Abstract:
A method of transferring a thin layer from a source substrate having a surface layer of a first material along a free surface thereof to a target substrate having at least one surface layer of a second material along a free surface thereof, where the first material differs from the second material, includes forming within the surface layer of the source substrate a weakened zone delimiting a thin layer with respect to the free surface, and assembling the free surface of the source substrate to the free surface of the target substrate in a stack of alternating layers comprising the first and second materials, so that there are, on either side of an interface formed by bringing the free surfaces into intimate contact. The cumulative thicknesses of the layers of the first material are substantially equal to the cumulative thickness of the layers of the second material, the layers having thicknesses at least equal to 50 microns and at least 1000 times the depth at which the weakened zone is formed. The thin layer is detached by applying at least partially thermal energy to fracture the weakened zone.

Description:
RELATED APPLICATIONS 
     This application claims the benefit of priority to French Patent Application No. 0954126, filed Jun. 18, 2009, which is incorporated by reference herein. 
     FIELD OF THE INVENTION 
     The invention concerns the transfer of a thin layer from a source substrate onto a target substrate having a coefficient of thermal expansion significantly different from that of the source substrate. 
     BACKGROUND 
     A conventional method for such layer transfer is known as the “Smart Cut™” method; it consists mainly in carrying out the following steps (see in particular the French Patent Application No. FR-2 681 472 or its equivalent U.S. Pat. No. 5,374,564 and its various developments and improvements): 
     creation by ionic implantation of a buried weakened zone within the source substrate, delimiting with the free surface the future thin layer to be transferred, 
     assembly of the source substrate and the target substrate at said free surface, and 
     input of thermal and/or mechanical energy to provoke a fracture in the weakened zone within the source substrate. 
     During fabrication by this “Smart Cut™” method of a heterostructure (in particular, a structure made up of at least two different materials, generally in a plurality of layers, and having a thickness typically between 1 μm and 1 cm inclusive), control of internal stresses is very important if the materials of the heterostructure have significantly different coefficients of thermal expansion and it is required to induce the fracture at a temperature significantly different from that at which bonding was effected (for example when it is required to use a heat treatment to induce some or all of the fracture in the weakened zone). 
     For example, in the case of the transfer of a film of silicon from a source substrate (of which at least a surface portion is in silicon) onto a target substrate the coefficient of thermal expansion of which is very different from that of the silicon source substrate (for example a fused silica target substrate), the two solid substrates are conventionally bonded at room temperature, for example by molecular bonding. When, to transfer the film, the choice is made to use an input of thermal energy, it is known that the bonding interface is then consolidated; however, this heat treatment also has the effect that internal stresses, which can be very high, are generated as a consequence of the difference between the coefficients of expansion on either side of this bonding interface; it follows from this that when the transfer of the silicon film is effected (in particular, when the fracture induced by the “Smart Cut™” method occurs), the two substrates (or a portion of the two substrates if the fracture does not extend over the whole area of the substrates) are brutally separated and then immediately relax. This stress jump, if it is of too high a magnitude, risks damaging one or the other of the two parts of the heterostructure separated in this way (formed, in the example considered here, by the silica substrate carrying the transferred thin film of silicon and the silicon substrate in which the fracture has been provoked). 
     There would be a benefit in being able to minimize the stress jump that occurs on the separation of a heterostructure at a temperature different from its creation temperature. 
     To minimize any such stress jump, thought may be given to creating the heterostructure at a higher temperature, preferably at least approximately at the temperature at which the fracture is subsequently to be provoked. However, when the heterostructure is produced by molecular bonding, the bonding energy decreases greatly when bonding above 200° C., although this is a low temperature at which application of the “Smart Cut™” technology can prove difficult, simply by input of thermal energy, in a silicon/fused silica system, for example (to transfer a silicon film onto a fused silica substrate); it follows from this that, when it is required to provoke fracture only by input of thermal energy, it is required in practice to proceed at a temperature much higher than 200° C. Now, if the bonding energy is too low, the stresses of thermal origin can be sufficient to provoke unsticking of the structure at the interface (rather than in the weakened zone) or at least lead to poor functioning of the “Smart Cut™” technology: the bonding interface may then not withstand the vertical pressure imposed by the development of microcavities that this method generates (on this subject see “Silicon on insulator material technology”, M. Bruel, Electron. Lett. Vol. 31-No. 14 (1995) p. 1201). 
     To minimize the stress jump it has already been proposed to bond the parts of the heterostructure under conditions such that the stress regime at the interface falls below a given threshold when this heterostructure is brought to the temperature at which it is wished to provoke the fracture in a weakened zone in one of the wafers near the bonding interface. Thus French Patent Application No. FR-2 848 336 or its equivalent U.S. Patent Publication No. 2006/0205179 proposes to effect the bonding of two wafers that have been subject beforehand to deformation. To be more precise, the above document teaches imposing a stress on the wafers at the moment of bonding at room temperature by bending the two plates before molecular bonding; if the curvature is carefully chosen, it is possible to minimize or even to eliminate internal stresses generated by thermal annealing of the heterostructure at the fracture temperature. However, to enable separation by the “Smart Cut™” method during thermal annealing of short duration, this method generally calls for bonding the structures with fairly high radii of curvature which, from the technological point of view, can prove relatively difficult to achieve on an industrial scale; moreover, the conditions of the future fracture must be known at the time that bonding is effected. On the other hand, this technology has the advantage that the molecular bonding can be effected at room temperature and thus makes it possible to have a good bonding energy at the moment of the transfer. 
     It follows from this that it is therefore possible to transfer a thin layer at a temperature as high as may be required from one of the wafers to the other wafer, the fracture occurring in the weakened zone previously formed, whereas the bonding interface between this thin layer and the wafer to which it is henceforth fixed can have a high bonding energy. It must nevertheless be noted that, on returning to room temperature, the thin layer may be stressed in traction or in compression because its coefficient of thermal expansion is different from that of the wafer to which it has been firmly attached by molecular bonding; because the target wafer is in practice more solid than the thin layer, it is hardly deformed when the temperature changes after fracture, imposing a change in the dimensions of the thin layer because of the change of temperature. 
     This kind of phenomenon had already been exploited in the case of a homostructure (in particular, a structure formed of layers or substrates in the same material); Feijoo et al. have proposed to impose a stress within a homostructure at room temperature by application of a deformation just before the formation of this homostructure by bonding (see D. Feijoo, I. Ong, K. Mitani, W. S. Yang, S. Yu and U. M. Gösele, “Prestressing of bonded wafers”, Proceedings of the 1st international symposium on semiconductor wafer bonding, Science, Technology and Applications, Vol. 92-7, The Electrochemical Society (1992) p. 230). To be more precise, in the above paper, a homostructure consists of two silicon wafers that are bonded with a certain radius of curvature (the paper states that the plates are bonded and unbonded several times during deformation). The authors propose thinning one of the silicon crystals thereafter at room temperature by mechanical means (lapping) so as to be able to impose a high stress in the thinned silicon film after return of the other plate to a plane shape. 
     It should be noted that the above document does not envisage obtaining the thin layer by fracture within one of the plates of the homostructure; a fortiori, the above document does not address in any way the problem of the separation of a heterostructure at a temperature different from the creation temperature (in fact, there would have been no particular problem with regard to a homostructure, since there is no thermal effect on the stress state at the interface). 
     SUMMARY 
     An object of the invention is to minimize the stress jump between two substrates during transfer of a thin layer from one of the substrates to the other by fracture in a previously weakened zone, even by simple input of thermal energy, at any temperature, without having to provide for stressing by deformation at the moment of bonding between the two substrates. It is evident that it might be of benefit to be able to proceed to the assembly by bonding at any temperature, for example at room temperature, and thus without having to sacrifice the bonding energy level, without having to impose deformation beforehand, and thus for example flat, and without having to know in advance the conditions of the future fracture effecting the transfer. 
     To this end, the invention proposes a method of transferring a thin layer from a source substrate of which a surface layer along a free surface is in a first material to a target substrate of which at least one surface layer along a free surface is in a second material different from the first material, wherein: 
     there is formed within the surface layer of the source substrate a weakened zone delimiting with its free surface a future thin layer, 
     the free surface of the source substrate is assembled to the free surface of the target substrate in a stack of alternating layers formed of the first and second materials so that there are layers of the first and second materials on either side of the interface formed by the assembly of said free surfaces brought into intimate contact, the cumulative thickness of the layers of the first material situated on a first side of this interface being equal to the cumulative thickness of the layers of this first material situated on the other side of this interface and the cumulative thickness of the layers of the second material situated on this first side of the interface being equal to the cumulative thickness of the layers of this second material situated on the other side of this interface, the layers having thicknesses at least equal to 50 microns and at least equal to 1000 times the depth at which the weakened zone is formed, 
     fracture in the weakened zone is provoked by input of at least partially thermal energy to detach the thin layer. 
     It is to be noted that the invention minimizes the stress jump that occurs during fracture in the weakened zone without seeking to minimize the stresses in the heterostructure; in contrast to the prior art solution that sought to minimize the stress regime on respective opposite sides of the weakened zone at the moment of fracture, the invention aims to generate stresses which are substantially the same before and after fracture: there is therefore no sudden variation of stress during fracture; it is the sharp variations of stress that are liable to degrade the layers of the heterostructure, not the absolute value of the stress. 
     According to preferred features of the invention, where appropriate in combination: 
     said stack is produced from a material such that each of the two parts situated on either side of the interface has a plane of symmetry parallel to said interface; 
     said stack is formed only of layers formed of one or the other of the first and second materials; 
     one of the parts of the stack includes between two other layers of the second material having substantially equal thicknesses a layer of the first material having a thickness substantially equal to twice the thickness of these other layers and the other part of the stack includes between two other layers formed of the first material having substantially equal thicknesses a layer of the second material having a thickness substantially equal to twice the thickness of these other layers; 
     the first part includes a double layer of the first material sandwiched between two identical layers of the second material and the other part includes a double layer of the second material sandwiched between two identical layers of the first material; 
     after fracture in the weakened zone, separation is provoked at a bonding interface within the part to which the thin layer has been transferred; 
     separation is provoked at an interface with a lower bonding energy formed within the assembly; it may be noted that the fact that this detachment is not effected on the side of the transferred film has the benefit that there is no risk of damage (in contrast to mechanical transfer); 
     the part of the stack the thin layer of which has been separated is used in a new stack after forming a new weakened zone delimiting with the free surface liberated by the fracture a future thin layer; 
     the weakened zone is formed by ionic implantation; 
     the first material is silicon. 
    
    
     
       BRIEF DESCRIPTION OF DRAWING 
       Objects, features and advantages of the invention emerge from the following description, given by way of illustrative and nonlimiting example with reference to the appended drawings, in which: 
         FIG. 1  is a diagram representing a stack of a first embodiment of the invention, 
         FIG. 2  is a diagram representing a stack of a second embodiment of the invention, 
         FIG. 3  consists of graphs representing the evolution of the stresses in the layers of the  FIG. 1  part of the stack, above the weakened zone, as a function of temperature before and then after fracture, 
         FIG. 4  consists of graphs representing the evolution of the stresses in the layers of the  FIG. 1  part of the stack, below the weakened zone, as a function of temperature before and then after fracture, 
         FIG. 5  consists of graphs representing the evolution of the stresses on either side of the source substrate on top of which is a target substrate to which a thin layer of the source substrate must be transferred as a function of temperature before and then after fracture, and 
         FIG. 6  consists of graphs representing the evolution of the stresses on either side of the target substrate to which the thin layer from  FIG. 5  must be transferred as a function of temperature before and then after fracture. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1 and 2  represent two examples of stacks making it possible, according to the invention, to proceed reliably to the transfer, by input of at least partially thermal energy, of a thin layer from a target substrate to a source substrate, even when the substrates have significantly different coefficients of thermal expansion. 
     It is in fact clear that when two layers of different materials are bonded to each other and are then subjected to the input of thermal energy, this input of thermal energy generates, at the level of and parallel to the bonding interface, tensile stresses in the surface layer the coefficient of thermal expansion of which is lower and compressive stresses in the surface layers of the other layer the coefficient of thermal expansion of which is higher (the layer that expands more tends to stretch the one that expands less, and the latter tends to prevent the natural expansion of this layer that expands more). 
     As these two embodiments show, the invention aims to enable transfer of a thin layer from a first layer in a first material to another layer in a second material, these first and second materials having significantly different coefficients of thermal expansion and these layers being situated in a median position of the stack concerned. These stacks are not designed to minimize the stresses existing along the surfaces freed by the fracture at the level of a weakened zone within the first layer, but to reduce the variations at the moment of fracture of the stresses existing locally on either side of this weakened zone. In other words, the invention aims to reduce the stress jumps occurring at the moment of fracture at the same time as accepting the existence of these stresses at a non-negligible level. 
     These stacks are produced at any temperature relative to the temperature at which it is intended to provoke the fracture; the simplest way is to proceed at room temperature. Furthermore, no prestressing is intentionally applied to the layers of this stack at the moment of their assembly by bonding. Since the layers are in practice plane, the assembly is in practice carried out flat. 
     In the  FIG. 1  example, the objective is to transfer a thin layer from a source layer  11  in a material A to a target layer  21  in a material B. Each of these layers has a free surface and the thin layer is to be transferred from one of these layers to the other after the respective free surfaces of these layers have been brought into intimate contact. These layers have a thickness of at least 50 microns, preferably at least 100 microns (they are thus not thin layers, but rather layers commonly referred to as “thick” layers). 
     Beforehand, a weakened layer Z has been produced at a chosen distance below the surface of the layer  11  which is then brought into intimate contact with a surface of the layer  21 . This weakened layer is typically produced by implantation (in practice by ionic bombardment) of one or more species, notably implantation of hydrogen, helium, or even other gases or heavier elements. The chosen distance between the free surface of the target layer and the weakened zone is in practice at most equal to 1/100 th  of the thickness of that layer; the future thin layer (which is delimited between this surface and this weakened zone) preferably has a thickness of at most 1/1000 th  of that of the layer.  FIG. 1  does not conform to this ratio for obvious reasons of legibility. 
     The layer  11  can be merely a surface layer of a source substrate formed of at least one other underlying layer; likewise, the layer  21  can be merely a surface layer of a target substrate formed of at least one other higher layer. 
     According to the invention, before the separation step during which fracture is to be provoked in the weakened layer Z, the source substrate and the target substrate are assembled at their free surfaces within a stack of alternate layers formed of the first or the second material such that, on either side of the interface formed by bringing the free surfaces into intimate contact: 
     the cumulative thickness of layers formed of the first material are substantially equal, 
     the cumulative thickness of the layers formed of the second material are substantially equal. 
     This stack is advantageously such that each of the two parts of the stack situated on either side of the interface between the layers  11  and  21  has a plane of symmetry diagrammatically represented by the chain-dotted lines X-X and Y-Y. 
     There can be thin intermediate layers between the layers in material A or material B, but the stack is preferably formed only of layers formed of one or the other of these materials A and B (if there are intermediate attachment layers, their cumulative thickness does not represent more than 1% of the total thickness of the stack). 
     To be more precise, it is clear from  FIG. 1  that the stack is formed: of a lower part  10  formed of the layer  11  in material A on top of a layer  12  in material B on top of a layer  13  in material A, the layer  12  having a thickness twice that of the layer  11  and the layer  13  having the same thickness as the layer  11 , 
     an upper part  20  formed of the layer  21  in material B on top of which is a layer  22  in material A on top of which is a layer  23  formed of the material B, the thickness of the layer  22  being twice that of the layer  21  and the layer  23  having the same thickness as this layer  21 . 
     As a result, the layer  11  from which it is wished to transfer a thin layer to the layer  21  is sandwiched between layers ( 12  and  21 ) in material B and the layer  21  is also sandwiched between layers ( 11  and  22 ). It follows from this that, during a temperature variation after assembly, each of the layers  11  and  21  is loaded in a similar manner along its upper and lower faces, whence an approximately homogeneous stress field. 
     It follows from this that during a heat treatment applied after assembly is advantageously effected at room temperature the stresses existing in the layer  11  on either side of the weakened zone Z are similar, with the result that the fracture does not involve any stress jump in the two parts of the layer  11  separated by the fracture of sufficient magnitude to be liable to degrade one of these parts. 
     It may be noted that if the mechanical calculations developed by Z-C Feng et al. (Zhe-Chuan Feng and Hong-du Liu J; Appl. Phys. 54 (1), 1983, p. 83 “Generalized formula for curvature radius and layer stresses caused by thermal strain in semiconductor multilayer structures”), it is possible to predict the stresses that will appear within the layers  10 + 20  of the stack (forming a heterostructure) before and after separation by fracture in the weakened zone. 
     It may be noted that the stack may be considered to be formed of a stack of four pairs of layers A-B (starting from the bottom, the  FIG. 1  stack can in fact be described as being the succession of a pair A-B, a pair B-A, a pair B-A and then a pair A-B). 
     In the  FIG. 1  stack the layers  11  and  21  (and thus the layers  13  and  23 ) have equal thickness a=b, and the layers  12  and  22  have equal thicknesses  2   a=   2 B, the breakdown into pairs A-B corresponds to pairs of layers of the same thickness and the stack may be represented as the assembly of a lower sub-stack ABBA and an upper stack BAAB, and the fracture in the weakened layer leads to the formation of a lower assembly ABBA′ and an upper assembly aBAAB (A′ representing what remains of the layer  11  after separation of the thin layer “a”). 
     The invention nevertheless applies also to the case of layers having different thicknesses, as shown diagrammatically in  FIG. 2  where the thickness b is ⅔ the thickness a. Designating the layers by the same references as in  FIG. 1  with the addition of a “prime” suffix, it is found that the upper intermediate layer  22 ′ has a thickness that is three times the thickness of the layer  21 ′ or  23 ′ and the intermediate layer  12 ′ has a thickness hardly greater than that of the layer  11 ′ or  13 ′. 
     The aforementioned calculations nevertheless make it possible to verify that, even with such a difference, stress fields are produced enabling fracture without stress jumps of great magnitude at the moment of fracture. 
       FIGS. 3 and 4  represent curves of variation of the stress within the various layers after assembly at room temperature during the increase in temperature for fracture heat treatment (the fracture is represented diagrammatically by an asterisk on the right-hand side of the frames of these curves) and then during return to room temperature. 
     To be more precise,  FIG. 3  groups curves corresponding to each of the layers of the upper part of the  FIG. 1  stack, starting from the top, in the case where the intermediate layer  22  is itself formed of two identical layers  22 - 1  and  22 - 2 , and with the transferred thin layer  11   a.    
     As for  FIG. 4 , it groups curves corresponding to each of the layers of the lower part of the  FIG. 1  stack, starting from the layer  11 , in the case where the intermediate layer  12  is itself formed of two identical layers  12 - 1  and  12 - 2 . 
     These curves are calculated in the following case: 
     the layers  11 ,  13 ,  22 - 1  and  22 - 2  are in silicon and have thicknesses equal to 750 microns, 
     the layers  21 ,  23  and  12 - 1  and  12 - 2  are in fused silica and have thicknesses of 1200 microns. 
     It is seen that, because the silicon expands more than the fused silica, a rise in temperature generates, parallel to the interface between the layers, tensile stressing of the silica by the silicon and therefore compressive stressing of the silica by the silicon; in other words, the silica layers are the seat of positive (tension) stresses along similar well-defined curves within the layers  23 ,  21 ,  12 - 1  and  12 - 2 ; in contrast, the silicon layers are the seat of negative (compression) stresses along similar well-defined curves within the layers  22 - 1 ,  22 - 2 ,  11   a ,  11  and  13 . 
     The arrows directed toward the right indicate the direction of travel of the curves during an increase in temperature and the arrows directed toward the left indicate the direction of travel of the same curves during cooling; it is seen that the same curves are traveled in the heating direction and during cooling although fracture has occurred at the maximum temperature with separation of the structure into two sub-structures. 
     In fact, the stresses are not exactly identical within the layers because a film is taken off one of the substrates, which very slightly unbalances the two sub-structures, with the result that there is a small stress jump on fracture in the weakened zone of the layer  11 ; however, in the example considered of an alternation of silicon and silica layers and a thin layer with a thickness of less than 1/1000 th  of the thickness of the silicon and silica layers, the jump is only of the order of 0.1 MPa, which does not degrade the layers (including the thin layer) at the time of fracture. This jump also influences slightly the evolution of the sag of each structure, but this changes very little (less than 0.5 micron). 
     It is interesting to note that the layers of the stack remain substantially plane during temperature variations, including during fracture, which facilitates manipulation of the layers separately or in combination (as and when they are assembled) during these heat treatments. 
     As mentioned hereinabove, the source substrate can consist of the layer  11  alone or be formed of the layers  11  and  12 - 1  or even layers  11  and  12  or layers  11 ,  12  and  13 . Likewise, the target substrate can consist of the layer  21  alone, the layers  21  and  22 - 2  or even the layers  21  and  22  or the layers  21 ,  22  and  23 . It is clear that in each case it is possible, possibly by adding layers, to produce the  FIG. 1  (or  FIG. 2 ) stack as a function of the relative thicknesses of the layers. 
     In the case where, after transfer and fracture, it is required to recover the target substrate with the transferred layer, it is useful to be able to detach the layer(s) added to this target substrate to form the stack. 
     To this end, this starting target substrate is advantageously assembled to the adjacent layer necessary for forming the required stack with a reduced bonding energy imparted to the bonding interface, for example by roughening one or both of the surfaces assembled in this way. Consequently, after cooling of the assembly  11   a - 21 - 22 - 23  obtained after fracture, detachment at the reduced energy interface can easily be obtained, for example by inserting a blade into the interface to be freed; it is to be noted that, if this is done at room temperature, there is no stress jump at the moment of detachment. If, on the other hand, the choice is made to effect such detachment at a temperature different from room temperature (thus at a temperature different from that at which the stack was produced), the stress jump, if any, generated will have no significant consequence for the thin layer since this stress jump, if any, will take place at a face of the target substrate opposite the transferred thin layer. It may be noted that since the low-energy bonding is effected at a distance from the weakened zone, the rupture can be effectively localized to this weakened zone, provided that the low-energy bonding is nevertheless sufficient to resist the overall stresses generated at the various interfaces during the heat treatment. 
     In fact, detachment at the aforementioned bonding interface can be controlled under good conditions even if the bonding energy is not to be downgraded, since mechanical detachment remains possible up to high bonding energies such as 0.5 J/m 2 . 
     As for the lower part of the stack, including the source substrate, it can be re-used directly to transfer a new thin layer from the layer  11  by bonding it to a target substrate analogous to the starting one, after further weakening treatment, and adding to it the part of the stack that has been detached at the aforementioned bonding level. 
     As has also been mentioned, it is possible for attachment of the layers formed of the materials A and B to be facilitated by the interposition of attachment layers. This remains entirely valid provided that the cumulative thickness of the intermediate layers not formed of A or B remains less than about 0.1% of the thickness of the layer concerned. 
     Clearly the advantages of the invention are retained when it is wished to provoke the fracture by application of mechanical energy (fluid, blade, vibrations, ultrasound), as well as heat treatment. 
       FIGS. 5 and 6  represent, by way of comparison, curves representing the variations of the stresses along the opposed faces of a source layer and a target layer similar to the aforementioned layers  11  and  21  alone, in the absence of the additional layers  12  and  13 , on the one hand, and  22  and  23 , on the other hand. 
     Clearly the advantages of the invention may be obtained even in the event of a slight departure from the aforementioned dimensional conditions; thus some of these advantages are preserved up to differences of some 20% of the recommended thicknesses. 
     EXAMPLE 
     Layers of silicon and fused silica are used. 
     Four silicon substrates and four fused silica substrates are prepared by preparing the two surfaces of each substrate for molecular bonding. The two faces of one of the silicon substrates are roughened by chemical treatment with SCI (H2O/H2O2/NH4OH solution, in relative proportions 5-1-1) for 20 minutes at 70° C. The rear face of this substrate is then polished so that the bonding energy on the rear face is not downgraded. 
     Another silicon substrate is implanted with hydrogen ions at a dose of 6.1016 at/cm 2  and at an energy of 76 keV. A stack B-A-A(rough)-B-A(implanted)-B-B-A is then constructed by successive molecular bonding. 
     An annealing treatment is applied for one hour at 500° C., which provokes separation of the assembly into two structures, respectively B-A-A(rough)-B-a(film of A) and A(less the thin layer)-B-B-A. 
     The required final product B-a is then detached by inserting a blade at the level of the previously roughened bonding interface of A(rough) and B-a. The  FIGS. 3 and 4  curves correspond to calculations corresponding to the example described above, taking:
         Young&#39;s modulus of silicon: 130 GPa   Young&#39;s modulus of silica: 70 GPa   Poisson&#39;s coefficient of silicon: 0.3   Poisson&#39;s coefficient of silica: 0.17   thickness of each layer of silicon: 750 microns   thickness of each layer of silica: 1200 microns   coefficient of thermal expansion of silica: 0.55.10−6   coefficient of thermal expansion of Si: varying between 2.4 10 −6  and 4.2 10 −6  along an increasing curve with the concave side facing down and toward the right, as indicated in the literature.