Microelectromechanical system with improved compensation of radiation measurement effects

Abstract

The present disclosure relates to a microelectromechanical system with improved compensation of radiation measurement effects. The microelectromechanical system comprises an acceleration transducer generating an acceleration signal, a first resonator and a second resonator arranged in a stack along a first direction and laterally arranged with respect to the acceleration transducer along a second direction, and an electronic circuit. The first resonator and the second resonator generate a first oscillation signal and a second oscillation signal representing a first resonance frequency and a second resonance frequency, the first resonance frequency and the second resonance frequency depending on a temperature of the first resonator and the second resonator. The electronic circuit determines an uncompensated value of the acceleration based on the acceleration signal, determines a current value of the first resonance frequency and the second resonance frequency based on the first oscillation signal and the second oscillation signal, determines an estimate of an offset of the acceleration signal caused by a temperature gradient along the first direction based on the current value, and determines a compensated value of the acceleration based on the uncompensated value and the offset estimate.

Description

Priority requirements

[0001] This application claims priority to Italian Patent Application No. 102025000006609, filed on March 28, 2025, the contents of which are incorporated herein by reference in their entirety to the fullest extent permitted by law. Technical Field

[0002] This invention relates to a microelectromechanical system (MEMS) that exhibits improved compensation for the radiometric effect. Background Technology

[0003] In the field of microelectromechanical sensors, it is known that a temperature gradient along the so-called out-of-plane direction of the sensor can cause a shift that negatively affects the sensor's sensing capability. This shift is caused by a so-called radiometric effect, which occurs on the sensor's movable block when it is subjected to an out-of-plane temperature gradient.

[0004] For example only, Figure 1A An accelerometer 1 is shown, which includes a movable block 2 suspended above a substrate 4 having a planar shape parallel to the XY plane by an insertion of a support structure 6. The support structure 6 allows the movable block 2 to rotate about an H-axis parallel to the XY plane, functioning as an acceleration received by the accelerometer 1 along a Z-axis perpendicular to the XY plane.

[0005] In particular, the movable block 2 has an asymmetrical shape relative to the H-axis, such that the acceleration along the Z-axis is converted into the rotation angle of the movable block 2, which is capacitively sensed using electrodes C1 and C2 arranged on the substrate 4, and forms a corresponding variable capacitor with the corresponding portion of the movable block 2 covering the electrodes C1 and C2.

[0006] More specifically, the movable block 2 is formed by the top surface S at the top and bottom. top and bottom surface S bottom Delineation, top surface S top and bottom surface S bottom It is roughly flat and in a static state, i.e., without acceleration along the Z-axis and at the top surface S. top and bottom surface S bottom In the absence of a thermal gradient, they are arranged parallel to the XY plane, such as... Figure 1A As shown. In fact, the top surface S top and bottom surface S bottomRepresents the two opposite sides of movable block 2. On the top surface S... top and bottom surface S bottom Even without acceleration along the Z-axis, when there is a temperature difference, the movable block 2 will rotate relative to its stationary position due to the radiation force acting on it. Figure 1B As shown; this generates an unwanted offset in the signal generated by the accelerometer 1, and thus generates an error in the acceleration measurement.

[0007] Nevertheless, various solutions have been proposed to minimize the offset caused by radiative forces in microelectromechanical sensors, particularly accelerometers. For example, some of these solutions envision using a perforated movable block with regions of varying thicknesses, but symmetrical about the axis of rotation in a top view, to maintain asymmetry that allows acceleration to be converted into rotation of the movable block, while simultaneously making the shape of the movable block symmetrical with respect to its interaction with gas molecules present in the sensor (an interaction that is a function of the number and size of the perforations), in order to balance the radiative forces acting on the movable block. However, this solution has been shown to be affected by non-negligible residual radiation measurement effects.

[0008] U.S. Patent Application Publication No. 2022 / 0057423 (in its entirety incorporated herein by reference) describes a sensor system including a sensor comprising processing circuitry and an accelerometer. The processing circuitry is configured to sense one or more temperature-dependent variables and / or characteristics of the sensor and, by means of these temperature-dependent variables and / or characteristics, correct for offsets in the accelerometer signal caused by temperature gradients. However, the improvement in accelerometer performance achievable through this solution is limited by the fact that the sensor temperature represents a relatively coarse approximation of the actual temperature gradient experienced by the movable block of the accelerometer. As stated above, this temperature gradient is the actual cause of the radiative force acting on the movable block; therefore, the offset correction is relatively approximate and may be insufficient for some applications.

[0009] It is necessary to overcome, at least partially, the shortcomings of existing technologies. Summary of the Invention

[0010] A microelectromechanical system (MEMS) is provided that can compensate for radiation measurement effects affecting acceleration measurements. The system includes: an acceleration transducer configured to generate an acceleration signal; a first resonator and a second resonator stacked along a first direction and laterally arranged relative to the acceleration transducer along a second direction; and electronic circuitry operatively coupled to the acceleration transducer and the resonators.

[0011] The first and second resonators generate respective oscillation signals representing their respective resonant frequencies, each frequency depending on the temperature of the first and second resonators. Electronic circuitry determines an uncompensated acceleration value based on the acceleration signals and determines the current values ​​of the first and second resonant frequencies based on the oscillation signals. Based on the current resonant frequency values, the electronic circuitry determines a offset estimate indicating a radiation measurement offset caused by a temperature gradient acting on the accelerometer along a first direction. The compensated acceleration value is then determined by correcting the uncompensated acceleration value using the offset estimate.

[0012] In some implementations, the electronic circuitry stores coefficients indicating a linear relationship between the offset estimate and a frequency quantity derived from the ratio between a first resonant frequency and a second resonant frequency. The frequency quantity can be defined as the difference between the ratio of the current resonant frequency measured at a reference temperature and the ratio of a reference resonant frequency. The coefficients can be determined during the calibration step and stored in non-volatile memory.

[0013] In some implementations, a first resonator, a second resonator, and an accelerometer are formed above a semiconductor body and arranged within a cavity defined by the semiconductor body and a cover, such that the resonators and accelerometer are exposed to the same pressure. The first resonator may be arranged above the second resonator, and the electronic circuitry may include a temperature sensor configured to generate an estimate of the temperature of the second resonator, wherein the offset estimate is further determined based on the estimated temperature.

[0014] The accelerometer and resonator may extend along a first direction between a first height and a second height, and the acceleration signal may indicate acceleration oriented along the first direction. Each resonator may include a movable structure having a curved arm suspended above a substrate structure and capacitively coupled to an electrode structure configured to excite and sense oscillating motion.

[0015] The disclosed system and method can compensate for radiation measurement offsets without directly measuring the temperatures on opposite sides of a movable block of an accelerometer. The use of spatially separated resonators allows for estimation of the temperature gradient acting on the accelerometer based on resonant frequency information, thereby improving measurement accuracy while reducing system complexity. Attached Figure Description

[0016] For better understanding, preferred embodiments are presented by way of non-limiting example with reference to the accompanying drawings, wherein:

[0017] Figure 1A and Figure 1B A cross-section of a portion of a microelectromechanical sensor under two different operating conditions is schematically shown;

[0018] Figure 2 A cross-section of the MEMS system disclosed herein is schematically shown;

[0019] Figure 3 A schematic top view of a MEMS resonator is shown; and

[0020] Figure 4 A block diagram illustrating the operations performed by the MEMS system disclosed herein is shown. Detailed Implementation

[0021] Figure 2 The MEMS system 10 is shown, which includes a first semiconductor die and second semiconductor dies 12, 14, a substrate 15, a cap 16 and a package region 18.

[0022] The substrate 15 is formed of a dielectric material (e.g., FR4) and extends parallel to the XY plane; conductive traces and contacts (not shown) may extend within the substrate 15. A second semiconductor die 14 is disposed above the substrate 15, for example, by inserting a first bonding region B1. Electronic circuitry 20 is formed within the second semiconductor die 14; the electronic circuitry 20 is, for example, an ASIC and includes a non-volatile memory 31 and a temperature sensor 32.

[0023] The first semiconductor die 12 is positioned above the second semiconductor die 14.

[0024] Specifically, the first semiconductor die 12 includes a semiconductor body 22, which is disposed above the second semiconductor die 14, for example, by inserting into the second bonding region B2. The semiconductor body 22 has a front surface S parallel to the XY plane at its top. top 22 defines the space; in addition, cavity 99 extends within semiconductor body 22, cavity 99 opening at the top and laterally defined by semiconductor body 22 at the bottom.

[0025] A first semiconductor die 12 forms a first MEMS resonator and second MEMS resonators 24, 26, and a MEMS-type accelerometer transducer 28. The first MEMS resonator 24, second MEMS resonator 26, and accelerometer transducer 28 are arranged in a cavity 99 and electrically coupled to electronic circuitry 20. Without loss of generality, the accelerometer transducer 28 may, for example, be connected to… Figure 1A and Figure 1B The accelerometer transducer shown is the same as 1.

[0026] More specifically, the first MEMS resonator and the second MEMS resonators 24 and 26 are stacked vertically, i.e., parallel to the Z-axis. Specifically, the first MEMS resonator 24 covers the second MEMS resonator 26, which in turn covers a corresponding portion of the semiconductor body 22, the corresponding portion of which defines a cavity 99 at the bottom. Furthermore, along the Y-axis, the entire assembly formed by the first MEMS resonator 24 and the second MEMS resonator 26 is arranged on one side of the accelerometer 28, which covers a corresponding portion of the semiconductor body 22, the corresponding portion of which defines a cavity 99 at the bottom. Due to the insertion of the trench 29 extending parallel to the X-axis, the entire assembly formed by the first MEMS resonator and the second MEMS resonators 24 and 26 is separated from the accelerometer 28.

[0027] Without loss of generality, the accelerometer 28 extends between a first height and a second height h1, h2; furthermore, the integral formed by the first MEMS resonator and the second MEMS resonators 24, 26 also extends between the first height and the second height h1, h2. Therefore, the integral formed by the first MEMS resonator 24 and the second MEMS resonator 26 has the same thickness along the Z-axis as the accelerometer 28. This is merely an example, and therefore without loss of generality, in Figure 2 In the middle, the first height and the second height h1 and h2 are respectively the front surface S of the semiconductor body 22 top The height of the bottom extension of 22 and cavity 99.

[0028] In fact, the first semiconductor die 12 can be formed from the first semiconductor wafer (not shown) using the corresponding manufacturing process, and the second semiconductor die 14 can be formed from the second semiconductor wafer (not shown).

[0029] The cap 16 is formed, for example, of a semiconductor material and can be formed, for example, starting from a third semiconductor wafer (not shown). Furthermore, the cap 16 is coupled to the front surface S of the semiconductor body 22, for example, by inserting a coupling region 98 formed, for example, of a glass frit or metal alloy. top twenty two.

[0030] Specifically, the cap 16 covers the first MEMS resonator 24 and the accelerometer 28. Air may be present between the cap 16 and the first MEMS resonator 24 and the accelerometer 28, as well as within the trench 29.

[0031] The encapsulation region 18 is formed of resin, for example, and extends to cover the cap 16 and to laterally coat the group formed by the first semiconductor die and the second semiconductor dies 12, 14, the cap 16, and the coupling region 98, until the encapsulation region 18 contacts the substrate 15 at the bottom to cooperate with the substrate 15 to seal the group.

[0032] In practice, the cap 16, coupling region 98, and semiconductor body 22 define a chamber 30, which includes a cavity 99, and the first MEMS resonator and the second MEMS resonators 24, 26 and the accelerometer 28 are arranged within this chamber 30. In this way, the first MEMS resonator 24, the second MEMS resonator 26, and the accelerometer 28 are subjected to the same pressure.

[0033] More specifically, the first MEMS resonator 24 and the second MEMS resonator 26 may each include a movable block (not shown) configured to oscillate according to a respective driving mode; specifically, the driving modes of the first MEMS resonator and the second MEMS resonator 24, 26 have a first resonant frequency and a second resonant frequency f1, f2, respectively. Furthermore, in a manner known per se, the electronic circuit 20 implements a closed-loop control circuit (not shown) configured such that the movable blocks of the first MEMS resonator and the second MEMS resonator 24, 26 oscillate at frequencies equal to the first resonant frequency and the second resonant frequency f1, f2, respectively, which depend on temperature.

[0034] Alternatively, and again by way of example only, the first MEMS resonator and the second MEMS resonators 24, 26 may be of the same type as any embodiment described in European patent application EP 18172940.1, filed May 17, 2018 and published as EP 3407492A1, and in the corresponding U.S. Patent No. 10,501,310B2 (incorporated herein by reference). In this case, as Figure 3 As shown, it is used as an example involving the first MEMS resonator 24 (the same considerations also apply to the second MEMS resonator 26), and the following description applies.

[0035] The first MEMS resonator 24 includes a corresponding substrate 213 and a movable structure 212 suspended above the substrate 213. The movable structure 212 has a main extension in a plane parallel to the XY plane and includes a first curved arm and second curved arms 212a and 212b, which are parallel to each other and have an elongated shape parallel to the Y-axis. The first curved arms and second curved arms 212a and 212b are connected at their respective ends by a first lateral connecting element and a second lateral connecting element 214a and 214b, which have an elongated shape parallel to the X-axis, thereby internally defining a window 215. The first MEMS resonator 24 also includes a first electrode structure 220 and a second electrode structure 221. The first electrode structure 220 is disposed outside the window 215 and capacitively coupled to the movable structure 212, and the second electrode structure 221 is disposed inside the window 215 and capacitively coupled to the movable structure 212. One of the first electrode structure and the second electrode structure 220, 221 has the function of causing the first curved arm and the second curved arm 212a, 212b to oscillate in opposite directions parallel to the X-axis, while the other of the first electrode structure and the second electrode structure 220, 221 has the function of sensing the oscillation.

[0036] Specifically, the first electrode structure 220 includes a first external electrode and second external electrodes 220a and 220b, which are arranged externally relative to the movable structure 212 and the window 215, respectively facing and parallel to the first and second curved arms 212a and 212b. The second electrode structure 221 includes a first internal electrode and second internal electrodes 221a and 221b arranged inside the window 215, respectively facing and parallel to the first and second curved arms 212a and 212b. Furthermore, in Figure 3 In the middle, the anchoring elements of the external electrodes 220a, 220b and the internal electrodes 221a, 221b are indicated by 220a', 220b' and 221', 221b', respectively.

[0037] Refer again Figure 3 The first and second curved arms 212a and 212b oscillate according to the oscillation mode of the first MEMS resonator 24. Furthermore, in the same case, electronic circuitry 20 implements a closed-loop control circuit (not shown) coupled to the first and second electrode structures 220 and 221, and is configured such that the first and second curved arms 212a and 212b oscillate at a frequency equal to a first resonant frequency f1, which is the resonant frequency of the oscillation mode of the first MEMS resonator 24 and depends on temperature.

[0038] Refer again Figure 3 The first MEMS resonator 24 also includes a suspension structure 216 that holds the movable structure 212 suspended above the substrate 213. The suspension structure 216 includes a suspension arm 217 and an anchoring structure 218. The suspension arm 217 extends within a window 215 between the first and second lateral connecting elements 214a, 214b. The anchoring structure 218 is coupled to the suspension arm 217 and the substrate 213 and is positioned centrally within the window 215, close to the second electrode structure 221. The anchoring structure 218 includes, for example, a first anchor, a second anchor, a third anchor, and a fourth anchor 218a-218d, formed, for example, by various cylindrical elements extending downwards from the Z-axis parallel to the substrate 213. The suspension structure 216 also includes a first connecting element and second connecting elements 219a, 219b. The first connecting element 219a connects the first anchor and the third anchors 218a and 218c to the central portion of the suspension arm 217, and the second connecting element 219b connects the second anchor and the fourth anchors 218b and 218d to the central portion of the suspension arm 217.

[0039] In fact, regardless of the specific implementation of the first MEMS resonator and the second MEMS resonators 24 and 26, Figure 4 The operations shown and described below all occur in MEMS system 10.

[0040] In use, the first MEMS resonator 24, the second MEMS resonator 26, and the accelerometer 28 generate (box 300) a first oscillation signal s1(t), a second oscillation signal s2(t), and an acceleration signal a(t), respectively. The acceleration signal indicates, for example, acceleration parallel to the Z-axis direction experienced by the MEMS system 10. The first oscillation signal and the second oscillation signals s1(t) and s2(t) represent the first and second resonant frequencies f1 and f2, which are the resonant frequencies of the oscillation modes of the first and second MEMS resonators 24 and 26.

[0041] Based on the first and second oscillation signals s1(t) and s2(t) and the acceleration signal a(t), the electronic circuit 20 determines (box 302) the current values ​​of the first and second resonant frequencies f1 and f2, as well as the aforementioned acceleration value Z. outraw This is referred to below as the original acceleration measurement Z. outraw .

[0042] Nevertheless, the following considerations apply before proceeding to describe the operations performed by the MEMS system 10.

[0043] Assuming the first MEMS resonator and the second MEMS resonators 24 and 26 are located at temperatures T1 and T2 respectively, the correlation between the first resonant frequency and the second resonant frequency f1 and f2 and temperatures T1 and T2 can be interpreted as representing the current values ​​of the first resonant frequency and the second resonant frequency f1 and f2 as f1(T1) and f2(T2) respectively. The following relationships apply:

[0044] f1(T1)=f1(T0)·[1+α·(T1-T0)]

[0045] f2(T2)=f2(T0)·[1+α·(T1-T0)]

[0046] Where f1(T0) and f2(T0) represent the values ​​of the first resonant frequency f1 and the second resonant frequency f2 when both the first MEMS resonator 24 and the second MEMS resonator 26 are at a reference temperature T0, respectively, and where α, in a first-order approximation, is a coefficient assumed to be valid for both the first MEMS resonator 24 and the second MEMS resonator 26. Specifically, the temperature T0 is the temperature applied during the calibration step of the MEMS system 10, and the values ​​f1(T0) and f2(T0) represent the measured values ​​of the first resonant frequency and the second resonant frequency f1, f2 determined by the electronic circuit 20 during the calibration step. The values ​​f1(T0) and f2(T0) can be stored, for example, in the memory 31 of the electronic circuit 20.

[0047] Also refer to the ratio R = f1(T1) / f2(T2) and the quantity ΔR = f1(T1) / f2(T2) - f1(T0) / f2(T0), which indicate the change in ratio R relative to the assumed value during the calibration step, caused by the temperature difference between the first MEMS resonator and the second MEMS resonators 24, 26. Nevertheless, the following equation applies:

[0048] Furthermore, under the first-order approximation, the following assumptions can be made:

[0049] Therefore, the following relationship applies:

[0050] Regarding the accelerometer transducer 28, given the temperature gradient on each movable block, the measured acceleration value Z... outraw The offset caused by the radiation measurement effect is referred to below as offset XLD.

[0051] Due to the arrangement of the first MEMS resonator and the second MEMS resonators 24, 26, under a first-order approximation, it can be assumed that the offset XLD depends linearly on the difference between temperatures T1 and T2, which represents an estimate of the temperature gradient existing on the movable block of the accelerometer 28. Therefore, the following relationship applies:

[0052] Where K is an unknown constant. Furthermore, as explained earlier, since the quantity ΔR depends on the difference between temperature T1 and temperature T2, the following relationship also applies:

[0053] Therefore, since the quantity K / α / [f1(T0) / f2(T0)] is constant, under the first-order approximation, the offset XLD caused by the radiometric measurement effect is proportional to the quantity ΔR, that is, the following occurs:

[0054] Where K' = K / α / [f1(T0) / f2(T0)].

[0055] Nevertheless, the electronic circuit 20 stores the value of K' in the memory 31; in particular, the value of K' can be initially determined in the characterization step of the MEMS system 10, wherein the temperature of the first MEMS resonator and the second MEMS resonators 24, 26 is applied, and thus the amount ΔR is applied indirectly.

[0056] Refer again Figure 4 Electronic circuit 20 calculates (box 304) the quantity ΔR. Specifically, at any given time, electronic circuit 20 can calculate the corresponding value of quantity ΔR based on the stored values ​​f1(T0) and f2(T0) and based on the current values ​​f1(T1) and f2(T2) of the first resonant frequency and the second resonant frequency f1 and f2.

[0057] Furthermore, electronic circuit 20 calculates (box 306) the offset XLD based on the stored value K' and the quantity ΔR. Additionally, electronic circuit 20 determines (box 308) the compensated acceleration measurement Z. outcomp ,equal:

[0058] Z outcomp =Z outraw -XLD

[0059] Compensated acceleration measurement Z outcomp The measured value of acceleration is represented, where the undesirable offset caused by the radiation measurement effect generated by the temperature gradient present in the accelerometer 28 has been eliminated under the first-order approximation.

[0060] Therefore, the advantages offered by this MEMS system are clear from the preceding description. In particular, the MEMS system enables acceleration measurement, under a first-order approximation, unaffected by undesirable offsets caused by radiation measurement effects, without requiring the measurement of the actual temperature existing on the surface of the movable block of the accelerometer.

[0061] Finally, it is clear that modifications and changes may be made to the content described and shown herein without departing from the scope of this disclosure as defined by the appended claims.

[0062] For example, the resonator and / or accelerometer may differ from the embodiments already described. However, the use of... Figure 3 The type of resonator shown allows for improved quality factor Q and reduced sensitivity of the resonant frequency to mechanical stresses caused by the package.

[0063] The first resonator and the second resonator are Figure 3 In the case of the type shown, the orientations relative to the X and Y axes may differ from the orientations described.

[0064] For example, the first and second resonators can be manufactured using the processes described in European Patent No. 3,912,953B1 and the corresponding U.S. Patent No. 11,945,712, the contents of which are incorporated herein by reference in their entirety.

[0065] The stacked arrangement of the first and second resonators can be achieved through any suitable support structure.

[0066] Accelerometers can sense acceleration along axes other than the Z-axis, although in this case, the estimation of the offset caused by radiation measurement effects may be less accurate.

[0067] The first and second MEMS resonators can also be arranged in a different chamber than the chamber containing the accelerometer. In this case, the first and second MEMS resonators can be subjected to different pressures relative to the accelerometer.

[0068] Finally, at the approximate value α If (T2-T0)=0 is unacceptable, the accuracy of the offset XLD estimation can be further improved by using the following relationship:

[0069] Right now:

[0070] In this case, the electronic circuit 20 calculates the offset XLD not only based on the stored value K' and the amount ΔR, but also based on the coefficient α and temperature T0 known through the calibration step and stored in the memory 31, as well as the temperature T2 estimated by the temperature sensor 32 due to the proximity of the second MEMS resonator 26 to the electronic circuit 20.

Claims

1. A microelectromechanical system, comprising: An accelerometer transducer configured to generate an acceleration signal; A first resonator and a second resonator are stacked along a first direction, and the first resonator and the second resonator are also arranged laterally relative to the accelerometer along a second direction transverse to the first direction. as well as Electronic circuits; The first resonator and the second resonator are configured to generate a first oscillation signal and a second oscillation signal, respectively. The first oscillation signal and the second oscillation signal indicate a first resonant frequency and a second resonant frequency, respectively. The first resonant frequency and the second resonant frequency depend on the temperature of the first resonator and the temperature of the second resonator, respectively. and The electronic circuit described therein is configured as follows: Based on the acceleration signal, determine the uncompensated value of the acceleration experienced by the microelectromechanical system; Based on the first oscillation signal and the second oscillation signal, determine the current value of the first resonant frequency and the current value of the second resonant frequency; Based on the current values ​​of the first resonant frequency and the second resonant frequency, a shift estimate of the acceleration signal caused by the temperature gradient along the first direction present on the acceleration transducer is determined; as well as Based on the uncompensated value and the offset estimate, the compensated value of the acceleration is determined.

2. The microelectromechanical system according to claim 1, wherein the electronic circuit is further configured as follows: The system stores coefficients indicating a linear relationship between the offset estimate and a frequency quantity that is a function of the ratio between the first resonant frequency and the second resonant frequency. Based on the current values ​​of the first resonant frequency and the second resonant frequency, determine the current value of the frequency quantity; as well as The offset estimate is determined based on the coefficients and the current value of the frequency quantity.

3. The microelectromechanical system of claim 2, wherein the frequency quantity is a function of the difference between the following ratios: the ratio between the first resonant frequency and the second resonant frequency, and the ratio between the value of the first resonant frequency at a reference temperature and the value of the second resonant frequency at the reference temperature.

4. The microelectromechanical system according to claim 2, wherein the frequency quantity is proportional to the difference between the temperature of the first resonator and the temperature of the second resonator.

5. The microelectromechanical system of claim 2, wherein the coefficients are determined during the calibration step and the coefficients are stored in the non-volatile memory of the electronic circuit.

6. The microelectromechanical system according to claim 1 further includes a semiconductor body, wherein the first resonator, the second resonator, and the accelerometer are formed above the semiconductor body.

7. The microelectromechanical system of claim 6, further comprising a cap that, together with the semiconductor body, defines a cavity, wherein the first resonator, the second resonator, and the accelerometer are disposed in the cavity.

8. The microelectromechanical system of claim 7, wherein the first resonator, the second resonator, and the accelerometer are exposed to the same pressure within the cavity.

9. The microelectromechanical system of claim 8, wherein the first resonator is arranged above the second resonator, wherein the electronic circuitry includes a temperature sensor configured to generate an estimate of the temperature of the second resonator, and wherein the electronic circuitry is further configured to determine the offset estimate based on the temperature of the second resonator.

10. The microelectromechanical system of claim 6 further includes a semiconductor die disposed beneath the semiconductor body, wherein the electronic circuitry is formed in the semiconductor die.

11. The microelectromechanical system of claim 1, wherein the accelerometer extends along the first direction between a first height and a second height, and wherein the first resonator and the second resonator also extend between the first height and the second height.

12. The microelectromechanical system of claim 1, wherein the acceleration signal indicates the acceleration experienced by the microelectromechanical system along the first direction.

13. The microelectromechanical system of claim 1, wherein each of the first resonator and the second resonator comprises: The corresponding substrate structure; A movable structure comprising a first curved arm and a second curved arm having an elongated shape along a longitudinal axis and coupled at respective ends by a first lateral connecting element and a second lateral connecting element to internally define a window; A first electrode structure is arranged outside the window and capacitively coupled to the movable structure. A second electrode structure is disposed inside the window and capacitively coupled to the movable structure. One of the first electrode structure and the second electrode structure is configured to cause oscillating motion of the first and second bent arms, and the other of the first electrode structure and the second electrode structure is configured to sense the oscillation. as well as A suspension structure configured to suspend the movable structure above the substrate structure, and the suspension structure includes: a suspension arm extending within the window between the first lateral connecting element and the second lateral connecting element; And an anchoring structure coupled to the cantilever arm and the substrate structure, centrally arranged within the window adjacent to the second electrode structure.

14. The microelectromechanical system of claim 1, wherein the offset estimate is determined by assuming a linear relationship between the offset estimate and the temperature difference between the first resonator and the second resonator.

15. The microelectromechanical system of claim 1, wherein the offset estimate is determined without directly measuring the temperature on opposite sides of the movable block of the accelerometer.

16. The microelectromechanical system of claim 1, wherein the first resonator and the second resonator are spaced apart along the first direction such that the temperature difference between the first resonator and the second resonator approximates the temperature gradient across the accelerometer.

17. A method for compensating for radiation measurement offset in a microelectromechanical system, the method comprising: A first oscillation signal is generated by a first resonator, and the first oscillation signal represents a first resonant frequency; A second oscillation signal is generated by second resonators arranged at different positions along the first direction, and the second oscillation signal represents the second resonant frequency; Based on the first oscillation signal and the second oscillation signal, determine the current values ​​of the first resonant frequency and the second resonant frequency; Based on the current values ​​of the first resonant frequency and the second resonant frequency, a offset estimate is determined, the offset estimate indicating a radiation measurement offset affecting an acceleration signal generated by an acceleration transducer arranged adjacent to the first resonator and the second resonator; as well as Compensated acceleration values ​​are generated by correcting the uncompensated acceleration values ​​using the offset estimation.

18. The method of claim 17, wherein determining the offset estimate comprises: The frequency estimate is determined based on the ratio of the first resonant frequency to the second resonant frequency.

19. The method of claim 17, wherein determining the offset estimate comprises: The offset estimate is applied to a linear relationship with the temperature difference between the first and second resonators, the linear relationship being defined by coefficients determined during the calibration step.

20. The method of claim 17, wherein the offset estimate is determined without directly measuring the temperature on opposite sides of the movable block of the accelerometer.

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