Patent Publication Number: US-2023135941-A1

Title: Mems gyroscope having quadrature compensation electrodes and method for compensating a quadrature error

Description:
BACKGROUND 
     Technical Field 
     The present disclosure relates to a MEMS gyroscope having quadrature compensation electrodes and to a method for compensating a quadrature error. 
     Description of the Related Art 
     As is known, a gyroscope made using MEMS (“Micro Electro-Mechanical Systems”) technology is formed in a die of semiconductor material, e.g., silicon, and comprises at least one or more movable masses suspended on a substrate and free to oscillate with respect to the substrate with one or more degrees of freedom. 
     The movable masses are capacitively coupled to the substrate through driving electrodes, configured to cause an oscillation of the movable masses along a driving direction, and detection electrodes, configured to detect a displacement of the movable masses along a detection direction. 
     When the MEMS gyroscope rotates with an angular speed around a rotation axis, a movable mass that oscillates with a linear velocity along a direction perpendicular to the rotation axis is subject to a Coriolis force directed along a direction perpendicular to the rotation axis and to the linear velocity direction. 
     In particular, MEMS gyroscopes of monoaxial, biaxial or triaxial type are known, configured to detect a movement of the movable mass perpendicular to an extension plane of the movable mass and associated with a roll or pitch angular speed of the MEMS gyroscope around an axis lying in the extension plane of the movable mass. 
     Due to imperfections, for example associated with variabilities in the manufacturing process of the MEMS gyroscope, the movable mass is subject, in use, when moving in the driving direction, to a quadrature force directed along the detection direction. 
     This quadrature force causes a movement of the movable mass in the detection direction, even in the absence of a Coriolis force, which is detected by the detection electrodes. 
     The quadrature error thus reduces the detection performances of the MEMS gyroscope. 
     In MEMS gyroscopes wherein the detection direction is perpendicular to the extension plane of the movable mass, one approach is to design quadrature-cancellation electrodes capacitively coupled to the movable mass and arranged below the movable mass, i.e., arranged between the substrate and the movable mass. In practice, in such MEMS gyroscopes, the quadrature-cancellation electrodes are arranged on one side with respect to the movable mass. 
     In use, the compensation electrodes are suitably biased, through an external control circuit, so as to generate an electrostatic force on the movable mass which compensates for the quadrature force. 
     However, the voltage applied to the quadrature-cancellation electrodes causes a phenomenon known as electrostatic softening, which causes a variation of the resonance frequency of a vibration mode of the MEMS gyroscope that is used to detect the Coriolis force. 
     During the life of these MEMS gyroscopes, external factors such as temperature, humidity and mechanical stress may cause a variation of the capacitive coupling between the quadrature-cancellation electrodes and the movable mass, for example they may modify the gap between the quadrature-cancellation electrodes and the movable mass. 
     The variation of capacitive coupling causes, in these MEMS gyroscopes, a variation of the extent of the electrostatic softening phenomenon which in turn causes a variation of the resonance frequency. As a result, these MEMS gyroscopes have an unstable resonance frequency. 
     The instability of the resonance frequency of MEMS gyroscopes degrades the detection performances of the same MEMS gyroscopes, in particular it degrades the sensitivity thereof. 
     According to one approach, in order to reduce the sensitivity of the MEMS gyroscope to variations of the capacitive coupling between the quadrature-cancellation electrodes and the movable mass, the MEMS gyroscope is encapsulated or packaged within a body of a specific material, for example ceramic. 
     However, such specific packages have a high cost. 
     Furthermore, even when using these specific materials for the package, the sensitivity of the MEMS gyroscope is not sufficiently stable for specific applications wherein a high accuracy and reliability of the MEMS gyroscope are desired. 
     BRIEF SUMMARY 
     Various embodiments of the present disclosure overcome the disadvantages of the prior art. 
     According to the present disclosure, a MEMS gyroscope and a method for compensating a quadrature error of a MEMS gyroscope are therefore provided. 
     The MEMS gyroscope is formed by a substrate and a movable mass suspended on the substrate and configured to carry out a movement in a driving direction and in a detection direction perpendicular to each other. The movable mass has a first face and a second face opposite to the first face. The gyroscope also has a first and a second quadrature compensation electrode group, fixed to the substrate and capacitively coupled to the movable mass. The first quadrature compensation electrode group faces the first face of the movable mass, and the second quadrature compensation electrode group faces the second face of the movable mass. 
     The first and the second quadrature compensation electrode groups each have a respective variable facing area on the movable mass as a result of the movement of the movable mass in the driving direction and are configured to exert an electrostatic force on the movable mass during the movement of the movable mass in the driving direction. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       For a better understanding of the present disclosure, some embodiments thereof are now described, purely by way of non-limiting example, with reference to the attached drawings, wherein: 
         FIG.  1    shows a top-plan view of the present MEMS gyroscope, according to an embodiment; 
         FIG.  1 A  shows a top-plan view of a portion of the MEMS gyroscope of  FIG.  1   ; 
         FIG.  2    shows a cross-section of the MEMS gyroscope of  FIG.  1   , at rest, along section line II-II of  FIG.  1   ; 
         FIG.  3    shows a cross-section of the MEMS gyroscope of  FIG.  1   , along section line II-II, in a condition of use; 
         FIG.  4    shows a cross-section of the MEMS gyroscope of  FIG.  1   , along section line II-II, in a different condition of use; 
         FIG.  5    shows a schematic representation of forces acting on a movable mass of the MEMS gyroscope of  FIG.  1   , in the conditions of use of  FIGS.  2 - 4   ; 
         FIGS.  6  and  7    show graphs of quantities associated with the operation of the MEMS gyroscope of  FIG.  1   ; 
         FIG.  8    shows a top-plan view of the present MEMS gyroscope, according to another embodiment; 
         FIG.  9    shows a cross-section of the MEMS gyroscope of  FIG.  8   , at rest, along section line IX-IX of  FIG.  8   ; and 
         FIG.  10    shows a top-plan view of the present MEMS gyroscope, according to a different embodiment. 
     
    
    
     The following description refers to the arrangement shown; consequently, expressions such as “above,” “below,” “top,” “bottom,” “right,” “left” relate to the attached figures and are not to be intended in a limiting manner. 
     DETAILED DESCRIPTION 
       FIGS.  1  and  2    show a MEMS gyroscope  1  in a Cartesian reference system XYZ comprising a first axis X, a second axis Y and a third axis Z. 
     The MEMS gyroscope  1  is formed in a die of semiconductor material, e.g., silicon, and comprises a substrate or support structure  2 . 
     The MEMS gyroscope  1  is of monoaxial type and comprises one or more detection units, here a first and a second detection unit  4 ,  5 , each configured to detect a roll angular speed Ω Y  of the MEMS gyroscope  1  around the second axis Y. 
     In this embodiment, the first and the second detection units  4 ,  5  are equal to each other and arranged symmetrically with respect to a central plane A passing through a center O of the MEMS gyroscope  1  and parallel to a plane YZ formed by the second axis Y and by the third axis Z. 
     Hereinafter, the description will refer, for sake of simplicity, to the first detection unit  4 . However, what has been described for the first detection unit  4  also refers to the second detection unit  5 , unless otherwise specified. 
     The first detection unit  4  comprises a movable mass  7 , for example of silicon or polysilicon, suspended on the substrate  2  and having a top surface  7 A and a bottom surface  7 B. 
     The first detection unit  4  comprises a quadrature compensation unit  6 , configured to cancel, in use, a quadrature force acting on the movable mass  7 , as described in detail below. 
     The movable mass  7  is substantially planar and has a main extent parallel to a plane XY formed by the first axis X and by the second axis Y. 
     The movable mass  7  has an opening  9 , here of rectangular shape and having a length L c  along the second axis Y, which extends between the top surface  7 A and the bottom surface  7 B of the movable mass  7 . 
     In detail, the movable mass  7  has a first inner wall  10 A and a second inner wall  10 B which laterally delimit, along the second axis Y, the opening  9 . 
     In this embodiment, the first inner wall  10 A and the second inner wall  10 B each extend parallel to a respective plane parallel to the plane YZ. 
     However, the opening  9  may have a different shape and/or the first and the second walls  10 A,  10 B may extend along different planes. 
     The movable mass  7  is coupled to anchoring regions  13 , fixed to the substrate  2 , through flexures  14  each extending between the movable mass  7  and a respective anchoring region  13 , parallel to the first axis X. 
     The MEMS gyroscope  1  further comprises a central anchoring region  15 , fixed to the substrate  2 . 
     The movable mass  7  is coupled to the central anchoring region  15  through a respective flexure  14 . 
     The flexures  14  may be linear or folded elastic elements and are configured to allow the movement of the movable mass  7  with one or more degrees of freedom. 
     In detail, in this embodiment, the flexures  14  allow the movement of the movable mass  7  along the first axis X and the third axis Z. 
     The first detection unit  4  further comprises a top compensation electrode group  20 , arranged on a first side along the third axis Z with respect to the movable mass  7  (at the top in  FIGS.  1  and  2   ), and a bottom compensation electrode group  21 , arranged on a second side opposite to the first side along the third axis Z with respect to the movable mass  7  (at the bottom in  FIG.  2   ). 
     The top compensation electrode group  20 , the bottom compensation electrode group  21  and the opening  9  form the quadrature compensation unit  6 . 
     In this embodiment, the top compensation electrode group  20  comprises a first top electrode  20 A and a second top electrode  20 B, of semiconductor material such as for example silicon or polysilicon. 
     The first top electrode  20 A and the second top electrode  20 B each extend at a higher coordinate, along the third axis Z, with respect to the top surface  7 A of the movable mass  7 , from a respective anchoring pillar  23 A,  23 B fixed to the substrate  2 . 
     The anchoring pillars  23 A,  23 B, identified for sake of clarity by a dashed line in  FIG.  1   , here extend externally to the movable mass  7 , on one side of the movable mass  7  along the second axis Y. 
     However, the number and the arrangement of the anchoring pillars  23 A,  23 B may be different, for example as a function of the specific shape of the movable mass  7 , of the opening  9  and of the first and the second top electrodes  20 A,  20 B. 
     With reference to  FIG.  2   , the first top electrode  20 A extends suspended above the movable mass  7 , at a first height gi along the third axis Z from the top surface  7 A of the movable mass  7 , and has a width W 1  along the first axis X, which may be chosen as a function of a maximum displacement of the movable mass  7 , in use, along the first axis X, as described below. 
     In this embodiment, the first top electrode  20 A extends along a direction parallel to the second axis Y on the second inner wall  10 B of the movable mass  7 , partially facing the top surface  7 A of the movable mass  7  and partially on the opening  9 . Stated differently, the first top electrode  20 A overlaps both the top surface  7 A of the movable mass  7  and the opening  9   
     The first top electrode  20 A extends throughout the length L c  of the opening  9 , in particular here it has a greater length. However, the first top electrode  20 A may have a smaller length than the length L c  of the opening  9 . 
     In detail, the first top electrode  20 A has, at the second inner wall  10 B, a variable surface Si facing and overlapping the top surface  7 A of the movable mass  7  and having, at rest, a width L ov1,r  along the first axis X, for example equal to half the width W 1 . 
     The second top electrode  20 B extends suspended on the movable mass  7 , at the first height gi along the third axis Z from the top surface  7 A of the movable mass  7 , and has a width W′ 2  along the first axis X, which may be chosen as a function of a maximum displacement of the movable mass  7 , in use, along the first axis X, as described below. 
     However, the first top electrode  20 A and the second top electrode  20 B may extend to heights different from each other from the top surface  7 A of the movable mass  7 . 
     In this embodiment, the width W′ 2  of the second top electrode  20 B is equal to the width W 1  of the first top electrode  20 A. However, the width W′ 2  and the width W 1  may be different from each other. 
     The second top electrode  20 B extends along a direction parallel to the second axis Y on the first inner wall  10 A of the movable mass  7 , partially facing the top surface  7 A of the movable mass  7  and partially on the opening  9 . Stated differently, the second top electrode  20 B overlaps both the top surface  7 A of the movable mass  7  and the opening  9   
     In detail, the second top electrode  20 B has, at the first inner wall  10 A, a variable surface S′ 2  facing and overlapping the top surface  7 A of the movable mass  7  and having, at rest, a width L&#39; ov2,r  along the first axis X, for example equal to half the width W 2 , here equal to the width L ov1,r  of the variable surface Si of the first top electrode  20 A. 
     The second top electrode  20 B is equal to the first top electrode  20 A, translated parallel to the first axis X. However, the first top electrode  20 A and the second top electrode  20 B may have shapes and dimensions different from each other. 
     In this embodiment, the bottom compensation electrode group  21  comprises a first bottom electrode  21 A and a second bottom electrode  21 B, of semiconductor material such as for example silicon or polysilicon. 
     The first bottom electrode  21 A and the second bottom electrode  21 B are fixed to the substrate  2  and each extend to a smaller coordinate along the third axis Z with respect to the bottom surface  7 B of the movable mass  7 . 
     In detail, the first bottom electrode  21 A extends below a respective portion of the movable mass  7 , at a second height g 2  along the third axis Z from the bottom surface  7 B of the movable mass  7 , and has a width W′ 1  along the first axis X, which may be chosen as a function of a maximum displacement of the movable mass  7 , in use, along the first axis X, as described below. 
     In this embodiment, the first bottom electrode  21 A extends parallel to the second top electrode  20 B, under the first inner wall  10 A of the movable mass  7 , partially facing the bottom surface  7 B of the movable mass  7  and partially under the opening  9 . 
     As shown in  FIG.  1 A , wherein the top compensation electrode group  20  is shown transparently for sake of clarity, the first bottom electrode  21 A has, in this embodiment, a length, parallel to the second axis Y, greater than the length L c  of the opening  9 . However, the first bottom electrode  21 A may have a smaller length than the length L c  of the opening  9 . 
     Furthermore, here, the first bottom electrode  21 A has a length, along the second axis Y, equal to the length, along the second axis Y, of the portion of the second top electrode  20 B facing the top surface  7 A of the movable mass  7 . 
     In detail, again with reference to  FIG.  2   , the first bottom electrode  21 A has, at the first inner wall  10 A, a variable surface S′ 1  facing and overlapping the bottom surface  7 B of the movable mass  7  and having, at rest, a width L&#39; ov1,r  along the first axis X, for example equal to half the width W′ 1 . 
     In this embodiment, the width L&#39; ov1,r  of the variable surface S′ 1  of the first bottom electrode  21 A is equal to the width L ov1,r  of the variable surface Si of the first top electrode  20 A. However, the width L&#39; ov1,r  may be different from the width L ov1,r . 
     The second bottom electrode  21 B extends below a respective portion of the movable mass  7 , at the second height g 2  along the third axis Z from the bottom surface  7 B of the movable mass  7  and has a width W 2  along the first axis X, which may be chosen as a function of a maximum displacement of the movable mass  7 , in use, along the first axis X, as described below. 
     The width W 2  of the second bottom electrode  21 B may be equal to or different from, here equal to, the width W′ 2  of the first bottom electrode  21 A. 
     In this embodiment, the second bottom electrode  21 B extends parallel to the first top electrode  20 A under the second inner wall  10 B of the movable mass  7 , partially facing the bottom surface  7 B of the movable mass  7  and partially under the opening  9 . 
     As shown in  FIG.  1 A , the second bottom electrode  21 B has a length, parallel to the second axis Y, greater than the length L c  of the opening  9 . However, the second bottom electrode  21 B may have a smaller length than the length L c  of the opening  9 . 
     The second bottom electrode  21 B may have a length, along the second axis Y, equal or different, here equal, with respect to the first bottom electrode  21 A. 
     In detail, again with reference to  FIG.  2   , the second bottom electrode  21 B has a variable surface S 2  facing and overlapping the bottom surface  7 B of the movable mass  7  and having, at rest, a width L ov2,r  along the first axis X, for example equal to half the width W 2 . 
     In this embodiment, the width L ov2,r  of the variable surface S 2  of the second bottom electrode  21 B is equal to the width L&#39; ov2,r  of the variable surface S′ 2  of the second top electrode  20 B. However, the width L ov2,r  may be different from the width L&#39; ov2,r . 
     In practice, in this embodiment, the first top electrode  20 A, the first bottom electrode  21 A, the second top electrode  20 B and the second bottom electrode  21 B have, at rest, a same facing area on the movable mass  7 . However, the first top electrode  20 A, the first bottom electrode  21 A, the second top electrode  20 B and the second bottom electrode  21 B may have different facing areas on the movable mass  7 . For example, the first top electrode  20 A may have a same facing area as the first bottom electrode  21 A, or the second top electrode  20 B may have a same facing area as the second bottom electrode  21 B. 
     The first detection unit  4  also comprises a fixed detection electrode  30  (represented by a dashed line in  FIG.  1   ), which is fixed to the substrate  2  and extends under a respective portion of the movable mass  7 , facing the bottom surface  7 B of the movable mass  7 . 
     The fixed detection electrode  30  is capacitively coupled to the movable mass  7  and is configured to detect a movement of the movable mass  7  along a detection axis S parallel to the third axis Z. 
     The first detection unit  4  also comprises a fixed driving electrode  33  extending at a distance, along the first axis X, from an outer wall  34  of the movable mass  7 . 
     The fixed driving electrode  33  is capacitively coupled to the movable mass  7  and is configured to cause a movement of the movable mass  7  along a driving axis D parallel to the first axis X. 
     The second detection unit  5  is equal to the first detection unit  4 ; as a result, the elements of the second detection unit  5  are indicated by the same reference numerals, with the addition of an apex, as the respective elements of the first detection unit  4  and are not further described in detail. 
     The second detection unit  5  is formed by a movable mass  7 ′ having an opening  9 ′ and coupled to the central anchoring portion  15  and to respective anchoring regions  13 ′ through flexures  14 ′. 
     The second detection unit  5  comprises a respective top compensation electrode group  20 ′ and a respective bottom compensation electrode group, not shown here. 
     The top compensation electrode group  20 ′ also includes here a first top electrode 20A′ and a second top electrode  20 B′ each fixed to the substrate  2  through a respective anchoring pillar  23 A′,  23 B′. 
     Furthermore, the second detection unit  5  comprises a respective fixed detection electrode  30 ′ and a respective fixed driving electrode  33 ′, coupled to the movable mass  7 ′ to detect a movement thereof along the detection axis S and, respectively, drive a movement thereof along the driving axis D. 
     Hereinafter an operation of the MEMS gyroscope  1  will be described with reference to the first detection unit  4 . However, as it will become clear to the person skilled in the art, what described with reference to the first detection unit  4  applies, mutatis mutandis, also to the second detection unit  5 , unless otherwise specified. 
     In use, when it is desired to detect a rotation of angular speed Ω Y  of the MEMS gyroscope  1  around the second axis Y, the fixed driving electrodes  33 ,  33 ′ of the first and the second detection units  4 ,  5  may be suitably biased so as to cause a movement of the movable mass  7  of the first detection unit  4  and of the movable mass  7 ′ of the second detection unit  5 , in particular to cause an oscillation at a respective resonance frequency, along the driving axis D. 
     In detail, the displacement of the movable mass  7  along the driving axis D, with respect to the equilibrium/rest position shown in  FIG.  2   , for example the position variation of the first inner wall  10 A or of the second inner wall  10 B with respect to the equilibrium/rest position of  FIG.  2   , will be indicated hereinafter as offset x D . 
     When the movable mass  7  oscillates along the driving axis D, in the presence of the angular speed Ω Y , the movable mass  7  is affected by a Coriolis force directed along the detection axis S. The Coriolis force causes a displacement of the movable mass  7  along the detection axis S, thus generating a capacitance variation between the movable mass  7  and the detection electrode  30 , which may be detected by an external control circuit, not shown here. 
     For example, to obtain a differential detection of the angular speed Ω Y  by the MEMS gyroscope  1 , the fixed driving electrodes  33 ,  33 ′ may be biased, in a per se known manner, such that the movable masses  7 ,  7 ′ mutually oscillate in counterphase along the driving axis D. 
     When the movable mass  7  is driven in oscillation along the driving axis D, the movable mass  7  may be subject to a quadrature force parallel to the detection axis S, even in the absence of the angular speed Ω Y . This quadrature force may be caused by structural asymmetries of the MEMS gyroscope  1 , for example asymmetries in the flexures  14  due to process variabilities during the manufacturing of the MEMS gyroscope  1 . 
     For the purposes of the discussion that follows, it is assumed, by way of example, that the movable mass  7  is subject, when moving towards increasing coordinates along the driving axis D ( FIG.  5   ), i.e., to the right in  FIGS.  1  and  2   , to a quadrature force parallel to the third axis Z and directed upwards, i.e., which would cause the movable mass  7  to move towards the top compensation electrode group  20 . 
     As a result, it is assumed that the movable mass  7  is subject, when moving towards decreasing coordinates of the driving axis D, i.e., to the left in  FIGS.  1  and  2   , to a quadrature force parallel to the third axis Z and directed downwards, i.e., which would cause the movable mass  7  to move towards the bottom compensation electrode group  21 . 
     To compensate for the contribution of the quadrature force on the movable mass  7 , a first voltage Vi is applied to the first top electrode  20 A and to the first bottom electrode  21 A and a second voltage V 2  is applied to the second top electrode  20 B and to the first bottom electrode  21 A, for example through the external control circuit. 
     In this regard, the first top electrode  20 A and the first bottom electrode  21 A may be coupled to respective voltage application elements  44 , for example connection tracks or pads, indicated schematically in  FIG.  2   , which allow the biasing thereof to the first voltage Vi. 
     The second top electrode  20 B and the second bottom electrode  21 B may be coupled to respective voltage application elements  45 , for example connection tracks or pads, indicated schematically in  FIG.  2   , which allow the biasing thereof to the second voltage V 2 . 
     The first voltage Vi may be equal to V CM  - ΔV and the second voltage V 2  may be equal to V CM  + ΔV, where V CM  is a common mode voltage and ΔV a differential corrective voltage. The common mode voltage V CM  and the differential corrective voltage ΔV, for example of continuous type, may be determined in a calibration step of the MEMS gyroscope  1 . 
     Each of the first top electrode  20 A, the second top electrode  20 B, the first bottom electrode  21 A and the second bottom electrode  21 B exerts a respective electrostatic force on the movable mass  7 . 
     In detail, at rest, the first and the second top electrodes  20 A,  20 B exert, on the movable mass  7 , respectively a force F 1,r  and a force F′ 1,r  equal in magnitude but directed along two opposite directions parallel to the detection axis S. 
     In fact, at rest, in the embodiment shown in  FIGS.  1  and  2   , the first and the second top electrodes  20 A,  20 B are at a same distance (first height gi and second height g 2 ) from the movable mass  7 , have a same facing surface on the movable mass  7 , and are at the same voltage with respect to the movable mass  7 . 
     Similarly, the first and the second bottom electrodes  21 A,  21 B exert, on the movable mass  7 , respectively a force F 2,r  and a force F′ 2,r  equal in magnitude but directed along two opposite directions parallel to the detection axis S. 
     In fact, in the embodiment shown in  FIGS.  1  and  2   , the first and the second bottom electrodes  21 A,  21 B are at a same distance (first height gi and second height g 2 ) from the movable mass  7 , have a same facing surface on the movable mass  7 , and are at the same voltage with respect to the movable mass  7 . 
     Furthermore, the force F 1,r  exerted by the first top electrode  20 A is lower than the force F′ 2,r  exerted by the second top electrode  20 B, since the first voltage Vi is lower than the second voltage V 2 . 
     In practice, as also schematically shown in  FIG.  5   , in the equilibrium position ( FIG.  2   ), the movable mass  7  is subject, as a whole, to a quadrature compensation force F Q,comp,r  that is zero. 
     Furthermore, in the equilibrium position, the quadrature force is also zero. In fact, the quadrature force is proportional to the offset x D  of the movable mass  7 . 
     When the movable mass  7  has a positive offset x D , i.e., it moves towards increasing coordinates along the driving axis D (to the right in  FIG.  3   ), the movable mass  7  is subject to a variable quadrature compensation force F Q,comp , parallel to the detection axis S and directed downwards in  FIG.  3   . 
     In detail, when the movable mass  7  moves to the right, the area of the variable surface Si of the first top electrode  20 A and the area of the variable surface S 2  of the second bottom electrode  21 B increase with respect to the rest condition of  FIG.  2   . 
     Conversely, the area of the variable surface S′ 2  of the second top electrode  20 B and the area of the variable surface S′ 1  of the first bottom electrode  21 A decrease with respect to the rest condition of  FIG.  2   . 
     By way of example,  FIG.  3    shows the MEMS gyroscope  1  along section line II-II of  FIG.  1   , when the movable mass  7  is subject to a maximum and positive offset x D , equal to +X D , with respect to the equilibrium position. In  FIG.  3   , the rest position of the movable mass  7  is indicated for sake of clarity by a dashed line. 
     In the condition of maximum positive offset +X D , a maximum positive quadrature force F Q,+ , directed upwards in  FIG.  3   , acts on the movable mass  7 . 
     In detail, in the condition of maximum positive offset +X D  of  FIG.  3   , the variable surface Si of the first top electrode  20 A has a maximum width L ov1,+ , greater than the respective width L ov1,r  of the rest condition of  FIG.  2   . 
     In particular, here, it is L ov1,+  = L ov1,r  + X D . 
     As a result, the first top electrode  20 A exerts, on the movable mass  7 , an electrostatic force F 1,+  that is greater than the electrostatic force F 1,r  of the rest condition of  FIG.  2   . 
     Similarly, in the condition of maximum positive offset +X D  of  FIG.  3   , the variable surface S 2  of the second bottom electrode  21 B has a maximum width L ov2,+ , greater than the respective width L ov2,r  of the rest condition of  FIG.  2   . 
     In particular, here, L ov2,+  = L ov2,r  + X D . 
     As a result, the second bottom electrode  21 B exerts, on the movable mass  7 , an electrostatic force F 2,+  that is greater than the electrostatic force F 2,r  of the rest condition of  FIG.  2   . 
     Furthermore, the electrostatic force F 1,+  exerted by the first top electrode  20 A is lower, in magnitude, than the electrostatic force F 2,+  exerted by the second bottom electrode  21 B, since the first voltage Vi is lower than the second voltage V 2 . 
     Again with reference to the condition of maximum positive offset +X D  of  FIG.  3   , the variable surface S′ 2  of the second top electrode  10 B has a minimum width L&#39; ov2,+ , smaller than the respective width L&#39; ov2,r  of the rest condition of  FIG.  2   . 
     In particular, here, it is L&#39; ov2,+  = L&#39; ov2,r  - X D . 
     As a result, the second top electrode  20 B exerts, on the movable mass  7 , an electrostatic force F′ 2,+  that is lower than the respective electrostatic force F′ 2,r  of the rest condition of  FIG.  2   . 
     Similarly, the variable surface S′ 1  of the first bottom electrode  21 A has a minimum width L&#39; ov1,+ , lower than the respective width L&#39; ov1,r  of the rest condition of  FIG.  2   . 
     In particular, here, L&#39; ov1,+  = L&#39; ov1,r  - X D . 
     As a result, the first bottom electrode  21 A exerts, on the movable mass  7 , an electrostatic force F′ 1,+  that is lower than the electrostatic force F′ 1,r  of the rest condition of  FIG.  2   . 
     Furthermore, the electrostatic force F′ 1,+  exerted by the first bottom electrode  21 A is lower, in magnitude, than the electrostatic force F′ 2,+  exerted by the second top electrode  20 B, since the first voltage Vi is lower than the second voltage V 2 . 
     In practice, as also shown in the force diagram of  FIG.  5   , in the condition of maximum positive offset +X D  of the movable mass  7  along the driving axis D, the movable mass  7  is subject to a total quadrature compensation force F Q,comp,+  different from zero, parallel to the detection axis S and directed downwards in  FIG.  3   . 
     As a result, the total quadrature compensation force F Q,comp,+  may compensate for the maximum positive quadrature force F Q,+ . 
     When the movable mass  7  has a negative offset x D , i.e., it moves towards decreasing coordinates along the driving axis D (to the left in  FIG.  4   ), the movable mass  7  is subject to a variable quadrature compensation force F Q,Comp , parallel to the detection axis S and directed upwards in  FIG.  4   . 
     In detail, when the movable mass  7  moves to the left, the area of the variable surface Si of the first top electrode  20 A and the area of the variable surface S 2  of the second bottom electrode  21 B decrease with respect to the rest condition of  FIG.  2   . 
     Conversely, the area of the variable surface S′ 2  of the second top electrode  20 B and the area of the variable surface S′ 1  of the first bottom electrode  21 A increase with respect to the rest condition of  FIG.  2   . 
     By way of example,  FIG.  4    shows the MEMS gyroscope  1  along section line II-II of  FIG.  1   , when the movable mass  7  is subject to an offset x D  that is maximum and negative, equal to -X D , with respect to the equilibrium position xd=0. In  FIG.  4   , the rest position of the movable mass  7  is indicated for sake of clarity by a dashed line. 
     In the condition of maximum negative offset -X D , a maximum negative quadrature force F Q,- , directed downwards in  FIG.  3   , acts on the movable mass  7 . 
     In detail, in the condition of maximum negative offset -X D  of  FIG.  4   , the variable surface Si of the first top electrode  20 A has a minimum width L ov1,- , smaller than the respective width L ov1,r  of the rest condition of  FIG.  2   . 
     In particular, here, it is L ov1,-  = L ov1,r  - X D . 
     As a result, the first top electrode  20 A exerts, on the movable mass  7 , an electrostatic force F 1,-  that is lower than the electrostatic force F 1,r  of the rest condition of  FIG.  2   . 
     Similarly, again with reference to the condition of maximum negative offset -X D  of  FIG.  4   , the variable surface S 2  of the second bottom electrode  21 B has a minimum width L ov2,- , smaller than the respective width L ov2,r  of the rest condition of  FIG.  2   . 
     In particular, here, L ov2,-  = L ov2,r  - X D . 
     As a result, the second bottom electrode  21 B exerts, on the movable mass  7 , an electrostatic force F 2,-  that is lower than the electrostatic force F 2,r  of the rest condition of  FIG.  2   . 
     Furthermore, the electrostatic force F 1,-  exerted by the first top electrode  20 A is lower, in magnitude, than the electrostatic force F 2,-  exerted by the second bottom electrode  21 B, since the first voltage Vi is lower than the second voltage V 2 . 
     Again with reference to the condition of maximum negative offset -X D  of  FIG.  4   , the variable surface S′ 2  of the second top electrode  10 B has a maximum width L&#39; ov2,- , greater than the respective width L&#39; ov2,r  of the rest condition of  FIG.  2   . 
     In particular, here, it is L&#39; ov2,-  = L&#39; ov2,r  + X D . 
     As a result, the second top electrode  20 B exerts, on the movable mass  7 , an electrostatic force F′ 2,-  that is greater than the respective electrostatic force F′ 2,r  of the rest condition of  FIG.  2   . 
     Similarly, the variable surface S′ 1  of the first bottom electrode  21 A has a maximum width L&#39; ov1,- , greater than the respective width L&#39; ov1,r  of the rest condition of  FIG.  2   . 
     In particular, here, L&#39; ov1,-  = L&#39; ov1,r  + X D . 
     As a result, the first bottom electrode  21 A exerts, on the movable mass  7 , an electrostatic force F′ 1,-  that is greater than the electrostatic force F′ 1,r  of the rest condition of  FIG.  2   . 
     Furthermore, the electrostatic force F′ 1,-  exerted by the first bottom electrode  21 A is lower, in magnitude, than the electrostatic force F′ 2,-  exerted by the second top electrode  20 B, since the first voltage Vi is lower than the second voltage V 2 . 
     In practice, as also shown in the force diagram of  FIG.  5   , in the condition of maximum negative offset -X D  of the movable mass  7  along the driving axis D, the movable mass  7  is subject to a total quadrature compensation force F Q,comp,-  different from zero, parallel to the detection axis S and directed upwards in  FIG.  4   . 
     As a result, the total quadrature compensation force F Q,comp,-  may compensate for the maximum negative quadrature force F Q,- . 
     With reference to  FIGS.  3  and  4    and to what has been described above, the width along the first axis X of the electrodes of the top compensation electrode group  20  and/or of the bottom compensation electrode group  21 , may be chosen so that even in the condition of maximum positive offset +X D  the variable surfaces of the electrodes of the top compensation electrode group  20  and/or of the bottom compensation electrode group  21  which face the movable mass  7  have a non-zero width. 
     Additionally or alternatively, the width along the first axis X of the electrodes of the top compensation electrode group  20  and/or of the bottom compensation electrode group  21 , may be chosen so that even in the condition of maximum negative offset -X D  the variable surfaces of the electrodes of the top compensation electrode group  20  and/or of the bottom compensation electrode group  21  which face the movable mass  7  have a non-zero width. 
     In other words, the electrodes of the top compensation electrode group  20  and/or of the bottom compensation electrode group  21  may be designed to have, in any driving condition of the movable mass  7 , a portion facing directly, along the third axis Z, the movable mass  7 . 
     For example, assuming that the maximum positive offset +X D  and the maximum negative offset -X D  are equal in magnitude and comprised, for example, between 2 µm and 12 µm, the width W 1 , W′ 2  of the electrodes of the top compensation electrode group  20  and/or the width W 2 , W′ 1  of the bottom compensation electrode group  21  may be chosen so as to be greater than or equal to twice the value, in magnitude, of the maximum positive offset +X D , for example said widths may each be comprised between 4 µm and 26 µm. 
     The presence of the top compensation electrode group  20  and of the bottom compensation electrode group  21  allows to obtain a total quadrature compensation force that is greater than a known MEMS gyroscope having, for example, the bottom compensation electrode group without the top compensation electrode group. 
     For example, in the simulation of  FIG.  6    performed by the Applicant, the solid line curve and the dashed line curve show the trend of the quadrature compensation force F Q,comp  (normalized with respect to the quadrature compensation force of the respective rest condition) as a function of the offset x D , respectively for the MEMS gyroscope  1  and for a known MEMS gyroscope having the bottom quadrature compensation electrode group without the top compensation electrode group. 
     As is noted, in the MEMS gyroscope  1 , the movable mass  7  is subject to a quadrature compensation force that is greater, in magnitude, than the known MEMS gyroscope indicated by the dashed line curve. 
     For example, the movable mass of the present MEMS gyroscope may be subject to a quadrature compensation force that is greater than an amount comprised between 40% and twice the known gyroscope, according to the specific implementation of the present MEMS gyroscope. 
     It will be clear to the person skilled in the art that what has been described above for the first detection unit  4  also applies to the second detection unit  5 . 
     In fact, when the movable mass  7 ′ is driven in motion along the driving direction, the facing surfaces of the top electrode group  20 ′ and of the bottom electrode group vary as a function of the displacement along the driving axis D of the movable mass  7 ′. By biasing the top electrode group  20 ′ and the bottom electrode group of the second detection unit  5 , it is thus possible to compensate for the quadrature force acting, in use, on the movable mass  7 ′. 
     Thus, in practice, the MEMS gyroscope  1  is able to effectively compensate for the quadrature force acting on the movable masses  7 ,  7 ′, for example reducing the die area occupation, and therefore the cost, of the MEMS gyroscope  1  and using lower voltages, and thus decreasing the energy consumption of the MEMS gyroscope  1 . 
     Furthermore, again with reference to the first detection unit  4  for simplicity, the presence of the bottom compensation electrode group  21  and of the top compensation electrode group  20  allows to prevent that variations at rest of the first height gi and/or of the second height g 2  ( FIG.  2   ), for example caused by temperature, humidity, mechanical stress or other external factors, degrade the performances of the MEMS gyroscope  1 . 
     Consider, for example, that the MEMS gyroscope  1  is accommodated in an encapsulating body or package, not shown here, for example to protect the MEMS gyroscope  1  from external contaminants, and consider that the package is subject, during the life of the MEMS gyroscope  1 , to a deformation caused by external agents such as temperature, mechanical stresses, etc. 
     This deformation may generate a variation Δg in the first height gi and in the second height g 2 . For example, the deformation may cause an average approach of the movable mass  7  towards the top compensation electrode group  20  by an amount equal to the variation Δg, and an average separation of the movable mass  7  away from the bottom compensation electrode group  21  by an amount equal to the variation Δg. 
     As a result, taking by way of example the first top electrode  20 A, it is possible to demonstrate that the electrostatic force exerted by the first top electrode  20 A on the movable mass  7  as a function of the offset x D  of the movable mass  7  is proportional to the amount x d ·V 2   1 /(g 1  - Δg) 2 . 
     Similarly, the electrostatic force exerted by the first bottom electrode  21 A on the movable mass  7  as a function of the offset x D  of the movable mass  7  is proportional to the amount x d ·V 2   1 /(g 2  + Δg) 2 . 
     In a similar manner it is obtained that the electrostatic force exerted by the second top electrode  20 B is proportional to x d ·V 2   2 /(g 2  - Δg) 2  and the electrostatic force exerted by the second bottom electrode  21 B is proportional to x d ·V 2   2 /(g 2  + Δg) 2 . 
     It is also possible to demonstrate that the presence of the bottom compensation electrode group  21  and of the top compensation electrode group  20  allows the electrostatic softening variation to be reduced as a function of the variation Δg, with respect, for example, to a known MEMS gyroscope having the bottom quadrature compensation electrode group without the top compensation electrode group. 
     For example, in the simulation of  FIG.  7    performed by the Applicant, the solid line curve and the dashed line curve show the behavior of the electrostatic softening percentage variation Δ χ  as a function of the variation Δg, respectively for the MEMS gyroscope  1  and for a known MEMS gyroscope having the bottom quadrature compensation electrode group without the top compensation electrode group. 
     As is noted, the MEMS gyroscope  1  is subject to a much lower electrostatic softening percentage variation than the known MEMS gyroscope indicated by the dashed line curve, in particular even up to ten times lower. 
     It will be clear to the person skilled in the art that this reduction in the electrostatic softening percentage variation described above for the first detection unit  4  also applies to the second detection unit  5 . 
     As a result, the MEMS gyroscope  1  has a higher sensitivity stability and therefore a higher accuracy and reliability in detecting the angular speed Ω Y . 
       FIGS.  8  and  9    show another embodiment of the present MEMS gyroscope, here indicated by  100 . 
     The MEMS gyroscope  100  has a general structure similar to the MEMS gyroscope  1  of  FIG.  1   ; as a result, elements in common are indicated by the same reference numerals and are not further described. 
     In detail, the MEMS gyroscope  100  is formed by the substrate  2  and comprises a first detection unit, here indicated by  104 , and a second detection unit, here indicated by  105 , each configured to detect a roll angular speed Ω Y  of the MEMS gyroscope  1  around the second axis Y. 
     The first detection unit  104  comprises a movable mass, here indicated by  107  and having a top surface  107 A and a bottom surface  107 B. 
     The first detection unit  104  further comprises also a quadrature compensation unit, here indicated by  106 , and configured to cancel, in use, a quadrature force acting on the movable mass  107 , as described in detail below. 
     The movable mass  107  is formed by a discontinuous portion  108  and by a solid portion  110 , which here surrounds the discontinuous portion  108 . 
     The solid portion  110  is coupled to the anchoring regions  13  and to the central anchoring region  15  via flexures  14 . 
     The discontinuous portion  108  has a length L c  along the second axis Y and is formed by one or more arms, here a plurality of arms  112  mutually separated from each other, along the second axis Y, by a plurality of openings  109 . 
     The arms  112 , here rectangular in shape, each extend along a direction parallel to the first axis X, between two ends integral with the solid portion  110  of the movable mass  107 , and have a width L s  along the second axis Y for example comprised between 0,5 µm and 2 µm. 
     However, the arms  112  may have a different shape, for example squared or trapezoidal, and may for example extend along a direction transverse to the first axis X. 
     The openings  109  are each delimited, along the first axis X, by a respective first inner wall  110 A and a respective second inner wall  110 B of the solid portion  110  of the movable mass  107 . 
     In this embodiment, the openings  109  each have a width L g , along the second axis Y, greater than 1 µm, for example comprised between 1 µm and 5 µm, which is uniform throughout the respective length along the first axis X. 
     In practice, in this embodiment, the first inner walls  110 A and the second inner walls  110 B each have a length, along the second axis Y, equal to the width L g  of the openings  109 . 
     The number of arms  112 , the width L s  of the arms  112  and the width L g  of the openings  109  may be determined, during the design step, according to the specific application, in particular as a function of specific manufacturing desires, as described in greater detail below. 
     The first detection unit  104  further comprises, here as well, the top electrode group  20 , including the first top electrode  20 A and the second top electrode  20 B, and the bottom electrode group  21 , including the first bottom electrode  21 A and the second bottom electrode (not shown here). 
     The discontinuous portion  108  of the movable mass  107 , the top electrode group  20  and the bottom electrode group  21  form the quadrature compensation unit  106 . 
     The first top electrode  20 A and the second top electrode  20 B each extend suspended above the movable mass  107 , from a respective anchoring pillar  23 A,  23 B integral with the substrate  2 . 
     The first top electrode  20 A extends at the first height gi along the third axis Z from the top surface  107 A of the movable mass  107 , on the second inner walls  110 B of the solid portion  110  of the movable mass  107 . 
     In detail, the first top electrode  20 A extends partially on the solid portion  110  of the movable mass  107  and partially on the discontinuous portion  108  of the movable mass  107 . 
     In this embodiment, the first top electrode  20 A extends throughout the length L c  of the discontinuous portion  108 ; in particular, the first top electrode  20 A here has a length that is greater than the length L c  of the discontinuous portion  108 , along the second axis Y. 
     The second top electrode  20 B extends at the first height gi along the third axis Z from the top surface  107 A of the movable mass  107 , on the first inner walls  110 A of the solid portion  110  of the movable mass  107 . 
     In detail, in this embodiment, the second top electrode  21 B is equal to the first top electrode  20 A and translated parallel to the first axis X, so as to partially extend on the solid portion  110  of the movable mass  107  and partially on the discontinuous portion  108  of the movable mass  107 . 
     The first bottom electrode  21 A and the second bottom electrode  21 B are fixed to the substrate  2  and extend below the movable mass  107 , at the second height g 2  along the third axis Z from the bottom surface  107 B of the movable mass  107 . 
     In detail, in this embodiment, the first bottom electrode  21 A and the second bottom electrode (not shown) extend parallel to the second top electrode  20 B, under the first inner wall  110 A of the solid portion  110  of the movable mass  107 , and, respectively, parallel to the first top electrode  20 A, under the second inner wall  110 B of the solid portion  110  of the movable mass  107 . 
     In this embodiment, the first bottom electrode  21 A and the second bottom electrode (not shown) extend throughout the length L c  of the discontinuous portion  108 ; in particular, for a length that is greater than the length L c  along the second axis Y. 
     The first detection unit  104  further comprises the fixed detection electrode  30  (represented by a dashed line in  FIG.  8   ), which is fixed to the substrate  2  and extends under the solid portion  110  of the movable mass  107 , facing the bottom surface  107 B of the movable mass  107 . 
     The first detection unit  104  also comprises the fixed driving electrode  33  extending at a distance, along the first axis X, from the movable mass  107 . 
     Also in this embodiment, the second detection unit  105  is equal to the first detection unit  104  and arranged symmetrically thereto with respect to the central plane A. As a result, the elements of the second detection unit  105  are indicated by the same reference numerals, with the addition of an apex, of the respective elements of the first detection unit  104  and are not further described in detail. 
     The second detection unit  105  is formed by a movable mass  107 ′ comprising a discontinuous portion  108 ′ and a solid portion  110 ′, and is coupled to the central anchoring portion  15  and to respective anchoring regions  13 ′ through flexures  14 ′. 
     The second detection unit  105  comprises a respective top compensation electrode group  20 ′ including a first and a second top electrode  20 A′,  20 B′, and a respective bottom compensation electrode group, not shown here. 
     The top compensation electrode group  20 ′ also includes here a first top electrode 20A′ and a second top electrode  20 B′ each fixed to the substrate  2  through a respective anchoring pillar  23 A′,  23 B′. 
     Furthermore, the second detection unit  5  comprises a respective fixed detection electrode  30 ′ and a respective fixed driving electrode  33 ′, coupled to the movable mass  107 ′ to detect a movement thereof along the detection axis S and, respectively, to drive a movement thereof along the driving axis D. 
     In use, with reference to the first detection unit  104 , the presence of the top electrode group  20  and of the bottom electrode group  21  allows to cancel a quadrature force acting on the movable mass  107 , similarly to what has been discussed for the MEMS gyroscope  1 . 
     Furthermore, also in the MEMS gyroscope  100 , the top electrode group  20  and the bottom electrode group  21  ensure that any variation of the first and the second heights gi, g 2 , does not cause, as a first approximation, an electrostatic softening variation of the MEMS gyroscope  100 . 
     In practice, also the MEMS gyroscope  100  therefore has a high reliability and accuracy in detecting the angular speed Ω Y . 
     Furthermore, the arms  112  may be useful during the manufacturing of the MEMS gyroscope  100 . In fact, the top electrode group  20  may be manufactured by depositing a sacrificial layer, for example of oxide, on the top surface  107 A of the movable mass  107 , by growing a silicon or polysilicon epitaxial layer on the sacrificial layer, and by removing the sacrificial layer. 
     The arms  112  may act as a support base for the sacrificial layer and therefore may increase the mechanical stability of the MEMS gyroscope  1  during manufacturing, improving its reliability. 
     The arms  112  may be designed so that the width L g  of the openings  109  is as large as possible. In this manner, it is possible to maximize the variation of the variable facing surface of the top compensation electrode group  20  on the movable mass  7  (and therefore to maximize the quadrature compensation force variation), as a function of the offset x D  of the movable mass  7 . 
       FIG.  10    shows a different embodiment of the present MEMS gyroscope, here indicated by  200 , in the Cartesian reference system XYZ. 
     The MEMS gyroscope  200  is of biaxial type and is configured to detect a roll angular speed Ω Y  of the MEMS gyroscope  100  around the second axis Y and a pitch angular speed Ω X  of the MEMS gyroscope  100  around the first axis X. 
     The MEMS gyroscope  200  comprises a first and a second detection unit  204 ,  205 , configured to detect the roll angular speed Ω Y , and a third and a fourth detection unit  216 ,  217 , configured to detect the pitch angular speed Qx. 
     The first and second detection units  204 ,  205  are here equal to each other and are arranged symmetrically with respect to a first central plane A passing through a center O of the MEMS gyroscope  200  and parallel to a plane YZ formed by the second axis Y and the third axis Z. Furthermore, the first and the second detection units  204 ,  205  have a general structure similar to the first and the second detection units  4 ,  5  of the MEMS gyroscope  1  of  FIG.  1   . As a result, elements in common are indicated by the same reference numerals and are not further described. 
     In detail, the first detection unit  204  is formed by a movable mass  207  comprising a detection mass  210  and a compensation mass  208 , mutually coupled by a connection element  211 . 
     The connection element  211  may be a flexure, for example linear or folded, or rigid, depending on the specific application. 
     The compensation mass  208  laterally delimits an opening  209 , which crosses the compensation mass  208  throughout its thickness along the third axis Z, as described for the opening  9  of the MEMS gyroscope  1  of  FIG.  1   . 
     The compensation mass  208  is coupled to respective anchoring regions  13 , fixed to the substrate  2 , through respective flexures  14 . 
     The detection mass  210  is coupled to a central anchoring region  15  through a respective flexure  14 . 
     The first detection unit  204  further comprises, as described with reference to the MEMS gyroscope  1  of  FIGS.  1  and  2   , the top compensation electrode group  20  extending on the compensation mass  208 , facing, at rest, partially the compensation mass  208  and partially the opening  209 , and the bottom compensation electrode group (not shown here), extending under the compensation mass  208  parallel to the top compensation electrode group  20 . 
     The top electrode group  20 , the bottom electrode group and the opening  209  form a quadrature compensation unit, here indicated by  215 . 
     The first detection unit  204  also comprises the driving electrode  33  and the detection electrode  30 . 
     The driving electrode  33  is capacitively coupled to the compensation mass  208  and is configured to cause a movement thereof, in particular an oscillation at a resonance frequency, along a first driving axis D1 parallel to the first axis X. 
     The detection electrode  30  is capacitively coupled to the detection mass  210  and is configured to detect a movement thereof along the detection axis S, parallel to the third axis Z. 
     Here as well, the elements of the second detection unit  205  are indicated with the same reference numerals, with the addition of an apex, as the respective elements of the first detection unit  204  and are not further described in detail. 
     The second detection unit  205  comprises a quadrature compensation unit  215 ′ and is formed by a movable mass  207 ′ comprising a compensation mass  208 ′ having an opening  209 ′, and a detection mass  210 ′, mutually coupled by a connection element  211 ′. 
     The third detection unit  216  is formed by a movable mass  227  comprising a respective compensation mass  230  and a respective detection mass  231 , mutually coupled by a respective connection element  233 , which may be elastic or rigid, depending on the specific application. 
     The compensation mass  230  is coupled to respective anchoring regions  237  through respective flexures  238 , which extend along the second axis Y and allow the movement of the compensation mass  230  with one or more degrees of freedom, here along the second axis Y and along the third axis Z. 
     The compensation mass  230  laterally delimits an opening  239 , which extends through the compensation mass  230  throughout its thickness, along the third axis Z. 
     The detection mass  231  is coupled to the central anchoring region  15  by a respective flexure  238 . 
     The third detection unit  216  further comprises a top compensation electrode group  241  and a bottom compensation electrode group (not shown here), which form, with the opening  239 , a quadrature compensation unit  246 , in a similar manner to what has been described for the compensation unit  6  of the MEMS gyroscope  1  of  FIG.  1   . 
     In detail, also in this embodiment, the top compensation electrode group  241  extends on the compensation mass  230  and comprises a first and a second top electrode  251 A,  251 B, fixed to the substrate  2  through respective anchoring pillars  252 A,  252 B. 
     The first and the second top electrodes  251 A,  251 B extend along a direction parallel to the first axis X, facing, at rest, partially on the compensation mass  230  and partially on the opening  239 . 
     The electrodes of the bottom compensation electrode group, not shown here, extend under the compensation mass  230 , parallel to the first and the second top electrodes  251 A,  251 B, similarly to what has been described for the bottom compensation electrode group  21  of the MEMS gyroscope  1 . 
     The third detection unit  205  further comprises a respective driving electrode  260  and a respective detection electrode  262 . 
     The driving electrode  260  extends at a distance, along the second axis Y, from a wall  263  of the compensation mass  230 . 
     The driving electrode  260  is capacitively coupled to the compensation mass  230  and is configured to cause a movement thereof, in particular an oscillation at a resonance frequency, along a second driving axis D2 parallel to the second axis Y. 
     The detection electrode  262  extends on the substrate  2 , under the detection mass  231 , facing thereto, and is configured to detect a movement of the detection mass  231  along the detection axis S. 
     The fourth detection unit  217  is here equal to the third detection unit  216  and symmetrically arranged thereto with respect to a second central plane B passing through the center O of the MEMS gyroscope  200  and parallel to a plane XZ formed by the first axis X and by the third axis Z. 
     The elements of the fourth detection unit  217  are indicated by the same reference numerals, with the addition of an apex, as the respective elements of the third detection unit  216 , and are not further described in detail. 
     The fourth detection unit  217  is formed by a movable mass  227 ′ comprising a compensation mass  230 ′ and a detection mass  231 ′, mutually coupled by a connection element  233 ′. 
     The compensation mass  230 ′ laterally delimits an opening  239 ′ and is coupled to respective anchoring regions  237 ′ through flexures  238 ′. The detection mass  231 ′ is coupled to the central anchoring region  15  by a respective flexure  238 ′. 
     The fourth detection unit  217  is further formed by a top compensation electrode group  241 ′ and a bottom compensation electrode group (not shown here), which form, with the opening  239 ′, a quadrature compensation unit  246 ′. 
     The top compensation electrode group  241 ′ comprises a first top electrode  251 A′ and a second top electrode  251 B′, each fixed to the substrate  2  by a respective anchoring pillar  252 A′,  252 B′. 
     The fourth detection unit  217 ′ comprises a driving electrode  260 ′, coupled to the compensation mass  230 ′, and a detection electrode  262 ′, coupled to the detection mass  231 ′. 
     In use, the first and the second detection units  204 ,  205  have a behavior similar to what has been discussed for the first and the second detection units  4 ,  5  of the MEMS gyroscope  1 . 
     Furthermore, it will be clear to the person skilled in the art that the third and the fourth detection units  216 ,  217  also have a behavior similar to that of the first and the second detection units  204 ,  205 , as regards the pitch angular speed Qx. 
     In practice, the MEMS gyroscope  200  has high detection performances both with respect to the roll angular speed Ω Y , and with respect to the pitch angular speed Qx. 
     Finally, it is clear that modifications and variations may be made to the MEMS gyroscopes  1 ,  100 ,  200  described and illustrated herein without thereby departing from the scope of the present disclosure. 
     For example, the total value of the compensation force applied to the movable mass may be adjusted by modifying the number of quadrature compensation units, i.e., by increasing the number of openings, top compensation electrodes and bottom compensation electrodes, depending on the specific application. 
     Shape and number of the anchoring pillars  23 A,  23 B,  252 A,  252 B of the top compensation electrode group  20 ,  241  may be different from what has been shown. For example, the top compensation electrode group  20 ,  241  may be constrained on two ends, i.e., the electrodes may be of the clamped-clamped type, so as to have a bridge shape on the respective movable mass. 
     Finally, the described embodiments may be combined to form further solutions. 
     A MEMS gyroscope ( 1 ;  100 ;  200 ) may be summarized as including a substrate ( 2 ); a movable mass ( 7 ,  7 ′;  107 ,  107 ′;  207 ,  207 ′,  227 ,  227 ′) suspended on the substrate and configured to carry out a movement in a driving direction (X, D; X, Y, D1, D2) and in a detection direction (Z, S) perpendicular to each other, the movable mass having a first face ( 7 A;  107 A) and a second face ( 7 B;  107 B) opposite to the first face; a first quadrature compensation electrode group ( 20 ,  20 ′;  241 ,  241 ′), fixed to the substrate and capacitively coupled to the movable mass, the first quadrature compensation electrode group facing the first face of the movable mass; and a second quadrature compensation electrode group ( 21 ,  21 ′), fixed to the substrate and capacitively coupled to the movable mass, the second quadrature compensation electrode group facing the second face of the movable mass, the first and the second quadrature compensation electrode groups each having a respective variable facing area (Si, S 2 , S′ 1 , S′ 2 ) on the movable mass as a result of the movement of the movable mass in the driving direction, wherein the first and the second quadrature compensation electrode groups are configured to exert an electrostatic force on the movable mass during the movement of the movable mass in the driving direction. 
     The movable mass may have a through opening ( 9 ;  109 ;  209 ,  239 ), the through opening extending through the movable mass ( 7 ,  7 ′;  107 ,  107 ′;  207 ,  207 ′,  227 ,  227 ′) between the first and the second faces of the movable mass, parallel to the detection direction (Z, S), the first quadrature compensation electrode group extending at a first height (gi), parallel to the detection direction, with respect to the first face of the movable mass and the second quadrature compensation electrode group extending at a second height (g 2 ), parallel to the detection direction, with respect to the second surface of the movable mass. 
     The first quadrature compensation electrode group ( 20 ,  20 ′;  241 ,  241 ′) may partially face the first face of the movable mass and partially faces the through opening and the second quadrature compensation electrode group ( 21 ,  21 ′) may partially face the second face of the movable mass and partially faces the through opening. 
     The movable mass may have an inner wall ( 10 A,  10 B;  110 A,  110 B) delimiting the through opening ( 9 ;  109 ) and extending in a direction (Y) transverse to the driving direction (D) and perpendicular to the detection direction (S), the first quadrature compensation electrode group comprising a first electrode ( 20 A,  20 B) arranged at the first height with respect to the inner wall, the second quadrature compensation electrode group comprising a first electrode ( 21 A,  21 B) arranged at the second height with respect to the inner wall. 
     The inner wall of the movable mass may extend in a direction perpendicular to the driving direction and the detection direction. 
     The inner wall ( 10 A;  110 A) of the movable mass may be a first inner wall forming a first side of the through opening ( 9 ;  109 ), the movable mass further having a second inner wall ( 10 B;  110 B) forming a second side of the through opening arranged at a distance from the first side along the driving direction (D), the second inner wall extending in a direction (Y) transverse to the driving direction (D) and perpendicular to the detection direction (S), the first quadrature compensation electrode group comprising a second electrode ( 20 B) arranged at the first height with respect to the second inner wall, the second quadrature compensation electrode group comprising a second electrode ( 21 A) arranged at the second height with respect to the second inner wall. 
     The first height (gi) may be equal to the second height (g 2 ). 
     The movable mass ( 107 ,  107 ′) may include at least one arm ( 112 ) extending along the driving direction (X, D), through the through opening ( 109 ). 
     The at least one arm may be a first arm, the MEMS gyroscope may further include a second arm extending at a distance that is greater than 1 µm from the first arm along a direction (Y) perpendicular to the driving direction (X, D) and the detection direction (Z, S). 
     The MEMS gyroscope may further include a driving electrode ( 33 ,  33 ′;  260 ,  260 ′) and a detection electrode ( 30 ,  30 ′;  262 ,  262 ′), the driving electrode being fixed to the substrate ( 2 ), capacitively coupled to the movable mass ( 7 ,  7 ′;  107 ,  107 ′;  207 ,  207 ′,  227 ,  227 ′) and configured to cause the movement of the movable mass in the driving direction (D; D1, D2), the detection electrode being fixed to the substrate, capacitively coupled to the movable mass and configured to detect the movement of the movable mass in the detection direction (S), wherein the movable mass, the first quadrature compensation electrode group, the second quadrature compensation electrode group, the driving electrode and the detection electrode form a first rotation detection unit ( 4 ,  5 ;  104 ,  105 ;  204 ,  205 ,  217 ,  217 ) configured to detect a rotation (Ω Y ; Ω X ) of the MEMS gyroscope around a first direction (Y; X) perpendicular to the detection direction (S) and to the driving direction (D; D2). 
     The driving direction of the first rotation detection unit ( 204 ,  204 ′) may be a first driving direction (D1), the MEMS gyroscope may further include a second rotation detection unit ( 216 ,  217 ) configured to detect a rotation of the MEMS gyroscope around the first driving direction, the second rotation detection unit having a respective movable mass ( 227 ,  227 ′) configured to move in the detection direction and in a second driving direction parallel to the first direction (Y). 
     A method for compensating a quadrature error of a MEMS gyroscope comprising a substrate ( 2 ); a movable mass ( 7 ,  7 ′;  107 ,  107 ′;  207 ,  207 ′,  227 ,  227 ′) suspended on the substrate and configured to carry out a movement in a driving direction (X, D; X, Y, D1, D2) and in a detection direction (Z, S) perpendicular to each other, the movable mass having a first face ( 7 A;  107 A) and a second face ( 7 B;  107 B) opposite to the first face; a first quadrature compensation electrode group ( 20 ,  20 ′;  241 ,  241 ′), fixed to the substrate and capacitively coupled to the movable mass, the first quadrature compensation electrode group facing the first face of the movable mass; and a second quadrature compensation electrode group ( 21 ,  21 ′), fixed to the substrate and capacitively coupled to the movable mass, the second quadrature compensation electrode group facing the second face of the movable mass, the first and the second quadrature compensation electrode groups each having a respective variable facing area (Si, S 2 , S′ 1 , S′ 2 ) on the movable mass as a result of the movement of the movable mass in the driving direction, may be summarized as including providing a first compensation voltage (Vi) to the first quadrature compensation electrode group; and providing a second compensation voltage (V 2 ) to the second quadrature compensation electrode group. 
     The MEMS gyroscope may further include a third quadrature compensation electrode group ( 20 B) facing the first face ( 7 A;  107 A) of the movable mass and a fourth quadrature compensation electrode group ( 21 A) facing the second face ( 7 B;  107 B) of the movable mass, wherein the variable facing area (Si) of the first quadrature compensation electrode group ( 20 A) and the variable facing area (S 2 ) of the second quadrature compensation electrode group ( 21 B) may increase when the movable mass moves in the driving direction (D), the third and the fourth quadrature compensation electrode groups each having a respective variable facing area on the movable mass, wherein the variable facing area (S′ 2 ) of the third quadrature compensation electrode group ( 20 B) and the variable facing area (S&#39;i) of the fourth quadrature compensation electrode group ( 21 A) may decrease when the movable mass moves in the driving direction, the method may further include providing the second compensation voltage (V 2 ) to the third quadrature compensation electrode group ( 20 B) and providing the first compensation voltage (Vi) to the fourth quadrature compensation electrode group ( 21 A). 
     The first compensation voltage (Vi) may be given by the sum of a common mode voltage (V CM ) and a first correction voltage (ΔV), and the second compensation voltage (V 2 ) may be given by the sum of the common mode voltage and a second correction voltage (ΔV). 
     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. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.