MEMS devices with optimized geometry to reduce deflection caused by radiation effects

Abstract

The present disclosure relates to a MEMS device having an optimized geometric structure to reduce deflection caused by radiation effects. The MEMS device having a seesaw structure includes a movable mass having an area in a plane and a thickness in a direction perpendicular to the plane. The movable mass is tiltable about a rotation axis extending parallel to the plane and is formed by a first and a second mass half arranged on opposite sides of the rotation axis. The first and second mass halves respectively have a first and a second centroid, which are arranged at a first distance b1 and a second distance b2 from the rotation axis, respectively. A first through-opening is formed in the first mass half and, together with the first mass half, has a first total circumference p1 in the plane. A second through-opening is formed in the second mass half and, together with the second mass half, has a second total circumference p2 in the plane, wherein the first circumference p1 and the second circumference p2 satisfy the following equation: p1×b1=p2×b2.

Description

Technical Field

[0001] The present disclosure relates to MEMS devices. In particular, the present disclosure relates to MEMS (micro-electromechanical systems) inertial sensors (such as accelerometers or gyroscopes). Background Art

[0002] As is known, the use of MEMS devices of the type described above is increasing in an ever-widening range of technical fields due to their ability to supply accurate signals, their low cost, and their high versatility.

[0003] In particular, inertial sensors of the type described above are increasingly being used in consumer applications and in the automotive sector, for example for indoor navigation and as an aid to autonomous driving. That is, inertial sensors of the type described above are increasingly being used in applications where it is important to have high accuracy and also to provide an output that is as stable as possible when environmental and / or internal parameters vary. In particular, in these applications, it is desirable for the output signal of the device to be stable with respect to temperature, both with respect to external effects that operate in a uniform manner across the entire die in which the device is integrated, and with respect to internal effects that operate differently within the die. In order to take into account external effects, many MEMS devices have arrangements for compensating for signal variations due to external temperature. With respect to internal effects, as discussed below, this issue has only recently been recognized and addressed.

[0004] In general, there are various reasons for the non-uniform temperature distribution within a MEMS device of the type described above. A first reason is related to the high integration density of electronic devices in complex devices; other reasons may be related to accidental circumstances.

[0005] For example, Figure 1 An example case is shown in which a printed circuit board 1 carries two inertial MEMS devices 2, one of which is arranged above and one below the printed circuit board 1, and a processing device (CPU) 3 or an application-specific integrated circuit (ASIC). In some applications, the printed circuit board 1 may carry only one MEMS device or a plurality of MEMS devices or other integrated devices, arranged next to each other and also in a plane extending in front of or behind the sheet plane, on only one side or both sides of the printed circuit board 1, in a manner not shown. In this case, the small distance and the large number of energy dissipating devices on one side of the MEMS device in question or at a short distance on the opposite surface of the printed circuit board 1 may result in a temperature profile that is variable in the horizontal or vertical direction (with reference to the sheet plane).

[0006] Other causes of uneven temperature distribution are related to operational considerations. Indeed, in some cases, such as when turning on the device, rapid temperature changes can lead to uneven distribution within the die, such as Figure 2 As shown in FIG. Here, sensor 5 includes a MEMS device 6, which is carried by a printed circuit board 7, which in turn carries an integrated device 8 (such as an ASIC (Application Specific Integrated Circuit)). In this case, at least under certain operating conditions, a non-constant temperature profile exists in the vertical direction due to the heat generated by the integrated device 7 during its operation. In this case, the MEMS device 6 may have a variable temperature profile, specifically decreasing from a high value on the top surface of the MEMS device 6 to a lower value on the bottom surface of the MEMS device 6.

[0007] It has been demonstrated that a temperature gradient along the Z-axis (out-of-plane direction) in a sensor movable in the Z-axis direction can result in a static deviation in the offset of the output signal representing movement along the Z-axis, whereas the output signals representing movement along the other axes (X and Y) are not affected by this phenomenon. Figure 3 and Figure 4 is a schematic diagram of an inertial sensor with a "seesaw" structure, which shows this situation.

[0008] In detail, Figure 3 and Figure 4 A MEMS accelerometer 10 is shown formed of a movable mass 11 having a top surface 11A and a bottom surface 11B, and suspended above a substrate 12. The movable mass 11 is generally formed of a platform or plate having a main extension in a plane parallel to the plane XY of a Cartesian reference system XYZ when at rest. The movable mass 11 can, for example, have a generally rectangular shape (in top view) and is carried by a post 13 extending from the substrate 12 parallel to the Z axis of the Cartesian reference system XYZ. The post 13 is coupled to the movable mass 11 via a hinge and a spring (not shown), thereby allowing the movable mass 11 to rotate about an axis of rotation O, which extends through the movable mass 11 parallel to the Y axis.

[0009] In particular, in these devices, the rotation axis O is eccentric and spaced apart from the centroid (not shown) of the movable mass 11, and the rotation axis O divides the movable mass 11 into a first mass half 14A and a second mass half 14B, which are arranged on opposite sides relative to the rotation axis O. The first mass half 14A and the second mass half 14B have different sizes, and therefore the corresponding centroids (not shown) are located at different distances from the rotation axis O. In the example shown, the first mass half 14A has a smaller size than the second mass half 14B.

[0010] The first electrode 16A and the second electrode 16B are arranged below the first and second mass halves 14A, 14B (facing the bottom surface 11B of the movable mass 11). Specifically, the first and second electrodes 16A, 16B face the first and second mass halves 14A, 14B, respectively, and form a first and second capacitive element 17A, 17B with the first and second mass halves 14A, 14B, respectively. The first and second capacitive elements 17A, 17B have capacitances C1 and C2, respectively.

[0011] Figure 3 The ideal situation is shown, in which no forces (internal or external) act on the movable mass 11. In this case, as described above, the movable mass 11 is in a rest position, and its main extension plane is parallel to the plane XY. In this case, the first and second mass halves 14A, 14B are arranged at the same distance from the respective electrodes 16A, 16B, and the capacitive elements 17A, 17B have a capacitance C10 = C20. A processing circuit (not shown) connected to the capacitive elements 17A, 17B is capable of converting the difference between the capacitances C1 and C2 into a voltage output signal. In the absence of acceleration, the output of this circuit is zero.

[0012] exist Figure 4 In FIG. 1 , the heat source 21 is arranged above the movable mass 11 , facing the top surface 11A, and the cold source 22 is arranged below the movable mass 11 , facing the bottom surface 11B.

[0013] Sources 21 and 22 generate a temperature gradient within movable mass 11 in a direction parallel to the Z-axis. In this case, even without an external force applied, movable mass 11 rotates (here, in a clockwise direction, arrow 25). As a result, capacitive elements 17A and 17B have different capacitances (i.e., C2 > C1), and the output signal becomes non-zero.

[0014] The rotation of the movable mass 11 following the internal temperature gradient is caused by radiation effects. These effects, discovered in 1873 by William Crookes and exploited in the Crookes radiometer (also known as the "light windmill"), are related to the effects exerted by gas molecules acting in different ways on opposing surfaces heated at different temperatures. In particular, according to Einstein's radiation theory, the radiation force depends on the mean free path λ of the gas molecules in which the considered body (MEMS device 10) is immersed; the mean free path, in turn, depends on the gas density and the molecular cross-section. Moreover, the radiation force depends on the value and direction of the temperature gradient and, for a plate-shaped structure with a cavity, follows the law:

[0015]

[0016] in:

[0017] F 2p is the force acting on the structure;

[0018] P0 is the standard pressure (1 bar);

[0019] P c is the pressure in the cavity;

[0020] λ is the pressure P c The mean free path of gas molecules at

[0021] λ0 is the mean free path of gas molecules at pressure P0;

[0022] T0 is the standard temperature (25°C);

[0023] L is the circumference of the cavity; and

[0024] is the temperature profile of the entire structure.

[0025] Assuming that the temperature variation depends only on the space and due to the small thickness of the plate-shaped structure, we obtain:

[0026]

[0027] Among them, T h is the temperature of the thermal surface of the structure, T h is the temperature of the cold surface of the structure, and t p is the thickness of the structure.

[0028] Therefore, equation (1) becomes:

[0029]

[0030] The problem of radiation forces acting on the movable mass (with a flat shape) of a MEMS device has not been well addressed so far. Solutions are described in the papers by J. Classen et al., “ADVANCED SURFACE MICROMACHINING PROCESS–AFIRST STEP TOWARDS 3D MEMS”, MEMS 2017, Las Vegas, NV, USA, January 22-26, 2017, IEEE, 978-1-5090-5078-9 / 17, and C. Nagel et al., “Radiometric effects in MEMS Accelerometers”, IEEE, 978-1-5090-1012-7 / 17, which describe accelerometers with a symmetrical structure (in Figures 5 to 7 ), the accelerometer is configured to detect forces acting in the Z direction (out of the plane of the movable platform).

[0031] In detail, the accelerometer described in the above paper ( Figures 5 to 7 30) has a movable mass 31 of rectangular shape, which is hinged to a column 33 in the middle position, in particular Figure 6 As can be seen from the top view of the rectangle, the rotation axis is designated as O1 and extends parallel to the short side of the rectangle, equidistant from the short side. The movable mass 31 is formed by a platform of semiconductor material, which includes two half-masses 32A and 32B with a plurality of through holes 34. In particular, as Figure 6 As can be seen in FIG. 3 , in a plane parallel to the plane XY of the Cartesian reference system XYZ, the through holes 34 have the same area, and the through holes 34 are arranged symmetrically with respect to the rotation axis O1 .

[0032] As can be noted, in particular, Figure 7 In the cross section, each half-mass 32A, 32B includes: a first portion 35A, 35B adjacent to the rotation axis O1, and a second portion 36A, 36B arranged farther away from the rotation axis O1, and the second portion 36A, 36B serves as an extension of the corresponding first portion 35A, 35B.

[0033] The first portions 35A, 35B are identical to one another and in particular have the same area in a plane parallel to the plane XY (e.g. Figure 6 ), and have the same thickness along the Z axis (as Figure 7 It can be noticed that Figure 7shows a cross-sectional view of a plane XY parallel to the Cartesian reference system XYZ). The second parts 36A, 36B have the same area but different thicknesses along the Z axis: the second part 36A of the first half mass 32A (at Figures 5 to 7 The thickness of the second half mass 32B is less than that of the second portion 36B (on the left side) of the second half mass 32B. Figures 5 to 7 In particular, in the example shown, the second portion 36A of the first mass half 32A has the same thickness as the first portions 35A, 35B, and the second portion 36B of the second mass half 32B has a greater thickness.

[0034] The substrate 44 , the top electrodes 40A, 40B (carried by the movable mass 31 ), and the bottom electrodes 41A, 42B (carried by the substrate 44 ), and the cover 43 together complete the structure of the accelerometer 30 .

[0035] Figure 7 The forces acting on the half-masses 32A and 32B are shown as hot air molecules move from bottom to top (as indicated by arrows 46, dark grey in the hotter area at the top, and light grey in the cooler area at the bottom) in the presence of a temperature gradient within the movable mass 31.

[0036] In this case, assuming that the thickness of the portions 35A, 35B, 36A (and hence 36B) of the two half-masses 32A, 32B is greater than the mean free path λ of the gas molecules, the first and second radiation forces F1, F2 ( Figure 7 ) acts on first and second mass halves 32A, 32B, and due to the different thicknesses of the two mass halves 32A, 32B, the first and second radiation forces differ from each other. Since the two mass halves 32A, 32B have centroids located at the same distance from the rotation axis O1 and thus have the same application arm for forces F1, F2, it can be demonstrated that the ratio between the moments acting on the mass halves 32A, 32B is inversely proportional to the ratio of their respective thicknesses and therefore differs from 1.

[0037] Therefore, in the example considered (where the temperature of the top surface of the movable mass 31 is higher than the temperature on the bottom surface), different moments act on the two half-masses 32A, 32B and cause the movable mass 31 to rotate in the clockwise direction.

[0038] Thus, also with this known structure, radiation effects generate a non-negligible torsional moment, which leads to an offset deviation in the output signal of the accelerometer. Summary of the Invention

[0039] One or more embodiments of the present disclosure relate to MEMS devices having an optimized geometry for reducing deflections caused by radiation effects. In one embodiment, the present disclosure relates to a MEMS (micro-electromechanical system) inertial sensor (such as an accelerometer or gyroscope) having a so-called "seesaw" structure, in which a suspended mass is tiltable about a horizontal rotation axis that belongs to the plane of extension of the suspended mass and extends through the suspended mass, so that two parts of the suspended mass arranged on opposite sides of the rotation axis move transversely to the plane of extension and in opposite directions (so-called out-of-plane movement or Z movement). BRIEF DESCRIPTION OF THE DRAWINGS

[0040] For a better understanding of the present disclosure, embodiments of the present disclosure will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

[0041] Figure 1 is a schematic diagram of a system including a plurality of MEMS sensors and corresponding electronic units on a printed circuit board;

[0042] Figure 2 is a schematic diagram of another MEMS sensor having a different arrangement of the sensor and the electronic unit;

[0043] Figure 3 is a schematic side view of a "seesaw" type MEMS sensor in a static condition and without stress;

[0044] Figure 4 is a schematic side view of a "seesaw" type MEMS sensor in the presence of stress due to radiation effects;

[0045] Figure 5 is a simplified perspective view of a known accelerometer;

[0046] Figure 6 yes Figure 5 A top view of the accelerometer;

[0047] Figure 7 It is along Figure 6 A schematic longitudinal section taken along the cross-sectional plane VII-VII of FIG. 1 , which illustrates the forces caused by the radiation effect;

[0048] Figure 8 is a schematic top view of a movable mass layout according to one embodiment of the present apparatus;

[0049] Figure 9 This device is along Figure 8 A schematic longitudinal section taken along a cross-sectional plane IX-IX;

[0050] Figure 10is a top view of a possible embodiment of the device;

[0051] Figure 11A and 11B Shown in known devices and Figure 10 the results of measurements performed on the equipment; and

[0052] Figure 12 Shown is an overall block diagram of an electronic device including the present device. DETAILED DESCRIPTION

[0053] Figure 8 and Figure 9 is a schematic diagram of a sensor 50 of the inertial type having a so-called “seesaw” structure.

[0054] In detail, the sensor 50 includes a movable mass 51, which is suspended on a substrate 52 ( Figure 9 ), the column 53 extends from the base plate 52 parallel to the Z axis of the Cartesian reference system XYZ. The column 53 is coupled to the movable mass 51 by a hinge and a spring (not shown), which enables the movable mass 51 to tilt around the rotation axis A.

[0055] The movable mass 51 has a characteristic mass (here, length in the X direction) that is much larger than its thickness, for example, ten times larger. In particular, at rest, the movable mass 51 has main surfaces (top surface 51A and bottom surface 51B) extending in a plane parallel to the plane XY of the Cartesian reference system XYZ, and a thickness t extending parallel to the Z axis. p .like Figure 9 As can be seen in the figure, the thickness t of the movable mass block 51 is p is uniform over its entire area. In the example shown, the movable mass 51 has a generally rectangular shape (in a top view) with sides parallel to the X-axis and the Y-axis, and the rotation axis A (which extends parallel to the Y-axis) is eccentric relative to the rectangular shape of the movable mass 51. The rotation axis A thus divides the movable mass 51 into a first mass half 54 and a second mass half 55, which are arranged on opposite sides relative to the rotation axis A and have different areas. Thus, as Figure 9 As shown, the first half mass 54 and the second half mass 55 each have their own centroids B1 and B2, which are respectively arranged at a first distance b1 and a second distance b2 from the rotation axis A, the first distance and the second distance being different from each other. Figure 8 and Figure 9 In the device 50 shown, b1 < b2.

[0056] The first electrode 56 and the second electrode 57 are arranged in front of the bottom surface 51B, facing the first and second mass-half 54 and 55 , respectively, and form a first and second capacitive elements 58 and 59 with the first and second mass-half 54 and 55 , respectively.

[0057] The mass halves 54 , 55 are perforated in a non-uniform manner; in particular, the first mass half 54 has first holes 60 and the second mass half 55 has second holes 61 .

[0058] The first and second holes 60, 61 are provided in a plurality and have dimensions so as to (together with the corresponding half-masses 54, 55) globally define a first perimeter p1 and a second perimeter p2, which are different from each other, wherein p1>p2, and so as to satisfy the following equation:

[0059] p1×b1=p2×b2 (3)

[0060] In particular, in the above equation (3), the first perimeter p1 is given by the sum of all perimeters of the first hole 60 and the outer perimeter of the half mass 54, and similarly, the second perimeter p2 is given by the sum of all perimeters of the second hole 61 and the outer perimeter of the half mass 55.

[0061] exist Figure 8 In

[0045] , this is represented by forming the first holes 60, which are different in number from the second holes 61 and have a rectangular shape with a short side of length W1 and a long side of length L1, while the second holes 61 have a square shape with sides L2>L1. However, the number, shape, and arrangement of the holes 61, 62 are infinite, and the only condition to be satisfied is equation (3) to minimize drift due to radiation effects.

[0062] For example, the second hole 61 may also have a rectangular shape having a short side of length W2 and a long side of length L2. Therefore, generally, and assuming that both the first hole 60 and the second hole 61 have rectangular shapes, equation (3) becomes:

[0063] N1(W1 L1)b1=N2(W2 L2)b2 (3.1)

[0064] Here, N1 is the number of first holes 60 , and N2 is the number of second holes 61 .

[0065] In this case, equation (2) becomes (the quantities are indexed by 1 or 2, depending on whether they refer to the first mass 54 or the second mass 55; or have no index if the quantity is the same for both masses):

[0066]

[0067]

[0068] Furthermore, the moments M1 and M2 acting on the first mass 54 and the second mass 55 are respectively given by:

[0069] M1=F1 b1 (4.1)

[0070] M2=F2 b2 (4.2)

[0071] Combining equations (2.1), (2.2), (4.1) and (4.2), and considering equation (3), we obtain:

[0072]

[0073] Therefore, equal moments M1 and M2 act on the first mass 54 and the second mass 55, respectively, and compensate for each other. As a result, using the indicated geometric conditions, the radiation force acts on the movable mass 51, but does not cause the movable mass 51 to rotate and thus does not generate an offset signal.

[0074] exist Figure 10 An embodiment of an accelerometer is shown in FIG, which satisfies the above conditions (3) or (3.1) and thus has compensated radiation effects, in Figure 10 For simplicity, Figure 8 and Figure 9 Those parts of the sensor 50 that are equivalent are designated by reference numerals increased by 100 and are therefore not described again in detail.

[0075] In particular, Figure 10 The accelerometer 150 comprises a suspended mass 151 (only half of the structure is shown; the entire structure of the suspended mass 151 can be Figure 10 The structure shown in FIG is flipped around the horizontal axis B).

[0076] The suspended mass 151 has a first mass half 154 and a second mass half 155 which are carried by a plurality of columns 153 (four columns 153 in the embodiment shown, two of which are visible). Figure 10, a spring 170 connects the column 153 to the two half-masses 154, 155 (obviously, a similar spring, not shown, is provided in the movable half-mass 151, not shown). In the embodiment shown, the spring 170 has a broken line structure having a pair of first portions 170A extending from and around the respective columns 153, a single central portion 170B that is an extension of the first portions and extends along the rotation axis A, and two diverging portions 170C that extend from the central portion 170B toward the respective half-masses 154, 155, perpendicular to the rotation axis A. However, the shape of the spring 170 may vary and is not part of the present patent application.

[0077] According to the above, each half-mass 154 , 155 has a plurality of openings that are asymmetric about the rotation axis A, and the number and size of the openings satisfy the relationship of the above-mentioned equation (3) or equation (3.1).

[0078] In the embodiment shown, the half-mass 154 having the smaller area has a damping opening 175 that accommodates a plurality of damping structures 176 ( Figure 10 Two of them are shown in FIG), which are not part of this patent application.

[0079] Furthermore, in the embodiment shown, the first mass half 154 has a delimiting side 177 which is approximately parallel to the axis of rotation A and has a projection 178 which receives a rectangular opening 179 .

[0080] The further openings 180 may extend asymmetrically in the first mass half 154 relative to the second mass half 155 .

[0081] In the accelerometer 150, all through openings (damping opening 175, rectangular opening 179, and other openings 180) are studied so that their circumference, together with the sum of the circumference of the first hole 160, the circumference of the first half mass block 154 and the circumference of half the slot of the spring 170, satisfies the relationship given by equation (3) relative to the sum of the circumference of the second hole 161, the circumference of the second half mass block 155 and the circumference of the other half slot of the spring 170.

[0082] Thus, by simply setting the dimensions at the design stage, the deviation of the output signal due to radiation effects can be greatly reduced or even completely eliminated without additional stress.

[0083] Studies conducted by the applicant have confirmed theoretical results such as Figure 11A and Figure 11B As shown, Figure 11A and Figure 11Brepresents hysteresis measurements performed on a device of similar structure that was initially reheated on one side from -80°C up to about 60°C and then cooled from about 60°C down to -80°C. In particular, Figure 11A shows the acceleration (in mg, where g is the acceleration due to gravity) obtained by a conventional accelerometer having a through-opening which is only relevant for usual geometrical and functional considerations and does not satisfy the above relation (3), and Figure 11B Shown by Figure 10 The results obtained with a device that differs from a conventional accelerometer only in the geometry of the through-opening. It can be noted that in the conventional device ( Figure 11A ), the heating and cooling curves show high hysteresis, while in the device satisfying condition (3) ( Figure 11B ), the heating and cooling curves are almost overlapping, with almost no hysteresis.

[0084] By changing only the first half mass 54 (ie Figure 8 The above results can be obtained by modifying the geometry and perimeter of the openings, holes and through-holes in the second half-mass (of the smaller size); however, in order to satisfy relation (3), it is also possible to modify the through-holes only with respect to the second half-mass 55 (of the larger size). Advantageously, this condition can be achieved without affecting the electromechanical parameters, dimensions and mechanical strength of the movable mass, and therefore without affecting the other performance parameters of the inertial sensor, while improving the behavior with respect to radiation forces.

[0085] Furthermore, the sought-after dimensioning can be achieved without modifying the manufacturing process of the inertial sensor and thus at unchanged manufacturing costs.

[0086] like Figure 12 As shown, the described inertial sensor is particularly suitable for integration into an electronic device 200, which can be used in a variety of electronic systems intended to process, store, transmit and receive signals and information. For example, the electronic device 200 can be, for example, an inertial navigation system, an automotive system, or a portable system such as a PDA (personal digital assistant), a portable computer, a mobile phone, a wearable device (such as a smart watch), a digital audio player, a camera, or a video camera.

[0087] The electronic device 200 may, for example, comprise a sensor 50 (here forming an accelerometer), an electronic circuit 205 (typically an ASIC) and an electronic control unit 220 (e.g. a microprocessor), the electronic circuit 205 being operatively coupled to the sensor 50, forming a reading interface for the sensor 50, supplying a bias signal to the sensor 50 (in a manner known per se, not shown in detail here), detecting the movement of the movable mass 51 ( Figure 8) and thereby determine the acceleration along the Z axis acting on the movable mass 51; the electronic control unit 220 is connected to the electronic circuit 205 and is configured to supervise the general operation of the electronic device 200, for example, based on the detected acceleration. Furthermore, the electronic device 200 may include an input / output interface 240 (e.g., having a keyboard and a display) connected to the electronic control unit 220, a speaker 250 for generating sound on an audio output (not shown), and an internal memory 260. The sensor 50 and the electronic circuit 205 may be packaged in a package structure to form the inertial device 230.

[0088] Finally, it is obvious that modifications and variations may be made to the MEMS device described and illustrated herein without thereby departing from the scope of the present disclosure. In particular, as already mentioned, the arrangement and number of the through-openings may vary greatly with respect to those illustrated, and the shape and arrangement of the movable mass and the envisaged structure may also be any shape and arrangement relevant to the respective function, provided that the openings satisfy the above relation (3).

[0089] Furthermore, the various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above detailed description. Generally, in the appended claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and claims, but should be construed to include all possible embodiments and the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by this disclosure.

Claims

1. A MEMS device comprising: a movable mass having an area in a plane and a thickness in a direction perpendicular to the plane, the movable mass being tiltable about a rotation axis extending parallel to the plane and thereby forming a first mass portion and a second mass portion arranged on opposite sides of the rotation axis, the first mass portion and the second mass portion respectively having a first centroid and a second centroid, the first centroid and the second centroid respectively being arranged at a first distance b1 and a second distance b2 from the rotation axis; a plurality of first through-openings in the first mass portion, wherein the plurality of first through-openings and the first mass portion have a first total perimeter p1 in the plane; as well as a plurality of second through-openings in the second mass part, wherein the plurality of second through-openings and the second mass part have a second total perimeter p2 in the plane, Wherein the first total perimeter p1 and the second total perimeter p2 satisfy the equation: p1×b1=p2×b2; and The movable mass block has a uniform thickness.

2. The MEMS device of claim 1, wherein the MEMS device is at least one of an accelerometer or a gyroscope.

3. The MEMS device of claim 1 , wherein the movable mass forms part of a Z-axis accelerometer. The MEMS device of claim 1 , wherein the movable mass is made of a monolithic semiconductor body. The MEMS device according to claim 1 , wherein a number of the second plurality of through-openings is different from a number of the first plurality of through-openings. The MEMS device according to claim 1 , wherein a shape of the plurality of second through-openings is different from a shape of the plurality of first through-openings.

7. An electronic device comprising: MEMS devices, including: a movable mass having an area in a plane and a thickness in a direction perpendicular to the plane, the movable mass being tiltable about a rotation axis extending parallel to the plane and thereby forming a first mass portion and a second mass portion arranged on opposite sides of the rotation axis, the first mass portion and the second mass portion respectively having a first centroid and a second centroid, the first centroid and the second centroid respectively being arranged at a first distance b1 and a second distance b2 from the rotation axis; a plurality of first through-openings in the first proof-mass portion, wherein the plurality of first through-openings and the first proof-mass portion have a first total perimeter p1 in the plane; and a plurality of second through-openings in the second mass part, wherein the plurality of second through-openings and the second mass part have a second total perimeter p2 in the plane, Wherein the first total perimeter p1 and the second total perimeter p2 satisfy the equation: p1×b1=p2×b2; an application specific integrated circuit coupled to the MEMS device; a processing unit coupled to the ASIC; an interface coupled to the processing unit; a storage device coupled to the processing unit; and The movable mass block has a uniform thickness.

8. The electronic device of claim 7, wherein the electronic device is at least one of: an inertial navigation system, an automotive system, a personal digital assistant, a laptop, a mobile phone, a wearable device, a smart watch, a digital audio player, a camera, or a video camera.

9. The electronic device of claim 7, wherein the movable mass is made of a monolithic semiconductor body.

10. The electronic device of claim 7, wherein the movable mass forms part of a Z-axis accelerometer or gyroscope. 11 . The electronic device according to claim 7 , wherein a number of the second plurality of through-openings is different from a number of the first plurality of through-openings. 12 . The electronic device according to claim 7 , wherein a shape of the plurality of second through-openings is different from a shape of the plurality of first through-openings.

13. A MEMS device comprising: substrate; a first electrode and a second electrode coupled to the substrate; a pillar having a first end and a second end, wherein the first end is coupled to the substrate between the first electrode and the second electrode; as well as a movable mass tiltably coupled to the second end of the column, the movable mass comprising: an area in a plane and a thickness in a direction perpendicular to the plane, the movable mass being tiltable about a rotation axis extending parallel to the plane and thereby forming a first mass portion and a second mass portion arranged on opposite sides of the rotation axis, the first mass portion and the second mass portion respectively having a first centroid and a second centroid, the first centroid and the second centroid respectively being arranged at a first distance b1 and a second distance b2 from the rotation axis; a plurality of first through-openings in the first mass portion, wherein the plurality of first through-openings and the first mass portion have a first total perimeter p1 in the plane; as well as a plurality of second through-openings in the second mass part, wherein the plurality of second through-openings and the second mass part have a second total perimeter p2 in the plane, wherein the first distance b1, the second distance b2, the first total perimeter p1, and the second total perimeter p2 satisfy the equation: p1×b1=p2×b2; and The movable mass block has a uniform thickness. The MEMS device of claim 13 , wherein the shape of the first proof-mass portion is different from the shape of the second proof-mass portion.

15. The MEMS device of claim 13, wherein the post is positioned offset from a central axis of the movable mass.

16. The MEMS device of claim 13, wherein the movable mass is made of a monolithic semiconductor body. The MEMS device of claim 16 , wherein the monolithic semiconductor body is silicon.

18. The MEMS device of claim 13, wherein the movable mass forms part of a Z-axis accelerometer.

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