Abstract:
The invention pertains to a contactor actuatable by a magnetic field wherein:
       first and second strips comprise pads forming several pairs of pads P 1i , P 2i  facing each other, immediately consecutive along the longitudinal direction, and   each strip comprises at least one bridge Pt ji , each bridge mechanically and directly linking two immediately consecutive pads P ji , P j,i+1  of a same strip, the cross-section of this bridge Pt ji  being reduced as compared with the cross-section of the pads P ji  et P j,i+1 , and the surface area S Ptji  of the smallest cross-section of the bridge Pt ji  verifying the following relationship: 0&lt;S Ptji &lt;⅔S Zi , where S Zi  is the surface area of an overlap zone between the contact faces of a pair of pads P 1i , P 2i , j is an index identifying the strip and i is an index identifying the pad of this strip.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The invention pertains to a contactor actuatable by a magnetic field as well as to a switch comprising this contactor. 
         [0002]    Contactors that can be actuated by a magnetic field are also called Reed switches. 
         [0003]    Prior-art contactors comprise at least one first strip and one second strip made out of magnetic material extending along a longitudinal direction: 
         [0004]    the first strip comprising at least one pad having a contact face F 1i , 
         [0005]    the second strip having at least one pad P 2i  facing the pad P 1i  and having a contact face F 2i , the pads P 1i  and P 2i  facing each other when the intersection of the face F 2i  and of the projection in a transversal direction, perpendicular to the longitudinal direction, of the face F 1i  on the face F 2i  forms an overlap zone Z i , the surface area S zi  of which is strictly greater than zero, 
         [0006]    at least one pad of each pair of pads P 1i , P 2i  facing each other being capable of being shifted along the transversal direction, under the effect of the magnetic field, between:
       a closed position in which the faces F 1i  and F 2i  are directly in mechanical contact with each other to enable the passage of a current, and       
 
         [0008]    an open position in which the faces F 1i  and F 2i  are separated from each other by an air gap so as to be electrically insulated from each other. 
         [0009]    When at least one of the pads is in the closed position, the contactor is said to be in the closed position. The contactor is in the open position when all the pads are in the open position. 
       SUMMARY OF THE INVENTION 
       [0010]    The invention is aimed at reducing the resistance of this contactor in the closed position. An object of the invention is a contactor in which: 
         [0011]    the first and second strips comprise pads forming several pairs of pads P 1i , P 2i  facing each other, immediately consecutive along the longitudinal direction, and 
         [0012]    each strip comprises at least one bridge Pt ji , each bridge mechanically and directly linking two pads P ji , P j,i+1  that are immediately consecutive in the same strip, the cross-section of this bridge Pt ji  being reduced as compared with the cross-section of the pads P ji  et P j,i+1 , and the surface area S Ptji  of the smallest cross-section of the bridge Pt ji  verifying the following relationship: 0&lt;S Ptji &lt;⅔S Zi , where j is an index identifying the strip and i is an index identifying the pad of this strip. 
         [0013]    The above contactor has a resistance in the closed position that is smaller than that of an identical reference contactor which however is provided with only one pair of pads. Indeed, since the cross-section of the bridges Pt ji  is smaller than the surface area S Zi  of the overlap zone (i.e. since the surface area S Ptji  is smaller than two-thirds of the surface area S Zi ), the majority of the magnetic flux concentrated by the pad P 1i  crosses the overlap zone rather than the bridge Pt 1i . The pads of each pair of pads P 1i , P 2i  are therefore drawn to each other under the effect of the magnetic field by a force close to that observed for the reference contactor. The resistance R i  between the pads of each pair of pads P 1i , P 2i  in the closed position is therefore fairly close to that observed for the reference contactor. However, the above contactor has  n  pairs of pads P 1i , P 2i  and therefore  n  parallel-connected resistors R i  when the switch is in the closed position. The resistance in the closed position of the above contactor is therefore far smaller than that of the reference contactor because of this parallel-mounting of several resistors R i . 
         [0014]    In fact, the resistance of the above contactor in the closed position is close to that which would be obtained by the parallel connection of  n  reference contactors. However, as compared with this parallel connection of  n  reference contactors, the above contactor has a far smaller space requirement. Indeed, the bridges Pt ji  mechanically and electrically connect the different pads to one another. It is therefore not necessary to provide for specific electrical tracks to set up the parallel connection of the pairs of pads as would be the case if  n  reference contactors were to be parallel connected. Furthermore, the space requirement of the above contactor is reduced. More specifically, the greater the number  n  of pairs of pads, the greater the overlap between the first and second strips. Thus, it has been estimated that the space requirement of the above contactor is smaller than nS/2 where S is the space requirement of the reference contactor while the space requirement of  n  parallel-connected reference contactors is substantially equal to nS. The space requirement of the contactor is represented by the surface area that it occupies in a plane parallel to the longitudinal and transversal directions. 
         [0015]    The embodiments of this contactor may have one or more of the following characteristics:
       the surface area S Zi  of each overlap zone verifies the following two relationships: 0&lt;S zi ≦S 1i /3 and 0&lt;S zi ≦S 2i ≦/3, where S ij  is the surface area of the contact face F ij ;   each pad P ji  is a parallelepiped extending in parallel to the longitudinal direction, with a thickness e pji  in the transversal direction and the overlap zone is a rectangle with a length x in the longitudinal direction, the length x being equal to e pji /2 plus or minus 30%,   at least one of the pads P ji  faces the pads P 2i  and the pad P 2,i+1 ;   the surface areas S Zi  of the overlap zones are all equal and the dimensions of the pads P ij  are also all equal to one another;   the contactor has a plane substrate within which there is hollowed out a well and the strips are entirely received within this well;   each bridge Pt ji  corresponds to the bottom of a groove whose opening is pointed towards the air gap.       
 
         [0022]    These embodiments of the contactor furthermore have the following advantages: 
         [0023]    having a smaller overlap zone than the surface area S 1i  or S 2i  of the pad concentrates a magnetic flux in this overlap zone, thus increasing the contact force in the closed position and consequently diminishing the resistance of the contactor in the closed position; 
         [0024]    choosing a length x for the overlap zone close to half the thickness e pji  maximizes the contact force while at the same time minimizing the space requirement of the contactor; 
         [0025]    having a pad P 1i  facing the pads P 2i  and the pad P 2,i+1  increases the number of contactors in the closed position and therefore further diminishes the resistance of the contactor in the closed position; 
         [0026]    sizing the different pads and their position to obtain substantially equal contact forces between each pair of pads diminishes the resistance of the contactor in the closed position while at the same time limiting the increase of its space requirement; 
         [0027]    housing the strips entirely within a well facilitates the making of a hood insulating this well from the external environment. 
         [0028]    An object of the invention is also a switch comprising: 
         [0029]    the above contactor, and 
         [0030]    a source of induction B 0  parallel to the longitudinal direction under the effect of which the pads shift from their open position to their closed position, 
         [0000]    wherein the dimensions of the pads are such that the intensity of the magnetic induction B 0  makes it possible to saturate these pads P 1i  and P 2i  while a magnetic induction B 1 , which is identical to the induction B 0  except that its intensity is equal to 80% of the intensity of the induction B 0 , does not enable these pads P 1i  and P 2i  to be saturated. 
         [0031]    Sizing the pads P ji  so that they are just saturated by the field B 0  limits the space requirement of the contactor and therefore that of the switch to the maximum degree. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]    The invention will be understood more clearly from the following description given purely by way of a non-exhaustive example and made with reference to the appended drawings, of which: 
           [0033]      FIG. 1  is a schematic illustration of a switch equipped with a contactor actuatable by a magnetic field, 
           [0034]      FIG. 2  is a schematic illustration in partial cross-section of the contactor of  FIG. 1 , 
           [0035]      FIG. 3  is a schematic illustration of the conformation of the ends of strips of the contactor of  FIG. 1 , 
           [0036]      FIG. 4  is a flowchart of a method for sizing ends of the contactor of  FIG. 1 , 
           [0037]      FIG. 5  is a flowchart of a method for fabricating the contactor of  FIG. 1 , 
           [0038]      FIGS. 6 to 10  are schematic illustrations in vertical section of a contactor of  FIG. 1  in different states of fabrication, 
           [0039]      FIGS. 11 and 12  are schematic illustrations in a top view of two other possible embodiments for the ends of the contactor of  FIG. 1 , 
           [0040]      FIG. 13  is a flowchart of a method for sizing the ends of the embodiment of  FIG. 12 , and 
           [0041]      FIG. 14  is a schematic illustration in a top view of another possible embodiment of the ends of the contactor of  FIG. 1 . 
       
    
    
       [0042]    In these Figures, the same references are used to designate the same elements. 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0043]    Here below in this description, the characteristics and functions well known to those skilled in the art are not described in detail. 
         [0044]      FIG. 1  shows a switch  1  equipped with: 
         [0045]    a micro-contactor  2  actuatable by a magnetic field, and 
         [0046]    a controllable magnetic-field source  3 . 
         [0047]    The source  3 , when activated, generates a magnetic field or a magnetic induction B 0  parallel to a longitudinal direction X. When there is no command, the source  3  generates no magnetic field. 
         [0048]    The micro-contactor  2  is a contactor. However, it differs from macroscopic contactors inter alia by its method of fabrication. The micro-contactors are made by using the same batch manufacturing methods as those used to make microelectronic chips. For example, the micro-contactors are made out of a monocrystalline silicon or glass machined by photolithography and etching and/or structured by epitaxial growth and deposition of metallic material. 
         [0049]    This micro-contactor  2  is made in a plane substrate  4  that extends horizontally, i.e. in parallel to the orthogonal directions X and Y. Here below in this description, the vertical direction, orthogonal to the directions X and Y, is denoted as Z. 
         [0050]    The substrate  4  is a rigid substrate. To this end, its thickness in the direction Z is greater than 200 μm and preferably greater than 500 μm. It is advantageously an electrically insulating substrate. 
         [0051]    For example, here, this substrate  4  is a silicon substrate, i.e. a substrate comprising at least 10% and typically more than 50% by mass of silicon. This substrate is inorganic and non-photosensitive. The substrate  4  has a horizontal plane upper face  6 . 
         [0052]    The micro-contactor  2  has electrodes  8  and  10  through which there flows the current that passes through this micro-contactor. These electrodes  8  and  10  are fixed without any degree of freedom to the substrate  4 . Here, these electrodes  8  and  10  are parallelepipeds whose upper faces are situated in the same plane as the upper face  6 . The vertical faces of these electrodes extend into the substrate  4 . The vertical faces are connected to one another within the substrate by a lower face, for example parallel to the upper face. 
         [0053]    Strips  12 ,  14  extend in parallel to the direction X starting from the electrodes, respectively  8  and  10 . These strips  12 ,  14  can be shifted relatively to each other, under the effect of a magnetic field parallel to this direction X, between: 
         [0054]    an open position (shown in  FIG. 1 ) in which the strips are electrically insulated from each other by an air gap  15  filled with a dielectric gas, and 
         [0055]    a closed position in which the strips are directly mechanically in contact with each other to enable the passage of the current between the electrodes  8  and  10 . 
         [0056]    Here, each strip has the shape of a parallelepiped that extends in parallel to the direction X. Thus, like the electrodes, each strip has: 
         [0057]    an upper face situated on the same plane as the upper face  6  of the substrate  4 , 
         [0058]    vertical faces which penetrate into the interior of the substrate  4 , and 
         [0059]    a lower face situated beneath the face  6  of the substrate  4 , and, for example, parallel to the upper face of this strip. 
         [0060]    Each strip  12 ,  14  has a proximal end, respectively  16 ,  18  mechanically and electrically connected respectively to the electrodes  8  and  10 . Here, the proximal ends  16  and  18  are connected without any degree of freedom to their respective electrodes. Thus, these proximal ends  16 ,  18  are immobile. 
         [0061]    In this embodiment, the strips form one and the same block of material with the electrode to which they are mechanically connected. 
         [0062]    Each strip  12 ,  14  also has a distal end respectively  20 ,  22 . These distal ends  20  and  22  face each other and are separated from each other by the air gap  15  in the open position. The thickness of the air gap in the direction Y is denoted as d. Conversely, these distal ends are directly supported on each other in the closed position. 
         [0063]    Here, in this embodiment, both distal ends  20 ,  22  are flexible so as to shift between the open and closed positions. 
         [0064]    The distal ends  20 ,  22  move solely in parallel to the horizontal plane X, Y. To this end, they are received within a well  24  filled with a dielectric gas such as air or the like. More specifically, each distal end  20 ,  22  bends in order to reach the closed position from the open position. The deformations undergone by each distal end  20 ,  22  between the closed and open positions are all elastic to enable it to return automatically to the open position when there is no external force applied. 
         [0065]    To be flexible, each distal end  20 ,  22  is far longer in the direction X than it is thick in the direction Y. For example, each distal end  20 ,  22  is five, ten or fifty times longer than it is thick. Here, the thickness of each distal end  20 ,  22  is smaller than 100 μm and preferably smaller than 50 or 10 μm. 
         [0066]    The height e c  of each distal end  20 ,  22  in the direction Z is typically, in this example, of the order of 20 to 50 μm. 
         [0067]    Here, the distal ends  20 ,  22  are formed to limit the resistance of the micro-contactor in the closed position. One example of such forming is described with reference to  FIG. 3 . 
         [0068]    The essential part of the strips  12 ,  14  and of the electrodes  8 ,  10  is made out of soft magnetic material. A soft magnetic material is a material having a relative permeability for which the real part at low frequency is greater than 1,000. Such a material typically has a coercive excitation in order to be demagnetized that is below 100 A·m −1 . For example, the soft magnetic material used here is an alloy of iron and nickel. 
         [0069]    To increase the electrical conductivity of the strips, the vertical and lower faces of these strips are covered with a conductive coating  28 . This is also the case for the vertical and lower faces of the electrodes  8 ,  10 . For example, this coating is made out of rhodium (Ro) or ruthenium (Ru) or platinum (Pt). The micro-contactor  2  can also comprise a hood  30  ( FIG. 2 ) that covers the well  24 . To simplify  FIG. 1 , this hood is not shown therein. 
         [0070]      FIG. 2  shows the micro-contactor  2  in a vertical section along a section plane I-I shown in  FIG. 1 . In this  FIG. 2 , the hood  30  which covers the well  24  is shown. This hood  30  prevents impurities from penetrating into the interior of the well  24  and hampers the shifting of the strips  12 ,  14 . It also prevents the oxidation of the contact. 
         [0071]    When an external magnetic field is applied in parallel to the direction X, it is concentrated and guided by the strips  12  and  14 . The field lines of this magnetic field are symbolized by an arrow F in  FIG. 1 . This creates forces in the air gap  15  which tend to reduce this air gap. These forces cause each distal end  20 ,  22  to bend until they come into contact with each other. Thus, an external magnetic field makes it possible to shift the strips  12 ,  14  between the open position and the closed position. When the external magnetic field disappears, the distal ends  20 ,  22  return to the open position in the manner of a spring leaf, i.e. by elastic deformation. 
         [0072]      FIG. 3  gives a more detailed view of the forming of the ends  20  and  22  implemented to reduce the resistance of the micro-contactor  2  in the closed position. Here, each end  20 ,  22  has several pads P ji  positioned beside one another in the direction X, where the index j identifies a strip and the index i identifies the pad of this strip. More specifically, here below in this description, the index j takes the value “1” to designate the strip  12  and the value “2” to designate the strip  14 . 
         [0073]    Two pads P ji  and P j,i+1  immediately consecutive in the direction X are mechanically connected to each other by means of a bridge Pt ji . 
         [0074]    Each pad P ji  has a plane face F ji  pointing toward the air gap  15 . Here, each pad P 1i  faces a pad P 2i  of the other strip. Two pads P 1i  and P 2i  are placed so as to be facing each other if the intersection of the face F 2i  and the projection, in the direction Y, of the face F 1i  on the face F 2i  forms an overlap zone Z i  whose surface area S Zi  is strictly greater than zero. Here below in this description, two pads P 1i  and P 2i  facing each other have the same index i. 
         [0075]    The surface area S Pji  of the cross section of the bridge Pt ji  is strictly smaller than the surface area of the cross section of the pads P ji  and P i,j+1  that it connects. Here, the term “surface area of the cross section” designates the surface area of the section of the pad or of the bridge parallel to the plane defined by the directions YZ. 
         [0076]    Here, the forming of the ends  20  and  22  is represented in the particular case where the number  n  of pairs of pads P 1i , P 2i  facing each other is equal to two. 
         [0077]    Furthermore, here, the ends  20  and  22  are identical except that they are pointed towards each other. Indeed, the faces F 1i  are pointed to the faces F 2i . Thus, here below, only the end  20  is described in detail. 
         [0078]    The pad P 11  is directly connected to the end  16  by a parallelepiped arm B 1  with a length l in the direction X, a thickness e in the direction Y and a height e c  in the direction Z. The pad P 11  is connected to the pad P 12  by the bridge Pt 11 . In this particular embodiment, the dimensions of the pads P 11  and P 12  are identical. Thus here below, only the dimensions of the pad P 11  are described in greater detail. 
         [0079]    The pad P 11  is a parallelepiped with a length βx, a thickness e p  and a height e c . The face F 11  and the overlap zone Z 1  are therefore rectangles. The length of the overlap zone Z 1  in the direction X is denoted as “x”. Here, the length of the pad P 11  is taken to be proportional to the length x of the overlap zone Z 1 . It is therefore noted in the form of a product: a constant β multiplied by the length x. 
         [0080]    The bridge Pt 11  is a parallelepiped with a length e s , a thickness e pt  and a height e c . The bridge Pt 11  is sized so its transversal surface area S Pt11  is at least smaller than two-thirds of the surface area S Z1  of the overlap zone Z 1 . When the surface area S Pt11  is smaller than two-thirds of the surface area S Z1  or S Z2 , the greater part of the magnetic flux concentrated by the pads P 11  or P 12  passes through the air gap  15  rather than through the bridge Pt 11 . This therefore increases the quantity of magnetic flux that passes through the air gap  15  by means of the overlap zones. Now, the contact force f contact  between the pairs of pads facing each other is proportional to the magnetic flux divided by the surface area crossed by this flux. Thus, minimizing the vertical section of the bridges Pt 1i  increases the force of contact between the pads in the closed position and therefore reduces the resistance of the contactor in the closed position. 
         [0081]    Here, the thickness e pt  of this bridge Pt 11  is at least smaller than one third of the thickness e p  of the pads P 11  and P 12 . Thus, this bridge Pt 11  also corresponds to the bottom of a groove with a depth t p  between the faces F 11  and F 12 . The width of this groove is equal here to the length e s  of the bridge Pt 11 . 
         [0082]    It will be noted that the thickness e p  of the pad P 11  is equal to the sum of the depth t p  and the width e pt  of the bridge Pt 11 . 
         [0083]    The total length of the end  20  is denoted as l p . Here, the length l p  is equal to 2βx+e s . 
         [0084]    The ends  20  and  22  are offset relatively to each other in the direction X by a distance g to reduce the overlapping surfaces S Zi . In this embodiment, the distance g is chosen so that the following two relationships are verified: 
         [0000]        S   Zi   ≦S   1i /3 
         [0000]        S   Zi   ≦S   2i /3, 
         [0000]    where S 1i  and S 2i  are the surface areas respectively of the faces F 1i  and F 2i . 
         [0085]    In order to simplify the figures, the representations of the ends  20 ,  22  are not drawn to scale, and these two relationships are not shown. 
         [0086]    Preferably, the surface area S Zi  is smaller than a quarter or one eighth of the surface areas S 1i  and S 2i . 
         [0087]    Reducing the overlap surface S Zi  concentrates the magnetic flux on a smaller surface area than the surface area of the faces F ji . This therefore increases the contact force f contact  between these pads and thus reduces the resistance of the contactor in the closed position. 
         [0088]    The sizing of the ends  20  and  22  shall now be described with reference to the method of  FIG. 4 . 
         [0089]    Here, the sizing of the ends  20  and  22  is illustrated by numerical examples given for the following condition: 
         [0090]    the intensity of the magnetic field B 0  produced by the source  3  to shift the micro-contactor  2  towards its closed position is 50 mT, 
         [0091]    the voltage that must be switched by the micro-contactor  2  is at most 50 volts, 
         [0092]    the contact force f contact  exerted between each pair of pads and the closed position is 150 μN, 
         [0093]    the restoring force f rappel  which brings the pads back to their open position is 20 μN per contact, 
         [0094]    the restoring force f amin  exerted by the bridge Pt 11  to bring the pad P 12  back towards its open position is 20 μN, 
         [0095]    the relative permeability of the magnetic material used to make the strips  20  and  22  is 1000, 
         [0096]    the Young&#39;s modulus E of the magnetic material is equal to 1.85.10 11  Pa, and 
         [0097]    the polarization J s  of the magnetic material at saturation is equal to 1 T. 
         [0098]    The contact force f contact  is the force exerted by the pad P 1i  on the pad P 2i  in the closed position. The greater this contact force, the greater is the reduction of the resistance of the contact. 
         [0099]    The restoring force f rappel  is a restoring force exerted on each pad, and permanently pulls them toward the open position. 
         [0100]    The polarization J s  is the polarization of the magnetic material observed when it is saturated. As a first approximation, the polarization is the ratio between the intensity of the magnetic field B 0  and the demagnetization factor Nd. 
         [0101]    At a step  27 , the distance d of the air gap in the open position is chosen. This distance d must be great enough to electrically insulate the pads P 1i  from the pads P 2i  in the open position. It therefore depends especially on the voltage present between the terminals  8  and  10  of the micro-contactor  2  in the open position. Here, this distance d is chosen to be greater than 5 μm so as to electrically insulate the pads P 1i  from the pads P 2i  even when there is a voltage of 220 volts between the pads  8  and  10 . This value of 5 μm is given in the special case where the air gap  15  is filled with air. Indeed, the disruptive field of air is of the order of 50V/μm for dimensions as small as those of the ends  20  and  22 . 
         [0102]    Besides, the distance d is chosen to be small enough to remain within the zone of elastic deformation of the strips  12  and  14 . The maximum limit for the distance d therefore depends on the characteristics of the magnetic material chosen such as its Young&#39;s modulus E. Here, to remain within this zone of elastic deformation, d is chosen to be smaller than 15 μm. 
         [0103]    In this example, the distance d is fixed to be equal to 5 μm to minimize the space requirement of the micro-contactor  2 . 
         [0104]    At a step  29 , the height e c  is fixed. The greater this height e c  the greater the decrease in the resistance of the micro-contactor  2  in the closed position. However, technological constraints of manufacture dictate an upper limit on the height e c . Thus, here, the height e c  is chosen to be to most equal to 30 μm and at least equal to 10 μm. For numerical applications, the height e c  is chosen to be equal to 20 μm. 
         [0105]    At a step  31 , the thickness e p  of the pads is calculated so as to obtain a magnetic force f f  which draws the pad P 1i  to the pad P 2i  in the presence of the magnetic field B 0  equal to 170 μN. This force f f  counters the restoring force f rappel  and the force f amin  which are taken here to be equal to 20 μN. More specifically, the forces f contact , f f  and f rappel  are connected to one another by the following relationship: f contact =f f −f rappel . 
         [0106]    Thus, to obtain a contact force f contact  of 150 μN, the force f f  is taken here to be equal to 170 μN. 
         [0107]    To calculate the thickness e p , different numerical simulations using software programs have been made to experimentally establish a relationship linking the force f f  to the thickness e p . The relationship established is the following: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     f 
                   
                   = 
                   
                     
                       ( 
                       
                         3 
                         , 
                         
                           
                             4 
                              
                             
                                 
                             
                              
                             
                               e 
                               p 
                             
                           
                           + 
                           25 
                         
                       
                       ) 
                     
                      
                     
                       
                         e 
                         c 
                       
                       20 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0108]    In this relationship (1) the thickness e p , the height e c  are expressed in μm and the force f f  is expressed in μN. 
         [0109]    This relationship (1) has been established with the following assumptions: 
         [0110]    the pads P ji  are saturated by the magnetic field B 0 , 
         [0111]    the presence of the bridges Pt ij  and of the arms B j  has been overlooked, and 
         [0112]    the thickness e p  is assumed to range from 10 to 100 μm. 
         [0113]    Furthermore, the relationship (1) has been established on the assumption that the length x of the overlap zone Z i  is equal to half of the thickness e p . In other words, the following relationship is verified: 
         [0000]        x=e   p /2  (2)
 
         [0114]    By means of this relationship (1), we obtain here the value of 40 μm for the thickness e p . 
         [0115]    At a step  32 , the length x is calculated by means of the relationship (2). The length x is therefore equal here to 20 μm. 
         [0116]    At a step  33 , the length βx of the pads P ji  is calculated. This length βx is determined so that each pad P ji  is completely saturated magnetically when the field B 0  is present. Here, the length βx is calculated so that each pad P ji  is just saturated. The term “just saturated” designates to the fact that each pad is saturated by the field B 0  and is not saturated by a field B 1  which is identical to the field B 0  except that its intensity is equal to 80% and, preferably, 90% of the intensity of the field B 0 . To this end, different relationships obtained by modeling the pad P ji  by means of the laws of electromagnetism are used. 
         [0117]    More specifically, the following relationship linking the polarization J s  of the material at saturation to the field B 0  is used: 
         [0000]    
       
         
           
             
               
                 
                   
                     J 
                     s 
                   
                   = 
                   
                     
                       
                         B 
                         0 
                       
                       
                         
                           1 
                           
                             
                               μ 
                               r 
                             
                             - 
                             1 
                           
                         
                         + 
                         Nd 
                       
                     
                     ≈ 
                     
                       
                         B 
                         0 
                       
                       Nd 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0118]    In this relationship (3) Nd is the factor of demagnetization of the pad P ji . This factor Nd is a function of the dimensions of the pad P ji . The following relationship which links the factor Nd to the dimensions of the pad is used: 
         [0000]    
       
         
           
             
               
                 
                   Nd 
                   = 
                   
                     
                       
                         
                           e 
                           c 
                         
                          
                         
                           e 
                           p 
                         
                       
                       
                         
                           ( 
                           
                             β 
                              
                             
                                 
                             
                              
                             x 
                           
                           ) 
                         
                         2 
                       
                     
                      
                     
                       ( 
                       
                         
                           ln 
                            
                           
                             ( 
                             
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     β 
                                      
                                     
                                         
                                     
                                      
                                     x 
                                   
                                   ) 
                                 
                               
                               
                                 
                                   e 
                                   c 
                                 
                                 + 
                                 
                                   e 
                                   p 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0119]    This relationship was obtained in assuming that the relationship relating the demagnetization factor Nd to the dimensions, established in the case of an ellipsoid, can also be applied in the case of a parallelepiped. 
         [0120]    Thus, to obtain the value of the constant β, the following equation must be resolved: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       B 
                       0 
                     
                     
                       J 
                       s 
                     
                   
                   = 
                   
                     
                       
                         
                           e 
                           c 
                         
                          
                         
                           e 
                           p 
                         
                       
                       
                         
                           ( 
                           
                             β 
                              
                             
                                 
                             
                              
                             x 
                           
                           ) 
                         
                         2 
                       
                     
                      
                     
                       ( 
                       
                         
                           ln 
                            
                           
                             ( 
                             
                               
                                 4 
                                  
                                 
                                   ( 
                                   
                                     β 
                                      
                                     
                                         
                                     
                                      
                                     x 
                                   
                                   ) 
                                 
                               
                               
                                 
                                   e 
                                   c 
                                 
                                 + 
                                 
                                   e 
                                   p 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0121]    The resolution of this equation gives the value “7” for the constant β. Thus the length of the pad P ji  here is 140 μm. 
         [0122]    Then, at the step  34 , the length l, the thickness e, the width e s  and the depth t p  are determined to obtain a restoring force f rappel  equal to 20 μN and a force f amin  equal to 20 μN. Here, for this purpose, e is fixed so as to minimize the space requirement of the micro-contactor  2 . For example, e is chosen to be equal to 5 μm. 
         [0123]    The distance g is also fixed in this particular case so that the pad P 1i  is facing only one pad P 2i . For example, g is chosen to be equal to 50 μm. Once the distance g has been fixed, the width e s  and the total length l p  of the end  20  are given by the following relationships: 
         [0000]        e   s   =g+βx−x,   (6)
 
         [0000]        l   p =2 βx+e   s   (7)
 
         [0124]    The force f amin  is given by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     amin 
                   
                   = 
                   
                     
                       2 
                        
                       
                         Γ 
                         amin 
                       
                     
                     
                       
                         e 
                         s 
                       
                       + 
                       
                         β 
                          
                         
                             
                         
                          
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0125]    Γ amin  is the mechanical restoring torque exerted by the bridge Pt 11  on the pad P 12 . 
         [0126]    The torque Γ amin  is given by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     Γ 
                     amin 
                   
                   = 
                   
                     
                       S 
                       amin 
                     
                      
                     
                       d 
                       2 
                     
                      
                     
                       ( 
                       
                         
                           e 
                           s 
                         
                         + 
                         
                           β 
                            
                           
                               
                           
                            
                           x 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0127]    The value S amin  is itself given by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     S 
                     amin 
                   
                   = 
                   
                     E 
                     
                       
                         
                           
                             e 
                             s 
                             3 
                           
                           
                             3 
                              
                             
                               I 
                               3 
                             
                           
                         
                         + 
                         
                           
                             
                               ( 
                               
                                 β 
                                  
                                 
                                     
                                 
                                  
                                 x 
                               
                               ) 
                             
                             3 
                           
                           
                             3 
                              
                             
                               I 
                               4 
                             
                           
                         
                         + 
                         
                           
                             1 
                             
                               I 
                               3 
                             
                           
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       β 
                                        
                                       
                                           
                                       
                                        
                                       x 
                                     
                                     ) 
                                   
                                   2 
                                 
                                  
                                 
                                   e 
                                   s 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     β 
                                      
                                     
                                         
                                     
                                      
                                     x 
                                   
                                   ) 
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       e 
                                       s 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                           
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0128]    The coefficients I 3  and I 4  are given by the following relationships: 
         [0000]    
       
         
           
             
               
                 
                   
                     I 
                     3 
                   
                   = 
                   
                     
                       
                         e 
                         C 
                       
                       · 
                       
                         
                           ( 
                           
                             
                               e 
                               p 
                             
                             - 
                             
                               t 
                               p 
                             
                           
                           ) 
                         
                         3 
                       
                     
                     12 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     4 
                   
                   = 
                   
                     
                       
                         e 
                         c 
                       
                       · 
                       
                         e 
                         
                           p 
                           3 
                         
                       
                     
                     12 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0129]    Thus, the constraint set on the force f admin  in enables the depth t p  to be calculated from the preceding relationships. 
         [0130]    Imposing the force f amin ≧20 μN ensures that, if the pad P 11  returns to its position under the action of the restoring force f rappel , the pad P 12  will do the same because the bridge Pt 11  is rigid enough for this purpose. 
         [0131]    Once the depth t p  has been calculated, the length l is calculated, enabling verification of the constraint according to which the force f rappel  is equal to 20 μN. The force f rappel  is given by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     rappel 
                   
                   = 
                   
                     
                       Γ 
                       r 
                     
                     
                       21 
                       + 
                       
                         l 
                         p 
                       
                       + 
                       
                         
                           ( 
                           
                             β 
                             - 
                             1 
                           
                           ) 
                         
                          
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0132]    Γ r  is the torque of the restoring force. This torque is equal to twice the restoring torque Γ meca  exerted by each of the strips  12  and  14 . Thus, the restoring torque Γ r  is defined by the following relationship: 
         [0000]      2Γ meca =Γ r   (14)
 
         [0133]    The torque Γ meca  of a single strip is defined by the following relationship: 
         [0000]      Γ meca   =S·f   0 ·( l+l   p )
 
         [0000]    where f 0  is the maximum bending of the strip  12 . 
         [0134]    Here, this bending f 0  is approximated by means of the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     0 
                   
                   ≈ 
                   
                     
                       - 
                       d 
                     
                     
                       
                         
                           
                             - 
                             l 
                           
                           + 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 β 
                               
                               ) 
                             
                              
                             x 
                           
                         
                         
                           l 
                           + 
                           
                             l 
                             p 
                           
                         
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0135]    The factor S of the relationship (15) is given by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   S 
                   = 
                   
                     E 
                     
                       
                         
                           
                             
                               
                                 l 
                                 3 
                               
                               
                                 3 
                                  
                                 
                                   I 
                                   1 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   ( 
                                   
                                     β 
                                      
                                     
                                         
                                     
                                      
                                     x 
                                   
                                   ) 
                                 
                                 3 
                               
                               
                                 3 
                                  
                                 
                                   I 
                                   2 
                                 
                               
                             
                             + 
                             
                               
                                 e 
                                 x 
                                 3 
                               
                               
                                 3 
                                  
                                 
                                   I 
                                   3 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   ( 
                                   
                                     β 
                                      
                                     
                                         
                                     
                                      
                                     x 
                                   
                                   ) 
                                 
                                 3 
                               
                               
                                 3 
                                  
                                 
                                   I 
                                   4 
                                 
                               
                             
                             + 
                             
                               1 
                               
                                 I 
                                 1 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     l 
                                     2 
                                   
                                    
                                   
                                     l 
                                     P 
                                   
                                 
                                 + 
                                 
                                   
                                     l 
                                      
                                     
                                       ( 
                                       
                                         l 
                                         p 
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                               
                               ) 
                             
                             + 
                             
                               
                                 1 
                                 
                                   I 
                                   3 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           β 
                                            
                                           
                                               
                                           
                                            
                                           x 
                                         
                                         ) 
                                       
                                       2 
                                     
                                      
                                     
                                       e 
                                       s 
                                     
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         β 
                                          
                                         
                                             
                                         
                                          
                                         x 
                                       
                                       ) 
                                     
                                      
                                     
                                       
                                         ( 
                                         
                                           e 
                                           x 
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the coefficients I1 and I2 are given by the following relationships: 
         [0000]    
       
         
           
             
               
                 
                   
                     I 
                     1 
                   
                   = 
                   
                     
                       
                         e 
                         c 
                       
                       · 
                       
                         e 
                         3 
                       
                     
                     12 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     2 
                   
                   = 
                   
                     
                       
                         e 
                         c 
                       
                        
                       
                         e 
                         p 
                         3 
                       
                     
                     12 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
         [0136]    The coefficients I 3  and I 4  have already been defined here above. On the basis of the previous relationships, the length l is calculated. 
         [0137]    With the numerical data taken into account here, the results obtained are the following: l=40 μm, e=5 μm, t p =30 μm and g=50 μm. 
         [0138]    At a step  35 , it is verified that a torque Γ 0  exerted by the magnetic forces in the open position when the field B 0  is present is strictly greater than the restoring torque Γ r  for the mechanical forces. If this is the case, then it ensures that the micro-contactor  2  will shift to its closed position when the magnetic field B 0  is present. Different numerical simulations made by the present filing party have established a relationship which approximates a force F 0  exerted by the magnetic forces on the strip  12  in the open position. This relationship is the following: 
         [0000]    
       
         
           
             
               
                 
                   
                     F 
                     0 
                   
                   = 
                   
                     
                       ( 
                       
                         36.790 
                         + 
                         
                           2.310 
                           · 
                           
                             e 
                             p 
                           
                         
                         - 
                         
                           10.465 
                           · 
                           d 
                         
                         + 
                         
                           0.54 
                            
                           
                             d 
                             2 
                           
                         
                         - 
                         
                           0.116 
                           · 
                           
                             e 
                             p 
                           
                           · 
                           d 
                         
                       
                       ) 
                     
                     · 
                     
                       
                         e 
                         c 
                       
                       20 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0139]    On the basis of the force F 0 , it is also possible to reduce the torque of the magnetic forces that is exerted on the end  20 . This torque is given here by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     Γ 
                     0 
                   
                   = 
                   
                     
                       ( 
                       
                         36 
                         , 
                         
                           790 
                           + 
                           2 
                         
                         , 
                         
                           
                             310 
                              
                             
                               e 
                               p 
                             
                           
                           - 
                           10 
                         
                         , 
                         
                           
                             465 
                              
                             d 
                           
                           + 
                           0 
                         
                         , 
                         
                           
                             54 
                              
                             
                               d 
                               2 
                             
                           
                           - 
                           0 
                         
                         , 
                         
                           116 
                            
                           
                             e 
                             p 
                           
                            
                           d 
                         
                       
                       ) 
                     
                      
                     
                       
                         e 
                         c 
                       
                       20 
                     
                      
                     
                       ( 
                       
                         21 
                         + 
                         
                           l 
                           P 
                         
                         + 
                         
                           
                             ( 
                             
                               β 
                               - 
                               1 
                             
                             ) 
                           
                            
                           x 
                         
                       
                       ) 
                     
                      
                     
                       10 
                       
                         - 
                         12 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0140]    The previous two relationships (20) and (21) were established by using the same assumptions as for the relationship (1). Furthermore, in both these relationships, the thickness e p , the distance d, the thickness e c  are expressed in μm, the torque Γ 0  in N·m, the force F 0  is expressed in μN and the thickness e p  ranges from 10 to 100 μm. 
         [0141]    If the torque Γ 0  is not greater than the torque Γ r , then a step  36  is performed during which the thickness e p  is incremented or the thickness e is diminished. At the end of the step  36 , there is a return to the step  34  so as to again calculate the length l and the depth t p . 
         [0142]    Should the torque Γ 0  be greater than the torque Γ r , then, at a step  37 , a check is made to see if the force f amin  is truly greater than or equal to 20 μN. If the answer is negative, a step  38  is performed during which the distance g is modified. For example, the distance g is diminished. At the end of the step  38 , the method returns to the step  34 . 
         [0143]    If the contrary is the case, the operation proceeds to a step  39  during which the micro-contactor  2  having determined dimensions is fabricated. 
         [0144]    The micro-contactor having the dimensions given above occupies an approximate surface area of silicon of 650 μm (=2l+l p +βx−x) by 85 μm (=2e p +d) in addition to contact pad in the plane XY. 
         [0145]    An example of the method for fabricating the micro-contactor  2  shall now be described in greater detail by means of the method shown in  FIG. 5 . 
         [0146]    The fabrication method described is a collective or batch fabricating method using the technologies of fabrication methods of microelectronics. It therefore starts with the supply of a silicon wafer on which several micro-contactors  2  will be fabricated simultaneously by means of the same operations. To simplify the following description, the different fabricating steps are described solely in the case of a single micro-contactor. Different states of fabrication obtained during the method of  FIG. 3  are shown in vertical section in  FIGS. 6 to 10 . 
         [0147]    At a step  40 , a layer  41  ( FIG. 6 ) of photosensitive resin is deposited on the upper face  6  of the substrate  4 . Then, the zones in which cavities have to be hollowed out in the substrate  4  are defined by insolation of the resin. These zones correspond to the location of the electrodes and of the strips. Here, this is a classic step of photolithography. 
         [0148]    At a step  42 , an anisotropic etching of the defined zones is carried out to etch cavities  44 ,  46  ( FIG. 6 ) in the substrate, forming a hollow model for the strips  12  and  14  and the electrodes  8  and  10 . The term “anisotropic” etching herein designates an etching whose etching speed in the direction Z is at least ten times and preferably fifty or a hundred times greater than the etching speed in the horizontal directions X and Y. In other words, the horizontal etching speed is negligible relatively to the etching speed in the vertical direction. This gives flanks that are more vertical than if the etching were to be done by means of other etching methods. In particular, the flanks of the cavities  44 ,  46  thus hollowed out are more vertical than they would be if they had been hollowed out in a photosensitive resin or by means of another etching method. For example, the method used here is a plasma etching or a deep silicon chemical etching. 
         [0149]    At a step  48 , the layer  41  of photosensitive resin is removed and the conductive coating  28  is deposited on the entire upper face. Thus, this conductive coating covers not only the vertical flanks of the cavities but also the bottom of the cavities as well as the upper face  6  of the substrate. 
         [0150]    At a step  50 , the cavities are filled with a soft magnetic material  52  ( FIG. 5 ). Here, the filling is done by electrolytic deposition by using the coating  28  as a conductive electrode. Thus, this coating  28  also fulfills the function of a seed layer. Since the coating  28  extends over the entire face of the substrate  4 , the material  52  is also deposited on the entire upper face of the substrate  4  as well as inside the cavities  44  and  46 . Thus, the state shown in  FIG. 7  is obtained. 
         [0151]    At a step  54 , the mechanical/chemical planarization of the substrate  4  is performed to restore the plane upper face  6  of the substrate  4 . Chemical mechanical planarization is also known by the acronym CMP. This planarization step is used herein to eliminate the material  52  and the coating  58  situated beneath the cavities  44  and  46 . At the end of this step, the state shown in  FIG. 8  is obtained. 
         [0152]    At a step  56 , the hood  30  is deposited at the location in which the well  24  is to be hollowed out. To this end, an excess thickness  58  ( FIG. 9 ) of material is deposited above the zone in which the well  24  has to be hollowed out. The material used to create this excess thickness  58  is capable of being etched by the same isotropic etching agent as the substrate  4 . For example, here, the material is silicon. This excess thickness  58  insulates the hood  30  from the upper face of the distal ends  20  and  22 . Then, again in this step  56 , a thin layer  59  is deposited on the entire upper face of the substrate  4 . This thin layer  59  is made out of a material resistant to the isotropic etching agent. Finally, in this thin layer  59  forming the hood  30 , intake holes  60  are made for the isotropic etching agent. To simplify  FIG. 9 , only one of the holes  60  has been shown. These holes are laid out above the location at which the well  24  has to be hollowed out. 
         [0153]    At a step  62 , the substrate  4  is etched directly to make the well  24 . During this step, the etching done is isotropic. An isotropic etching is a step of etching in which the etching speeds in the directions X, Y are equal to the etching speed in the direction Z plus or minus 50% and preferably plus or minus 20 or 10%. 
         [0154]    At the step  62 , the isotropic etching agent is put into direct contact with the silicon to be etched through the intake holes  60 . The etching agent used is chosen so as not to react with the soft magnetic material  52  and the coating  28 . For example, the etching agent is a gas XeF 2 . 
         [0155]    Since the etching agent is an isotropic etching agent, it clears the vertical faces of the ends  20  and  22  and, at the same time, the bottom, i.e. the lower face of the distal end  20  ( FIG. 10 ). 
         [0156]    Thus, at the end of this isotropic etching step, the well  24  is made. 
         [0157]    Finally, at a step  66 , the intake holes  60  are closed again if necessary and the wafer on which the different micro-contactors had been made in a batch is cut out to separate them mechanically from one another. 
         [0158]      FIG. 11  shows a micro-contactor  80 . This micro-contactor  80  is identical to the micro-contactor  2  except that the end  20  is replaced by a fixed end  82 . The end  82  is herein identical to the end  20  except that it is fixed without any degree of freedom to the substrate  4 . The arm B 1  is therefore omitted. 
         [0159]    The size of the pads P 21  and P 22  is identical to what was described with reference to  FIG. 4  except that the bending f 0 , the torque Γ meca , the force F amin  and the torque Γ amin  are defined by the following relationships: 
         [0000]        f   0   =d   (22)
 
         [0000]      Γ meca =Γ r   (23)
 
         [0000]                    F   amin     =       Γ   amin         e   s     +     β                 x                 (   24   )               Γ amin   =S   amin   ·d ·( e   s   +βx )
 
         [0160]    As in the above embodiment, the pads P 11  and P 22  as well as the bridge Pt 11  are identical respectively to the pads P 21  and P 22  and to the bridge Pt 21 . 
         [0161]      FIG. 12  shows a micro-contactor  90  identical to the micro-contactor  2  except that the end  20  is replaced by an end  92 . To simplify this figure, only the ends  92  and  22  are shown in detail. 
         [0162]    The end  92  is identical to the end  20  except that the distance g is chosen in this embodiment to be equal to −x to create a new overlap zone Z′ 1  between the pads P 12  and the pad P 21 . In addition, g is chosen so that the dimensions of this overlap zone Z′ 1  are identical to those of the zones Z 1  and Z 2  so as to uniformly distribute the contact forces between the different contact points between the pads. Thus, in this embodiment, there are three contact points obtained with only two pairs of pads instead of two contact points as in the previous embodiment. The increase in the number of contact points makes it possible to reduce the resistance of the micro-contactor in the closed position since, as shall now be described with reference to  FIG. 13 , the ends  22  and  92  are sized so that the contact forces which are exerted at each contact point are identical to those that would be obtained if there were only one contact point. 
         [0163]    The method of sizing the micro-contactor  90  shown in  FIG. 13  is identical to the one shown in  FIG. 4  except that the step  34  is replaced by a step  100  and the steps  37  and  38  are omitted. 
         [0164]    More specifically, at the step  100 , the width e s  of the groove is set by the following relationship: 
         [0000]        e   s   =βx− 2 x   (26)
 
         [0165]    Thus, only the length l, the thickness e and the depth t p  are to be determined to obtain a restoring force f rappel  and a force f amin  equal to 20 μN. 
         [0166]    As above, here the thickness e is chosen in order to restrict the space requirement of the micro-contactor  90 . Here, e is chosen to be equal to 5 μm. 
         [0167]    The thickness t p  is determined from the constraint imposed on the force f amin  in using the following relationships similarly to what was described here above with reference to the step  34 . 
         [0168]    The force f amin  is given by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     amin 
                   
                   = 
                   
                     
                       2 
                        
                       
                         Γ 
                         amin 
                       
                     
                     
                       
                         2 
                          
                         
                           e 
                           s 
                         
                       
                       + 
                       
                         β 
                          
                         
                             
                         
                          
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
         [0169]    Γ amin  is the mechanical restoring torque exerted by the bridge Pt 11  on the pad P 12 . It is given by the relationship (9). Thus, the constraint set on the force f amin  enables the depth t p  to be calculated from the above relationships. 
         [0170]    Then, the length l is determined from the constraint laid down on the force f rappel . However, unlike what was described in the step  34 , the restoring force is given this time by the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     F 
                     rappel 
                   
                   = 
                   
                     
                       Γ 
                        
                       
                           
                       
                        
                       r 
                     
                     
                       31 
                       + 
                       
                         
                           ( 
                           
                             
                               6 
                                
                               β 
                             
                             - 
                             
                               7 
                               / 
                               2 
                             
                           
                           ) 
                         
                          
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
         [0171]    As here above, the restoring force Γ r  is given by the following relationship: 
         [0000]      2Γ meca =Γ r   (29)
 
         [0172]    The torque Γ meca  is given by the following relationship: 
         [0000]      Γ meca   =S·f   0 ·( l+l   p )  (30)
 
         [0173]    In the preceding relationship, the length l p  of the end  92  is given by the following relationship: 
         [0000]        l   p =2 βx+e   s   (31)
 
         [0174]    The factor S of the relationship (30) is determined from the same relationship (17) as that given with reference to the step  34 . 
         [0175]    With the same numerical examples as above, we obtain the following values. The length l is equal to 35 μm, the thickness e is equal to 5 μm and the depth t p  is equal to 35 μm. 
         [0176]    The total space requirement, apart from the contact pads, of the micro-contactor  90  is given by the product: total length L t  multiplied by the total thickness e t . The total length L t  is given by the following relationship: 
         [0000]        L   t =2 l+l   p +(β−1) x   (32)
 
         [0177]    The thickness e t  is given by the following relationship: 
         [0000]        E   t =2 e   p   +d   (33)
 
         [0178]    Thus, the silicon surface area occupied by the strips is here 570×85 μm 2 . The micro-contactor  90  therefore takes up slightly less space than the micro-contactor  2  and its resistance in the closed position is weaker. 
         [0179]      FIG. 14  shows a micro-contactor  110  identical to the micro-contactor  90  but wherein the end  92  is replaced by a fixed end  112 . 
         [0180]    The end  112  is fixed without any degree of freedom to the substrate  4 . The arm B 1  is omitted. 
         [0181]    The sizing of the micro-contactor  110  is deduced from the description given with reference to  FIG. 13 . However, the following relationships are used instead of the corresponding relationships in  FIG. 13 . 
         [0000]        f   0   =d   (34)
 
         [0000]      Γ meca =Γ r   (35)
 
         [0000]      Γ meca   =S·d ·( l+l   p )  (36)
 
         [0000]                    F   amin     =       Γ   amin         2        e   s       +     β                 x                 (   37   )               Γ amin   =S   amin   ·d ·( e   s   +βx )  (38)
 
         [0182]    Numerous other embodiments are possible. For example, it is not necessary to lay down that the length x should be equal to half the thickness e p  although this seems to make it possible to achieve an optimum between, on the one hand, the reduction of the resistance and, on the other hand, low space requirement or compactness. For example, as a variant, x is chosen so that it ranges from e p /3 to e p /1.5. Preferably, the length x is chosen to be equal to e p /2 plus or minus 30%. 
         [0183]    Other methods of sizing the ends of the strips are possible. In particular, it is possible, for one set of dimensions and using a simulation software, to simulate the working of the micro-contactor. If the constraints dictated on the simulated functioning of the micro-contactor are not satisfactory, the dimensions are modified and a new simulation is carried out. Thus, by successive trials, it becomes possible to determine the dimensions of the ends that meet the constraints imposed. 
         [0184]    During the sizing of the ends of the strips, the constraints on the force f amin  can be omitted. 
         [0185]    To limit the transversal surface area of the bridge P ij , it is also possible to limit its height in the vertical direction. In one particular case, only the height of the bridge P ij  in the vertical direction is limited in order to satisfy the relationship S Ptij ≦⅔S Zi . 
         [0186]    The above description with regard to the forming of the ends can also be applied to the micro-contactor in which the strips shift perpendicularly to the plane of the substrate. 
         [0187]    It is not necessary for the different contact forces at the different contact points to be all identical with one another. For example, at least one of the pads can be sized to produce a contact force greater than that produced by the other pads. For example, this can also be obtained by choosing different lengths for the different overlap zones. 
         [0188]    In order that the micro-contactor may work properly, it is not necessary to saturate each of the pads magnetically. For example, only some pads are sized in order to be saturated by the field B 0 . As a variant, none of the pads is saturated. 
         [0189]    What has been described here in the particular case of micro-contactors can also be applied to contactors having macroscopic dimensions. These contactors with macroscopic dimensions are not fabricated by the same fabrication methods as those used in microelectronics. Furthermore, their dimensions are generally far greater. For example, the length of the strips often exceeds 1 or 3 mm.