Abstract:
The disclosure relates to a micro-electromechanical membrane arrangement with a substrate, which has a multiplicity of recesses on a surface, a first electrically conductive electrode layer, which is arranged on the surface of the substrate and has a multiplicity of first depressions coinciding with the recesses, and an electrically conductive membrane layer, which can be deflected in a direction perpendicular to the active surface of the substrate, is arranged over the first electrode layer and is kept at a distance therefrom by a first distance value.

Description:
This application is a 35 U.S.C. §371 National Stage Application of PCT/EP2013/054418, filed on Mar. 5, 2013, which claims the benefit of priority to Serial No. DE 10 2012 205 921.0, filed on Apr. 12, 2012 in Germany, the disclosures of which are incorporated herein by reference in their entirety. 
     The disclosure relates to a membrane arrangement for a microelectromechanical measuring transducer and to a method for producing a membrane arrangement for a microelectromechanical measuring transducer, in particular for microelectromechanical pressure sensors, microphones and loudspeakers. 
     BACKGROUND 
     Miniaturized pressure sensors and acoustic signal transducers such as microphones or loudspeakers are used for various applications, for example for acoustic component parts in portable telecommunications devices. 
     The sensors and actuators can in this case be produced from microelectromechanical structures (MEMS, “microelectromechanical systems”). 
     Such sensors and signal transducers can be based on the capacitive principle of action, i.e. voltage is applied to two membrane elements arranged with a predetermined geometry with respect to one another. By changing the voltage, movements of the membranes relative to one another can be induced. Alternatively, externally induced membrane movements can result in detectable changes in the capacitance and therefore in the voltage present. 
     The document DE 102 47 847 A1, for example, discloses a method for producing a membrane for an MEMS component comprising a mating electrode on a substrate. The document DE 10 2006 055 147 B4 discloses a method for producing an acoustic signal transducer structure comprising an oscillatory membrane over a mating electrode on a substrate. The document EP 2 071 871 A1 discloses a membrane for an MEMS component part comprising a corrugated peripheral region for reducing mechanical stresses of the membrane. 
     There is a need for membrane arrangements, in particular for microelectromechanical acoustic signal transducers, with which the sensitivity of the signal pickup can be improved and the installation space requirement can be correspondingly reduced. 
     SUMMARY 
     The present disclosure in accordance with one aspect provides a microelectromechanical membrane arrangement comprising a substrate which has a multiplicity of cutouts in a surface, a first electrically conductive electrode layer, which is arranged on the surface of the substrate and which has a multiplicity of first depressions corresponding to the cutouts, and an electrically conductive membrane layer, which can be deflected in a direction perpendicular to the surface of the substrate, is arranged over the first electrode layer and is spaced apart from said first electrode layer by a first distance value. 
     The present disclosure in accordance with a further aspect provides a microelectromechanical component comprising a microelectromechanical membrane arrangement according to the disclosure. In a preferred embodiment, the microelectromechanical component can comprise a pressure sensor, a microphone or a loudspeaker. 
     In accordance with a further aspect, the present disclosure provides a method for producing a microelectromechanical membrane arrangement, in particular for a microelectromechanical component, comprising the steps of introducing cutouts into a surface of a semiconductor substrate, forming a first electrically conductive electrode layer on the surface of the substrate, which electrode layer has a multiplicity of first depressions coinciding with the cutouts, forming an oxide layer on the first electrically conductive electrode layer, depositing an electrically conductive membrane layer on the oxide layer, forming first through-holes in the substrate and the first electrically conductive electrode layer, and etching the oxide layer through the first through-holes in order to free the electrically conductive membrane layer, with the result that the membrane layer is deflectable with respect to the first electrode layer and is spaced apart from said first electrode layer by a first distance value. 
     One concept of the present disclosure consists in configuring at least one membrane of a microelectromechanical membrane arrangement based on a capacitive principle of action to have depressions or a predetermined corrugated nature, with the result that capacitive vertical regions of the membrane arrangement are produced, whose membrane sections are shifted laterally with respect to one another during a vertical movement of the membranes. As a result, a vertical membrane movement causes a change in capacitance of the vertical regions which has a linear profile with the membrane deflection. 
     A considerable advantage of this membrane arrangement consists in that, even in the case of small vertical membrane deflections, a large change in capacitance is caused or, in the case of slight changes in capacitance owing to small changes in voltage between the membranes, high membrane deflections result. Overall, there is a considerably larger signal excursion in the case of small changes in measured value, i.e. greater sensitivity of the membrane arrangement results for such membrane arrangements. 
     Such membrane arrangements with high sensitivity can be configured so as to have correspondingly smaller dimensions since the effective active capacitive area is increased. This advantageously results in a lower installation space requirement and a less expensive design. 
     When using such membrane arrangements in actuators, relatively high acceleration values for the membranes at a relatively low voltage can be achieved. In the case of sensors, relatively large signal excursions can be achieved for the same reasons. 
     A further positive effect of the membrane arrangements according to the disclosure consists in the improved mechanical stability and rigidity which can be set by the selection of the geometry of the depressions or the corrugated nature. 
     In accordance with one embodiment of the membrane arrangement according to the disclosure, the membrane layer can have a multiplicity of second depressions formed over the first depressions. As a result, a region of overlap between the electrode layer and the membrane layer which changes linearly with a vertical movement of the membrane layer can be provided. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the second depressions can be configured so as to engage in the first depressions one inside the other without any touching contact when the membrane layer is deflected perpendicular to the surface of the substrate. As a result, advantageously a lateral sensor or actuator capacitance with a high acceleration even from the zero position can be provided. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the second depressions can have outer walls having a vertical extent which is greater than the first distance value. Alternatively, the second depressions can have outer walls with a vertical extent which is precisely the same size as the first distance value. In this way, either a particularly compact and flat membrane geometry can be configured or a membrane geometry without parasitic capacitances in the zero position of the deflectable membrane layer. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the outer walls of the first depressions can have a second distance value from the outer walls of the second depressions parallel to the surface of the substrate. By virtue of setting the second distance value, the sensitivity of the membrane arrangement can advantageously be adjusted. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the membrane arrangement can furthermore comprise a second electrically conductive electrode layer, which is arranged over the membrane layer, and is spaced apart from said membrane layer by the first distance value and which has a multiplicity of third depressions formed over the first depressions. A relatively large signal excursion or a relatively large acceleration of the membrane layer can be achieved by virtue of this double-membrane structure. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the outer walls of the second depressions can have the second distance value from the outer walls of the third depressions parallel to the surface of the substrate. As a result, a symmetrical double-membrane structure is provided which achieves high signal excursions and high acceleration values of the membrane layer. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the first electrode layer and the substrate can have a multiplicity of first pressure compensation holes, which are formed in the first depressions. These pressure compensation holes are used for allowing the air located in the interspaces between the electrode layer and the membrane layer to escape during a movement of the membrane layer, with the result that the flow resistance through the pressure compensation holes is advantageously lower than along the interspaces. 
     In accordance with a further embodiment, the first electrode layer is formed directly by the substrate. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the membrane layer can have a multiplicity of second pressure compensation holes, which are formed in the membrane layer between the second depressions. These pressure compensation holes are used to allow the air located in the interspaces between the electrode layer and the membrane layer to escape during a movement of the membrane layer, with the result that the flow resistance through the pressure compensation holes is advantageously lower than along the interspaces. 
     In accordance with a further embodiment of the membrane arrangement according to the disclosure, the second electrode layer can have a multiplicity of third pressure compensation holes, which are formed in the third depressions and/or between the third depressions. These pressure compensation holes are used to allow the air located in the interspaces between the second electrode layer and the membrane layer to escape during a movement of the membrane layer, with the result that the flow resistance through the pressure compensation holes is advantageously lower than along the interspaces. 
     In accordance with one embodiment of the method according to the disclosure, furthermore, at least one second through-hole can be formed in the electrically conductively membrane layer. This through-hole can then act as pressure compensation hole. 
     Further features and advantages of embodiments of the disclosure result from the description below with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The described configurations and developments can, where expedient, be combined with one another as desired. Further possible configurations, developments and implementations of the disclosure also include combinations of features of the disclosure, which have been described previously or below with respect to the exemplary embodiments, which have not been explicitly mentioned. 
       The attached drawings are intended to provide improved understanding of the embodiments of the disclosure. They illustrate embodiments and, in conjunction with the description serve to explain principles and concepts of the disclosure. Other embodiments and many of the mentioned advantages can be gleaned from the drawings. The elements in the drawings are not necessarily shown true to scale with respect to one another. Directional indications such as “left”, “right”, “top”, “bottom”, “above”, “below”, “next to” or the like are merely used for explanatory purposes in the description below without any loss of generality. 
       In the drawings: 
         FIG. 1  shows a schematic illustration of a microelectromechanical membrane arrangement in a cross-sectional view in accordance with one embodiment of the present disclosure; 
         FIG. 2  shows a schematic illustration of a microelectromechanical membrane arrangement in a cross-sectional view in accordance with a further embodiment of the present disclosure; 
         FIG. 3  shows a schematic illustration of a microelectromechanical membrane arrangement in a cross-sectional view in accordance with a further embodiment of the present disclosure; 
         FIG. 4  shows a schematic illustration of a microelectromechanical membrane arrangement in a cross-sectional view in accordance with a further embodiment of the present disclosure; 
         FIG. 5  shows a schematic illustration of a microelectromechanical membrane arrangement in a cross-sectional view in accordance with a further embodiment of the present disclosure; 
         FIG. 6  shows a schematic illustration of a microelectromechanical membrane arrangement in a plan view in accordance with a further embodiment of the present disclosure; 
         FIG. 7  shows a schematic illustration of a microelectromechanical membrane arrangement in a plan view in accordance with a further embodiment of the present disclosure; 
         FIG. 8  shows a schematic illustration of a microelectromechanical membrane arrangement in a plan view in accordance with a further embodiment of the present disclosure; 
         FIGS. 9 to 13  show schematic illustrations of process steps in a method for producing a microelectromechanical membrane arrangement in accordance with a further embodiment of the present disclosure; and 
         FIGS. 14 to 18  show schematic illustrations of the process steps in a method for producing a microelectromechanical membrane arrangement in accordance with a further embodiment of the present invention disclosure. 
     
    
    
     The microelectromechanical membrane arrangements (MEMS membrane arrangements) shown can each be used for microelectromechanical components (MEMS components) such as, for example, signal transducers or measuring transducers, MEMS sensors, MEMS actuators or membrane-based inertial sensors. Such MEMS components can include, for example, pressure sensors, microphones, loudspeakers or other acoustic energy transducers. 
     DETAILED DESCRIPTION 
     Depressions within the meaning of the present disclosure are all deviations in shape of the component which are perpendicular or substantially perpendicular to a surface of a substantially planar component. In particular, depressions within the meaning of the present disclosure can be grooves, corrugations, beads, flutes, channels, troughs or similar angular or wavy convexities of the substantially planar component. In this case, the depressions can be arranged along the surface of the substantially planar component at regular or irregular distances from one another. The depressions can have a multiplicity of depression sections running perpendicular to the lateral extent of the substantially planar component. 
     Two substantially planar components which are arranged planar-parallel one above the other and spaced apart from one another in the direction of their lateral extent, can in this case have depressions which substantially coincide with one another in such a way that the individual depressions engage in one another in the case of a movement of the substantially planar components towards one another without the two components touching one another. In other words, the depressions in one component have a similar physical configuration to those of the other component, wherein the depressions of one component have smaller physical dimensions than the depressions of the other component. In this way, meshing of the components one inside the other can be achieved, with the result that a relative movement of the two substantially planar-parallel components perpendicular to their lateral extents is possible without the components touching one another. 
     Similarly, three substantially planar components can be arranged planar-parallel with respect to one another, with the result that it is possible for the components located in the center and in each case one of the components arranged on the outside to engage one inside the other without any touching contact in the event of an up-and-down movement relative to the outer components. 
       FIG. 1  shows a schematic illustration of a microelectromechanical membrane arrangement  100  in a cross-sectional view. The membrane arrangement  100  comprises a substrate  4  having cutouts, a first electrically conductive electrode layer  1 , which is applied to a surface of the substrate  4 . The first electrode layer  1  can be, for example, a monocrystalline silicon layer. Alternatively, it may also be possible to configure the first electrode layer  1  to have a metallization layer. In another variant embodiment, the first electrode layer  1  can be a first functional layer on a silicon-on-insulator wafer  4  (SOI wafer). The first electrode layer  1  can have first depressions  1   a , which are designed to substantially coincide with the cutouts in the substrate  4 . In the example in  FIG. 1 , the cutouts are in the form of right-parallelepipedal grooves with outer walls which are substantially perpendicular to the surface of the substrate  4  and which extend over a predetermined, for example constant depth into the substrate  4 . 
     An electrically conductive membrane layer  2  which is deflectable in a direction perpendicular to the surface of the substrate  4  can be arranged over the first electrode layer  1 . In a variant embodiment, the membrane layer  2  can consist of polysilicon, for example. The membrane layer  2  can be suspended on the substrate via one or more suspension webs at suspension points outside the section area illustrated in  FIG. 1 , with the result that the membrane layer  2  is mounted in pendulous fashion over the first electrode layer  1 . The membrane layer  2  is spaced apart from the first electrode layer  1  by a first (vertical) distance value x G . The distance value x G  can be, for example, between 0.1μ and 10μ. 
     In this case, the membrane layer  2  has second depressions  2   a , which are arranged substantially over the first depressions  1   a  in such a way that the outer dimensions of the second depressions  2   a  are slightly smaller than the corresponding dimensions of the first depressions  1   a . As a result, the second depressions  2   a  can engage in the first depressions  1   a  without any touching contact. The outer walls  2   b  of the second depressions  2   a  are spaced apart from the outer walls  1   b  of the first depressions  1   a  by a distance value y G . 
     By virtue of the vertical movement of the membrane layer  2 , for example in the event of actuation of the membrane layer  2 , the membrane layer  2  can be moved up and down substantially perpendicular to the surface of the substrate  4 , as indicated in  FIG. 1  by means of the dashed lines. For example, the maximum deflection upwards can result in a position  2 U of the membrane layer  2 , while the maximum deflection downwards can result in a position  2 D of the membrane layer  2 . 
     The membrane arrangement  100  furthermore has a second electrically conductive electrode layer  3 , which is arranged over the membrane layer  2  and is spaced apart from said membrane layer by the first distance value x G . The second electrically conductive electrode layer  3  can be produced from polysilicon or a metallization layer, for example. The second electrode layer  3  can have a multiplicity of third depressions  3   a  formed over the first depressions  1   a . For the third depressions  3   a , substantially the same can apply in respect of the relationship with respect to the second depressions  2   a  as for the relationship of the second depressions  2   a  with respect to the first depressions  1   a . In other words, the membrane arrangement  100  is structured in such a way that the geometric structures of the depressions  1   a ,  2   a  and  3   a  coincide with one another in such a way that a movement of the membrane layer  2  in the interspace between the electrode layers  1  and  3  is enabled in such a way that the second depressions  2   a  mesh with the first and third depressions  1   a  and  3   a , respectively, without any touching contact. 
     The first electrode layer  1  and the substrate  4  can have first through-holes or pressure compensation holes  5   a , which are formed in the base of the first depressions  1   a . An exchange of air or another medium filling the first interspaces  6   a  between the first electrode layer  1  and the membrane layer  2  is enabled via the first pressure compensation holes  5   a . Preferably, the dimensions of the first pressure compensation holes  5   a  are configured such that the flow resistance of the air or of the other medium through the first pressure compensation holes  5   a  is less than along the first interspace  6   a . As a result, the air or the other medium preferably escapes through the first pressure compensation holes  5   a.    
     The second electrode layer  3  can have second through-holes or pressure compensation holes  5   b , which are formed between the third depressions  3   a . An exchange of air or another medium filling the second interspaces  6   a  between the second electrode layer  3  and the membrane layer  2  is enabled via the second pressure compensation holes  5   b . Preferably, the dimensions of the second pressure compensation holes  5   b  are configured in such a way that the flow resistance of the air or of the other medium through the second pressure compensation holes  5   b  is less than along the second interspace  6   b . As a result, the air or the other medium preferably escapes through the second pressure compensation holes  5   b.    
     The number of first and second pressure compensation holes  5   a  and  5   b , respectively, is in this case not limited, in principle. In particular, provision can be made of pressure compensation holes  5   a  and  5   b , respectively, not to be formed in each first depression  1   a  or between each pair of third depressions  3   a.    
     The outer walls  2   b  of the second depressions  2   a  can have the same second distance value y G  from the outer walls of the third depressions  3   a  parallel to the surface of the substrate  4  as the outer walls  2   b  of the second depressions  2   a  from the outer walls  1   b  of the first depressions  1   a.    
       FIG. 2  shows a schematic illustration of a further microelectromechanical membrane arrangement  200  in a cross-sectional view. The microelectromechanical membrane arrangement  200  differs from the microelectromechanical membrane arrangement  100  substantially only in that the vertical distance x G  between the membrane layer  2  and the first and second electrode layers  1  and  3 , respectively, is selected to be precisely the same size as the vertical extent x k  of the depressions  2   a  and  1   a  and  3   a , respectively. In addition, through-holes or pressure compensation holes  5   c  can also be formed in the base of third depressions  3   a  in the microelectromechanical membrane arrangement  200 . The parasitic capacitance components can advantageously be reduced with the membrane arrangement  200  in comparison with the membrane arrangement  100  at the expense of the amount of installation space required. 
       FIG. 3  shows a schematic illustration of a further microelectromechanical membrane arrangement  300  in a cross-sectional view. The microelectromechanical membrane arrangement  300  differs from the microelectromechanical membrane arrangement  200  substantially only in that a membrane layer  7 , which is formed planar-parallel to the surface of the substrate  4 , is used between the first and second electrode layers  1  and  3  instead of a membrane layer  2  with depressions  2 , which membrane layer  7  is movable between a maximum deflection  7 U upwards and a maximum deflection  7 U downwards with respect to the electrode layers  1  and  3 . 
       FIG. 4  shows a schematic illustration of a further microelectromechanical membrane arrangement  400  in a cross-sectional view. The microelectromechanical membrane arrangement  400  differs from the microelectromechanical membrane arrangement  100  substantially only in that there is no second electrode layer  3 . Instead, the membrane layer  2  has through-holes or pressure compensation holes  5   d  between the depressions  2   a  in the membrane layer  2 . 
       FIG. 5  shows a schematic illustration of a further microelectromechanical membrane arrangement  500  in a cross-sectional view. The microelectromechanical membrane arrangement  500  differs from the microelectromechanical membrane arrangement  400  substantially only in that the vertical distance x G  between the membrane layer  2  and the first electrode layer  1  is selected to be precisely the same size as the vertical extent x k  of the depressions  2   a  and  1   a . In this way, as mentioned above, a reduction in the parasitic capacitance components can be provided at the expense of the amount of installation space required. 
       FIGS. 6, 7 and 8  show schematic illustrations of microelectromechanical membrane arrangements in plan views. The membrane arrangements illustrated in  FIGS. 6, 7 and 8  can correspond to the membrane arrangements  100 ,  200 ,  300 ,  400 ,  500  in  FIGS. 1 to 5 . In  FIG. 6 , the membrane layer  2  is circular, and the depressions  2   a  are in the form of circular and concentrically arranged channels or beads. The membrane layer  2  can be suspended on a substrate via suspension webs  8   a ,  8   b ,  8   c . By way of example, the number of suspension webs is three in  FIG. 6 , but any other number of suspension webs is likewise possible. 
     In  FIG. 7 , the membrane layer  2  is formed with longitudinal channels or longitudinal beads in the form of depressions  2   a . The suspension of the membrane layer  2  in this case takes place via a suspension web  8   d . In  FIG. 8 , the membrane layer  2  is formed with polygonal troughs as depressions  2   a , with the result that, for example, an eggbox-like surface structure of the membrane layer  2  is produced. It is of course also possible for other polygonal or rounded structures to be selected for the troughs in  FIG. 8 . By way of example, the number of suspension webs  8   d  in  FIGS. 7 and 8  is one, but any other number of suspension webs  8   d  is likewise possible. 
     With the present membrane arrangements  100 ,  200 ,  300 ,  400 ,  500 , as illustrated in  FIGS. 1 to 8 , in the case of actuated membranes, for example in the case of a loudspeaker, in the case of a linear out-of-plane drive or in the case of an ultrasonic transducer, a high degree of acceleration of the membrane even from a rest position is possible. This advantageously results in high acoustic pressures and therefore in efficient operation of an MEMS actuator using the membrane arrangement. 
     In principle, it is true that the acoustic pressure p is proportional to the acceleration a of the membrane. The acceleration a of the membrane results from its motion equation. If an electrostatic force is used between a planar membrane layer and an electrode layer arranged planar-parallel thereto for acceleration purposes and if it is further assumed that the membrane layer is approximately freely movable, the following results for the acceleration a: 
               a   =           d   2     ⁢   x       dt   2       =         ɛ   0     ·     ɛ   r     ·   A   ·     U   2         2   ·   m   ·       (     x   ·     x   G       )     2             ,         
where ∈ 0  is the dielectric constant in a vacuum, ∈ r  is the dielectric constant of the medium between the membrane and the electrode layer, x is the instantaneous deflection of the membrane, x G  is the distance between the membrane and the electrode layer, t is time, U is the voltage present between the membrane and the electrode layer, m is the mass of the membrane, and A is the planar-parallel area of the membrane and the electrode layer.
 
     In the case of a membrane suspended in a resilient manner, in addition acceleration is necessary also counter to the spring force kx, where k is the spring constant, which is ever increasing with the deflection, such that the acceleration a is reduced by a magnitude of kx. The acceleration a is therefore particularly high whenever the retarding forces, for example the spring force kx or the damping of the membrane, are particularly high. 
     If the electrode layer or the membrane layer has additional depressions, i.e. sections in which the membrane layer is laterally shifted in the case of a vertical movement of the membrane with respect to the electrode layer, the following results for the electrostatic force F onto a membrane layer section moving vertically with respect to fixed electrode layer sections: 
               F   =         1   2     ·       dC   y     dx     ·     U   2       =         ɛ   0     ·     ɛ   r     ·     L   y         2   ·     y   G   2             ,         
where C y  is the value of the capacitance between vertical membrane layer sections and vertical electrode layer sections, y G  is the distance between vertical membrane layer sections and vertical electrode layer sections, and L y  is the length of all of the vertical membrane layer sections. The vertical membrane layer sections can in this case be the sections  2   b  in  FIGS. 1, 2, 4 and 5 . The vertical electrode layer sections can in this case be the sections  1   b  in  FIGS. 1 to 5 .
 
     With this additional retarding force, a total motion equation for membrane arrangements with interleaved depressions, such as, for example, for the membrane arrangements  100 ,  200 ,  300 ,  400 ,  500  shown in  FIGS. 1 to 5  results as follows: 
     
       
         
           
             
               a 
               = 
               
                 
                   
                     
                       d 
                       2 
                     
                     ⁢ 
                     x 
                   
                   
                     dt 
                     2 
                   
                 
                 = 
                 
                   
                     
                       
                         ɛ 
                         0 
                       
                       · 
                       
                         ɛ 
                         r 
                       
                       · 
                       
                         U 
                         2 
                       
                     
                     
                       
                         2 
                         · 
                         ρ 
                       
                       ⁣ 
                       
                         · 
                         d 
                         · 
                         
                           ( 
                           
                             A 
                             + 
                             
                               
                                 x 
                                 k 
                               
                               · 
                               
                                 L 
                                 y 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   · 
                   
                     ( 
                     
                       
                         A 
                         
                           
                             ( 
                             
                               x 
                               - 
                               
                                 x 
                                 G 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       + 
                       
                         
                           L 
                           y 
                         
                         
                           y 
                           G 
                         
                       
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
     where ρ is the density of the membrane layer material, d is the thickness of the membrane layer and x k  is the depth or vertical extent of the depressions. Thus, an adjustable acceleration term can be provided via the vertical depression sections or the geometric dimensions thereof which permits high accelerations even from the rest position of the membrane. 
     With the present membrane arrangements  100 ,  200 ,  300 ,  400 ,  500 , as illustrated in  FIGS. 1 to 8 , conversely a large signal excursion is possible in the case of sensing membranes, for example in the case of a microphone, or in the case of an acoustic pressure sensor, as a result of an acceleration of the membrane out of the rest position. As a result, an MEMS sensor using the membrane arrangement can be operated efficiently and with a high degree of measurement sensitivity. 
     The measured capacitance C x  between a planar membrane and an electrode layer arranged planar-parallel with respect thereto is as follows: 
     
       
         
           
             
               C 
               x 
             
             = 
             
               
                 
                   
                     ɛ 
                     0 
                   
                   · 
                   
                     ɛ 
                     r 
                   
                   · 
                   A 
                 
                 
                   ( 
                   
                     x 
                     - 
                     
                       x 
                       G 
                     
                   
                   ) 
                 
               
               . 
             
           
         
       
     
     A change in the vertical distance x between the membrane and the electrode layer results in a change in capacitance of 
                   dC   x     dx     =             ɛ   0     ·     ɛ   r     ·   A         (     x   -     x   G       )     2       ⇒       dC   x       C   x         =     dx     (     x   -     x   G       )           ,         
i.e. the change in capacitance is relatively low for small deflections. For a membrane layer or an electrode layer with depressions, as explained in connection with the membrane arrangements  100 ,  200 ,  300 ,  400 ,  500  in  FIGS. 1 to 5 , a measured capacitance C G  of
 
               C   G     =           ɛ   0     ·     ɛ   r     ·   A       (     x   -     x   G       )       +         ɛ   0     ·     ɛ   r     ·     (       x   k     +   x     )     ·     L   y         y   G               
results.
 
     Accordingly, the change in capacitance of such a measured capacitance C G  is: 
     
       
         
           
             
               
                 dC 
                 G 
               
               dx 
             
             = 
             
               
                 
                   
                     
                       
                         ɛ 
                         0 
                       
                       · 
                       
                         ɛ 
                         r 
                       
                       · 
                       A 
                     
                     
                       
                         ( 
                         
                           x 
                           - 
                           
                             x 
                             G 
                           
                         
                         ) 
                       
                       2 
                     
                   
                   + 
                   
                     
                       
                         ɛ 
                         0 
                       
                       · 
                       
                         ɛ 
                         r 
                       
                       · 
                       
                         L 
                         y 
                       
                     
                     
                       y 
                       G 
                     
                   
                 
                 ⇒ 
                 
                   
                     dC 
                     G 
                   
                   
                     C 
                     G 
                   
                 
               
               = 
               
                 
                   
                     
                       ( 
                       
                         
                           A 
                           
                             ( 
                             
                               x 
                               - 
                               
                                 x 
                                 G 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             L 
                             y 
                           
                           
                             y 
                             G 
                           
                         
                       
                       ) 
                     
                     · 
                     dx 
                   
                   
                     ( 
                     
                       
                         A 
                         
                           ( 
                           
                             x 
                             - 
                             
                               x 
                               G 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           
                             ( 
                             
                               
                                 x 
                                 k 
                               
                               + 
                               x 
                             
                             ) 
                           
                           · 
                           
                             L 
                             y 
                           
                         
                         
                           y 
                           G 
                         
                       
                     
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
     In comparison with planar-parallel membranes and electrode layers, there is therefore an improved signal excursion even in the case of small deflections or in the case of large vertical distance values. In particular, the signal excursion can be adjusted via the geometry of the depressions. 
     In order to avoid parasitic capacitances it is possible, as illustrated by way of example for the membrane arrangements  200  or  500  in  FIGS. 2 and 5 , for the vertical distance x G  between the membrane layer  2  and the electrode layers  1  and  3  to be selected to be precisely the same size as the vertical extent x k  of the depressions  2   a  and  1   a  and  3   a , respectively. Therefore, in the rest position of the membrane layer  2 , the vertical capacitance component is substantially zero. At the same time, however, a small deflection results in the production of an overlap or meshing between the depressions  2   a  and  1   a  and  3   a , respectively, which brings about a non-vanishing vertical capacitance component. 
       FIGS. 9 to 13  show process steps in a method for producing a membrane arrangement. The method can be used, for example, to produce a membrane arrangement  100 ,  200 ,  300 ,  400 ,  500  as shown in  FIGS. 1 to 8 . 
     First, cutouts  4   a  are produced in a substrate  4 , for example an SOI wafer. A first electrically conductive electrode layer  1  can be introduced into these cutouts  4   a  and over the surface of the substrate  4 , wherein the electrode layer  1  has a multiplicity of first depressions  1   a  coinciding with the cutouts  4   a . Furthermore, sacrificial webs  4   b  can be formed in the cutouts  4   a , for example by generating trenches in the cutouts  4   a . The sacrificial webs  4   b  can be used as oxidation points for forming an oxide layer  4   c . The oxide layer in  FIG. 11  completely fills the cutouts  4   a  and covers the surface of the substrate  4 . If appropriate, a chemical-mechanical processing step (CMP) for planarizing and thinning the oxide layer  4   c  can be performed. Then, the oxide layer  4   c  can be etched selectively in the cutouts  4   a , for example via a lithography step. 
     Then, an electrically conductive membrane layer  2  is deposited on the oxide layer  4   c . The electrically conductive membrane layer  2  can be formed by deposition of polysilicon, for example. In this case, the membrane layer  2  can have depressions  2   a  coinciding with the cutouts  4   a . First through-holes  5   a  can be formed in the substrate  4  and the first electrically conductive electrode layer  1 , through which through-holes the oxide layer  4   c  can be etched. As a result, the electrically conductive membrane layer  2  is freed, with the result that the membrane layer  2  is deflectable with respect to the first electrode layer  1  and is spaced apart from said first electrode layer by a first distance value x G . Optionally, through-holes  5   d  can also be formed in the membrane layer  2 . 
       FIGS. 14 to 18  show process steps in a further method for producing a membrane arrangement. The method can be used, for example, to produce a membrane arrangement  100 ,  200 ,  300 ,  400 ,  500  as shown in  FIGS. 1 to 8 . 
     In a similar manner to that shown in  FIG. 9 , firstly cutouts  4   a  are formed in a substrate  4 , over which an electrode layer  1  is formed. Nitride strips can be formed, for example, vertically on the outer walls of the cutouts  1   a  by means of a deposition process and subsequent targeted etching process. An oxide layer  9   b , for example a LOCOS oxide, can be formed over the surface of the substrate  4  and the cutouts  4 . In a further deposition process, for example, TEOS oxide layers  9   c  can be formed over the oxide layers  9   b  and the nitride layer  9   a . Then, a membrane layer  2 , for example consisting of polysilicon, can be deposited over the TEOS oxide layers  9   c.    
     In turn, it is then possible for first through-holes  5   a  to be formed in the substrate  4  and the first electrically conductive electrode layer  1 , through which holes the oxide layers  9   b  and  9   c  can be etched. As a result, the electrically conductive membrane layer  2  is freed, with the result that the membrane layer  2  is deflectable with respect to the first electrode layer  1  and is spaced apart from said first electrode layer by a first distance value x G . Optionally, through-holes  5   d  can also be formed in the membrane layer  2 . 
     In order to prevent distortions in the outer walls  2   b  and  1   b  of the depressions  2   a  and  1   a , respectively, bending radii at the lines of abutment of the layer sections which are vertical with respect to one another can be rounded, for example, by means of isotropic etching steps or vacuum annealing measures, for example. Similar measures can also be performed to improve the emission impedance in the case of the through-holes  5   a  to  5   d.