension parameter, For the first Angular modulation amplitude parameters, A positive integer greater than or equal to 1. f m It is a periodic function.

[0110] By adjusting the average radial dimension parameter With the first angular modulation amplitude parameters The proportional relationship between these parameters allows for the adjustment of the frequency-temperature characteristics of the micromechanical resonator.

[0111] The periodic function f m These can be trigonometric functions, exponential functions, polynomial functions, spline functions, or combinations of the above functions.

[0112] For example, trigonometric functions can be represented as: A polynomial function can be represented as: where p is the degree of the polynomial; an exponential function can be expressed as: Where, a is the amplitude modulation parameter, controlling the overall offset of the irregular contour relative to the average size; b is the shape modulation parameter, controlling the degree of nonlinearity in the angular modulation; the spline function can be expressed as: , For spline basis functions, Here, is the control coefficient, and N is the number of control points. All of the above-mentioned function forms cause the irregular profile to exhibit periodic radial dimensional variations in the circumferential direction.

[0113] For example, when Figure 6-a The irregularly shaped square plate resonator shown is made of n-type heavily doped single-crystal silicon material with a doping concentration greater than 1.2 × 10⁻⁶. 20 / cm 3 And the resonator along the single-crystal silicon <100> When arranging crystal orientations, the average radial dimension parameter is adjusted. r 0 and the angular modulation amplitude parameters a m The proportional relationship allows adjustment of the resonator's frequency offset-temperature curve. (See also...) Figure 7 Different a m / r Different frequency offset-temperature curves corresponding to 0 parameter ratio.

[0114] Under the aforementioned hyperheavy doping conditions, the second-order frequency-temperature coefficient of the micromechanical resonator is tuned to near zero or within the target range. Based on this, the first-order and second-order frequency-temperature coefficients are further adjusted using irregular profile parameters to satisfy the target matching relationship required by the cubic frequency-temperature curve. Thus, the frequency offset-temperature curve of the micromechanical resonator can be transformed from a traditional quadratic dominant curve into a cubic frequency offset-temperature curve similar to that of a quartz crystal, forming two temperature inflection points over a wide temperature range.

[0115] By selecting appropriate average radial dimension parameters r 0 and the angular modulation amplitude parameters a m The proportional relationship allows the frequency shift to be kept within ±10ppm over a wide temperature range of -70℃ to 140℃, while simultaneously achieving a higher temperature inflection point.

[0116] Example 3: Example 3 provides a method for controlling the frequency-temperature curve of a micromechanical resonator. Example 3 controls the frequency-temperature characteristics of the micromechanical resonator by adjusting the mechanical coupling structure parameters.

[0117] exist Figures 8-a to 8-h In this structure, the main resonant unit 81 and the secondary resonant unit 83 are connected by a coupling block 82 to form a mechanical coupling structure. This mechanical coupling structure allows resonant units with different frequency-temperature characteristics to be combined into an overall resonant structure. Furthermore, by changing the participation ratio of different resonant units or different resonant modes in the overall structure, the overall frequency-temperature characteristics can be controlled. Figure 8-a , Figure 8-g and Figure 8-h The structure showing the mechanical coupling between the rectangular plate resonant unit and the circular ring resonant unit via the coupling block 82 is illustrated. Figure 8-b , Figure 8-d , Figure 8-e and Figure 8-f The structure showing the mechanical coupling between the rectangular plate resonant unit and the disk resonant unit via the coupling block 82 is illustrated. Figure 8-c The structure of the rectangular plate resonant unit being mechanically coupled to the rectangular plate resonant unit through the coupling block 82 is shown.

[0118] In Example 3, different resonant units or different resonant modes have different first-order and second-order frequency-temperature coefficients. By adjusting the proportion of the equivalent mass or equivalent stiffness of the resonant units, the contribution weight of different resonant modes to the overall frequency-temperature characteristics of the coupled resonator can be changed. Therefore, the first-order and second-order frequency-temperature coefficients of the mechanically coupled resonator can be controlled to meet the target matching relationship required by the cubic frequency-temperature curve. The frequency-temperature coefficient of the overall structure after coupling is shown in the figure. TCF It can be approximated as a weighted combination of the frequency-temperature coefficients of different resonant unit states, as follows:

[0119] in, m i ( i =1,2) represent the equivalent mass of each resonant structure, respectively. TCF m1 and TCF m2 These are the frequency-temperature coefficients of the resonant modes corresponding to the main resonant unit 81 and the secondary resonant unit 83, respectively.

[0120] The frequency-temperature characteristics of a mechanically coupled resonator can be effectively adjusted by changing the proportion of the equivalent mass or equivalent stiffness of a single type of resonant structure in the mechanical coupling system.

[0121] Therefore, Example 3 utilizes the differences in frequency-temperature characteristics between different resonant units or different resonant modes through a mechanical coupling structure to regulate the overall frequency-temperature curve. This mechanical coupling regulation method can be combined with other regulation methods to increase the degree of freedom in regulating the cubic frequency-temperature curve and enable the micromechanical resonator to achieve lower frequency drift within the target operating temperature range.

[0122] Example 4: Example 4 provides a method for controlling the frequency-temperature curve of a micromechanical resonator. Example 4 controls the frequency-temperature characteristics of the micromechanical resonator by adjusting the structural material layer ratio parameters (i.e., composite material layer structure).

[0123] For example, a micromechanical resonator is a combination structure of a heavily doped silicon structural layer and a compensation material layer. Figure 9-a As shown, the micromechanical resonator may include a heavily doped silicon structure layer 901 and a compensation material layer 902. By adjusting the thickness ratio of the heavily doped silicon structure layer 901 and the compensation material layer 902, the contribution weights of the two material layers to the overall equivalent stiffness and frequency-temperature characteristics of the resonator can be changed, thereby controlling the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

[0124] For example, a micromechanical resonator is a combination structure of a heavily doped silicon structural layer, a piezoelectric layer, and a top electrode layer. Figure 9-b As shown, the micromechanical resonator may include a heavily doped silicon structural layer 901, a piezoelectric layer 903, and a top electrode layer 904. This structure is suitable for piezoelectric micromechanical resonators. By adjusting the thickness ratio between the heavily doped silicon structural layer 901, the piezoelectric layer 903, and the top electrode layer 904, the contribution weight of the composite structure to the overall equivalent stiffness and frequency-temperature characteristics of the resonator can be changed, thereby controlling the first-order and second-order frequency-temperature coefficients.

[0125] For example, a micromechanical resonator is a combination structure of a bottom electrode layer, a heavily doped silicon structure layer, a piezoelectric layer, and a top electrode layer. Figure 9-c As shown, the micromechanical resonator may include a bottom electrode layer 904, a heavily doped silicon structure layer 901, a piezoelectric layer 903, and a top electrode layer 904 (all electrode layers are denoted as 904). This structure forms a piezoelectric transduction field together through the bottom electrode layer 904 and the top electrode layer 904. By adjusting the thickness ratio among the bottom electrode layer 904, the heavily doped silicon structure layer 901, the piezoelectric layer 903, and the top electrode layer 904, the contribution weight of the composite structure to the overall equivalent stiffness and frequency-temperature characteristics of the resonator can be changed, thereby controlling the first-order and second-order frequency-temperature coefficients.

[0126] For example, a micromechanical resonator is a combination structure of a heavily doped silicon layer, a piezoelectric layer, a top electrode layer, and a compensation material layer. Figure 9-d As shown, the micromechanical resonator may include a heavily doped silicon structure layer 901, a piezoelectric layer 903, a top electrode layer 904, and a compensation material layer 902. This structure achieves piezoelectric transduction while introducing the compensation material layer 902 for further tuning of the frequency-temperature characteristics. By adjusting the thickness ratio among the heavily doped silicon structure layer 901, the piezoelectric layer 903, the top electrode layer 904, and the compensation material layer 902, synergistic control of the first-order and second-order frequency-temperature coefficients can be achieved.

[0127] In Example 4, the adjustment of the composite material layer structure is not limited to changing the type of material, but also includes changing the thickness ratio of each material layer. Different material layers have different temperature coefficients of elastic modulus and thermal expansion characteristics; therefore, by changing the thickness or volume ratio of the material layers, the overall frequency-temperature characteristics of the resonator can be adjusted. The equivalent frequency-temperature coefficient of the composite material layer structure is shown in the figure. TCF This can be approximated as a weighted combination of the frequency-temperature coefficients of each material layer, as follows:

[0128] in, TCF i No. iThe contribution of each material layer to the frequency-temperature coefficient, λ i This represents the contribution weight of the corresponding material layer.

[0129] Example 4 achieves coordinated control of the first-order and second-order frequency-temperature coefficients by adjusting the thickness or volume ratio of each material layer in the composite material layer structure, thereby changing the contribution weight of different material layers to the frequency-temperature characteristics. This composite material layer control method can be combined with other control methods to achieve precise construction of the third-order frequency-temperature curve.

[0130] In summary, the frequency-temperature curve control method for micromechanical resonators proposed in this invention adjusts the doping concentration of silicon material to bring the second-order frequency-temperature coefficient within a preset target range. Combined with structural design techniques such as structural geometric parameters, mechanical coupling parameters, crystal orientation parameters, and structural material layer ratio parameters, the first-order frequency-temperature coefficient is matched and adjusted, and the second-order frequency-temperature coefficient is synergistically corrected. This transforms the frequency-temperature characteristics of the micromechanical resonator from a quadratic dominant curve to a cubic frequency-temperature curve, enabling adjustable design of the temperature inflection point or central symmetry point of the cubic curve. This invention provides a pre-controllability method for the frequency-temperature characteristics of temperature-compensated and temperature-controlled micromechanical oscillators, and is suitable for applications such as high-stability frequency sources and communication systems.

[0131] Based on the frequency-temperature curve control method of the micromechanical resonator provided by the present invention, a corresponding micromechanical device is further provided, which will be described below with reference to Embodiments 5 and 6.

[0132] Example 5: Example 5 provides a micromechanical device, which is a micromechanical resonator. The micromechanical resonator has a cubic frequency-temperature curve formed using the frequency-temperature curve modulation method for micromechanical resonators as described in Example 1.

[0133] The frequency-temperature curve of the micromechanical resonator in Example 5 can be adjusted by various parameters, including doping concentration, structural geometry parameters, mechanical coupling structure parameters, crystal orientation angle parameters, and structural material layer ratio parameters, to form a cubic frequency-temperature curve. The micromechanical resonator provided in Example 5 exhibits good frequency-temperature stability.

[0134] Example 6: Example 6 provides a micromechanical device, which is a micromechanical oscillator. The micromechanical oscillator includes a micromechanical resonator and an oscillation holding circuit connected to the micromechanical resonator, the oscillation holding circuit being used to provide closed-loop oscillation excitation for the micromechanical resonator.

[0135] The micromechanical resonator has a cubic frequency-temperature curve formed using the frequency-temperature curve control method for the micromechanical resonator as described in Example 1.

[0136] Specifically, the micromechanical resonator can be configured as an uncompensated micromechanical oscillator, a temperature-compensated micromechanical oscillator, or a temperature-controlled micromechanical oscillator, depending on the application scenario.

[0137] When the micromechanical oscillator is a temperature-compensated micromechanical oscillator, it further includes a temperature sensor and a frequency compensation circuit. The temperature sensor is used to acquire the ambient temperature, and the frequency compensation circuit is used to compensate the output frequency based on the ambient temperature. Preferably, the temperature inflection point of the micromechanical resonator is located near room temperature to reduce frequency drift within the target operating temperature range and decrease the compensation range and complexity of the frequency compensation circuit.

[0138] When the micromechanical oscillator is a temperature-controlled micromechanical oscillator, it further includes a temperature sensor, a temperature control circuit, and a heating cavity. The micromechanical resonator is disposed within the heating cavity, and the temperature control circuit adjusts the temperature of the heating cavity based on the temperature obtained by the temperature sensor, so that the micromechanical resonator operates near a preset temperature point. Preferably, the preset temperature point is located near the temperature inflection point of the frequency-temperature curve of the micromechanical resonator to reduce the impact of temperature fluctuations on the stability of the output frequency.

[0139] The following description, in conjunction with the accompanying drawings, further explains various types of micromechanical oscillators.

[0140] (1) Micromechanical oscillator without temperature compensation.

[0141] Figure 10-a This is an uncompensated micromechanical oscillator architecture. For example... Figure 10-a As shown, the uncompensated micromechanical oscillator includes a micromechanical resonator 1001 and an oscillation holding circuit 1002. The oscillation holding circuit 1002 is connected to the micromechanical resonator 1001 and provides closed-loop oscillation excitation to the micromechanical resonator 1001, enabling the micromechanical resonator 1001 to maintain stable oscillation and output a frequency signal. In this structure, the micromechanical oscillator does not have an additional temperature sensor, frequency compensation circuit, or temperature control circuit; its output frequency is mainly determined by the frequency-temperature characteristics of the micromechanical resonator 1001 itself. Therefore, by pre-designing the cubic frequency-temperature curve of the micromechanical resonator 1001 during the device design stage using the method of this invention, frequency drift within the target operating temperature range can be reduced, thereby improving the frequency stability of the uncompensated micromechanical oscillator.

[0142] (2) Temperature-compensated micromechanical oscillator.

[0143] Figure 10-b This is a temperature-compensated micromechanical oscillator architecture. For example... Figure 10-b As shown, the temperature-compensated micromechanical oscillator includes a micromechanical resonator 1001, an oscillation holding circuit 1002, a frequency synthesizer 1003, and a temperature sensor 1004. The oscillation holding circuit 1002 provides closed-loop oscillation excitation for the micromechanical resonator 1001; the temperature sensor 1004 acquires the ambient temperature or the temperature near the micromechanical resonator 1001 and transmits the temperature information to the frequency synthesizer 1003; the frequency synthesizer 1003 adjusts the output frequency according to the temperature information to compensate for the frequency shift of the micromechanical oscillator caused by temperature changes.

[0144] In this example, the frequency-temperature curve of the micromechanical resonator 1001 has been subjected to cubic curve tuning using the method of the present invention. Preferably, the second-order frequency-temperature coefficient can be brought close to zero or into the target range by adjusting the doping concentration, and the first-order and second-order frequency-temperature coefficients can be adjusted by crystal orientation, irregular profile, mechanical coupling relationship, or the proportion of composite structure materials, so that the central symmetry point of the cubic frequency-temperature curve is located at the center of the target operating temperature range. As a result, the original frequency drift of the micromechanical resonator 1001 in the target temperature range is reduced, and the compensation range and compensation complexity required by the frequency synthesizer 1003 are correspondingly reduced, thereby improving the output frequency stability of the temperature-compensated micromechanical oscillator.

[0145] (3) Thermostatic control micromechanical oscillator.

[0146] Figure 10-c This is a temperature-controlled micromechanical oscillator architecture. For example... Figure 10-c As shown, the thermostatically controlled micromechanical oscillator includes a micromechanical resonator 1001, an oscillation holding circuit 1002, a temperature sensor 1004, a temperature control circuit 1005, and a heating cavity 1006. The micromechanical resonator 1001 is disposed within the heating cavity 1006; the oscillation holding circuit 1002 provides closed-loop oscillation excitation for the micromechanical resonator 1001; the temperature sensor 1004 acquires the real-time temperature within the heating cavity 1006 or near the micromechanical resonator 1001 and transmits the temperature information to the temperature control circuit 1005; the temperature control circuit 1005 adjusts the temperature of the heating cavity 1006 according to the temperature information, so that the micromechanical resonator 1001 operates near a preset temperature point.

[0147] In this example, the preset temperature point can be determined based on the third frequency-temperature curve of the micromechanical resonator 1001. Preferably, the high-temperature inflection point of the third frequency-temperature curve is adjusted to a preset temperature range above the target operating temperature range using the method of the present invention, and the micromechanical resonator 1001 operates near this high-temperature inflection point under isothermal control. Since the frequency is less sensitive to temperature near the temperature inflection point, the impact of ambient temperature fluctuations on the output frequency can be reduced, thereby improving the frequency stability of the isothermal-controlled micromechanical oscillator.

[0148] Example 6 combines the frequency-temperature curve control method for the micromechanical resonator provided by this invention with an oscillation holding circuit, a frequency synthesizer, a temperature sensor, a temperature control circuit, and a heating cavity to construct uncompensated micromechanical oscillators, temperature-compensated micromechanical oscillators, and temperature-controlled micromechanical oscillators, respectively. This invention allows for pre-design of the frequency-temperature curve at the device level according to different application requirements, reducing frequency drift with temperature. It also reduces the difficulty of subsequent circuit temperature compensation or temperature control at the device structure level, which is beneficial for improving the frequency stability, temperature adaptability, and engineering feasibility of the micromechanical oscillator.

[0149] In summary, this invention provides a method for controlling the third-order frequency-temperature coefficient of micromechanical resonators. By establishing a material parameter temperature model that varies the elastic constants of the structural material with temperature and doping concentration, and combining it with a parameterized structural model of the micromechanical resonator, the method can predict the frequency-temperature characteristics under different doping concentrations, structural geometric parameters, mechanical coupling structural parameters, crystal orientation parameters, and structural material layer ratio parameters during the device design stage. Specifically, this invention first controls the second-order frequency-temperature coefficient by adjusting the doping concentration, bringing it close to zero or controlling it to a target range. Furthermore, it controls the first-order and second-order frequency-temperature coefficients by adjusting design degrees of freedom such as size characteristics, crystal orientation, closed irregular profiles, mechanical coupling relationships, or the proportion of composite structural materials, ensuring that the first-order and second-order frequency-temperature coefficients meet the target matching relationship. This transforms the frequency-temperature curve of the micromechanical resonator from a traditional linear or quadratic dominant curve into a cubic frequency-temperature curve. This method allows for the reverse determination of the design parameters of the micromechanical resonator corresponding to the third-order frequency-temperature curve, based on the target operating temperature range, target frequency drift index, target temperature inflection point location, or the location of the central symmetry point of the cubic curve. This ensures that the temperature inflection point or the central symmetry point of the cubic curve is located within the target operating temperature range, thereby reducing the maximum frequency drift within the target temperature range and improving the frequency-temperature stability of the resonator.

[0150] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for controlling the frequency-temperature curve of a micromechanical resonator, characterized in that, Includes the following steps: Based on the set target third frequency-temperature curve, determine the initial control target range of the second-order frequency-temperature coefficient; select the doping type of the micromechanical resonator, compare the difference between the second-order frequency-temperature coefficient corresponding to different doping concentrations and the initial control target range of the second-order frequency-temperature coefficient, and select the doping concentration based on the difference; By adjusting the design parameters of the micromechanical resonator, the first-order frequency-temperature coefficient is matched and adjusted, and the second-order frequency-temperature coefficient is synergistically corrected, so that the deviation between the formed third-order frequency-temperature curve and the target third-order frequency-temperature curve is within a preset tolerance range.

2. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 1, characterized in that, The target third frequency-temperature curve is set in the following manner: Determine the operating temperature range, frequency drift index, and operating frequency range of the micromechanical resonator; Set target control information; wherein, the target control information includes at least one of the target position of temperature inflection point and the target position of central symmetry point, wherein the temperature inflection point is the temperature point corresponding to the first derivative of the cubic frequency-temperature curve being equal to zero, and the central symmetry point is the temperature point corresponding to the second derivative of the cubic frequency-temperature curve being equal to zero. The target cubic frequency-temperature curve is determined based on the operating temperature range, the frequency drift index, the operating frequency range, and the target control information.

3. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 1, characterized in that, The initial target range for adjusting the second-order frequency-temperature coefficient is a preset numerical range in which the absolute value approaches 0.

4. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 1, characterized in that, A material parameter temperature model and a parameterized structural model corresponding to the micromechanical resonator are established. After selecting the doping type of the micromechanical resonator, the second-order frequency-temperature coefficient corresponding to different doping concentrations is calculated based on the material parameter temperature model and the parameterized structural model. The material parameter temperature model is a model of how the elastic constants of the structural material in the micromechanical resonator change with temperature and doping concentration. The structural material is N-type heavily doped silicon or P-type heavily doped silicon. The material parameter temperature model includes the first-order and second-order temperature dependence of the elastic constants of silicon material. The material parameter temperature model can be used to predict the changing trends of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient of the micromechanical resonator with doping concentration. The parameterized structural model includes mandatory parameters and optional parameters. The mandatory parameters include doping concentration and structural geometry parameters. The optional parameters include some or all of the structural material layer ratio parameters, crystal orientation angle parameters, and mechanical coupling structural parameters.

5. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 4, characterized in that, Adjusting the design parameters of a micromechanical resonator includes adjusting some or all of the structural geometric parameters, mechanical coupling structural parameters, crystal orientation angle parameters, and structural material layer ratio parameters.

6. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 5, characterized in that, The resonant oscillator of the micromechanical resonator is a single continuous structure, and the resonant oscillator has a closed standard geometric profile or an irregular profile in the plane; the structural geometric parameters include the in-plane dimensions and thickness of the resonant oscillator; when the resonant oscillator has an irregular profile, the irregular profile exhibits a non-constant radial dimension distribution along the circumference, and the in-plane dimensions include the radial dimensions, local width, or local curvature of the resonant oscillator at different positions in the circumference. By adjusting the geometric parameters of the structure, the equivalent stiffness distribution of the resonant oscillator in different crystal orientations can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

7. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 5, characterized in that, The micromechanical resonator is formed by connecting at least two resonant units through a coupling block; the mechanical coupling structure parameters include the structural form and working mode of the resonant unit; the structural form is any one or more combinations of rectangular plate, fixed beam, disk, and ring; the working mode is any one or more combinations of volume mode, shear mode, and bending mode. By adjusting the parameters of the mechanical coupling structure, the participation ratio of different working modes can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

8. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 5, characterized in that, The crystal orientation angle parameter is the orientation angle of the main vibration direction of the micromechanical resonator relative to the crystal coordinate axis; By adjusting the crystal orientation angle parameter, the contribution weight of different elastic constants and their temperature dependence on the equivalent stiffness of the working mode is changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

9. The method for controlling the frequency-temperature curve of a micromechanical resonator according to claim 5, characterized in that, The micromechanical resonator is any one of the following structures: a combination of a heavily doped silicon structure layer and a compensation material layer; a combination of a heavily doped silicon structure layer, a piezoelectric layer and a top electrode layer; a combination of a bottom electrode layer, a heavily doped silicon structure layer, a piezoelectric layer and a top electrode layer; or a combination of a heavily doped silicon structure layer, a piezoelectric layer, a top electrode layer and a compensation material layer. The structural material layer ratio parameters include the thickness ratio of at least a portion of the material layers selected from the heavily doped silicon structural layer, the compensation material layer, the piezoelectric layer, the top electrode layer, and the bottom electrode layer. By adjusting the proportion parameters of the structural material layers, the contribution weight of different material layers to the frequency-temperature characteristics of the resonator can be changed, thereby achieving the control of the first-order frequency-temperature coefficient and the second-order frequency-temperature coefficient.

10. A micromechanical device, characterized in that, The micromechanical device is a micromechanical resonator or a micromechanical oscillator; the micromechanical oscillator includes the micromechanical resonator and an oscillation holding circuit connected to the micromechanical resonator; the micromechanical resonator has a cubic frequency-temperature curve formed using the frequency-temperature curve control method of the micromechanical resonator as described in any one of claims 1 to 9.

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