Patent Publication Number: US-10324418-B2

Title: Method for fabrication of a balance spring of predetermined thickness through the addition of material

Description:
This application claims priority from European Patent Application No 15201337.1 of Dec. 18, 2015, the entire disclosure of which is hereby incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The invention relates to a method for fabrication of a balance spring of predetermined stiffness and, more specifically, such a balance spring used as a compensating balance spring cooperating with a balance of predetermined inertia to form a resonator having a predetermined frequency. 
     BACKGROUND OF THE INVENTION 
     It is explained in EP Patent 1422436, incorporated in the present Application by reference, how to form a compensating balance spring comprising a silicon core coated with silicon dioxide and cooperating with a balance having a predetermined inertia for thermal compensation of said entire resonator. 
     The fabrication of such a compensating balance spring offers numerous advantages but also has drawbacks. Indeed, the step of etching several balance springs in a silicon wafer offers a significant geometric dispersion between the balance springs of the same wafer and a greater dispersion between the balance springs of two wafers etched at different times. Incidentally, the stiffness of each balance spring etched with the same etch pattern is variable, creating significant fabrication dispersions. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to overcome all of part of the aforecited drawbacks by proposing a method for fabrication of a balance spring whose dimensions are sufficiently precise not to require further operations. 
     The invention therefore relates to a method for fabrication of a balance spring of a predetermined stiffness including the following steps:
         a) Forming a balance spring in dimensions smaller than the dimensions necessary to obtain said balance spring of a predetermined stiffness;   b) determining the stiffness of the balance spring formed in step a) by measuring the frequency of said balance spring coupled with a balance having a predetermined inertia;   c) calculating the missing thickness of material, based on the determination of the stiffness of the balance spring determined in step b), to obtain said balance spring of a predetermined stiffness;   d) modifying the balance spring formed in step a), to compensate for said missing thickness of material in order to obtain the balance spring ( 5   c ) in the dimensions necessary for said predetermined stiffness.       

     It is thus understood that the method can guarantee very high dimensional precision of the balance spring, and incidentally, a more precise stiffness of said balance spring. Any fabrication parameter able to cause geometric variations in step a) can thus be completely rectified for each fabricated balance spring, or rectified on average for all the balance springs formed at the same time, thereby drastically reducing the scrap rate. 
     In accordance with other advantageous variants of the invention:
         in step a), the dimensions of the balance spring formed in step a) are between 1% and 20% smaller than those necessary to obtain said balance spring with said predetermined stiffness;   step a) is achieved by means of deep reactive ion etching or chemical etching;   in step a), several balance springs are formed in the same wafer in dimensions smaller than the dimensions necessary to obtain several balance spring of a predetermined stiffness or several balance springs of several predetermined stiffnesses;   the balance spring formed in step a) is made from silicon, glass, ceramic, metal or metal alloy;   step b) comprises phase b1): measuring the frequency of an assembly comprising the balance spring formed in step a) coupled with a balance having a predetermined inertia, and phase b2): deducing, from the measured frequency, the stiffness of the balance spring formed in step a);   according to a first variant, step d) comprises phase d1): depositing a layer on one part of the external surface of the balance spring formed in step a) in order to obtain the balance spring in the dimensions necessary for said predetermined stiffness;   according to a second variant, step d) comprises phase d2): modifying the structure, to a predetermined depth, of one part of the external surface of the balance spring formed in step a), in order to obtain the balance spring in the dimensions necessary for said predetermined stiffness;   according to a third variant, step d) comprises phase d3): modifying the composition, to a predetermined depth, of one part of the external surface of the balance spring obtained in step a), in order to obtain the balance spring in the dimensions necessary for said predetermined stiffness;   after step d), the method performs, at least once more, steps b), c) and d) to further improve the dimensional quality;   according to a first variant, step e) comprises phase e1): depositing a layer on one part of the external surface of said balance spring of a predetermined stiffness;   in a second variant, step e) comprises phase e2): modifying the structure, to a predetermined depth, of one part of the external surface of said balance spring of a predetermined stiffness;   according to a third variant, step e) comprises phase e3): modifying the composition, to a predetermined depth, of one part of the external surface of said balance spring of a predetermined stiffness.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other features and advantages will appear clearly from the following description, given by way of non-limiting illustration, with reference to the annexed drawings, in which: 
         FIG. 1  is a perspective view of an assembled resonator according to the invention. 
         FIG. 2  is an example geometry of a balance spring according to the invention. 
         FIGS. 3 to 5  are cross-sections of the balance spring in different steps of the method according to the invention. 
         FIG. 6  is a perspective view of a step of the method according to the invention. 
         FIG. 7  is a diagram of the method according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     As illustrated in  FIG. 1 , the invention relates to a resonator  1  of the type with a balance  3 -balance spring  5 . Balance  3  and balance spring  5  are preferably mounted on the same arbor  7 . In this resonator  1 , the moment of inertia I of balance  3  answers to the formula:
 
 I=mr   2   (1)
 
where m represents its mass and r the turn radius which also depends on temperature through the expansion coefficient α b  of the balance.
 
     Further, the stiffness C of balance spring  5  of constant cross-section responds to the formula: 
                   C   =       Ehe   3       12   ⁢           ⁢   L               (   2   )               
where E is the Young&#39;s modulus of the material used, h the height, e the thickness and L the developed length thereof.
 
     Further, the stiffness C of a balance spring  5  of constant cross-section responds to the formula: 
                   C   =       E   12     ⁢     1       ∫   0   L     ⁢       1       h   ⁡     (   l   )       ⁢       e   3     ⁡     (   l   )           ⁢   dl                   (   3   )               
where E is the Young&#39;s modulus of the material used, h the height, e the thickness and L the developed length and I the curvilinear abscissa along the balance spring.
 
     Further, the stiffness C of a balance spring  5  of variable thickness but constant cross-section responds to the formula: 
                   C   =       Eh   12     ⁢     1       ∫   0   L     ⁢       1       e   3     ⁡     (   l   )         ⁢   dl                   (   4   )               
where E is the Young&#39;s modulus of the material used, h the height, e the thickness and L the developed length and I the curvilinear abscissa along the balance spring.
 
     Finally, the elastic constant C of sprung balance resonator  1  answers to the formula: 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         C 
                         I 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     According to the invention, it is desired that a resonator has substantially zero frequency variation with temperature. The frequency variation f with temperature T in the case of a sprung-balance resonator substantially follows the following formula: 
                       Δ   ⁢           ⁢   f     f     =       1   2     ⁢       {           ∂   E       ∂   T       ⁢     1   E       +     3   ·     α   s       -     2   ·     α   b         }     ·   Δ     ⁢           ⁢   T             (   6   )               
where:
 
               Δ   ⁢           ⁢   f     f         
is a relative frequency variation;
         ΔT is the temperature variation;       

                 ∂   E       ∂   T       ⁢     1   E           
is the relative Young&#39;s modulus variation with temperature, i.e. the thermoelastic coefficient (TEC) of the balance spring;
         α s  is the expansion coefficient of the balance spring, expressed in ppm.° C. −1 ;   α b  is the expansion coefficient of the balance, expressed in ppm.° C. −1          

     Since the oscillations of any resonator intended for a time or frequency base must be maintained, the maintenance system may also contribute to thermal dependence, such as, for example, a Swiss lever escapement (not shown) cooperating with the impulse pin  9  of the roller  11 , also mounted on arbor  7 . 
     It is thus clear, from formulae (1)-(6), that through the choice of materials used to couple balance spring  5  with balance  3 , for the frequency f of resonator  1  to be virtually insensitive to temperature variations. 
     The invention more particularly concerns a resonator  1  wherein the balance spring  5  is used to thermally compensate the entire resonator  1 , i.e. all the parts and particularly the balance  3 . Such a balance spring  5  is generally called a temperature compensating balance spring. This is why the invention relates to a method that can guarantee very high dimensional precision of the balance spring, and incidentally, guarantee a more precise stiffness of said balance spring. 
     According to the invention, compensating balance spring  5 ,  15  is formed from a material, possibly coated with a thermal compensation layer, and intended to cooperate with a balance  3  having a predetermined inertia. However, there is nothing to prevent the use of a balance with movable inertia-blocks able to offer an adjustment parameter prior to or after the sale of the timepiece. 
     The utilisation of a material, for example made from silicon, glass or ceramic, for the fabrication of a balance spring  5 ,  15  offers the advantage of being precise via existing etching methods and of having good mechanical and chemical properties while being virtually insensitive to magnetic fields. It must, however, be coated or surface modified to be able to form a compensating balance spring. 
     Preferably, the silicon-based material used to make the compensated balance spring may be single crystal silicon, regardless of its crystal orientation, doped single crystal silicon, regardless of its crystal orientation, amorphous silicon, porous silicon, polycrystalline silicon, silicon nitride, silicon carbide, quartz, regardless of its crystal orientation, or silicon oxide. Of course, other materials may be envisaged, such as glass, ceramics, cermets, metals or metal alloys. For the sake of simplification, the following explanation will concern a silicon-based material. 
     Each material type can be surface-modified or coated with a layer to thermally compensate the base material as explained above. 
     Although the step of etching balance springs in a silicon-based wafer, by means of deep reactive ion etching (DRIE) is the most precise, phenomena which occur during the etch or between two successive etches may nonetheless cause geometric variations. 
     Of course, other fabrication types may be implemented, such as laser etching, focused ion beam etching (FIB), galvanic growth, growth by chemical vapour deposition or chemical etching, which are less precise and for which the method would be even more meaningful. 
     Thus, the invention relates to a method  31  for fabrication of a balance spring  5   c . According to the invention, method  31  comprises, as illustrated in  FIG. 7 , a first step  33  intended to form at least one balance spring  5   a , for example from silicon, in dimensions Da smaller than the dimensions Db necessary to obtain said balance spring  5   c  of a predetermined stiffness C. As seen in  FIG. 3 , the cross-section of balance spring  5   a  has a height H 1  and a thickness E 1 . 
     Preferably, the dimensions Da of balance spring  5   a  are substantially between 1% and 20% smaller than those Db of balance spring  5   c  necessary to obtain said balance spring  5   c  of a predetermined stiffness C. 
     Preferably according to the invention, step  33  is achieved by means of a deep reactive ion etch in a wafer  23  of silicon-based material, as illustrated in  FIG. 6 . It is noted that the opposite faces F 1 , F 2  are undulating since a Bosch deep reactive ion etch results in an undulating etch, structured by the successive etch and passivation steps. 
     Of course, the method is not limited to a particular step  33 . By way of example, step  33  could also be obtained by means of a chemical etch in a wafer  23 , for example of silicon-based material. Further, step  33  means that one or more balance springs are formed, i.e. step  33  can form individual loose balance springs or, alternatively, balance springs formed in a wafer of material. 
     Consequently, in step  33 , several balance springs  5   a  can be formed in the same wafer  23  in dimensions Da, H 1 , E 1  smaller than the dimensions Db, H 2 , E 2  necessary to obtain several balance springs  5   c  of a predetermined stiffness C or several balance springs  5   c  of several predetermined stiffnesses C. 
     Step  33  is also not limited to forming a balance spring  5   a  in dimensions Da, H 1 , E 1  smaller than the dimensions Db, H 2 , E 2  necessary to obtain a balance spring  5   c  of a predetermined stiffness C, produced using a single material. Thus, step  33  could also form a balance spring  5   a  in dimensions Da, H 1 , E 1  smaller than the dimensions Db,  H 2,  E 2 a necessary to obtain a balance spring  5   c  of a predetermined stiffness C made from a composite material, i.e. comprising several distinct materials. 
     Method  31  includes a second step  35  intended to determine the stiffness of balance spring  5   a . This step  35  may be performed directly on a balance spring  5   a  still attached to wafer  23  or on a balance spring  5   a  previously detached from wafer  23 , on all, or on a sample of the balance springs still attached to a wafer  23 , or on a sample of balance springs previously detached from a wafer  23 . 
     Preferably according to the invention, regardless of whether or not balance spring  5   a  is detached from wafer  23 , step  35  includes a first phase intended to measure the frequency f of an assembly comprising balance spring  5   a  coupled to a balance having a predetermined inertia I and then, using the relation (5), to deduce therefrom, in a second phase, the stiffness C of balance spring  5   a.    
     This measuring phase may, in particular, be dynamic and performed in accordance with the teaching of EP Patent 2423764, incorporated by reference in the present Application. However, alternatively, a static method, performed in accordance with the teaching of EP Patent 2423764, may also be implemented to determine the stiffness C of balance spring  5   a.    
     Of course, as explained above, since the method is not limited to the etching of only one balance spring per wafer, step  35  may also consist in the determination of the mean stiffness of a representative sample, or of all the balance springs formed on the same wafer. 
     Advantageously according to the invention, based on the determination of the stiffness C of balance spring  5   a , method  31  includes a step  37  intended to calculate, with the aid of relation (2), the missing thickness of material required to obtain balance spring  5   c  of a predetermined stiffness C, i.e. the volume of material to be added and/or to be modified in a homogeneous or non-homogeneous manner, on the surface of balance spring  5   a.    
     The method continues with a step  39  intended to modify balance spring  5   a  formed in step a), to compensate for said missing thickness of material required to obtain balance spring  5   c  in the dimensions Db, H 2 , E 2  necessary for said predetermined stiffness C. It is therefore understood that it does not matter whether geometric variations have occurred in the thickness and/or the height and/or the length of balance spring  5   a  given that, according to equation (2), it is the product h·e 3  that determines the stiffness of the coil. 
     Thus, a homogeneous thickness can be added and/or modified on the entire external surface, a non-homogeneous thickness can be added and/or modified on the entire external surface, a homogeneous thickness can be added and/or modified on only one part of the external surface, or a non-homogeneous thickness can be added and/or modified on only one part of the external surface. By way of example, step  39  could consist in only adding material to the thickness E 1  or to the height H 1  of balance spring  5   a.    
     In a first variant, step  39  includes a phase d1 intended to deposit a layer on one part of the external surface of balance spring  5   a  formed in step  33 , in order to obtain balance spring  5   c  in the dimensions Db, H 2 , E 2  necessary for said predetermined stiffness C. This phase d1 may, for example, be obtained by thermal oxidation, by galvanic growth, by physical phase deposition (PVD), by chemical phase deposition (CVD), by atomic layer deposition (ALD), or by any other method of addition. 
     This phase d1 may, for example, be achieved by a chemical vapour deposition allowing polysilicon to be formed on the single crystal silicon balance spring  5   a , to obtain balance spring  5   c  in the dimensions Db, H 2 , E 2  necessary for predetermined stiffness C. 
     As seen in  FIG. 4 , the cross-section of balance spring  5   c  has a height H 2  and a thickness E 2 . It is noted that balance spring  5   c  is formed of a central part  22  made from single crystal silicon and a peripheral part  24  made from polycrystalline silicon in the overall dimensions Db necessary for predetermined stiffness C. 
     In a second variant, step  39  may consist of a phase d2 intended to modify the structure, to a predetermined depth, of one part of the external surface of balance spring  5   a  in order to obtain balance spring  5   c  in the dimensions Db, H 2 , E 2  necessary for predetermined stiffness C. By way of example, illustrated in  FIG. 4 , if amorphous silicon is used to form balance spring  5   a , it could be crystallised to a predetermined depth to form an amorphous silicon central part  22  and a polycrystalline silicon peripheral part  24 , to obtain balance spring  5   c  in the dimensions Db, H 2 , E 2  necessary for predetermined stiffness C. 
     In a third variant, step  39  may consist of a phase d3 intended to modify the composition, to a predetermined depth, of one part of the external surface of balance spring  5   a  of a predetermined stiffness C. By way of example, illustrated in  FIG. 4 , if single crystal or polycrystalline silicon is used to form balance spring  5   a , it could be doped or diffused with interstitial or substitional atoms, to a predetermined depth, to form a single crystal or polycrystalline silicon central part  22  and a peripheral part  24  doped or diffused with different silicon atoms, to obtain balance spring  5   c  in the dimensions Db, H 2 , E 2  necessary for predetermined stiffness C. It is understood that this third variant does not necessarily involve an increase in volume but at least superficially increases the Young&#39;s modulus to obtain predetermined stiffness C. 
     For these three variants, it is seen that the undulating shape is always reproduced on a portion of peripheral part  24  and central part  22 . Thus, a smoothing step may be provided before step  39  to attenuate, or remove, any undulating shape of balance spring  5   a.    
     Method  31  may end with step  39 . However, after step  39 , method  31  may also perform, at least once more, steps  35 ,  37  and  39  in order to further improve the dimensional quality of the balance spring. These iterations of steps  35 ,  37  and  39  may, for example, be of particular advantage when the first iteration of steps  35 ,  37  and  39  is performed on all, or on a sample, of the balance springs still attached to a wafer  23 , and then, in a second iteration, on all, or a sample, of the balance springs previously detached from wafer  23  and having undergone the first iteration. 
     Method  31  may also continue with all or part of process  40  illustrated in  FIG. 7 , comprising optional steps  41 ,  43  and  45 . Advantageously according to the invention, method  31  may thus continue with step  41  intended to form, on at least one part of balance spring  5   c , a portion  26  for correcting the stiffness of balance spring  5   c  and for forming a balance spring  5 ,  15  that is less sensitive to thermal variations. 
     In a first variant, step  41  may consist of a phase e1 intended to deposit a layer on one part of the external surface of said balance spring  5   c  of a predetermined stiffness C. 
     In the case where parts  22 / 24  are made from a silicon-based material, phase e1 may consist in oxidising balance spring  5   c  to coat it with silicon dioxide to correct the stiffness of balance spring  5   c  and to form a balance spring  5 ,  15  which is temperature compensated. This phase e1 may, for example, be obtained by thermal oxidation. This thermal oxidation may, for example, be achieved between 800 and 1200° C. in an oxidising atmosphere with the aid of water vapour or dioxygen gas to form silicon oxide on balance spring  5   c.    
     There is thus obtained compensating balance spring  5 ,  15 , as illustrated in  FIG. 5  which, advantageously according to the invention, comprises a composite silicon core  22 / 24  and a silicon oxide coating  26 . Advantageously according to the invention, compensating balance spring  5 ,  15  therefore has a very high dimensional precision, particularly as regards height H 3  and thickness E 3 , and, incidentally, very fine temperature compensation of the entire resonator  1 . 
     In the case of a silicon-based balance spring, the overall dimensions Db may be found by using the teaching of EP Patent 1422436 to apply to the resonator  1  which is intended to be fabricated, i.e to compensate all of the constituent parts of resonator  1 , as explained above. 
     In a second variant, step  41  may consist in a phase e2 intended to modify the structure, to a predetermined depth, of one part of the external surface of said balance spring  5   c  of a predetermined stiffness C. By way of example, if an amorphous silicon is used for peripheral part  24  and possibly, central part  22 , it could be crystallised to a predetermined depth in peripheral part  24  and possibly in central part  22 . 
     In a third variant, step  41  may consist in a phase e3 intended to modify the composition, to a predetermined depth, of one part of the external surface of said balance spring  5   c  of a predetermined stiffness C. By way of example, if a single crystal silicon or polycrystalline silicon is used for peripheral part  24  and, possibly, central part  22 , it could be doped or diffused with interstitial or substitional atoms, to a predetermined depth, in peripheral part  24  and, possibly, in central part  22 . 
     Advantageously according to the invention, it is thus possible, with no further complexity, to fabricate, as illustrated in  FIG. 2 , a balance spring  5   c ,  5 ,  15  comprising in particular:
         one or more coils of more precise cross-section(s) than that obtained by means of a single etch;   variations in thickness and/or in pitch along the coil;   a one-piece collet  17 ;   an inner coil  19  of the Grossman curve type   a one-piece balance spring stud attachment  14 ;   a one-piece external attachment element;   a portion  13  of outer coil  12  and/or of inner coil  19  that is thicker than the rest of the coils.       

     Finally, method  31  may also comprise step  45  intended to assemble a compensating balance spring  5 ,  15  obtained in step  41 , or a balance spring  5   c  obtained in step  39 , to a balance having a predetermined inertia obtained in step  43 , to form a resonator  1  of the sprung balance type, which may or may not be temperature compensated, i.e. whose frequency f is or is not sensitive to temperature variations. 
     Of course, the present invention is not limited to the illustrated example but is capable of various variants and modifications that will appear to those skilled in the art. In particular, as explained above, the balance, even if it has an inertia predefined by design, may comprise movable inertia-blocks offering an adjustment parameter prior to or after the sale of the timepiece. 
     Further, an additional step could be provided, between step  39  and step  41 , or between step  39  and step  45 , for depositing a functional or aesthetic layer, such as, for example, a hardening layer or a luminescent layer. 
     It is also possible to envisage, when method  31  performs, after step  39 , one or more iterations of steps  35 ,  37  and  39 , that step  35  is not systematically implemented.