MEMS sensor structure comprising mechanically preloaded suspension springs

Abstract

A MEMS sensor comprising preloaded suspension springs and a method for mechanically preloading suspension springs of a MEMS sensor are described. The MEMS sensor comprises a MEMS support structure; a plurality of suspension springs connected to said support structure; and, a proof mass flexibly suspended by said suspension springs; wherein at least one of said suspension springs is mechanically preloaded with a compressive force for reducing the natural frequency of said proof mass.

Claims

1. A MEMS sensor comprising: a support structure; a plurality of suspension springs connecting a proof mass to the support structure, the plurality of suspension springs being further connected to one or more actuators, the proof mass flexibly suspended by the suspension springs forming a proof mass-spring system, the proof mass configured to move in a sensing direction along a sensing axis of the sensor; a parasitic spring connecting the proof mass to the support structure, the parasitic spring being further connected to a further actuator; wherein the suspension springs are mechanically preloaded by the one or more actuators with a compressive force for reducing a natural frequency of said proof mass-spring system; and, wherein the parasitic spring is mechanically preloaded with a compressive force by the further actuator in the sensing direction to compensate gravity when the sensing axis of the sensor has a component along a direction associated with the gravity.

2. The MEMS sensor according to claim 1, wherein each of the suspension springs includes a first connection point connecting a first end of the suspension spring to the support structure and a second connection point connecting a second end of the suspension spring to the proof mass, wherein each of the suspension springs being connected in a predetermined orientation with respect to the proof mass, the orientation comprising an initial offset angle φ.sub.0 defined by a first direction associated with the compressive force and a second direction defined by a line connecting the first connection point with the second connection point, wherein the initial offset angle φ.sub.0 introduces for each of the suspension springs a force component perpendicular to the sensing direction and a force component in the sensing direction.

3. The MEMS sensor according to claim 1 further comprising a locking mechanism for maintaining a predetermined compressive force to at least one suspension spring.

4. The MEMS sensor according to claim 3 wherein said locking mechanism is configured for switching said at least one suspension spring from a non-compressed state to one or more compressed states.

5. The MEMS sensor according to claim 4 wherein said locking mechanism comprises a ratchet and a pawl, the ratchet comprising one or more ratchet positions associated with the one or more compressed states respectively.

6. The MEMS sensor according to claim 3 wherein said locking mechanism comprises a two state locking spring system connected to said at least one suspension spring for switching said at least one suspension spring between a non-compressed state and a compressed state.

7. The MEMS sensor according to claim 1 wherein at least part of the suspension springs are configured as curved beams.

8. The MEMS sensor according to claim 1 wherein said reduced natural frequency is selected between 500 and 1 Hz.

9. The MEMS sensor according to claim 1 wherein said proof mass is a substantially planar element and wherein a direction of said compressive force is in a plane of said proof mass.

10. The MEMS sensor according to claim 1 wherein at least two suspension springs are connected to opposite sides of said proof mass and wherein said at least two suspension springs are preloaded with a compressive force of substantial similar magnitude.

11. The MEMS sensor according to claim 1 wherein said proof mass further comprises one or more capacitive elements for detecting movements of said proof mass, for actuating said proof mass and/or for using the MEMS sensor in a closed loop configuration.

12. The MEMS sensor according to claim 1 wherein the suspension springs are mechanically preloaded using one or more electro-thermal actuators comprising a V-shaped suspended conductive beam, wherein a tip of said V-shaped suspended conductive beam is displaced in a predetermined direction as a function of a current that runs through said conductive beam.

13. The MEMS sensor according to claim 1 wherein the suspension springs are configured for keeping the proof mass at an equilibrium position when a preloading force is applied on the suspension springs.

14. The MEMS sensor according to claim 1 further comprising a locking mechanism for maintaining a predetermined compressive force to the parasitic spring.

15. The MEMS sensor according to claim 1 wherein each of the suspension springs of the plurality of suspension springs is connected to the proof mass in a predetermined angular orientation with respect to the sensing axis of the proof mass, the predetermined angular orientation providing compensation for gravity when the sensing axis of the sensor has a component along the direction of gravity.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 depicts a MEMS structure comprising a compressive spring structure according to an embodiment.

(2) FIG. 2 depicts a compressive spring structure for use in an MEMS structure according to another embodiment.

(3) FIG. 3A and FIG. 3B depict a MEMS inertial sensor comprising a compressive spring structure according to an embodiment.

(4) FIG. 4A-4C depict schematics and a photograph of a mechanical locking structure for use in a MEMS structure according to an embodiment.

(5) FIG. 5A-5C depict schematics and a photograph of a mechanical locking structure for use in a MEMS structure according to another embodiment.

(6) FIG. 6 depicts a top view of at least part of an inertial MEMS sensor according to an embodiment.

(7) FIG. 7A and FIG. 7B depict an electro-thermal actuator for use in a MEMS sensor according to an embodiment.

(8) FIG. 8A and FIG. 8B depict a model describing a compressive spring structure for use in a MEMS sensor according to an embodiment.

(9) FIG. 9A and FIG. 9B depict graphs of the compression versus the natural frequency for two inertial MEMS sensors according to an embodiment.

(10) FIG. 10A-10E depicts a MEMS inertial sensor comprising suspension beams and compressive spring structure suitable to partial of full compensation of static gravity acceleration according to an embodiment.

(11) FIG. 11 depicts a comparison between the readout noise of a state of the art inertial MEMS sensor and an inertial MEMS sensor with a variable natural frequency.

(12) FIG. 12 depicts the measured output noise of an inertial MEMS sensor with variable natural frequency built according to an embodiment.

(13) FIG. 13A-13E represent pictures of a MEMS sensor according to an embodiment.

(14) FIG. 14 depict a schematic of MEMS sensor according to another embodiment.

DETAILED DESCRIPTION

(15) FIG. 1 depicts a schematic of a MEMS structure comprising a mechanically preloaded spring system 100 according to an embodiment. In particular, FIG. 1 depicts a top view of a MEMS structure comprising a suspended mass 101 (i.e. a planar sheet of material) that is kept in a suspending state using several suspension beams. A suspension beam behaves like a spring that is characterized by a spring constant. The springs in FIG. 1 may have any suitable geometry, including meandering and/or serpentine spring designs. The MEMS structure of FIG. 1 may comprise a main suspension spring 102 and one or more mechanically preloaded suspensions springs 104.sub.1,104.sub.2 that connect the mass to a support structure 106. This way, the proof mass forms a suspended mass that is connected by the suspension springs to the MEMS support structure. In this particular embodiment, the main suspension spring (aligned along the y-axis) may have a spring constant k and the two preloaded suspensions springs (aligned along the x-axis) may have a spring constant k.sub.c.

(16) The two lateral springs may be mechanically pre-loaded on the basis of an external compressive force F.sub.c. This force may be applied to a suspension spring using an actuator 108 that may be configured to compress the spring in a direction in the plane of the proof mass (in this case the x-direction) wherein the compressive force is approximately equal to δx*k.sub.c (δx being the compressive deformation of the spring along the x-direction). The length of such a pre-loaded spring may be defined as L(δx)=L.sub.0−δx, where L.sub.0 is the rest length. The compressive force applied to the first and second lateral springs may have substantially the same magnitude and may be of opposite sign so the total (vector) sum in the plane of the proof mass is zero and so that the position of the proof mass will not be affected when the springs are preloaded by the actuators.

(17) If the mass is subjected to an external force dF.sub.1 along the y-direction, the mass will be displaced over a distance dy along the y-direction. Due to the displacement dy, the preloaded springs will be slightly tilted so that the y-components

(18) $k_{\mathrm{tot}}\simeq k-\frac{2F_c}{L_0}$
of compressive forces F.sub.c in the preloaded springs will generate a net force dF.sub.3≅2F.sub.c.Math.dy/L in the same direction as dF.sub.1.

(19) The two forces dF.sub.1 and dF.sub.3 will be counteracted by a spring force dF.sub.2 which is equal to the spring constant k times the mass displacement dy. The compressive forces in the preloaded suspension springs thus effectively cause a reduction of the spring constant k (and thus in its stiffness) along the y-direction wherein the reduction is approximately equal to 2F.sub.c/L.sub.0 since in typical embodiments of the system δx/L.sub.0<<1. Hence, due to the lateral preloaded springs, the effective spring constant of the mass-spring system may be given by the expression (Eq. 5) as

(20) Hence, by controlling the compressive force in the springs (e.g. using an actuator), the total spring constant and thus the natural frequency of the MEMS structure may be controlled. As will be described hereunder, the natural frequency is a very important aspect in the design of any MEMS device. As will be shown hereunder in more detail, a MEMS mass-spring system that has a controllable natural frequency may be of particular use in MEMS sensors, in particular MEMS inertial sensors.

(21) In an embodiment, the stiffness reduction as described with reference to FIG. 1 may be obtained with conventional non-curved suspension beams. Alternatively, in another embodiment, a curved suspension beam as shown in FIG. 2 may be used. In particular, FIG. 2 depicts a curved elastic suspension beam (a curved cantilever beam or curved suspension spring) of length L, which is preloaded by a compressive force. In the non-compressed state, the curved beam has a predetermined non-stressed curved shape θ.sub.i(l), wherein l is a curvilinear position coordinate along the beam and θ is the beam orientation with respect to the (global) x-axis. The curved beam may comprise a base (l=0) that is fixed to part of a MEMS structure (e.g. a proof mass as described with reference to FIG. 1) and tip (l=L) that may be connected to an actuator beam. When forces are applied to the curved beam, the change of the curve (change of the shape) of the beam may be described by a function θ(l).

(22) FIG. 2 depicts a system wherein the tip (one side) of the beam may be subject to a compressive force F.sub.x along the x-axis and an external force F.sub.y along the y-axis. At low frequencies of interests, compared to the eigenmodes of the beam, F.sub.y may be described as the reaction force induced by a displacement between the proof mass and the frame of the MEMS structure (which in turn could be caused by an acceleration of the frame along the y-axis). In that case, the curve of the beam may

(23) $E\frac{d}{\mathrm{dl}}\left[I\left(l\right)\frac{d}{\mathrm{dl}}\left(\theta \left(l\right)-{\theta }_i\left(l\right)\right)\right]=F_x\sin \theta \left(l\right)-F_y\cos \theta \left(l\right)$
be described by the equation (Eq. 6) given by
where E represents the Young modulus of the blade beam material, I(l)=w(l)t(l).sup.3/12 is the second moment of area of the beam cross section, with t and w the beam thickness and beam width respectively, which—in general—both may depend on l and θ.sub.i(l), wherein θ.sub.i(l) is the beam orientation with respect to the (global) x-axis of the initially unstressed beam. Hence, in this particular case, the elastic beam may have a particular curved shape θ.sub.i(l) in the non-compressed state and a particular curved shape θ(l) in the compressed state. On the basis of this equation, the effective spring constant of the preloaded elastic member may be estimated.

(24) The curved beam configuration as shown in FIG. 2 has the advantage that it allows both preloading of the beam with a compressive force using e.g. an (electro-thermal) actuator and “locking” the thus preloaded beam using a mechanical locking structure. As will be described hereunder in more detail, the mechanical locking structure may be part of the same MEMS structure as the springs and e.g. a proof mass of a MEMS sensor. Although the preloading force in FIG. 2 is provided along the x-direction, in other embodiments other directions of the preloading force (e.g. y-axis or both x and y axis) are also foreseen.

(25) FIGS. 3A and 3B depict an inertial MEMS sensor comprising according to various embodiments. In particular, FIG. 3A depicts an inertial MEMS sensor comprising a proof mass 304 that is connected by suspension springs 306.sub.1-4 to a support structure 302. In particular, a first end of each suspension spring 306.sub.1-4 may be connected at first connection point 305 to a support structure and a second end of the suspension spring may be connected at a second connection point 307 to the proof mass. In this example, the direction of movement of the proof mass (the sensing direction) is along the y-direction. Control of the direction of movement may be realized by guiding structures around the proof mass (not shown). The MEMS sensor may comprise actuators 308.sub.1-4 for (on-chip) preloading of the suspension springs. In an embodiment, a curved suspension beam as described with reference to FIG. 2 may be used as suspension spring. An actuator beam 303 connected to the actuator 308.sub.1 may be connected to the first end of a suspension spring 306.sub.1. The actuator may move the actuator beam back and forward in a direction that is substantially perpendicular to the direction of movement of the proof mass. A guiding structure 310 attached to the MEMS support structure may ensure that the actuator beam controllably applies a compressive force to the suspension spring in a predetermined direction, in this example a direction perpendicular to the direction of movement of the proof mass. The curved suspension beams may be connected to the support structure and the proof mass such that when preloading the springs the proof mass is kept in balance in the sense that the position and orientation of the proof mass does not substantially change compared to the uncompressed state as depicted in FIG. 3A. The dimensions and geometry of the proof mass and the suspensions springs may be selected such that the mass-spring system has a certain natural frequency f.sub.0 when the suspensions springs are in their non-compressed state.

(26) The guiding structure and the actuator may be part of or may be rigidly connected to the support structure. The actuators may be activated in order to controllably apply a compressive force to the elastic beams as shown in FIG. 3B. Due to the compressive force, the elastic beams will be preloaded in a similar way as described with reference to FIG. 2 thereby effectively reducing the total stiffness of the mass-spring system of the inertial sensor. The proof mass may comprise electrodes for forming capacitive sensing elements 312, which may be used in order to detect movements of the proof mass with respect to the frame that are caused by frame vibrations within a certain low-frequency bandwidth, and to apply feedback forces in closed-loop operation.

(27) A plurality of capacitive actuation elements may be used to separate the function of static and dynamic balancing servo actions possibly resulting in a larger output dynamic range. Balancing actuators may provide compensation for: processing inaccuracies, thermos-elastic effects, differences in local gravity acceleration, full compensation of gravity to implement omni-directional configurations of the MEMS sensor.

(28) Hence, in the MEMS inertial sensor structure of FIG. 3B actuators may be used to apply a compressive force to the suspension springs in opposite directions such that the compressive forces applied to the springs do not affect the position of the mass. The force applied to the actuator beam and the guiding structure will cause deformation of the elastic beam so that a compression force is formed in the suspension beam. The magnitude of the compressive force may be controlled by controlling the displacement of the actuator. This way, the suspension springs may be mechanically pre-loaded in a controllable way, thereby effectively decreasing the spring constant of the suspension springs and thus the natural frequency of the mass-spring system. The preloaded suspension springs will effectively decouple the proof mass from the environment so that the responsivity of inertial sensing may be significantly increased. The increased responsivity to some accelerations may result in an inertial sensor having increased sensitivity.

(29) In an embodiment, the guiding structures 310 may comprise a mechanical locking structure preventing the preloaded spring to move back to its initial (unloaded) state if e.g. the actuator force is released. In one embodiment, the mechanical locking structure may comprise a first locking state associated with non-loaded suspension spring and a second locking state associated with a preloaded suspension spring. When the actuator is activated, the locking structure may allow the spring to be moved from a non-compressed first position into a compressed second position. This way the suspension spring may be preloaded with a predetermined compressive force even when the actuator itself moves back to its initial position. In an embodiment, the spring may be moved irreversibly to the compressed second position.

(30) In another embodiment, the mechanical locking mechanism may comprise multiple locking states wherein one state of the locking mechanism is associated with the suspension spring in an uncompressed state and at least two or more states are associated with different compressed states of the suspension spring. Hence, in this embodiment, the actuator may be used to mechanically set the suspension spring in one of the two or more positions associated with the different compressed states of the suspension spring.

(31) FIG. 4A-4C depict schematics and a photograph of a mechanical locking structure for use in a MEMS structure according to an embodiment. In particular, in FIG. 4A, a mechanical MEMS locking structure is depicted wherein an actuator beam 402 connected to an actuator 404 comprises one or more pawls 406 (e.g. elastic beams) that engage with one or more ratchets 408 that are formed in or onto the MEMS support structure 409. The actuator beam is further connected to an end 410 of the suspension spring 412. A guiding element 414 connected to the MEMS support structure may ensure that the actuator beam is moved in the desired direction and that the compressive force is applied to the elastic beam in that direction.

(32) The ratchet may be formed by a linear arrangement of asymmetrically formed sawtooths. As shown in FIG. 4B due to the sawtooth form of the ratchet, the one or more elastic pawl beams attached to the actuator beam may slide over the one or more ratchets, thereby allowing continuous linear motion of the actuator beam in the direction towards the suspension spring. In the reverse direction however, the elastic pawl beam will engage with a ratchet position thereby preventing the actuator beam from moving in the direction away from the suspension spring. This way, the ratchet and pawl structure ensures that the suspension spring is irreversibly preloaded

(33) Hence, by moving the elastic pawl beams over the ratchet and positioning the elastic pawl beams in a predetermined ratchet position, the suspension spring may be mechanically preloaded with a predetermined compressive force. Each ratchet position may correspond to a predetermined compressive (preload) state of the spring. FIG. 4C depicts a photograph of an example of a MEMS structure comprising a mechanically locking mechanism comprising an actuator beam, (two) elastic pawl beams that engage with (two) ratchet structures that are formed in the MEMS support structure. Methods for producing mechanical MEMS elements such as the ratchet-pawl system are known and e.g. described in U.S. Pat. No. 8,480,302 or in the article by Pham et al, “Single mask, simple structure micro rotational motor driven by electrostatic comb-drive actuators”, 2012, J. Micromech. Microeng. 22 (2012) 015008.

(34) FIG. 5A-5C depict schematics and a photograph of a mechanical locking structure for use in a MEMS structure according to another embodiment. In particular, in FIG. 5A, a mechanical MEMS locking structure is depicted wherein the actuator beam 502 is connected by a mechanical two-state switch structure 506 to MEMS support structure 516. The actuator beam may be further connected to an end 510 of the suspension spring 512. A guiding element 514 connected to the MEMS support structure 516 may ensure that the actuator beam is moving in a desired direction and that the compressive force is applied to the elastic beam in that direction. The mechanical switch may comprise one or more curved so-called bistable beams 506 that are connected between two opposite sides of the MEMS support structure and to the actuator beam. Methods for producing mechanical MEMS elements such as the bistable beams are known and e.g. described in US200302970. Such structure may have two stable positions, i.e. a first position of the elastic beam (as shown in FIG. 5A) and a second position of the elastic beam (as shown in FIG. 5B). Switching to the second position may be achieved by activating the actuator that pushes the actuator beam that is guided by guiding element 514 in the direction of the suspension spring 512. At a certain moment, the actuator will force the elastic beam into its second stable position as depicted in FIG. 5B. In that case, the suspension spring is preloaded by a (static) compressive force that is maintained by the mechanical switch. FIG. 5C depicts a photograph of an example of a MEMS structure comprising a mechanical two-state switch. In this particular example the actuator beam is connected to the suspension spring and an intermediate mass structure that allows stable suspension of a proof mass using the suspension springs. If the actuator can only push and not pull, the original unstressed state cannot be recovered. In that case this may also function as an anti-reverse system.

(35) FIG. 6 depicts a top view of at least part of an inertial MEMS sensor according to an embodiment. In particular, FIG. 6 depicts the top view of a MEMS inertial sensor comprising a proof mass 602 that is suspended by suspension springs 604 to a MEMS support structure 606. One end of the suspension spring may be connected to an actuator 608 via an actuator beam 610. In this particular example, the suspension spring may have dimensions of 1000×5×25 micron, the thermal actuator 1700×10×25 micron, bistable beam pair 400 (or 600)×5×25 micron, proof mass 3000×3000×25 micron. Depending on the desired properties of the system, the beam length L may be selected between 1000 and 5000 micron.

(36) The actuator beam may be further connected to a mechanical locking mechanism 612 (as e.g. described in detail with reference to FIGS. 4 and 5) for maintaining the compressive force onto the suspension springs. The proof mass may comprise capacitive coupling members 614,616, e.g. interdigitated capacitor members that may be used to sense displacements of the suspended proof mass or to actuate it. Contact pads 618.sub.1-3 may be used to contact (e.g. by wire bonding) elements of the MEMS sensor. For example, the contact pads 618.sub.1,2 may be used for applying a current through the electro-thermal actuator 608 and the contact pad 618.sub.3 may be used for applying a bias voltage to one of the capacitor electrodes.

(37) FIGS. 7A and 7B depict an electro-thermal actuator for use in a MEMS sensor according to an embodiment. In this particular embodiment, the electro-thermal actuator may be implemented as a MEMS structure comprising a suspended (slightly) V-shaped silicon beam 702 of a certain conductivity (see also the actuator beam 502 in FIG. 5C) that may be formed in the same silicon layer in which all other MEMS elements, including the proof mass, the suspension springs and the locking mechanisms, may also be formed. The beam may be connected to bonding pads 704.sub.1,2 for applying a current through the beam. Further, the tip 706 of the V shaped beam may be connected to or close to the actuator beam 708, which is connected to the suspension spring(s) as e.g. 710.

(38) When applying current I through the suspended V-shaped beam, Joule heating will occur and the thermal expansion of the beam will result in a displacement dx of the tip of the V-shape along the x-direction as shown in FIG. 7B. The displacement of the beam will push the actuator beam along the x-direction such that the suspension spring is mechanically preloaded with a certain compressive force. For example, when applying a current between 0 and 15 mA through a V-shaped silicon beam of 1700×10×25 micron, displacements dx of the order of 0 and 20 micron may be achieved. Although FIGS. 7A and 7B illustrate an electro-thermal actuator in combination with a locking mechanism of FIG. 5, other embodiments either with or without a locking mechanism are also foreseen.

(39) A simplified analytical mathematical description of the embodiment of

(40) $k_0=\frac{F_y}{y}\simeq \frac{12\mathrm{EI}}{L_0^3}$
the invention with reference to FIG. 2, 3A, 3B can be made by using the model depicted in FIG. 8A-B. FIG. 8A depicts a proof mass suspended by two curved clamped-clamped beams with initial (un-compressed) projected along x length L.sub.0. Hereafter the calculation is done for a single suspension beam and it can be straightforwardly generalized for any number of beams acting in parallel. Under the action of an external force F.sub.y (per beam), the proof-mass is pulled from equilibrium over a distance y. For small deflections the initial stiffness of each suspension beam k.sub.0 is close to that of a straight beam (Eq. 7),
where E is the beam material Young modulus and I is its second moment of area. Equivalently, one can define the beam tip rotational stiffness with respect to the beam base as

(41) $\begin{array}{cc}{\kappa }_0=\frac{M}{\varphi }=k_0{L}_0^2,& \left(\mathrm{Eq}.8\right)\end{array}$
with φ=y/L.sub.0 and where M=F.sub.yL.sub.0 is the torque acting on the beam support frame. The natural frequency of the mass-spring system as configured in FIG. 8A is f.sub.0=1/2π√k.sub.0/m, where m is the suspended mass per beam.

(42) FIG. 8B depicts the mass-spring system after a compressive force F.sub.x
M=F.sub.yL+F.sub.xy=αk.sub.0L.sub.y
has been applied to the suspension beams. Such a force contributes to the torque acting on the beam support frame which, at some mass displacement y, becomes (Eq. 9)
where α is a correction factor to the initial beam bending stiffness k.sub.0. The correction factor is a function of F.sub.x through the geometrical parameters of the suspension beams, and it can be calculated by numerical integration of Eq. 6 or by Finite

(43) $k_1=\alpha k_0-\frac{F_x}{L}$
Element Modeling (FEM). From Eq. 9 y can be solved, resulting in a reduced stiffness per beam (Eq. 10)
In typical embodiments of the invention L˜L.sub.0. The natural frequency of the mass-spring system in compressed state is f.sub.1=1/2π√k.sub.1/m.

(44) TABLE-US-00001 TABLE 1 Examples of design parameters for a MEMS inertial sensor according to the embodiments of the invention. Sensor 1 Sensor 2 Mass (mg) 0.45 30 Number of springs 4 16 L.sub.0 (μm) 960 1660 Uncompressed stiffness per beam k.sub.0(N/m) 0.55 1.1 Uncompressed frequency f.sub.0 (Hz) 355 122 Correction factor α 0.85 0.85 Beam compression (μm) 19 32.9 Compression force F.sub.x (μN) 423 1465 Compressed frequency f.sub.1 (Hz) 84 28
Table 1 shows two examples of MEMS inertial sensor design, based on the model depicted in FIG. 8A-8B, according to the embodiments of the invention.

(45) FIG. 9A-9B depict graphs of the measured natural frequency of MEMS inertial sensors that comprise preloaded suspension springs as described with reference to FIG. 3A-3B. FIG. 9A depicts the measurements done on two samples of a MEMS sensor comprising a proof mass of 0.45 mg. As reference the results of FEM model are also presented. As shown in the graph, the natural frequency f0 may be varied by controlling the compressive force on the suspensions springs. Here, the compressive force is expressed in terms of compressive deformation δx of the spring. Hence, for example, by controlling the actuators to induce a compressive deformation of around 9 micrometers in the suspension springs of MEMS-2, the natural frequency of the mass-spring system may be decreased from 290 Hz to approximately 190 Hz. Further increase of the spring compressive deformation up to 14 micrometers resulted in a natural frequency of around 130 Hz, i.e. less than half of the natural frequency of the MEMS sensor in its non-preloaded state thereby providing effective on-chip stiffness cancellation resulting in an increased sensitivity of the sensor. Further increase of the beam compression up to 19 micrometers provided a further decrease of the natural frequency down to 70 Hz, corresponding to a 17-fold stiffness reduction with respect to the as-processed state. It must be noticed that the out-of-plane (z-axis) natural frequency of the same device is 1300 Hz independently on the compression state. FIG. 9B depicts the same measurements done on a MEMS sensor com-prising a proof mass of 30 mg. In this case, the as-processed natural frequency was 100 Hz. By means of the on-chip anti-spring mechanism the natural frequency was lowered down to 28 Hz, corresponding to a 14-fold stiffness reduction compared to the as-processed state of the MEMS sensor. Further compression of the suspension beams may result into a lower than 20 Hz operational natural frequency of the device.

(46) Hence, this graph shows effective on-chip control of the natural frequency of the mass-spring MEMS structure is provided. By applying a compressive force to the suspension springs, the natural frequency of the mass-spring system may be controlled between f.sub.0 and 0.1.Math.f.sub.0, preferably between f.sub.0 and 0.2.Math.f.sub.0, more preferably between f.sub.0 and 0.3.Math.f.sub.0.

(47) FIG. 10A-10E depict an inertial MEMS sensor according to various embodiments. In particular, FIG. 10A depicts an inertial MEMS sensor that is similar to those described with reference to FIG. 3A-3B in the sense that the MEMS sensor comprises a proof mass 1005 that is connected by a plurality of suspension beams 1001.sub.1-4 to a support structure 1007. The MEMS sensor may comprise actuators 1002.sub.1-4 for on-chip preloading of the suspension beams. In an embodiment, a curved suspension beam as described with reference to FIG. 2 may be used as suspension spring. In another embodiment, a stiff suspension beam may be used. The suspension beam may be compressed in a predetermined direction by the actuators comprising an actuation beam 1008 and, optionally, a guiding structure 1003. The support structure may be provided with end stop structures 1009.sub.1-4 for limiting the displacement of the proof mass along the sensitive axis (y) of the MEMS sensor (i.e. the axis of movement of the proof mass). In FIG. 10A the beams are in an uncompressed state, with the MEMS surface in horizontal orientation

(48) When compared with FIGS. 3A and 3B, the MEMS sensor in FIG. 10A comprises curved suspension beams that comprise an initial offset angle φ.sub.0 1013 with respect to the direction of motion of the proof mass (in this particular example the x-direction). This predetermined offset angle may be introduced in the structure during fabrication process. As will be described hereunder in more detail the initial offset angle φ.sub.0 provides a means for compensating gravitational effects that may occur when the MEMS sensor is used in a vertical position, e.g. a position wherein the proof mass moves along the z-direction.

(49) When compared to the embodiment depicted in FIG. 3A-3B, in the design of FIG. 10A an offset has been introduced between the connection points of beams to the proof mass relative to the connection points to the support structure, while the proof mass is kept centered with respect to the capacitive sensing and actuation structures 1006.sub.1,2. The offset is along the direction of the movement of proof mass and scales with an angle, initial offset angle φ.sub.0, about the connection point to the compression structure. The dimensions and geometry of the proof mass and the curved suspensions springs may be selected such that the mass-spring system has a certain natural frequency f.sub.0 when the suspensions springs are in their non-compressed state.

(50) Thereafter, the curved suspension springs may be compressed by the built-in actuators until the desired compression state is reached. As an effect of the initial offset angle φ.sub.0 (the offset) the proof mass will move along the y-axis when the beams are compressed until they are pushed against the end stops 1009.sub.1,2. This intermediate compressed state of the MEMS sensor, in horizontal state, is depicted in FIG. 10B.

(51) Subsequently, the MEMS sensor is oriented in a vertical position. In that case, due to the effect of gravity, the proof-mass will move back to its initial position such that it is centered with respect to the sensing and actuation structures. This final configuration of the MEMS sensor is depicted in FIG. 10C. In this state, the natural frequency f.sub.1 of the MEMS inertial sensor is determined by the initial (uncompressed state) stiffness of the suspension (as described in detail with reference to FIG. 10A) and by the pre-loading force applied to the suspension springs. Hence, from the above, it follows that by changing the orientation the suspension springs with respect to the direction of the mechanical preloading force, the MEMS sensor can be preferably configured to measure acceleration in horizontal, vertical or along any different inclination with respect to the direction of gravity. This way both frequency reduction and gravity compensation are achievable without electrical power consumption.

(52) The embodiment of FIG. 10A-B may be simply described by using the model depicted in FIG. 10D-10E. FIG. 10D depicts a mass suspended by two curved beams with initial (uncompressed) projected along x length L.sub.0. In FIG. 10D the y axis is oriented horizontally. Due to the fact that the springs have an initial rotation angle φ.sub.0, the proof-mass position along y is shifted by an amount y.sub.0 with respect to the connection point between suspension springs and support structure of the suspension springs.

(53) FIG. 10E depicts the mass-spring system after a compressive force F.sub.x has been applied to the suspension springs and after the y-axis of the system has been oriented vertically. The new equilibrium position of the proof-mass is shifted by an amount y with respect to the initial configuration. With reference to Eq. 9, the torque M on the support structure is given by (Eq. 11)
M=F.sub.x(y+y.sub.0)−mgL−αk.sub.0Ly=0
By solving Eq. 11, y can be determined as (Eq. 12)

(54) $y=\frac{y_0{F}_x-\mathrm{mgL}}{L-F_x}$$y=\frac{\mathrm{mgL}}{F_x}$
By solving Eq. 12 the value of y.sub.0 (and therefore φ.sub.0) such that y=0 can be calculated (Eq. 13) as
The final stiffness (per spring) k.sub.1, determined by differentiating Eq. 12, amounts to (Eq. 14)

(55) 0$k_1=\alpha k_0-\frac{F_x}{L}$
which is the same as in Eq. 10. The natural frequency of the mass-spring system in the final state is f1=1/2π√k.sub.1/m. It must be noticed that a more precise determination of the suspension geometrical parameters and pre-loading force is made by integrating numerically Eq. 6 or by finite-element-modeling (FEM). As an example, the design parameters shown in Table 1 can also be used for a vertical MEMS inertial sensor, according to this embodiment of the invention, by introducing y.sub.0=2.5 micrometers and y.sub.0=83 micrometers, respectively in Sensor 1 and Sensor 2.

(56) This embodiment of the invention allows to design low natural frequency vertical MEMS inertial sensors in which the static effect of gravity on the proof-mass position is compensated passively by applying a suitable pre-loading to the suspension springs. The gravity compensation system is engaged once in the lifetime of the chip, after its fabrication, and does not require the application of any electrostatic field during the sensor operation. This will result in better noise performance and lower power consumption. Residual vertical imbalance, due to process inaccuracies, to local magnitude of gravity or to thermo-elastic effects, may be accommodated by the capacitive actuation system. Alternative configurations of the MEMS sensor with different orientation with respect to gravity, like Galperin (54.7 degrees from the vertical z-axis), may be implemented by adjusting φ.sub.0.

(57) FIG. 11 illustrates a graph showing a comparison between the acceleration noise contribution from the readout noise for a state-of-the-art MEMS seismic sensor that uses an optimized closed-loop readout scheme (in this case we refer to published results from U.S. Pat. No. 7,484,411B2) and several MEMS inertial sensors with twenty times larger displacement noise and with different lower natural frequencies. As shown in the graph an inertial sensor with a 90 Hz natural frequency and a 20 times worse displacement noise has substantially the same noise level as the best available MEMS sensors. When reducing the natural frequency from 70 down to 30 Hz, the readout noise is several orders of magnitude lower down to a few ng/√Hz which is close to the Brownian noise level of the system. These graphs show the significant impact of reducing the natural frequency on the sensitivity of the sensor.

(58) FIG. 12 depicts a graph showing the measured noise level, as a function of the natural frequency, of an inertial MEMS sensor comprising pre-loaded suspension springs as described with reference to FIG. 3A-3B. The measurement was performed with the MEMS sensor mounted on an in-vacuum ultra-quiet platform with a residual acceleration better than 10.sup.−10 g/√Hz above 3 Hz. The MEMS sensor has a proof-mass of 30 mg and 102 Hz natural frequency in uncompressed state. The position of the proof-mass with respect to the support structure was read by connecting a conventional discrete components charge amplifier to the MEMS capacitive sensing structures. The position readout noise was measured to be 3.Math.10.sup.−13 m/√Hz. In all data sets shown in the graph the vacuum level was adjusted in order to make the Brownian noise level contribution negligible: in particular the measurements with f0=102 Hz and f0=50.7 Hz were performed at 100 mTorr, while the measurement with f0=28 Hz was performed at 10 mTorr. The graph shows how the measured background signal decreases in level at low frequencies by reducing the natural frequency of the MEMS sensor by means of the anti-spring mechanism. Noise levels of the order of 10.sup.−9 g/√Hz are achieved. It has to be noticed that the noise shown in the graph below 3 Hz is due to the residual motion of the test platform and it is not a feature of the MEMS sensor output, for which, according to Eq. 1 and Eq. 2, the nano-g/√Hz level resolution is expected to extend down to very low frequencies (almost DC).

(59) The MEMS structure described within this application may be fabricated by using well known semiconductor processing techniques, including lithography, etching and deposition techniques. MEMS structures may be fabricated by using for example a Silicon On Glass (SOG) or a Silicon On Insulator (SOI) technology that is suitable for integration with CMOS. In SOG MEMS structures are formed in a silicon substrate that is bonded to a glass substrate. Similarly, in SOI MEMS structures may be formed in a silicon device layer between 10 and 50 micron, preferably 20 and 40 micron, that is bonded to a silicon support wafer of between 200 and 400 micron that is covered with an insulating dielectric layer, e.g. a SiO.sub.2 layer, of a thickness between 1 and 5 micron. The mechanical anti-spring achieves equivalent cross axis rejection ratio in just a single etching step and single wafer.

(60) By etching the silicon device layer and removing part of the SiO.sub.2 layer underneath the etched structures, free suspending MEMS structures may be realized in the silicon device layer. These MEMS structures may be designed such that the suspending proof masses, suspension springs and locking structures as described in this application are all realized in the same silicon device layer. This way, very sensitive inertial MEMS sensor may be realized in a relatively simple process that does not require complex multi-layer processing.

(61) FIG. 13A-13E represent pictures of a MEMS sensor according to an embodiment. This design relates to a sensor that can be used for vertical sensing similar to the one described with reference to FIG. 10A-10E. When using the sensor for vertical sensing gravity will pull the mass towards earth out of its equilibrium position. Hence in that case the springs may be rotated over a small angle phi in the plane of the mass. Preloading of these springs will cause a preloading force component on the mass in the sensing direction that counters the effect of gravity. Accurate control of the gravity compensation by introducing the angle phi in the design may be affected by fabrication tolerances. To counter this problem the MEMS sensor may include a further parasitic spring which can be used to fine tune the gravity compensation. In particular, the parasitic spring allows fine tuning the force required to lift the proof mass against gravity and overcome the accuracy limit set by fabrication tolerances.

(62) FIG. 13A-13E shows an overview of an implementation of a vertical seismic sensor with an implementation of such a parasitic compensation spring. FIG. 13A depicts a central proof mass which is suspended by one spring in each corner and can move in the direction indicated by the arrow. The proof mass in this case may in the order of mg, in this particular case 1.57 mg. A relatively light mass allows suspending it by only one curved spring in each corner, resulting in an uncompressed natural frequency of 210 Hz.

(63) To compensate for gravity the suspension springs should all be rotated by about an angle ϕ=0.16° to suspend the proof mass in a centered position when they are fully compressed. In this case however, the angle may be intentionally set to a somewhat smaller value of about 0.11° to be sure that the compression force would be too small to fully lift the proof mass towards is equilibrium position. The rest of the required force will then be provided by the compensation spring that is connected to the top of the proof mass as shown in FIG. 13A. FIG. 13B is an enhancement of the actuator and the locking mechanism connecting the parasitic spring to the mass. Hence, each of the springs is rotated over an angle ϕ to partly lift the mass against gravity and a parasitic spring connected at the top along with its actuation mechanism can be used to provide the rest of the required force for compensating gravity. To not defeat the purpose of the preloading of the suspension springs, the parasitic spring may only introduce a small amount of additional stiffness to the system. This way, the offset introduced by gravity can be accurately compensated mechanically.

(64) FIG. 14 depicts a schematic of MEMS sensor as described with reference to FIG. 13A-13D. The sensor comprises a proof mass 1404 that is connected by suspension springs 1406.sub.1-4 to a support structure 1402. In particular, a first end of each suspension spring 1406.sub.1-4 may be connected at first connection point 1405 to a support structure and a second end of the suspension spring may be connected at a second connection point 1407 to the proof mass. In this example, the direction of movement of the proof mass (the sensing direction 1409) is along the z-direction, which may be (partially) along the direction of the force of gravity. Control of the direction of movement may be realized by guiding structures around the proof mass. These guiding structures may for example include capacitive actuators 1416.sub.1-4 to keep the mass in a substantially fixed position the x direction. The MEMS sensor may comprise actuators 1408.sub.1-4 for (on-chip) preloading of the suspension springs. In an embodiment, a curved suspension beam as described with reference to FIG. 2 may be used as suspension spring. An actuator beam 1403 connected to the actuator 1408.sub.1 may be connected to the first end of a suspension spring 1406.sub.1. The actuator may move the actuator beam back and forward in a direction that is substantially perpendicular to the direction of movement of the proof mass. A guiding structure 1410 attached to the MEMS support structure may ensure that the actuator beam controllably applies a compressive force to the suspension spring in a predetermined direction.

(65) Similar to the embodiments of FIG. 10A-10C, an initial offset angle φ.sub.0 is introduced between the connection points of the suspension springs. When preloading the suspension springs the initial offset angle will introduce a preloading force which has a component in the direction perpendicular to the sensing direction and a component in the direction of the sensing direction. This way, when the sensing axis of the sensor has a component along the direction of gravity, this gravity component can be partially compensated by the component of the preloading force which is parallel to the sensing direction. The sensor further includes a parasitic spring 1420 connected to the support structure 1402 and the mass 1404, the parasitic spring being mechanically preloaded with a compressive force for providing a force in the sensing direction to further control and fine tune compensation of the gravity when the sensing axis of the sensor has a component along the direction of gravity. The parasitic spring may be comprising at least one actuator for mechanically applying the compressive force to the parasitic spring. Further, a locking mechanism for maintaining a predetermined compressive force to the parasitic spring may be used to fixate the compressive force after preloading. Any of the locking mechanisms described in the embodiments of this application may be used.

(66) The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

(67) The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.