Patent Publication Number: US-2021190814-A1

Title: Micromechanical device with elastic assembly having variable elastic constant

Description:
BACKGROUND 
     Technical Field 
     The present disclosure relates to a micromechanical device with an elastic assembly having a variable elastic constant. 
     Description of the Related Art 
     As is known, there is a desire to detect and measure effectively accelerations and shocks via sensors having small dimensions that can be easily integrated. Common applications include monitoring of shocks in electronic devices, such as mobile phones and smartwatches, for example for detecting car accidents or cases of people falling on the ground as a result of feeling unwell or fainting or because they suffer from an illness. 
     Currently, available on the market are low-G sensors (such as accelerometers and gyroscopes) adapted to detect low accelerations (for example, with a full-scale range of 16 g or 32 g) and high-G sensors adapted to detect high accelerations (for example, with a full-scale range of 128 g). The former are used for detecting usual movements of operators provided with the electronic device that integrates the sensors (such as approach of the mobile phone to the operator&#39;s ear, or movement of the wrist to which the smartwatch is connected), whereas the latter enable detection of high-intensity accelerations (and therefore, anomalous events). 
     In order to enable an electronic device to detect both low accelerations and high accelerations, known solutions envisage integration in the electronic device of both types of accelerometer. However, the simultaneous presence in a same electronic device of two different accelerometers entails disadvantages such as a larger number of pads necessary and a higher complexity in the control circuitry (for example, dedicated ASICs, PCBs, or CPUs, etc.), and more in general a greater integration area, a lower portability of the electronic device, and a higher manufacturing cost. 
     Given the drawbacks, the patent document US2006/107743A1 discloses the structure of an accelerometer that enables implementation of two different sensitivities in respective and different operating modes. In particular, the above accelerometer includes, in one embodiment (designated in  FIG. 1A  by the reference number  1   a ), a seismic mass  2  fixed to a first end  3   a  of a first spring element  3  having an elongated shape. The first spring element  3  is moreover fixed to a support  5  at a second end  3   b  thereof, opposite to the first end  3   a.  A second spring element  4 , having an elongated shape and having a first end  4   a  and a second end  4   b  opposite to one another, is moreover fixed to the support  5  at its second end  4   b.  The first and second spring elements  3 ,  4  have a main extension along a first direction orthogonal to a main extension of the support  5  (for example, orthogonal to a surface of the support  5 ), and are therefore set parallel to one another and with respect to the first direction. In addition, they are aligned with one another in a direction perpendicular to a second direction orthogonal to the first direction. In use, the first spring element  3  is deflected in a direction perpendicular to its main extension by a force F (for example, a force of gravity) acting in the second direction. When the force F is equal to a threshold force F th , the first spring element  3  presents a deflection such that it comes into contact, at a portion of a bottom surface  3   c  thereof, with the first end  4   a  of the second spring element  4 . For forces F lower than the threshold force F th , the accelerometer  1   a  has a first value K 1  of elastic constant (that depends just upon the characteristics of the first spring element  3 ); for forces F higher than the threshold force F th , the accelerometer  1   a  has, instead, a second value K 2  of elastic constant (that depends upon the characteristics of the second spring element  4 ) greater than the first value K 1 . The presence of the second spring element  4  therefore enables modification of the stiffness of the accelerometer  1   a  as a function of the force F applied. 
     According to a different embodiment of the accelerometer, disclosed in the same patent document US2006/107743A1 (designated in  FIG. 1B  by the reference number  1   b ), the seismic mass  2  is connected to the support  5  via a third spring element  7 , which that has a pyramidal tapering from the end in contact with the support  5  to the end in contact with the seismic mass  2 . The shape of the third spring element  7  makes it possible to obtain, in use, a non-linear profile of the elastic constant, and therefore a stiffness of the accelerometer  1   b  that varies as a function (in particular, logarithmically) of the force F applied. 
     However, the accelerometer  1   a  presents a low mechanical stability since, during an event of shock or in any case of marked acceleration, the spring elements  3 ,  4  may be overstressed and undergo damage or failure due to mutual contact. Instead, in the case of the accelerometer  1   b,  the real plot of stiffness is difficult to predict theoretically in an accurate way since it depends upon a multiplicity of structural factors, factors of use, and process factors. 
     BRIEF SUMMARY 
     In various embodiments, the present disclosure provides a micromechanical device that will overcome the problems of the prior art. 
     In one or more embodiments of the present disclosure, a micromechanical device is provided that includes a semiconductor body; a first mobile structure, having a first mass, configured to oscillate relative to the semiconductor body in a direction belonging to a plane; an elastic assembly, having an elastic constant, mechanically coupled to the first mobile structure and to the semiconductor body, and configured to expand and contract in the direction; and at least one abutment element. The elastic assembly is configured to enable the oscillation of the first mobile structure as a function of a force applied to the first mobile structure in the direction. The first mobile structure, the abutment element, and the elastic assembly are arranged with respect to one another in such a way that: when the force applied to the first mobile structure is lower than an abutment-force threshold, then the first mobile structure is not in contact with the abutment element, and the elastic assembly operates with a first elastic constant; and when the force applied to the first mobile structure is greater than the abutment-force threshold, then the first mobile structure is in contact with the abutment element and, under the action of the applied force, a deformation of the elastic assembly is generated such that the elastic assembly operates with a second elastic constant different from the first elastic constant. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       For a better understanding of the present disclosure, a preferred embodiment thereof is now described, purely by way of non-limiting example, with reference to the attached drawings, wherein: 
         FIGS. 1A and 1B  are cross-sectional views of respective accelerometers of a known type; 
         FIG. 2  is a top view of a micromechanical device, according to one embodiment of the present disclosure; 
         FIGS. 2A and 2B  illustrate the micromechanical device of  FIG. 2  in respective operating modes; 
         FIG. 3  is a top view of a further embodiment of the micromechanical device according to the present disclosure; 
         FIGS. 3A and 3B  are top views of the micromechanical device of  FIG. 3 , in respective operating modes; 
         FIG. 3C  is a top view of a further embodiment of the micromechanical device according to the present disclosure; 
         FIG. 4  is a top view of a further embodiment of the micromechanical device according to the present disclosure; 
         FIGS. 4A and 4B  are top views of the micromechanical device of  FIG. 4 , in respective operating modes; 
         FIG. 5  is a top view of a further embodiment of the micromechanical device according to the present disclosure; 
         FIGS. 5A and 5B  are top views of the micromechanical device of  FIG. 5 , in respective operating modes; 
         FIG. 6A  is a graph that represents an electrical signal generated at output by the micromechanical device of  FIG. 3  as a function of an acceleration to which the micromechanical device is subjected in use; and 
         FIG. 6B  is a graph that represents the plot of the stiffness of the micromechanical device of  FIG. 4  as a function of a displacement of a sensing mass belonging to the micromechanical device with respect to a resting position. 
     
    
    
     DETAILED DESCRIPTION 
     In particular, the figures are illustrated with reference to a triaxial cartesian system defined by a first axis X, a second axis Y, and a third axis Z, orthogonal to one another. 
     In the ensuing description, elements that are common to the different embodiments are designated by the same reference numbers. 
     Moreover, in the ensuing description, the term “substantially” is used to refer to a property that is considered verified to a first order. For instance, if two elements moving with respect to a reference point are said to be “substantially” fixed with respect to one another, it is meant that, even though there may exist a relative movement between them, this relative movement is negligible as compared to the movement with respect to the reference point (for example, the relative movement is less than 5% of the movement of each element with respect to the reference point). Likewise, if an element is said to present a “substantially” zero deformation along one axis, it is meant that a possible deformation of the element is negligible as compared to the extension of the element itself along the aforesaid axis (for example, the deformation is less than 5% of the extension of the element along said axis). 
       FIG. 2  shows a micromechanical device  50  configured to detect accelerations (hereinafter also referred to as sensor  50 ), according to one embodiment.  FIG. 2  is a top view (i.e., in the plane XY) of the sensor  50 . Illustrated in  FIG. 2  are just the elements useful for an understanding of the present embodiment, and elements or components that, albeit present in the finished sensor, are not important for the present disclosure are not illustrated. 
     The sensor  50  comprises a semiconductor body  51  of semiconductor material, such as silicon (Si), having a surface  51   a  extending parallel to a first plane XY defined by the first axis X and by the second axis Y (i.e., the third axis Z is orthogonal to the surface  51   a ). The sensor  50  further comprises a first mobile structure  53  having a first mass M 1 , and a second mobile structure  55  having a second mass M 2 , greater than the first mass M 1 . In what follows, the first mobile structure  53  will be referred to as “first seismic mass”, and the second mobile structure  55  will be referred to as “second seismic mass”. 
     Both the first seismic mass  53  and the second seismic mass  55  are, for example, of semiconductor material (such as silicon or polysilicon) and extend parallel to the surface  51   a  of the semiconductor body  51 , at a different height, along the axis Z, with respect to the height of the surface  51   a.    
     The first seismic mass  53  is physically coupled to the semiconductor body  51  via a first spring assembly  57  (in detail, a first spring, or first elastic element,  57   a  of the first spring assembly  57  and a second spring, or second elastic element,  57   b  of the first spring assembly  57 ), whereas the second seismic mass  55  is physically coupled to the semiconductor body  51  via a second spring assembly  59  (in detail, a first spring, or first elastic element,  59   a  of the second spring assembly  59  and a second spring, or second elastic element,  59   b  of the second spring assembly  59 ). Both the first spring assembly  57  and the second spring assembly  59  are, for example, of semiconductor material (such as silicon or polysilicon) and undergo deformation (i.e., they lengthen/shorten) along the first axis X. In other words, both the first spring assembly  57  and the second spring assembly  59  have respective axes along which deformation occurs parallel to the first axis X. In addition, deformation of the first and second spring assemblies  57 ,  59  occurs along a same direction of deformation  60 . 
     In the embodiment described by way of example, both the first portions  57   a,    59   a  and the second portions  57   b,    59   b  of the elastic elements  57 ,  59  are serpentine springs. In particular, such serpentine springs are of a planar type and are obtained with MEMS technology (i.e., by methods of machining of semiconductors). In greater detail, said serpentine springs may include first portions, which extend parallel to one another and to the second axis Y, and second portions, which extend parallel to one another and to the first axis X. The first and second portions are connected to one another and are mutually arranged so as to form a serpentine path: each first portion is connected, at its ends that are opposite to one another along the second axis Y, to respective second portions; and each second portion is connected, at its ends that are opposite to one another along the first axis X, to respective first portions, except for two second portions (each of which is set at a respective end of said path along the first axis X and is joined to just one respective first portion). 
     Each spring  57   a,    57   b  of the first spring assembly  57  has a respective first end  57   a ′,  57   b ′ and a respective second end  57   a ″,  57   b ″, which are opposite to one another along the first axis X. Each spring  59   a,    59   b  of the second spring assembly  59  has a respective end  59   a ′,  59   b ′ and a respective end  59   a ″,  59   b ″, which are opposite to one another along the first axis X. 
     In particular, the distance, measured along the axis X, between the end  57   a ′ and the end  57   a ″ of the first spring  57   a  of the first spring assembly  57 , is identified by the reference L 1a . The distance, measured along the axis X between the end  57   b ′ and the end  57   b ″ of the second spring  57   b  of the first spring assembly  57 , is identified by the reference L 1b . The distance, measured along the axis X between the end  59   a ′ and the end  59   a ″ of the first spring  59   a  of the second spring assembly  59 , is identified by the reference L 2a . The distance, measured along the axis X between the end  59   b ′ and the end  59   b ″ of the second spring  59   b  of the second spring assembly  59 , is identified by the reference L 2b . 
     The springs  57   a,    57   b  of the first spring assembly  57  have respective first elastic constants K 1  (having the same value), and the springs  59   a,    59   b  of the second spring assembly  59  have respective second elastic constants K 2  (having the same value as one another, but different from K 1 , for example greater than K 1 ). 
     In the embodiment of  FIG. 2 , two springs  57   a,    57   b  are present so that the equivalent elastic constant of the first spring assembly  57  is given by 2K 1 , and two springs  59   a,    59   b  are present so that the equivalent elastic constant of the second spring assembly  59  is given by 2K 2 . In general, for any number N 1  of springs of the first spring assembly  57 , the equivalent elastic constant of the first spring assembly  57  is given by N1·K 1 , and for any number N2 of springs of the second spring assembly  59 , the equivalent elastic constant of the second spring assembly  59  is given by N2·K 2 . 
     Each spring  57   a,    57   b  of the first spring assembly  57  is coupled, via the respective end  57   a ′,  57   b ′, to a respective first fixing element  64 ′ coupled to the surface  51   a  of the semiconductor body  51  (in particular, each first fixing element  64 ′ is fixed with respect to the surface of the semiconductor body  51 ). Each spring  57   a,    57   b  of the first spring assembly  57  is moreover coupled, at the respective end  57   a ″,  57   b ″, to the first seismic mass  53 . In detail, in the embodiment discussed by way of example, the first seismic mass  53  has a first lateral surface  53   a  and a second lateral surface  53   b  opposite to one another along the first axis X, and each end  57   a ″,  57   b ″ is fixed with respect to a respective one between the first and second lateral surfaces  53   a,    53   b.  Consequently, the first seismic mass  53  is set, along the first axis X, between the first and second springs  57   a,    57   b  of the first spring assembly  57 . 
     The second seismic mass  55  moreover has, in the view of  FIG. 2 , a cavity  62  that houses within it the first seismic mass  53 , the first spring assembly  57 , and the first fixing elements  64 ′. 
     Each spring  59   a,    59   b  of the second spring assembly  59  is coupled, via the respective end  59   a ′,  59   b ′, to a respective second fixing element  64 ″, which is in turn coupled to the semiconductor body  51  (in particular, the second fixing element  64 ″ is fixed with respect to the surface  51   a  of the semiconductor body  51 ). Each spring  59   a,    59   b  of the second spring assembly  59  is moreover coupled, at the respective end  59   a ″,  59   b ″, to the second seismic mass  55 . In detail, in the embodiment discussed, the second seismic mass  55  has a first lateral surface  55   a  and a second lateral surface  55   b  opposite to one another along the first axis X, and each end  59   a ″,  59   b ″ is fixed with respect to a respective one between the first and second lateral surface  55   a,    55   b.  Consequently, the second seismic mass  55  is set, along the first axis X, between the first and second springs  59   a,    59   b  of the second spring assembly  59 . 
     The first seismic mass  53  further includes a plurality of stopper elements  66   a  (for example, in  FIG. 2 , four stopper elements  66   a ), and the second seismic mass  55  includes a respective plurality of housing elements  66   b  (for example, in  FIG. 2 , four housing elements  66   b ). The stopper elements  66   a  and the housing elements  66   b  form an abutment assembly  66 . 
     The stopper elements  66   a  are protrusions of the first seismic mass  53 , whereas the housing elements  66   b  are respective portions of the second seismic mass  55 , which present a respective cavity and/or recess. In the embodiment illustrated by way of example in  FIG. 2 , both the stopper elements (protrusions)  66   a  and the housing elements  66   b  (cavities) have a substantially rectangular shape with a main extension parallel to the second axis Y. In particular, the first and second seismic masses  53 ,  55  are arranged in such a way that each stopper element  66   a  extends within the cavity of each respective housing element  66   b  or, in other words, each stopper element  66   a  is partially surrounded by a respective housing element  66   b,  to form a respective abutment assembly  66 . In the absence of external forces acting along the axis X, each stopper element  66   a  is not in contact with the respective housing element  66   b.  Each stopper element  66   a  has a first side wall  67   a  and a second side wall  67   b,  opposite to one another along the first axis X, whereas each housing element  66   b  has a first side wall  67   c  and a second side wall  67   d,  opposite to one another along the first axis X and facing the first side wall  67   a  and the second side wall  67   a,    67   b,  respectively, of the respective stopper element  66   a.  For each contact structure  66 , the side walls  67   a,    67   c  are at a distance equal to a first length L 1  from one another, whereas the side walls  67   b,    67   d  are at a distance equal to a second length L 2  from one another. 
     Furthermore, the first seismic mass  53  includes one or more first electrodes  68   a  (mobile electrodes), such as protrusions (for example, having a substantially rectangular shape in the plane XY), which, in use, displace in a way fixed with respect to the first seismic mass  53 . One or more second electrodes  68   b  (fixed electrodes) are fixed with respect to the semiconductor body  51 , in particular to the surface  51   a.    
     Each of the second electrodes is further divided into a first portion  68   b ′ and a second portion  68   b ″, which are separate from one another. The first electrode  68   a  extends between the first portion  68   b ′ and the second portion  68   b ″. In greater detail, each of the first electrodes  68   a  faces, and is set between, the first portion  68   b ′ of a respective second electrode  68   b  and the second portion  68   b ″ of said respective second electrode  68   b.    
     The first and second electrodes  68   a,    68   b  form a measurement structure  68  of the sensor  50  adapted, in use, to detect in a capacitive way displacements along the first axis X of the first and second seismic masses  53 ,  55 ; these displacements are indicative of external forces (e.g., accelerations) that act on the sensor  50 . 
     In particular, surfaces of the first electrode  68   a  and of the first portion  68   b ′ of the second electrode  68   b  that directly face one another form a first capacitor  68 ′. Likewise, surfaces of the first electrode  68   a  and of the second portion  68   b ″ of the second electrode  68   b  that directly face one another form a second capacitor  68 ″. The distance (along the axis X) between the first electrode  68   a  and the first portion  68   b ′ is designated by the reference d c1 , whereas the distance between the first electrode  68   a  and the second portion  68   b ″ is designated by the reference d c2 . 
     Moreover, first and second blocking elements  70 ′,  70 ″ are fixed with respect to the semiconductor body  51  (in particular, to the surface  51   a  of the semiconductor body  51 ).  FIG. 2  illustrates, by way of example, two blocking elements  70 ′ that are located at a distance L 1block  along the first axis X from the first lateral surface  55   a  of the second seismic mass  55 .  FIG. 2  likewise illustrates two blocking elements  70 ″ that are set at a distance L 2block  along the first axis X from the second lateral surface  55   b  of the second seismic mass  55 . 
     In detail, in order to prevent direct contact between the first electrode  68   a  and the portions  68   b ′,  68   b ″, the distance d c1  is designed to have a value such that d c1 &gt;L 1 +L 1block , and the distance d c2  is designed to have a value such that d c2 &gt;L 2 +L 2block . 
     During use of the sensor  50 , the first electrode  68   a  is biased at a first voltage V 1 , and the second electrode  68   b  is biased at a second voltage V 2 . In particular, the first voltage V 1  and the second voltage V 2  are the same as one another (V 1 =V 2 ). 
     Since, in use, the first and second distances d c1 , d c2  vary as a function of the external force applied to the sensor  50  (which causes, as has been said, a displacement of the first seismic mass  53 ), it is possible to correlate the variation of capacitance of the capacitors  68 ′,  68 ″ to this applied force. The measurements of capacitance can be performed via techniques in themselves known, for example, via transimpedance amplifiers. 
     With the sensor  50  in the resting condition, no external force is applied to the sensor  50 , and therefore both the first and second seismic masses  53 ,  55  are in the resting position. 
     The first seismic mass  53  has a first centroid B 1  and the second seismic mass  55  has a second centroid B 2 . In the resting condition:
         the first and second centroids B 1 , B 2  coincide with one another in the plane XY (B 1 =B 2 =B stat );   the first and second path lengths L 1 , L 2  are the same as one another (L 1 =L 2 =L stop );   the first and second distances d c1 , d c2  are the same as one another (d c1 =d c2 =d rest );   the first length L 1a  and the second length L 1b  are the same as one another (L 1a =L 1b =L 1rest );   the first length L 2a  and the second length L 2b  are the same as one another (L 2a =L 2b =L 2rest ); and   the first distance L 1block  and the second distance L 2block  are the same as one another (L 1block =L 2block =L blockmax ).       

       FIG. 2A  shows the sensor  50  in a first operating condition, where an external force (having a first value F 1  lower than a threshold value F th ) is applied to the sensor  50 . In the present description, the external force is considered, by way of example, as a force acting in the direction of the first axis X (in  FIG. 2A , from left to right); however, what is described hereinafter applies in a way in itself evident also to the case where the external force acts in the opposite direction. On account of its inertia, the first seismic mass  53  undergoes an apparent force equal to the external force applied to the sensor  50 , but in an opposite direction (since the reference system illustrated in  FIG. 2A  and fixed with respect to the semiconductor body  51  is not inertial). The apparent force causes a relative movement of the first seismic mass  53  with respect to the semiconductor body  51 . In particular:
         in the plane XY, the first centroid B 1  is displaced along the first axis X with respect to the position B stat  of the centroids at rest, whereas the second centroid B 2  substantially coincides with the position B stat  of the centroids at rest;   the first length L 1  is less than L stop , and the second length L 2  is greater than L stop ;   the first distance d c1  is less than the distance d rest , and the second distance d c2  is greater than the distance d rest ;   the first length L 1a  is less than the length at rest L 1rest , and the second length L 1b  is greater than the length at rest L 1rest ;   the first length L 2a  and the second length L 2b  are substantially the same as one another and substantially equal to the length at rest L 2rest ; and   the first distance L 1block  and the second distance L 2block  are the same as one another and equal to the distance L blockmax .       

     Therefore, considering by way of example N1=1, N2=1, in the first operating condition of  FIG. 2A , the sensor  50  has a resonance pulsation ω res  according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   K 
                   1 
                 
                 
                   M 
                   1 
                 
               
             
           
         
       
     
       FIG. 2B  shows the sensor  50  in a second operating condition, where the external force applied to the sensor  50  has a second force value F 2  greater than, or equal to, the threshold value F th . For the same reasons as those described previously, the first seismic mass  53  is displaced with respect to the resting position of  FIG. 2 , and the stopper elements  66   a  are in abutment against the respective housing elements  66   b.  In particular, the first centroid B 1  is displaced, in the plane XY along the first axis X, with respect to the position B stat  (centroid at rest) and the first seismic mass  53  is in direct physical contact with the second seismic mass  55  at the first side walls  67   a,    67   c  of the stopper elements  66   a  and of the housing elements  66   b.  In this operating condition, also the second seismic mass  55  is displaced with respect to the semiconductor body  51 , and to its resting position illustrated in  FIG. 2 , under the thrust of the first seismic mass  53 . Therefore, also the second centroid B 2  is displaced, in the plane XY along the first axis X, with respect to the position at rest B stat . Consequently, in the second operating condition, the second seismic mass  55  moves in a way fixed with respect to the first seismic mass  53 . In particular:
         the first length L 1  is zero and the second length L 2  is twice the length L stop ;   the first distance d c1  is less than the resting distance d rest  (moreover, it is less than the first distance d c1  of  FIG. 2A ), and the second distance d c2  is greater than the resting distance d rest  (moreover, it is greater than the second distance d c2  of  FIG. 2A );   the first length L 1a  is less than the first length at rest L 1rest  (moreover, it is less than the first length L 1a  of  FIG. 2A ), and the second length L 1b  is greater than the first length at rest L 1rest  (moreover, it is greater than the second length L 1b  of  FIG. 2A );   the first length L 2a  is less than the second length at rest L 2rest  (moreover, it is less than the first length L 2a  of  FIG. 2A ), and the second length L 2b  is greater than the second length at rest L 2rest  (moreover, it is greater than the second length L 2b  of  FIG. 2A ); and   the first distance L 1block  is less than the maximum distance L blockmax , and the second distance L 2block  is greater than the maximum distance L blockmax .       

     Therefore, considering by way of example N1=1, N2=1, in the second operating condition of  FIG. 2B  the resonance pulsation ω res  of the sensor  50  is obtained according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   
                     K 
                     1 
                   
                   + 
                   
                     K 
                     2 
                   
                 
                 
                   
                     M 
                     1 
                   
                   + 
                   
                     M 
                     2 
                   
                 
               
             
           
         
       
     
     In particular, if the external force applied to the sensor  50  has a value greater than, or equal to, a maximum force value F max  (greater than the threshold force value F th ), the second seismic mass  55  is in abutment against the first blocking element  70 ′ at a portion of the first lateral surface  55   a  of the second seismic mass  55 . In other words, the first distance L 1block  is zero, and the second distance L 2block  is twice the maximum distance L blockmax . The blocking elements  70  therefore enable limitation of any possible oscillations of the second seismic mass  55  (and, consequently, also of the first seismic mass  53 ), preventing them from overstepping a critical amplitude threshold that might cause damage to or failure of the sensor  50 . 
       FIG. 3  shows a different embodiment of the sensor (here designated by the reference number  150 ). The sensor  150  comprises the semiconductor body  51  and a mobile structure  153  (hereinafter referred to as “seismic mass”), having an own mass M 3 . The seismic mass  153  is, for example, of semiconductor material (such as silicon or polysilicon) and extends parallel to the surface  51   a  of the semiconductor body  51 . The seismic mass  153  has a first lateral surface  153   a  and a second lateral surface  153   b  opposite to one another along the first axis X. 
     The seismic mass  153  is supported by the first spring assembly  57  (described previously with reference to  FIG. 2 ) having a respective axis of deformation extending in a first direction of deformation  160 ′ parallel to the first axis X. In particular, the ends  57   a ″,  57   b ″ of the springs that form the spring assembly  57  are in contact with, and fixed with respect to, the first lateral surface  153   a  and the second lateral surface  153   b,  respectively. Consequently, the seismic mass  153  is set, along the first axis X, between the first and second springs  57   a,    57   b  of the spring assembly  57 . 
     In addition, at least one second spring assembly  159  is present. With the sensor  150  in resting conditions, i.e., when the seismic mass  153  is not subject to an external force that causes a displacement thereof, the second spring assembly  159  is physically separate from the seismic mass  153 ; in a different operating condition of the sensor  150 , when an external force acts on the seismic mass  153 , causing a displacement thereof in the direction of the axis X, the seismic mass  153  comes into abutment against abutment regions of the second spring assembly  159 . 
     The second spring assembly  159  is, for example, of semiconductor material (such as silicon or polysilicon) and has an elastic constant K 3  thereof different from the elastic constant K 1  of the first spring assembly  57  (for example, higher than the elastic constant K 1 ). The axis of deformation of the second spring assembly  159  extends parallel to the axis X and is staggered with respect to the axis of deformation of the first spring assembly  57 . The second spring assembly  159  includes a first elastic element (spring)  159   a  and a second elastic element (spring)  159   b.    
     In the embodiment described by way of example, both the first elastic element  159   a  and the second elastic element  159   b  are serpentine springs, i.e., strips arranged to form respective paths extending in a serpentine fashion (as described previously). Each elastic element  159   a,    159   b  has a respective end  159   a ′,  159   b ′ coupled to the semiconductor body  51  and a respective end  159   a ″,  159   b ″ coupled to the seismic mass  153 . In particular, each elastic element  159   a,    159   b  of the second spring assembly  159  is coupled, via the respective end  159   a ′,  159   b ′, to a respective fixing element  164  coupled to the surface  51   a  of the semiconductor body  51  (in particular, each fixing element  164  is fixed with respect to the surface of the semiconductor body  51 ). 
     In the embodiment of  FIG. 3 , four elastic elements  159   a,    159   b  are present, so that the equivalent elastic constant of the second spring assembly  159  is given by 4K 3 . In general, for any number N3 of elastic elements of the second spring assembly  159 , the equivalent elastic constant of the second spring assembly  159  is given by N3·K 3 . 
     Each first elastic element  159   a  has an extension, measured along the first axis X between the respective ends  159   a ′ and  159   a ″, equal to a first length L 3 a, and each second elastic element  159   b  has an extension, measured along the first axis X between the respective ends  159   b ′ and  159   b ″, equal to a second length L 3b . 
     Each elastic element  159   a,    159   b  of the second spring assembly  159  includes, in a position corresponding to the respective end  159   a ″,  159   b ″, a respective stopper element  166   a  obtained by a terminal protrusion having a main extension parallel to the second axis Y (i.e., perpendicular to the direction of the oscillations of the seismic mass  153 ). 
     The seismic mass  153  has a recess, within which the stopper element  166   a  extends. Portions of the seismic mass  153  that include said recess form a respective housing element  166   b  for the stopper element  166   a.  Each stopper element  166   a  and the respective housing element  166   b  form a respective abutment assembly  166 . 
     Each stopper element  166   a  has a first side wall  167   a  and a second side wall  167   b,  opposite to one another along the first axis X, while each housing element  166   b  has a first side wall  167   c  and a second side wall  167   d,  opposite to one another along the first axis X and facing the first and second side walls  167   a,    167   b,  respectively, of the respective stopper element  166   a.  For each abutment assembly  166 , the side walls  167   a,    167   c  are at a distance equal to a first length L 3  from one another, whereas the side walls  167   b,    167   d  are at a distance equal to a second length L 4  from one another. 
     Each stopper element  166   a  operates in a similar way to the stopper element  66   a  of  FIG. 2 , whereas the housing element  166   b  has a function similar to what has been described with reference to the housing element  66   b  of  FIG. 2 . 
     As better described hereinafter, in an operating condition, the seismic mass  153  and each elastic element  159   a,    159   b  abut against one another via each stopper element  166   a  and the respective housing element  166   b.    
     Furthermore, as has been described with reference to  FIG. 2 , the first seismic mass  153  includes the first and second electrodes  68   a,    68   b,  thus forming the measurement structure  68  already described with reference to  FIG. 2 . 
     In addition, the blocking elements  70  are present, here facing the first and second lateral surfaces  153   a,    153   b  of the seismic mass  153 . In particular, at least one (in  FIG. 3 , two) the first blocking element  70 ′ is at a distance L 3block  from the first lateral surface  153   a,  along the first axis X, and at least one (in  FIG. 3 , two) second blocking element  70 ″ is at a distance L 4block  from the second lateral surface  153   b,  along the first axis X. It may be noted that the distance d c1  is greater than L 3 +L 3block , and the distance d c2  is greater than L 4 +L 4block . 
     In use, the sensor  150  is biased, as discussed previously, for carrying out measurement of the external force applied. 
     With the sensor  150  in the resting condition as shown in  FIG. 3 , no external force is applied to the sensor  150 , and therefore the seismic mass  153  is in the resting position. In particular, in the plane XY, the seismic mass  153  has a centroid B (in the resting condition, equal to the centroidal position B stat ). In addition:
         the lengths L 3 , L 4  are the same as one another and equal to the stop length L stop ;   the first and second distances d c1 , d c2  are the same as one another and equal to the distance at rest d rest ;   the first length L 1a  and the second length L 1b  are the same as one another and equal to the first length at rest L 1rest ;   the first length L 3a  and the second length L 3b  are the same as one another and equal to a second length at rest L 3rest ; and   the first distance L 3block  and the second distance L 4block  are the same as one another and equal to the maximum distance L blockmax .       

       FIG. 3A  shows the sensor  150  in a first operating condition, where the external force (having the first force value F 1  less than the threshold force value F th ) is applied to the sensor  150 . As discussed previously, there is a relative movement of the seismic mass  153  with respect to the semiconductor body  51 . In particular, in the plane XY, the centroid B is displaced along the first axis X with respect to the centroid at rest B stat . In addition:
         the first length L 1  is greater than the stop length L stop , and the second length L 2  is less than the stop length L stop ;   the first distance d c1  is less than the distance at rest d rest , and the second distance d c2  is greater than the distance at rest d rest ;   the first length L 1a  is less than the first length at rest L 1rest , and the second length L 1b  is greater than the first length at rest L 1rest ;   the first length L 3a  and the second length L 3b  are the same as one another and equal to the length at rest L 3rest ; and   the first distance L 3block  is less than the maximum distance L blockmax , and the second distance L 4block  is greater than the maximum distance L blockmax .       

     Therefore, considering by way of example N1=1, N3=1, in the first operating condition of  FIG. 3A , the resonance pulsation ω res  of the sensor  150  is obtained according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   K 
                   1 
                 
                 
                   M 
                   3 
                 
               
             
           
         
       
     
       FIG. 3B  shows the sensor  150  in a second operating condition, where the external force applied to the sensor  150  has a second force value F 2  greater than, or equal to, the threshold value F th . For the same reasons as those described previously, the seismic mass  153  is displaced with respect to the resting position of  FIG. 3 , and each stopper element  166   a  bears upon the respective housing element  166   b  (i.e., the seismic mass  153  is in contact with the stopper element  166   a  of the second spring assembly  159 ). In particular, in the plane XY the centroid B has a displacement along the first axis X with respect to the position of the centroid at rest B stat  greater than in the case illustrated in  FIG. 3A , and the seismic mass  153  is in direct physical contact with the second spring assembly  159 . In addition:
         the first length L 1  is twice the length L stop , and the second length L 2  is zero;   the first distance d c1  is less than the distance at rest d rest  (moreover, it is less than the first distance d c1  of  FIG. 3A ), and the second distance d c2  is greater than the distance at rest d rest  (moreover, it is greater than the second distance d c2  of  FIG. 3A );   the first length L 1a  is less than the first length at rest L 1rest  (moreover, it is less than the first length L 1a  of  FIG. 3A ), and the second length L 1b  is greater than the first length at rest L 1rest  (moreover, it is greater than the second length L 1b  of  FIG. 3A );   the first length L 3a  is less than the second length at rest L 3rest , and the second length L 3b  is greater than the second length at rest L 3rest ; and   the first distance L 3block  is less than the maximum distance L blockmax  (moreover, it is less than the first distance L 3block  of  FIG. 3A ), and the second distance L 4block  is greater than the maximum distance L blockmax  (moreover, it is greater than the second distance L 4block  of  FIG. 3A ).       

     Therefore, considering by way of example N1=1, N3=1, in the second operating condition of  FIG. 3B , the resonance pulsation ω res  of the sensor  150  is obtained according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   
                     K 
                     1 
                   
                   + 
                   
                     K 
                     3 
                   
                 
                 
                   M 
                   3 
                 
               
             
           
         
       
     
     In particular, if the external force applied to the sensor  150  has a value greater than, or equal to, the maximum force value F max  (greater than the threshold force value F th ), the seismic mass  153  bears upon the first blocking element  70 ′ at a portion of the first lateral surface  153   a  of the seismic mass  153 . The blocking elements  70  therefore enable limitation of any possible oscillations of the seismic mass  153 , preventing them from overstepping a critical threshold of amplitude that might cause damage to or failure of the sensor  150 . 
     In addition,  FIG. 3C  shows a further embodiment of the sensor  150  (here designated by the reference  150 ′), similar to the one illustrated in  FIG. 3 . 
     In particular, in  FIG. 3C  the seismic mass  153  encloses and delimits at least one through opening, or cavity,  180 , where a second set  189  of springs extends (which takes the place of the second spring assembly  159  of  FIG. 3 ). In particular, the seismic mass  153  has side walls  180   a,    180   b  opposite to one another along the first axis X and directly facing the cavity  180 . 
     The second set  189  of springs comprises a first spring (elastic element)  189   a  and a second spring (elastic element)  189   b,  each having an elastic constant K 3′  thereof, for example higher than the elastic constant K 1  of the first spring assembly  57 . With the sensor  150 ′ in the resting condition, i.e., when the seismic mass  153  is not subject to an external force that causes a displacement thereof, the second set  189  of springs is physically separate from the seismic mass  153 . In a different operating condition of the sensor  150 ′, when an external force acts on the seismic mass  153 , causing a displacement thereof in the direction of the axis X, the seismic mass  153  comes into abutment against the abutment regions  186   a  of the second spring assembly  159 . 
     Each spring  189   a,    189   b  is a planar spring obtained with MEMS technology, in particular a spring including a strip (for example, of semiconductor material), extending in the plane XY and having a main extension parallel to the second axis Y and a width W 1  measured along the first axis X. The first spring  189   a  develops between an end  189   a ′ thereof and an end  189   a ″ thereof, opposite to one another with respect to the second axis Y, and the second spring  189   b  develops between an end  189   b ′ thereof and an end  189   b ″ thereof, opposite to one another with respect to the second axis Y. The ends  189   a ′,  189   b ′ are fixed with respect to respective fixing elements  184  coupled to the surface  51   a  of the semiconductor body  51  (in particular, each fixing element  184  is fixed with respect to the surface of the semiconductor body  51  and extends in the cavity  180 ). The abutment regions  186   a  are located at the ends  189   a ″,  189   b ″. In particular, the abutment regions  186   a  are fixed with respect to the ends  189   a ″,  189   b ″ and have a width W 2 , measured along the first axis X, greater than the width W 1 . Alternatively, the abutment regions  186   a  are portions of the springs  189   a,    189   b  that have a width W 2 , measured along the first axis X, greater than the width W 1 . 
     With the sensor  150 ′ in the operating condition where an external force acts on the seismic mass  153  causing a displacement thereof in the direction of the axis X, one of the side walls  180   a,    180   b  bears upon the abutment regions  186   a  of the second spring assembly  159 , causing a deflection (deformation) of the respective spring  189   a,    189   b  along the first axis X. The lengths, measured along the axis X, between the abutment regions  186   a  and the side walls  180   a,    180   b,  are here identified by L 3′ , L 4′  and are homologous to the lengths L 3 , L 4  of  FIG. 3 . 
     Each abutment region  186   a  and the side walls  180   a,    180   b  of the seismic mass  153  facing it therefore form a respective abutment assembly  186 , which enables variation of the elastic constant of the sensor  150 ′, as has been described with reference to  FIGS. 3-3B . 
     Furthermore, in the embodiment illustrated in  FIG. 3C , the abutment regions  186   a  have, in the plane XY, a round shape (i.e., a circular profile) in order to distribute better the mechanical stresses due to contact between the abutment regions  186   a  and the side walls  180   a,    180   b  of the seismic mass  153 . 
     As in  FIG. 3 , the blocking elements  70  are moreover present. The blocking elements  70  extend (see  FIG. 3C ) in the cavity  180 . They are fixed with respect to the surface  51   a  of the semiconductor body  51  (in particular, each blocking element  70  is fixed with respect to the respective fixing element  184 ) and face one of the side walls  180   a,    180   b  of the seismic mass  153 , from which they are separated by distances L 3block′ , L 4block′ , homologous to the distances L 3block , L 4block  of  FIG. 3 . 
     In the embodiment of  FIG. 3C , four springs  189   a,    189   b  are present, so that the equivalent elastic constant of the second set  189  of springs is given by 4K 3′ . In general, for any number N3′ of springs of the second set  189  of springs, the equivalent elastic constant of the second set  189  of springs is given by N3′·K 3′ . 
       FIG. 4  shows a different embodiment of the sensor (here designated by the reference number  250 ). The sensor  250  comprises the semiconductor body  51  and a mobile structure (hereinafter referred to as “seismic mass”)  253 , having a mass M 4 . The seismic mass  253  is, for example, of semiconductor material (such as silicon or polysilicon) and extends parallel to the surface  51   a  of the semiconductor body  51 . The seismic mass  253  has a through opening, or cavity,  262 . The seismic mass  253  surrounds and delimits said cavity  262 . The seismic mass  253  is externally delimited by a first lateral surface  253   a  and a second lateral surface  253   b  opposite to one another along the first axis X. The seismic mass  253  also has a third lateral surface  253   c  and a fourth lateral surface  253   d,  which are opposite to one another along the first axis X and directly face the cavity  262 . 
     The seismic mass  253  is physically coupled to the semiconductor body  51  via at least one spring assembly  259 , which extends in the cavity  262 . The spring assembly  259  is, for example, of semiconductor material (such as silicon or polysilicon) and has a respective axis of deformation in a direction of deformation  260  parallel to the first axis X. The spring assembly  259  includes a first spring (elastic element)  259   a  and a second spring (elastic element)  259   b.  In one embodiment (not illustrated), the springs  259   a,    259   b  are planar springs obtained with MEMS technology, more in particular springs that include a plurality of turns that define a serpentine path (as discussed previously; in particular, the springs  259   a,    259   b  include first and second portions similar to the ones defined previously). In a per se known manner, each turn is defined as the minimum ensemble of first and second portions of each spring  259   a,    259   b  (having a turn length, not illustrated, measured along the first axis X), which, when replicated a number of times by translating it by the turn length in the direction of deformation  260 , forms said spring  259   a,    259   b.  In the embodiment of  FIG. 4 , the springs  259   a,    259   b  are planar springs obtained with MEMS technology, more in particular springs that include a plurality of turns. Each turn extends in the plane XY and includes a strip, for example, of semiconductor material, arranged to form a polygonal closed path (for example, a rectangular path comprising minor sides parallel to the first axis X and major sides parallel to the second axis Y). 
     The number of turns is equal to a total number of turns n foldtot . 
     Both the first spring  259   a  and the second spring  259   b  of the spring assembly  259  have a respective end  259   a ′ and a respective end  259   b ″, opposite to one another along the first axis X. Each spring  259   a,    259   b  is coupled, via the respective end  259   a ′,  259   b ′, to a respective fixing element  264  fixed with respect to the semiconductor body  51  (in particular, with respect to the surface  51   a  of the semiconductor body  51 ). Each spring  259   a,    259   b  of the second spring assembly  59  is moreover coupled, via the respective end  259   a ″,  259   b ″, to the seismic mass  253 . In detail, the ends  259   a ″,  259   b ″ coupled to the seismic mass are in contact with the third lateral surface  253   c  and the fourth lateral surface  253   d,  respectively, of the seismic mass  253 . 
     The first spring  259   a  has an extension, measured along the first axis X between the end  259   a ′ and the end  259   a ″, equal to a first length L a . The second spring  259   b  has an extension, measured along the first axis X between the end  259   b ′ and the end  259   b ″ equal to a first length L b . Moreover, each spring  259   a,    259   b  includes at least one stopper element  266   a  arranged so as to come into abutment against the seismic mass  253  in an operating condition of the sensor  250 , as discussed more fully hereinafter. Said stopper element  266   a  is a protrusion of each portion  259   a,    259   b,  having a main extension parallel to the second axis Y, and extends within a recess of the seismic mass  253 . In what follows the portion of the seismic mass  253  that includes said recess is referred to as housing element  266   b.  The stopper element  266   a  and the housing element  266   b  form an abutment assembly  266 . 
     Each stopper element  266   a  has a first side wall  267   a  and a second side wall  267   b,  opposite to one another along the first axis X, while each housing element  266   b  has a first side wall  267   c  and a second side wall  267   d,  which are opposite to one another along the first axis X and face the first side wall  267   a  and the second side wall  267   b,  respectively, of the respective stopper element  266   a.  For each abutment assembly  266 , the side walls  267   a,    267   c  are at a distance equal to a first length L 5  from one another, while the side walls  267   b,    267   d  are at a distance equal to a second length L 6  from one another. 
     For the spring  259   a  of the spring assembly  259  there are identified a first region  261   a ′, which includes the turns comprised between the end  259   a ″ and the stopper element  266   a,  and a second region  261   a ″, which includes the turns comprised between the end  259   a ′ and the stopper element  266   a.  For the spring  259   b  of the spring assembly  259  there are identified a first region  261   b ′, which includes the turns comprised between the end  259   b ″ and the stopper element  266   a,  and a second region  261   b ″, which includes the turns comprised between the end  259   b ′ and the stopper element  266   a.    
     The length, measured along the axis X between the end  259   a ″ and the stopper element  266   a  is here identified by L a′ . It may be noted that, since in this example the stopper element  266   a  has a rectangular shape, the length L a′  is defined between the end  259   a ″ and an axis passing through the centroid of the stopper element  266   a  and lying parallel to the axis Y. The length, measured along the axis X between the end  259   a ′ and the stopper element  266   a  is here identified by L a″ . Likewise, the length L a″  is defined between the end  259   a ′ and the aforementioned axis passing through the centroid of the stopper element  266   a  and lying parallel to the axis Y. The length, measured along the axis X between the end  259   b ″ and the stopper element  266   a  is here identified by L b′ . Likewise, the length L b′  is defined between the end  259   b ″ and the aforementioned axis passing through the centroid of the stopper element  266   a  and lying parallel to the axis Y. The length, measured along the axis X, between the end  259   b ′ and the stopper element  266   a  is here identified by L b″ . Likewise, the length L b″  is defined between the end  259   b ′ and the aforementioned axis passing through the centroid of the stopper element  266   a  and lying parallel to the axis Y. 
     For the spring  259   a,  the sum of the length L a′  and of the length L a″  is therefore equal to the first length L a . For the spring  259   b,  the sum of the length L b′  and of the length L b″  is therefore equal to the second length L b . In the embodiment described by way of example, for each portion  259   a,    259   b  the lengths L a′ , L a″ , L b′ , and L b″  are the same as one another in the resting condition of the sensor  250 , and the number of turns present between the ends  259   a ″,  259   b ″ and the stopper element  266   a  is equal to the number of turns present between the stopper element  266   a  and the ends  259   a ′,  259   b ′. However, according to further embodiments, not illustrated, the lengths L a′  and L a″  may be, in the resting condition of the sensor  250 , different from one another, and the number of turns present between the end  259   a ″ and the stopper element  266   a  may be different from the number of turns present between the stopper element  266   a  and the end  259   a ′. Likewise, the lengths L b′  and L b″  may be, in the resting condition of the sensor  250 , different from one another, and the number of turns present between the end  259   b ″ and the stopper element  266   a  may be different from the number of turns present between the stopper element  266   a  and the end  259   b′.    
     In addition, as has been described with reference to  FIG. 2 , the seismic mass  253  includes the first and second electrodes  68   a,    68   b,  which form the measurement structure  68 . 
     Furthermore, the blocking elements  70  are present, facing the first and second lateral surfaces  253   a,    253   b  of the seismic mass  253 . In particular, at least one (in  FIG. 4 , two) first blocking element  70 ′ is at a distance L 5block , along the first axis X, from the first lateral surface  253   a  of the seismic mass  253 , and at least one (in  FIG. 4 , two) second blocking element  70 ″ is at a distance L 6block , along the first axis X, from the second lateral surface  253   b  of the seismic mass  253 . 
     In use, the sensor  250  is biased, as discussed previously, for carrying out measurement of the external applied force. 
     With the sensor  250  in the resting condition as shown in  FIG. 4 , no external force is applied to the sensor  250 , and therefore the seismic mass  253  is in the resting position. In particular, in the plane XY, the seismic mass  253  has a centroid B that coincides, in the resting condition, with a position B stat . In addition:
         the first and second lengths L 5 , L 6  are the same as one another and equal to the stop length L stop ;   the first and second distances d c1 , d c2  are the same as one another and equal to the distance at rest d rest ;   the first length L a  and the second length L b  are the same as one another and equal to a length at rest L rest ; and   the first distance L 5block  and the second distance L 6block  are the same as one another and equal to the maximum distance L blockmax .       

       FIG. 4A  shows the sensor  250  in a first operating condition, where the external force (having the first force value F 1  lower than the threshold force value F th ) is applied to the sensor  250 . As discussed previously, there is a relative movement of the seismic mass  253  with respect to the semiconductor body  51 , which causes a deformation of the spring assembly  259 . In particular, in the plane XY, the centroid B is displaced along the first axis X with respect to the centroid at rest B stat . In addition:
         the first length L 5  is greater than the stop length L stop , and the second length L 6  is less than the stop length L stop ;   the first distance d c1  is less than the distance at rest d rest , and the second distance d c2  is greater than the distance at rest d rest ;   the first length L a  is greater than the length at rest L rest , and the second length L b  is less than the length at rest L rest ; and   the first distance L 5block  is less than the maximum distance L blockmax , and the second distance L 6block  is greater than the maximum distance L blockmax .       

     In detail, since the stopper elements  266   a  are not yet in direct physical contact with (i.e., they do not abut against) the respective housing elements  266   b,  the stress is distributed over the entire spring assembly  259 , and all the turns undergo deformation. In this operating condition, for each portion  259   a,    259   b  the number of turns that undergo deformation is equal to n fold1 , which is in turn equal to the total number of turns n foldtot  (n fold1 =n foldtot ). 
     As is in itself known, the elastic constant of a spring, having an axis of deformation, is dependent upon the number of turns of the spring and upon the length of the spring measured along the axis of deformation (in particular, it is inversely proportional both to the number of turns and to said length). Consequently, each spring  259   a,    259   b  of the spring assembly  259  has, in the first operating condition, a first elastic constant K 4  depending upon the number n fold1  of turns effectively involved in deformation. In the embodiment of  FIG. 4 , two springs  259   a,    259   b  are present, so that the equivalent elastic constant of the spring assembly  259  in the first condition is given by 2K 4 . In general, for any number N4 of springs of the spring assembly  259 , the equivalent elastic constant of the spring assembly  259  in the first operating condition is given by N4·K 4 . 
     Therefore, considering by way of example N4=1, in the first operating condition of  FIG. 4A , the resonance pulsation ω res  of the sensor  250  is obtained by applying the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   K 
                   4 
                 
                 
                   M 
                   4 
                 
               
             
           
         
       
     
       FIG. 4B  shows the sensor  250  in a second operating condition, where the external force applied to the sensor  250  has a second force value F 2  greater than, or equal to, the threshold force value F th . For the same reasons as those described previously, the seismic mass  253  is displaced with respect to the resting position of  FIG. 4 , and the stopper elements  266   a  are in abutment against the respective housing elements  266   b.  In particular, in the plane XY, the centroid B presents a displacement along the first axis X with respect to the centroid at rest B stat  greater than in the case illustrated in  FIG. 4A , and the springs  259   a,    259   b  of the spring assembly  259  are set in direct physical contact with the seismic mass  253 . In addition:
         the first length L 5  is twice the stop length L stop , and the second length L 6  is zero;   the first distance d c1  is less than the distance at rest d rest  (moreover, it is less than the first distance d c1  of  FIG. 4A ), and the second distance d c2  is greater than the distance at rest d rest  (moreover, it is greater than the second distance d c2  of  FIG. 4A );   the first length L a  is greater than the length at rest L rest  (moreover, it is greater than the first length L a  of  FIG. 4A ), and the second length L b  is less than the length at rest L rest  (moreover, it is less than the second length L b  of  FIG. 4A ); and   the first distance L 5block  is less than the maximum distance L blockmax  (moreover, it is less than the first distance L 5block  of  FIG. 4A ), and the second distance L 6block  is greater than the maximum distance L blockmax  (moreover, it is greater than the second distance L 6block  of  FIG. 4A ).       

     In detail, since the stopper elements  266   a  are in direct physical contact with (i.e., in abutment against) the respective housing elements  266   b,  the further stress (i.e., the difference between the stress applied and the minimum stress necessary for bringing the stopper elements  266   a  into abutment against the respective housing elements  266   b ) is distributed only over the turns of the second regions  261   a ″,  261   b ″ of the springs  259   a  and  259   b,  which undergo further deformation: in other words, these are the turns comprised between the stopper element  266   a  and the end  259   a ′ (respectively,  259   b ′). In what follows, denoted by the reference n fold2  is the number of turns belonging to each second region  261   a ″,  261   b ″ of the springs  259   a  and  259   b.    
     In the embodiment provided by way of example presented in  FIG. 4 , we have n fold2 =n foldtot /2. Consequently, each spring  259   a,    259   b  of the spring assembly  259  has, in the second operating condition, a second elastic constant K 5  that depends upon the second number of turns n fold2  (the second elastic constant K 5  being higher than the first elastic constant K 4 ). In the embodiment of  FIG. 4 , two springs  259   a,    259   b  are present, so that the equivalent elastic constant of the spring assembly  259  in the second operating condition is given by 2K 5 . In general, given any number N4 of springs of the spring assembly  259 , the equivalent elastic constant of the spring assembly  259  in the second operating condition is given by N4·K 5 . 
     Therefore, considering by way of example N4=1, in the second operating condition of  FIG. 4B , the resonance pulsation ω res  of the sensor  250  is obtained according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   K 
                   5 
                 
                 
                   M 
                   4 
                 
               
             
           
         
       
     
     In particular, if the external force applied to the sensor  250  has a value greater than, or equal to, the maximum force value F max  (greater than the threshold force value F th ), the seismic mass  253  bears upon the first blocking element  70 ′. 
       FIG. 5  shows a further embodiment of a micromechanical device  350  (referred to hereinafter as “sensor  350 ”) according to one aspect of the present disclosure. The sensor  350  comprises the semiconductor body  51 , a first mobile structure (hereinafter “seismic mass”)  353  having a first mass M 5 , and a second mobile structure (hereinafter “seismic mass”)  355  having a second mass M 6 , for example greater than the first mass M 5 . Both the first and second seismic masses  353 ,  355  are, for example, of semiconductor material (such as silicon or polysilicon) and extend parallel to the surface  51   a  of the semiconductor body  51 . The second seismic mass  355  encloses and delimits a first through opening, or cavity,  362 . Moreover, the second seismic mass  355  includes: a first side wall  355   a  and a second side wall  355   b,  directly facing the first cavity  362  and opposite to one another along the first axis X; and a third side wall  355   c  and a fourth side wall  355   d,  opposite to one another along the first axis X, which delimit the second seismic mass  355  externally. 
     The first seismic mass  353  is completely contained within the cavity  362 . The first seismic mass  353  has, in turn, a second through opening, or cavity  363 . The first seismic mass  353  encloses and delimits the cavity  363 . Moreover, the first seismic mass  353  includes: a first side wall  353   a  and a second side wall  353   b,  directly facing the cavity  363  and opposite to one another along the first axis X; and a third side wall  353   c  and a fourth side wall  353   d,  facing the first cavity  362  and opposite to one another along the first axis X. The first seismic mass  353  is physically coupled to the semiconductor body  51  via a first set of springs (similar to what has been described with reference to the first spring assembly  57  of  FIG. 2 , and therefore designated in what follows as first spring assembly  57 ) completely contained in the second cavity  363 . In particular, the fixing ends  57   a ′,  57   b ′ of both of the springs  57   a,    57   b  are fixed with respect to a same fixing element  64  (which in turn extends in the second cavity  363 , in a way fixed with respect to the semiconductor body  51 , in particular to the surface  51   a  of the semiconductor body  51 ). The ends  57   a ″,  57   b ″ of the springs  57   a,    57   b  of the first spring assembly  57  are, instead, fixed with respect to the first side wall  353   a  and the second side wall  353   b,  respectively, of the first seismic mass  353 . 
     The first and second seismic masses  353 ,  355  are physically coupled to one another via a second spring assembly  359  (e.g., to the spring assembly  59  of  FIG. 2 ), which extends in the first cavity  362 . In particular, the second spring assembly  359  comprises a first spring (elastic element)  359   a  and a second spring (elastic element)  359   b.  Each spring  359   a,    359   b  is a planar spring obtained with MEMS technology, more in particular a spring having a plurality of turns that define a serpentine path. 
     The first spring  359   a  develops between an end  359   a ′ thereof and an end  359   a ″ thereof, while the second spring  359   b  develops between an end  359   b ′ thereof and an end  359   b ″ thereof. The ends  359   a ′,  359   b ′ are fixed with respect to the first side wall  355   a  and second side wall  355   b,  respectively, of the second seismic mass  355 . 
     The spring  359   a  has a length, measured along the axis X, between the ends  359   a ′ and  359   a ″, identified by the reference L 4a ; the spring  359   b  has a length, measured along the axis X, between the ends  359   b ′ and  359   b ″, identified by the reference L 4b . 
     The ends  359   a ″,  359   b ″ are, instead, fixed with respect to the third side wall  353   c  and fourth side wall  353   d,  respectively, of the first seismic mass  353 . 
     Each spring  359   a  and  359   b  has an elastic constant K 6  that is higher than the elastic constant K 1  of each portion  57   a,    57   b.  In the embodiment of  FIG. 5 , two springs  359   a,    359   b  are present, so that the equivalent elastic constant of the second spring assembly  259  is equal to 2K 6 . In general, given any number N5 of springs of the second spring assembly  359 , the equivalent elastic constant of the second spring assembly  359  is given by N5·K 6 . Likewise, in the embodiment of  FIG. 5 , two springs  57   a,    57   b  are present, so that the equivalent elastic constant of the first spring assembly  57  is equal to 2K 1 . In general, given any number N1 of springs of the first spring assembly  57 , the equivalent elastic constant of the first spring assembly  57  is given by N1·K 1 . 
     In addition, the first seismic mass  353  includes at least one third through opening, or cavity,  365 . The first seismic mass  353  encloses and delimits the cavity  365 . A measurement structure extends in the cavity  365 . Said measurement structure is similar to the measurement structure  68  described with reference to  FIG. 2 , and is therefore designated in what follows by the same reference number. In particular, the first seismic mass  353  includes at least one first electrode  68   a,  which extends in the third cavity  365  and faces, and is set (along the first axis X) between, a first portion  68   b ′ and a second portion  68   b ″ of the measurement structure  68 . 
     Furthermore, at least one first contact element  380   a  and at least one second contact element  380   b  are fixed with respect to the surface  51   a  of the semiconductor body  51  and face the third side wall  355   c  and the fourth side wall  355   d,  respectively, of the second seismic mass  355 . The first contact element  380   a  is at a distance from the third side wall  355   c  of the second seismic mass  355  equal to a first contact length L cont1 , and the second contact element  380   b  is at a distance from the fourth side wall  355   d  of the second seismic mass  355  equal to a second contact length L cont2 . The contact lengths L cont1 , L cont2  are less than the value of distance at rest d rest  (d rest  is the distance at rest between the electrode  68   a  and the electrode  68   b ′, which is equal to the distance at rest between the electrode  68   a  and the electrode  68   b ″). Consequently, the second seismic mass  355  is set, along the first axis X, between the first and second contact elements  380   a,    380   b  so that the first and second seismic masses  353 ,  355  can move with respect to the semiconductor body  51  in a direction of deformation  360  parallel to the first axis X. 
     Moreover, the blocking elements  70  are present, here facing the third and fourth side walls  353   c,    353   d  of the first seismic mass  353 . In particular, at least one (in  FIG. 5 , two) first blocking element  70 ′ is at a first distance L 7block  from the third side wall  353   c  of the first seismic mass  353 , along the first axis X, and at least one (in  FIG. 5 , two) second blocking element  70 ″ is at a second distance L 8block  from the fourth side wall  353   d  of the first seismic mass  353 , along the first axis X. The first capacitor distance d c1  is greater than L 7block , and the second capacitor distance d c2  is greater than L 8block . 
     In use, the sensor  350  is biased, as discussed previously, for carrying out measurement of the external force applied. 
     With the sensor  350  in the resting condition as shown in  FIG. 5 , no external force is applied to the sensor  350 , and therefore both the first and second seismic masses  353 ,  355  are stationary and in the resting position. In particular, the first seismic mass  353  has a first centroid B 1 , and the second seismic mass  355  has a second centroid B 2 . In the resting condition, in the plane XY, the first and second centroids B 1 , B 2  coincide with one another and with a position at rest B stat . In addition:
         the first and second contact lengths L cont1 , L cont2  are the same as one another and equal to a length at rest L contrest ;   the first and second distances d c1 , d c2  are the same as one another and equal to the distance at rest d rest ;   the first length L 1a  and the second length L 1b  are the same as one another and equal to the length at rest L 1rest ;   the first length L 4a  and the second length L 4b  are the same as one another and equal to a length at rest L 4rest ; and   the first distance L 7block  and the second distance L 8block  are the same as one another and equal to the maximum distance L blockmax .       

       FIG. 5A  shows the sensor  350  in a first operating condition, where the external force (having the first force value F 1  lower than a threshold force value F th ) is applied to the sensor  350 . In a way similar to what has been discussed previously, there is a relative movement of the first and second seismic masses  253 ,  255  with respect to the semiconductor body  51 . In particular, considering the greater stiffness of the second spring assembly  359  as compared to the stiffness of the first spring assembly  57 , the first and second seismic masses  353 ,  355  move in a way fixed with respect to one another. In detail, both the first centroid B 1  and the second centroid B 2  are displaced, in the plane XY along the first axis X, with respect to the position of the centroid at rest B stat  and substantially coincide with one another. In addition:
         the first contact length L cont1  is less than the length at rest L contrest , and the second contact length L cont2  is greater than the length at rest L contrest ;   the first distance d c1  is less than the distance at rest d rest , and the second distance d c2  is greater than the distance at rest d rest ;   the first length L 1a  is greater than the first length at rest L 7rest , and the second length L 1b  is less than the length at rest L 7rest ;   the length L 4a  and the length L 4b  are substantially the same as one another and substantially equal to the length at rest L 8rest ; and   the first distance L 7block  is less than the maximum distance L blockmax , and the second distance L 8block  is greater than the maximum distance L blockmax .       

     Therefore, considering by way of example N1=1 and N5=1, in the first operating condition of  FIG. 5A , the sensor  350  has a resonance pulsation ω res  according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   K 
                   1 
                 
                 
                   
                     M 
                     5 
                   
                   + 
                   
                     M 
                     6 
                   
                 
               
             
           
         
       
     
       FIG. 5B  shows the sensor  350  in a second operating condition, where the external force applied to the sensor  350  has the second force value F 2  greater than, or equal to, the threshold force value F th . For the same reasons as those described previously, both the first and second seismic masses  353 ,  355  are displaced with respect to the resting position of  FIG. 5 , and the second seismic mass  355  bears upon the first contact element  380   a  at the third side wall  355   c  of the second seismic mass  355 . In particular, in the plane XY, both the first centroid B 1  and the second centroid B 2  present respective displacements along the first axis X with respect to the position at rest B stat  of the centroid greater than the displacements in the case illustrated in  FIG. 5A , and the displacement of the first centroid B 1  with respect to the position at rest B stat  of the centroid is greater than that of the second centroid B 2  with respect to the position at rest B stat  of the centroid. Consequently, in the second operating condition, the second seismic mass  355  is fixed with respect to the semiconductor body  51 , whereas the first seismic mass  353  can oscillate and move further. In addition:
         the first contact length L cont1  is zero, and the second contact length L cont2  is twice the length at rest L contrest ;   the first distance d c1  is less than the distance at rest d rest  (moreover, it is less than the distance d c1  of  FIG. 5A ), and the second distance d c2  is greater than the distance at rest d rest  (moreover, it is greater than the distance d c2  of  FIG. 5A );   the first length L 1a  is greater than the first length at rest L 1rest  (moreover, it is greater than the length L 1a  of  FIG. 5A ), and the second length L 1b  is less than the first length at rest L 1rest  (moreover, it is less than the length L 1b  of  FIG. 5A );   the first length L 4a  of the second spring assembly  359  is less than the second length at rest L 2rest , and the second length L 4b  is greater than the second length at rest L 2rest ; and   the first distance L 7block  is less than the maximum distance L blockmax  (moreover, it is less than the first distance L 7block  of  FIG. 5A ), and the second distance L 8block  is greater than the maximum distance L blockmax  (moreover, it is greater than the distance L 8block  of  FIG. 5A ).       

     Therefore, considering by way of example N1=1 and N5=1, in the second operating condition of  FIG. 5B , the resonance pulsation ω res  of the sensor  350  is obtained according to the following mathematical expression: 
     
       
         
           
             
               ω 
               res 
             
             ≈ 
             
               
                 
                   
                     K 
                     1 
                   
                   + 
                   
                     K 
                     6 
                   
                 
                 
                   M 
                   5 
                 
               
             
           
         
       
     
     The contact elements  380  therefore enable limitation of any possible oscillations of the second seismic mass  355  and cause deformation of the second spring assembly  359  thanks to the inertia of the first seismic mass  353  (which, in the second operating mode, is no longer fixed with respect to the second seismic mass  355 ), thus providing a threshold mechanism for modifying the elastic response of the sensor  350 . 
     Furthermore, if the external force applied to the sensor  350  has a value greater than, or equal to, the maximum force value F max  (greater than the threshold force value F th ), the first seismic mass  353  bears upon the first blocking element  70 ′ at a portion of the third side wall  353   c  of the first seismic mass  353 . In other words, the first distance L 7block  is zero, and the second distance L 8block  is twice the maximum distance L blockmax . The blocking elements  70  therefore enable limitation of any possible oscillations of the first seismic mass  353 , preventing them from overstepping a critical threshold of amplitude that might cause damage to or failure of the sensor  350 . 
     From an examination of the characteristics of the disclosure provided according to the present disclosure, the advantages that it affords are evident. 
     In particular, the present disclosure makes it possible to provide acceleration sensors that present a variable and/or nonlinear response to accelerations/decelerations. This enables just one sensor to measure different ranges of accelerations/decelerations and therefore detect and discriminate events that are very different from one another. In detail, having a same sensor that measures both accelerations of a low value (for example, equal to 16 g or 32 g) and accelerations of a high value (for example, equal to 128 g) guarantees a saving in terms of power dissipated for its operation, of area of integration dedicated thereto, and of overall cost of the device that houses the sensor. 
     In greater detail, the sensor  50  has two seismic masses  53 ,  55  and two spring assemblies  57 ,  59 . It is possible to measure low accelerations via the first seismic mass  53  that deforms the first spring assembly  57  (while the second seismic mass  55  is fixed with respect to the semiconductor body  51 , and the second spring assembly  59  does not substantially undergo deformation). It is then possible to measure high accelerations when the seismic masses  53 ,  55  are in abutment against and are fixed with respect to one another, and contribute to causing deformation both of the first set  57  and of the second spring assembly  59 . Moreover, the spring assemblies  57 ,  59  are not in direct physical contact with one another, and this improves the mechanical stability of the sensor  50  by reducing the stresses to which the spring assemblies  57 ,  59  are subjected in the event of shocks. In the sensor  50 , the threshold mechanism that enables modification of the elastic response of the sensor  50  is given by the elements  66   a  and  66   b.  The physical contact that can, in use, occur between the elements  66   a  and  66   b  involves elements of a bulk type, which are able to withstand high stresses. Therefore, critical stresses are not reached, thus guaranteeing a better mechanical stability of the sensor  50 . 
     The sensor  150  has, instead, one seismic mass  153  and two sets  57 ,  159  of springs. It is possible to measure low accelerations via the deformations of the first spring assembly  57  caused by the seismic mass  153  (while the second spring assembly  159  is not stressed), and it is possible to measure high accelerations via the deformations, caused by the seismic mass  153 , of both of the sets  57 ,  159  of springs. The elastic response of the sensor  150  can moreover be easily calculated via FEM (Finite-Element Modelling) simulations, in a per se known manner. In particular, as illustrated in  FIG. 6A , the signal generated by the sensor  150  presents, as the acceleration increases (positive values), a first rectilinear stretch having a first slope followed by a second rectilinear stretch having a second slope, lower than the first slope. The first and second stretches are joined together in a continuous way (i.e., there is no zero-degree discontinuity but only a first-degree discontinuity). The plot of the signal generated by the sensor  150  at negative accelerations (i.e., decelerations) is specular (in particular, symmetrical with respect to the origin) to that of positive accelerations. 
     The sensor  250  has a seismic mass  253  and a spring assembly  259 . The nonlinear elastic response of the sensor  250  is obtained by the operation described of the stopper elements  266   a  and housing elements  266   b,  which modify, in use, the properties of the spring assembly  259 : by reducing the number of turns of the spring assembly  259  that can withstand the stresses due to the external force applied (i.e., by reducing the number of active turns), the elasticity of the spring assembly  259  changes, and therefore the response of the sensor  250 . In this case, as illustrated in  FIG. 6B , the stiffness of the spring assembly  259  (and therefore, the overall stiffness of the sensor  250 ) presents, as the displacement of the seismic mass  253  increases, a first rectilinear stretch (which indicates a first stiffness) followed by a second rectilinear stretch (which indicates a second stiffness). These two stretches are separated from one another by a zero-degree discontinuity of the stiffness corresponding to the instant when the physical contact between the stopper elements  266   a  and housing elements  266  occurs. 
     The sensor  350  has two seismic masses  353 ,  355  and two sets  57 ,  359  of springs. The threshold mechanism that enables measurement of different ranges of acceleration is given by the physical contact of the second seismic mass  355  with the contact elements  380  fixed with respect to the semiconductor body  51 , which decouples the seismic masses  353 ,  355  and causes activation of the second spring assembly  359 . The response at output from the sensor  350  as a function of the acceleration is similar to the one described with reference to  FIG. 6A  for the sensor  150 . 
     Furthermore, the elastic elements of the sensors discussed previously have a main extension and direction of deformation parallel to the surface  51   a  of the semiconductor body  51 . In particular, the external force acts in the direction of deformation of the elastic elements. This enables distribution of the stresses on the elastic elements in an efficient way, thus reducing the likelihood of damage or failure thereof. 
     Finally, it is clear that modifications and variations may be made to the disclosure described and illustrated herein, without thereby departing from the scope of the present disclosure, as defined in the annexed claims. 
     In particular, the measurement structure  68  may be of an interdigitated type (i.e., it may include a plurality of first and second electrodes  68   a,    68   b  facing one another to form an array), to improve measurement sensitivity. Moreover, the measurement structure  68  may be based upon an effect different from the capacitive one discussed previously. For instance, the measurement structure  68  may be a structure, of a type in itself known, that implements a detection of a resistive, piezoelectric, or optical type. 
     In addition, each stopper element  66   a  (equivalently,  166   a  and  266   a,  and each contact element  380   a,    380   b ) may include a crowned portion adapted to improve contact with, and reduce the risk of its adhesion to, the respective housing element  66   b  (respectively,  166   b  and  266   b,  and the second mass  355 ) during mutual contact. In particular, the side walls of each stopper element may have a convex shape. 
     The abutment assemblies  66 ,  166 ,  266  may be in a number and occupy positions different from what has been described herein, as likewise the blocking elements  70 . 
     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.