Patent Publication Number: US-7907025-B2

Title: Electromechanical resonator and manufacturing method thereof

Description:
BACKGROUND 
     The present invention relates to an electromechanical resonator fabricated by using the MEMS (Micro Electro Mechanical Systems) and a manufacturing method thereof. 
     In related electromechanical devices, configurations for operating an oscillator with various driving systems are applied. An electromechanical element that translates in parallel with respect to a substrate is used in a large number of devices. To mechanically operate the oscillator of such an electromechanical device, an input/output terminal of a fixed electrode arranged over the side face of the oscillator is required. 
     A method has been proposed for changing the vibration mode by changing the thickness of an electrode in the electromechanical devices. 
     For example, an electromechanical resonator described in Non-patent Reference 1 is proposed. 
     As shown in  FIG. 18 , the electromechanical resonator includes a beam-shaped oscillator which has both ends supported as free ends. A uniform air gap  53  is formed between a fixed electrode  51  and an oscillator  52  provided on a substrate  50 . An electrostatic force is exerted in the air gap to control the oscillator to vibrate mechanically. While a resonance frequency is determined mainly by a vibration mode that depends on the electrode arrangement of the fixed electrode  51 , a secondary flexural vibration mode is excited ( FIG. 18(   b )) in a configuration where two electrodes  51  of input and output terminals are arranged in the lower layer of the oscillator  52  as shown in  FIG. 18(   a ). When three electrodes  51  are arranged in the lower layer of the oscillator  52 , a tertiary flexural vibration mode is excited at a resonance frequency higher than that of the secondary mode. Positioning of the electrode arrangement means that the vibration mode is different depending on an arrangement of the electrode  51  with respect to an anti-node position of vibration. 
     Therefore, in case an electromechanical resonator having various resonance frequencies is required, it is necessary to make variable the size and arrangement of a fixed electrode depending on the vibration mode to be excited. Also, a manufacturing method for simply manufacturing such an electrode is required. 
     Patent Reference 1 describes a method for manufacturing an electronic gun and a quantum wire and uses a structure where a sacrifice layer and an electrode layer are formed in an upper layer of a triangular section structure. This manufacturing method causes the apex of an electrode to protrude and removes the protruding part of the electrode to form a final electrode by applying a resist of a thick film and through etching-back. The electrode is formed over each of the side faces of the structure and the electrodes serve as input and output terminals. 
     By using a manufacturing method for fabricating, as described in [Patent Reference 1], fixed electrodes to be arranged over the side faces of an oscillator in a single layer, is made possible by simultaneously forming multiple fixed electrodes in an electrode layer formed with one process step. 
     [Non-patent Reference 1] M. Demirci, C. T.-C. Nguyen, “Higher-mode Free-Free Beam Micromechanical Resonators,” Proceeding, 2003 IEEE Int. Frequency Control Symposium, Tampa, Fla., May 5-8, 2003, pp. 810-818. 
     [Patent Reference 1] JP-A-06-310029 
     A resonator of the vertical driving type described in Non-patent Reference 1 determines a resonance frequency of a selected vibration mode depending on the arrangement of fixed electrodes. In this configuration, the electrodes are formed only in a lower layer of an oscillator. Therefore, the electrodes are bounded in limited locations. 
     Patent Reference 1 uses a configuration where electrodes are arranged over the side faces of an oscillator and the electrodes are driven in parallel on a substrate. This approach solves the problem of Non-patent Reference 1. However, in Patent Reference 1, the height of an electrode arranged over each of the side faces of the structure is determined by the control time of resist etching-back in the manufacturing process, thus requiring sophisticated film thickness control in order to vary the electrode height. It is difficult to independently control the film thickness of multiple fixed electrodes. With this approach, it is necessary to have a multilayer electrode configuration. A multilayer configuration adds to the number of processes to complicate the manufacturing method with a rise in the manufacturing costs. 
     In case an electromechanical resonator of the parallel driving type is provided with the configuration of Patent Reference 1, it is necessary to remove the sacrifice layer in the lower layer of the oscillator to form released structure.  FIG. 19  shows a cross section of this electromechanical resonator. A sacrifice layer  54  in the lower layer of an oscillator  56  is removed in  FIG. 19 . In case an electrode  55  is thin, the sacrifice layer  54  in the lower layer of the electrode  55  is simultaneously etched. As a result, undercutting may occur in the electrode. This results in problems that the electrode  55  is stuck and fixed to a substrate  57  and that the electrode  55  is excited with an input signal. 
     SUMMARY 
     An object of the invention is to provide an electromechanical resonator of the parallel driving type capable of varying variable the height of an electrode as required and maintaining the electrode strength. 
     In order to solve the problems, the invention provides an electromechanical resonator which includes a plurality of fixed electrodes formed in a single layer and an oscillator arranged between the fixed electrodes with gap. A part of the gap is larger than the another parts of the gap. In other words, the invention provides an electromechanical resonator comprising a resonator portion which includes a fixed electrode and an oscillator formed separately from the fixed electrode with a gap. The gap has a first gap region and a second gap region which are arranged in a thickness direction of the fixed electrode. The first gap region is different in width from the second gap region. 
     The thickness direction of the fixed electrode refers to the laminating direction of fixed electrodes and corresponds to the length direction of the gap. The length direction of the gap is perpendicular to the width direction of the gap. This allows free choice of a substantial gap width. It is thus possible to form an electromechanical resonator having a desired resonance frequency by solely adjusting the gap width. The fixed electrode can be formed without reducing its thickness. It is thus possible to maintain the strength of the fixed electrode. There is no such disadvantage described above that the electrode is stuck to a substrate or that the fixed electrode is excited with an input signal. 
     Preferably, a width of the first gap region is constant. The second gap region has a width enough for neglecting a capacitance between the fixed electrode and the oscillator. 
     With this configuration, only the first gap region is used as an operating region, as a result, the design for making the electromechanical resonator can be facilitated. Even in case a plurality of resonator portions having different resonance frequencies are formed on the same substrate, it is possible to change the size of the first gap region and change the resonance frequency only by adjusting the width of a groove or the like, thus allowing easy design work. 
     Preferably, the fixed electrode has a first fixed electrode and a second fixed electrode. The oscillator is arranged between the first fixed electrode and the second fixed electrode with the gaps. 
     Preferably, the gap has only an air gap. 
     Preferably, the gap has an air gap and a dielectric gap. 
     Preferably, the gap has only a dielectric gap. 
     Preferably, the oscillator is made of monocrystalline silicon. 
     Preferably, the oscillator is made of polysilicon. 
     Preferably, the fixed electrode is formed on a substrate via a predetermined supporting portion. Side faces of the oscillator are inclined with respect to a surface of the substrate. 
     Preferably, the fixed electrode is formed on a substrate via a predetermined supporting portion. Side faces of the oscillator are perpendicular to a surface of the substrate. 
     Preferably, a thickness of the fixed electrode is greater than that of the oscillator. 
     Preferably, a thickness of the fixed electrode is equal to that of the oscillator. 
     Preferably, a thickness of the fixed electrode is smaller than that of the oscillator. 
     Preferably, a plurality of the resonator portions have different resonance frequencies respectively which are formed on a substrate. 
     Preferably, the resonator portion includes a first resonator portion and a second resonator portion, each of which having the fixed electrode and the oscillator. The first gap region of the first resonator portion is different in the width from the first gap region of the second resonator portion. 
     The invention provides a method for manufacturing an electromechanical resonator, comprising: forming a first electrode on a substrate; forming an insulating film on the first electrode; forming a conductor layer on the insulating film and flattening the conductor layer to form a second electrode; and forming a gap between the first electrode and the second electrode. One of the first electrode and the second electrode is a fixed electrode, and the other of the first electrode and the second electrode is an oscillator. The gap has a first gap region and a second gap region which are arranged in a thickness direction of the fixed electrode. The first gap region is different in width from the second gap region. That is, the one of the fixed electrodes and the oscillator is patterned to form an insulating film serving as a sacrifice layer. The conductor layer serving as the other electrode is formed in an upper layer of the insulating film. Then the insulating film is removed to form a gap of a constant width and additionally a groove so as to form a gap of a width broader than that of the gap of a constant width. With this procedure, it is possible to readily form an electromechanical resonator having a gap width that varies in the direction of thickness. While generally an oscillator is patterned first, a fixed electrode may be patterned first. 
     The invention further includes processes of: forming an insulating film in an upper layer of an oscillator; forming a conductor layer in an upper layer of the insulating film and flattening the film; forming a mask pattern on the electrode layer and etching the layer in a direction normal to a substrate surface to form a groove; forming a protective film on the side face of the groove to selectively remove the conductor layer and form the pattern of a fixed electrode. 
     The invention also includes processes of: forming a groove on a substrate; forming a film on the groove; filling the groove with a conductor layer; and forming the groove reaching the insulating layer by etching the conductor layer in a slanting direction on the substrate. 
     With the above configuration, an electromechanical resonator adapting a plurality of resonance frequencies and having a fixed electrode of high strength is provided. 
     With the above manufacturing method, it is possible to form the fixed electrodes having plural resonance frequencies in the same layer thus reducing costs by way of simplified processes. 
     Preferably, the forming process of the gap includes: forming a groove on the conductor layer; and removing the insulating layer which is exposed from the groove to form an air gap. 
     Preferably, the forming process of the gap includes: doping impurities into the conductive layer to form a dielectric groove corresponding to the second gap region. A dielectric gap includes the second gap region and the first gap region which corresponds to the insulating film connected with the dielectric groove. 
     Preferably, the forming process of the gap includes: doping insulating impurities into the conductive layer to form a dielectric groove corresponding to the second gap region so that the dielectric groove connects with the first gap region having an air gap. 
     Preferably, the method further includes: etching the substrate to form the oscillator of a triangular section having an inclined surface, then forming an insulating layer on the oscillator; forming a conductor layer on the insulating layer; and etching the conductor layer in a vertical direction to form the groove reaching the insulating layer. 
     Preferably, the forming process of the gap includes: forming a groove on the substrate; forming the insulating layer on the groove, filling the groove with the conductor layer; and etching the conductor layer in slanting direction to form the groove reaching the insulating layer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above objects and advantages of the present invention will become more apparent by describing in detail preferred exemplary embodiments thereof with reference to the accompanying drawings, wherein: 
         FIGS. 1A and 1B  are cross-sectional views of an electromechanical resonator according to a first embodiment; 
         FIGS. 2A to 2D  are cross-sectional views of a method for manufacturing an electromechanical resonator according to the first embodiment; 
         FIGS. 3A and 3B  show an electromechanical resonator according to a second embodiment; 
         FIGS. 4A and 4B  show an electromechanical resonator according to a third embodiment; 
         FIGS. 5A to 5H  are cross-sectional views of a method for manufacturing an electromechanical resonator according to the third embodiment; 
         FIG. 6  shows an electromechanical resonator according to a fourth embodiment; 
         FIG. 7  shows an electromechanical resonator according to the fourth embodiment; 
         FIGS. 8A and 8B  shows variations of the electromechanical resonator according to the fourth embodiment; 
         FIGS. 9A to 9D  show an electromechanical resonator according to a fifth embodiment; 
         FIGS. 10A and 10B  show a process for manufacturing an electromechanical resonator according to the fifth embodiment; 
         FIG. 11  shows an electromechanical resonator according to a sixth embodiment; 
         FIGS. 12A to 12F  show a process for manufacturing an electromechanical resonator according to the sixth embodiment; 
         FIG. 13  shows an electromechanical resonator according to a seventh embodiment; 
         FIGS. 14A to 14E  show a process for manufacturing an electromechanical resonator according to a seventh embodiment; 
         FIGS. 15A to 15D  show a process for manufacturing an electromechanical resonator according to a eighth embodiment; 
         FIG. 16  shows an electromechanical resonator according to a ninth embodiment; 
         FIGS. 17A to 17E  show a process for manufacturing an electromechanical resonator according to the ninth embodiment; 
         FIG. 18  shows an electromechanical resonator according to the related art; and 
         FIG. 19  shows an electromechanical resonator according to the related art. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Embodiments of the invention will be described referring to drawings. 
     First Embodiment 
       FIGS. 1A and 1B  show an electromechanical resonator according to the first embodiment of the invention.  FIGS. 2A and 2B  show a method for manufacturing an electromechanical resonator according to the first embodiment. 
     As shown in  FIG. 1A , the electromechanical resonator according to this embodiment includes a resonator portion having fixed electrodes and an oscillator  109  formed separately from the fixed electrodes  107  with gaps. Each of the gaps has a first region ( 113 ) with a constant width in a thickness direction of the fixed electrode  107  and a second region ( 111 ) being large enough for the capacitance between the fixed electrode and the oscillator to be negligible. The oscillator  109  is formed by a beam-shaped body of a triangular section. The fixed electrodes  107  are arranged over two side faces of the oscillator with air gaps, the air gaps between the oscillator  109  and the fixed electrodes  107  including a portion of a varying gap width (a nonconstant gap width). The thickness of the fixed electrode  107  is formed so as to be greater than that of the oscillator  109 . To be precise, the air gap includes a gap  111  having a broad width and a gap  113  having a narrow width. A maximum electrostatic force is generated at the gap  113  having the narrow width in the air gap between the oscillator  109  and the fixed electrode  107 . The electrostatic force exerted in the capacitance is proportional to the square of the width of the gap. A small electrostatic force is generated in the gap  111  having the broad width and a small driving force is obtained.  FIG. 1B  shows the mode of vibration excited by the gap spacing (gap width). In case the gap  113  having the narrow width overlaps half the thickness of the oscillator  109 , a driving force is exerted in the region and, as a result, torsional vibration is excited with the beam of a triangular section working as an oscillator. Further, the thickness of the fixed electrode  107  is greater than that of the oscillator  109  thus enhancing the strength of the fixed electrode. To enhance the strength of the fixed electrode  107 , the electrode film thickness is desirably set equal to or greater than the height of the structure of the electromechanical resonator. 
       FIGS. 2A to 2D  show a method for manufacturing a resonator structure according to the first embodiment of the invention. 
     First, an SOI substrate, in which a monocrystalline silicon thin film is formed on a surface of a silicon substrate serving as a material substrate  101  via a silicon oxide layer serving as a first insulating film  103 , is prepared. 
     Next, as shown in  FIG. 2A , a mask pattern is formed by way of photolithography. Anisotropic etching is performed using the mask pattern, and an oscillator  109  in which a beam-shaped body of a triangular section having a slanted side face (with an inclination angle of 54.7 degrees) is formed. The silicon oxide film serving as the second insulating film  105  is formed on an upper layer of the oscillator  109 . 
     As shown in  FIG. 2B , a doped polycrystalline silicon layer as a fixed electrode  107  is formed on the second insulating film  105  by way of the CVD method. The depressurized CVD method or the like is desirably used in order to form a flat film. 
     As shown in  FIG. 2C , a mask pattern is formed and a groove is formed on the polycrystalline silicon layer working as the fixed electrode  107  to expose the second insulating film  105  formed in the upper layer of the oscillator  109 . 
     Finally, as shown in  FIG. 2D , the second insulating film  105  to be exposed is removed by etching to form a gap and remove the first insulating film  103 , thus forming an electromechanical resonator. 
     In this way, it is possible to form the electromechanical resonator shown in  FIG. 1  with good workability. 
     In the first embodiment, the fixed electrode  107  is formed via the first insulating film  103  as a post on a substrate. By removing the portion corresponding to the post under the oscillator  109  by way of etching, the oscillator  109  may be selectively made movable. 
     The side face of the oscillator  109  is an inclined surface. In the first region, the fixed electrode  107  is opposed to the oscillator  109  with a gap having a predetermined spacing along the inclined surface of the oscillator  109  so as to exert an electrostatic force in the first region appropriately. 
     In the second region, the side face of the fixed electrode  107  is a perpendicular cross section separated to a large extent from the side face of the oscillator  109 . In the second region, almost no electrostatic force is exerted. 
     The shape of each of these side faces may be changed as required, as long as there are arranged a first region of a constant gap width and formed narrow enough to cause an electrostatic force to be exerted and a second region having a gap width broad enough to neglect an electrostatic force. 
     In this embodiment, the beam-shaped body having a triangular section which serves as the oscillator  109  is formed of monocrystalline silicon. This material ensures shape machining with excellent control in the patterning of the oscillator  109  by way of anisotropic etching of silicon. 
     While an SOI substrate in which a monocrystalline silicon substrate is bonded on a silicon substrate is used as a material substrate of a starting material, an SOI substrate in which a polycrystalline silicon or amorphous silicon is bonded on the silicon substrate may be used instead. In such a case, there is no control to use anisotropic etching dependent on the monocrystalline surface as an etching end point. 
     Second Embodiment 
     The second embodiment of the invention will be described. While the gap is an air gap in the first embodiment, a capacitance insulating film  105  may be formed on the oscillator  109  or in the gap as a variation of the first embodiment. 
       FIGS. 3A and 3B  show variations of the electromechanical resonator according to the first embodiment shown in  FIG. 1 . In a configuration of the second embodiment, the capacitance ratio between a region having a broad gap and a region having a narrow gap is optimized by the capacitance insulating film  105  provided in the gap.  FIG. 3B  is an enlarged view of main parts of  FIG. 3A . 
     As shown in  FIGS. 3A and 3B , an electromechanical resonator according to the second embodiment is an electromechanical resonator of a capacitive coupling type for performing excitation and detection that uses, as a capacitance insulating film, the second insulating film  105  which is remained on the oscillator  109 , instead of removing the second insulating film for forming the gap in the process of manufacturing the electromechanical resonator according to the first embodiment. 
     In this embodiment, the silicon substrate  101  is etched from the rear face thereof so as to facilitate vibration of the oscillator  109 . 
     Third Embodiment 
       FIGS. 4A and 4B  show an electromechanical resonator according to the third embodiment of the invention.  FIGS. 5A to 5H  are explanation views of a method for manufacturing the electromechanical resonator according to the third embodiment. 
     The electromechanical resonator according to the third embodiment differs from that of the first embodiment in that the thickness of the fixed electrode  107  is almost equal to that of the oscillator  109 . In this configuration, the strength of the fixed electrode  107  of the third embodiment is smaller than that of the fixed electrode  107  of the first embodiment. However, the thickness of the fixed electrode  107  of this embodiment is utilized at a maximum. 
     As shown in  FIG. 4A , the electromechanical resonator according to this embodiment includes a resonator portion having fixed electrodes and an oscillator  109  formed separately from the fixed electrodes  107  with gaps. Each of the gaps has a first region ( 113 ) with a constant width in a thickness direction of the fixed electrode  107  and a second region ( 111 ) being large enough for the capacitance between the fixed electrode and the oscillator to be negligible. The oscillator  109  is formed by a beam-shaped body of a triangular section. The fixed electrodes  107  are arranged over two side faces of the oscillator with air gaps, the air gaps between the oscillator  109  and the fixed electrodes  107  including a portion of a varying gap width (a nonconstant gap width). The thickness of the fixed electrode  107  is formed so as to be substantially equal to that of the oscillator  109 . To be precise, the air gap includes a gap  111  having a broad width and a gap  113  having a narrow width. A maximum electrostatic force is generated at the gap  113  having the narrow width in the air gap between the oscillator  109  and the fixed electrode  107 . The electrostatic force exerted in the capacitance is proportional to the square of the width of the gap. A small electrostatic force is generated in the gap  111  having the broad width and a small driving force is obtained.  FIG. 4B  shows the mode of vibration excited by the gap spacing (gap width). In case the gap  113  having the narrow width overlaps half the thickness of the oscillator  109 , a driving force is exerted in the region and, as a result, torsional vibration is excited with the beam of a triangular section working as an oscillator. Further, the thickness of the fixed electrode  107  is substantially equal to that of the oscillator  109  thus taking maximum advantage of the height of the structure. 
       FIGS. 5A to 5H  show a method for manufacturing the resonator structure according to the third embodiment of the invention. The manufacturing method in this embodiment differs from the manufacturing method described referring to  FIG. 2  in the first embodiment in that the film thickness of the doped polycrystalline silicon layer for forming the fixed electrodes  107  is made larger and that a step of coating or covering the side wall of the doped polycrystalline silicon layer with a silicon nitride film  115  and performing etching-back up to the height of the oscillator  109  prior to the step of forming the gap is added. 
     The method for manufacturing the resonator structure according to the third embodiment will be described. 
     First, an SOI substrate, in which a monocrystalline silicon thin film is formed on a surface of a silicon substrate serving as a material substrate  101  via a silicon oxide layer serving as a first insulating film  103 , is prepared. 
     Next, as shown in  FIG. 5A , a mask pattern is formed by way of photolithography. Anisotropic etching is performed using the mask pattern, and an oscillator  109  in which a beam-shaped body of a triangular section having a slanted side face (with an inclination angle of 54.7 degrees) is formed. The silicon oxide film serving as the second insulating film  105  is formed on an upper layer of the oscillator  109 . 
     As shown in  FIG. 5B , a doped polycrystalline silicon layer as a fixed electrode  107  is formed on the second insulating film  105  by way of the CVD method. The depressurized CVD method or the like is desirably used in order to form a flat film. 
     As shown in  FIG. 5C , a mask pattern is formed and a groove is formed on the polycrystalline silicon layer working as the fixed electrode  107  to expose the second insulating film  105  formed in the upper layer of the oscillator  109 . 
     After that, a protective film  115  composed of a silicon nitride film is deposited ( FIG. 5D ) and anisotropic etching is carried out to remove the protective film  115  for an upper layer ( FIG. 5E ). As shown in  FIG. 5F , a polycrystalline silicon layer for forming a fixed electrode  107  is etched to determine the film thickness of the polycrystalline silicon layer. 
     Finally, as shown in  FIG. 2G , the second insulating film  105  to be exposed is removed by etching to form a gap and remove the first insulating film  103 , thus forming an electromechanical resonator as shown in  FIG. 5H . 
     In this way, it is possible to form the electromechanical resonator shown in  FIG. 4  with good workability. 
     In the third embodiment, same as the first embodiment, the fixed electrode  107  is formed via the first insulating film  103  as a post on a substrate. By removing the portion corresponding to the post under the oscillator  109  by way of etching, the oscillator  109  may be selectively made movable. 
     The side face of the oscillator  109  is an inclined surface. In the first region, the fixed electrode  107  is opposed to the oscillator  109  with a gap having a predetermined spacing along the inclined surface of the oscillator  109  so as to exert an electrostatic force in the first region appropriately. 
     In the second region, the side face of the fixed electrode  107  is a perpendicular cross section separated to a large extent from the side face of the oscillator  109 . In the second region, almost no electrostatic force is exerted. 
     The shape of each of these side faces may be changed as required, as long as there are arranged a first region of a constant gap width and formed narrow enough to cause an electrostatic force to be exerted and a second region having a gap width broad enough to neglect an electrostatic force. 
     In this embodiment, the beam-shaped body having a triangular section which serves as the oscillator  109  is formed of monocrystalline silicon. This material ensures shape machining with excellent control in the patterning of the oscillator  109  by way of anisotropic etching of silicon. 
     While an SOI substrate in which a monocrystalline silicon substrate is bonded on a silicon substrate is used as a material substrate of a starting material, an SOI substrate in which a polycrystalline silicon or amorphous silicon is bonded on the silicon substrate may be used instead. In such a case, there is no control to use anisotropic etching dependent on the monocrystalline surface as an etching end point. 
     Fourth Embodiment 
     The fourth embodiment of the invention will be described. While the gap is an air gap in the third embodiment, a capacitance insulating film is formed on the oscillator  109  or in the gap as a variation thereof. 
       FIGS. 6 and 7  show variations of the electromechanical resonator according to the third embodiment shown in  FIG. 4 . In a configuration of the fourth embodiment, the capacitance ratio between a region having a broad gap and a region having a small gap is optimized by the capacitance insulating film  105  provided in the gap and a shape of the gap, as similar to the second embodiment. 
     As shown in  FIG. 6 , an electromechanical resonator according to this embodiment is an electromechanical resonator of a capacitive coupling type for performing excitation and detection that uses, as a capacitance insulating film, the second insulating film  105  which is remained on the oscillator  109 , instead of removing the second insulating film for forming the gap in the process of manufacturing the electromechanical resonator according to the third embodiment. 
     In general, an expression for calculating a capacitance is as follows: 
     
       
         
           
             
               
                 
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                             e 
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                   [ 
                   
                     Expression 
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     e o =Dielectric constant of vacuum=8.854 E-12 F/m 
     e r =Relative dielectric constant of an insulating film 
     d=distance between electrodes 
     s=Capacitor area 
     While the relative dielectric constant (e r ) of air is approximately 1, that of an oxide film (SiO 2 ) is approximately 4.5 and that of a nitride film (Si 3 N 4 ) is approximately 7.5. 
     In  FIG. 7 , the insulating film  105  in the air gap region is removed so as to gain a more capacitance variation ratio than in  FIG. 6 . 
     Further, as shown in the variation in  FIG. 8A , a dielectric gap may be formed of materials having different relative dielectric constants with a geometric gap width unchanged. To be more precise, the second insulating film  105  may be formed of a first dielectric  105   a  having a high dielectric constant and a second dielectric  105   b  such as silicon oxide to provide a first dielectric gap and a second dielectric gap. The dielectric gaps  105   a ,  105   b  can assure a high capacitance ratio (20-60) without changing the gap width and substantially operate the same way as a gap width ratio of 20 or more, thus offering an optimum configuration when the dielectric gaps include a first region composed of silicon oxide or the like and a second region composed of hafnium oxide HFO 2  (e r =80), titanium oxide TiO 2  (e r =80), BST, BaSrTiO 3  (e r =300) or the like serving as a ferroelectric layer assure a high capacitance ratio (20-60). 
     Also, as shown in the variation in  FIG. 8B , an insulating impurities is doped into a part of the conductive layer  205  communicating with an air gap  213  so that the part of the conductive layer  205  is turned into a dielectric part  201  to form the second region constructed by a dielectric gap  201 . As a result, a gap constructed by the air gap  213  and the dielectric gap  201  is formed. 
     Fifth Embodiment 
     The fifth embodiment of the invention will be described. 
     The process of manufacturing an electromechanical resonator according to the fifth embodiment is shown in  FIGS. 9A to 9D . In this embodiment, a nondoped polycrystalline silicon layer is used instead of the broad gap  111  in the second region. The fixed electrode  205  is made of a heavily doped polycrystalline silicon layer and more distance is substantially provided between the oscillator  109  and the fixed electrode  205 , thus delivering the same working effect as a broad gap. In the manufacture of the electromechanical resonator, for example, ion implantation at a high dose may be made into the polysilicon  201  prior to doping except in some regions so as to control the coupling area (capacitive coupling area). 
     In the manufacture, same as the first embodiment shown in  FIG. 5A , an SOI substrate, in which a monocrystalline silicon thin film is formed on a surface of a silicon substrate serving as a material substrate  101  via a silicon oxide layer serving as a first insulating film  103 , is prepared. Next, a mask pattern is formed by way of photolithography. Anisotropic etching is performed using the mask pattern, and an oscillator  109  in which a beam-shaped body of a triangular section having a slanted side face with an inclination angle of 54.7 degrees is formed. The silicon oxide film serving as the second insulating film  105  is formed on an upper layer of the oscillator  109 . 
     As shown in  FIG. 9A , a nondoped polycrystalline silicon layer  201  as a fixed electrode is formed on the second insulating film  105  by way of the CVD method. The depressurized CVD method or the like is desirably used in order to form a flat film. 
     Next, as shown in  FIG. 9B , a mask  203  is formed in a region where a broad gap is to be formed and the polycrystalline silicon layer  201  of a region where a fixed electrode is to be formed is exposed. 
     After that, ion implantation is made in a state that the mask  203  is remained ( FIG. 9C ). As shown in  FIG. 9D , the polycrystalline silicon layer in the region to be exposed from the mask is heavily doped to form a fixed electrode  205 . The region covered with the mask  203  without being doped remains as a nondoped polycrystalline silicon layer which works as a dielectric gap  201 . 
     In this way, it is possible to form the electromechanical resonator with good workability. 
     In the first embodiment, a fixed electrode is formed via the first insulating film  103  as a post on a substrate. By removing the portion corresponding to the post under the oscillator  109  by way of etching, the oscillator  109  may be selectively made movable. Similar way for removing the first insulating film  103  provided under the oscillator  109  may be applied to the electromechanical resonator according to the fifth embodiment. 
     The insulating film  105  as a sacrifice layer may be removed to form an air gap or the insulating film  105  may be left without being removed for an electrostatic force to be exerted. Either choice may be made to provide an electromechanical resonator of a capacitive coupling type. 
     In the process of forming a gap, whose manufacturing process is shown in part in  FIGS. 10A and 10B , insulating impurities may be doped into a doped polycrystalline silicon layer  205  as a fixed electrode and turning the doped polycrystalline silicon layer into a dielectric to form a second region  201  composed of a dielectric groove, and an insulating film in a region communicating with the dielectric groove may be used as a first region to form a dielectric gap. 
     With this configuration, it is possible to readily form the second region including a broad dielectric gap only by doping insulating impurities in a state that the mask is remained. 
     The process of forming the gap may include a process of doping insulating impurities into the electrode which communicates with an air gap after removing the insulting film to form the air gap, and turning the electrode into a dielectric thus forming a second region composed of a dielectric groove in order to form a gap composed of the air gap and dielectric gap. 
     With this configuration, it is possible to remove a portion of a sacrifice layer to provide an air gap and turn a portion of the air gap into a dielectric gap. 
     The method for manufacturing an electromechanical resonator according to this embodiment includes steps of: performing etching to provide an inclined surface and form an oscillator of a triangular section, then forming a insulating layer in an upper layer of the oscillator; forming a conductor layer in an upper layer of the insulating layer; and etching the conductor layer in vertical direction to form the groove reaching the insulating layer. 
     As a result, the groove reaching the insulating layer is readily formed into a broad air gap. By removing the insulating layer, it is possible to provide an air gap of a constant width. 
     The method for manufacturing an electromechanical resonator according to this embodiment may include steps of: forming a groove on a material substrate; forming an insulating film on the groove, filling the groove with a conductor layer; and forming a mask pattern and etching the conductor layer in the slanting direction of the substrate. 
     With this approach, it is possible to readily form a broad air gap. The step of filling the groove with a conductor layer is readily made possible by forming a groove and then an insulating film, forming a conductor layer, and flattening the layer through etching-back or CSP. In this example, the conductor layer filled into the groove constitutes an oscillator or a fixed electrode. 
     Sixth Embodiment 
     The sixth embodiment of the invention will be described. While a single resonator portion is arranged on a substrate in the third embodiment, plural different resonator portions are arranged on a substrate in the sixth embodiment. 
       FIG. 11  shows an electromechanical resonator according to the sixth embodiment.  FIG. 12  is a cross-sectional view for explaining a method for manufacturing an electromechanical resonator according to the sixth embodiment. 
       FIG. 11  is an as-built drawing of the electromechanical resonator including the plural electromechanical resonators having different resonance frequencies on the single substrate. A numeral  121  represents a first oscillator having a beam of a trapezoidal section. A numeral  123  represents a second oscillator of a large-sized rectangular shape. Fixed electrodes  107  are formed in the same layer. The gap formed between the second oscillator  123  and the fixed electrode  107  has a constant width. The gap formed between the first oscillator  121  and the fixed electrode  107  includes a first region having a constant gap width and a second region having a broad gap width, same as the first embodiment. In the second region, a region where the gap between the oscillator  121  and the electrode  107  is broader. 
     With this configuration, the first oscillator  121  and the second oscillator  123  are excited in different vibration modes and have different resonance frequencies. It is thus possible to readily provide an electromechanical resonator supporting a plurality of frequencies. 
     While two resonators having different resonance frequencies are arranged side by side in this embodiment, the overlap region of a constant gap width occurring between a fixed electrode and an oscillator formed in the same layer can be arbitrarily changed, so that three or more electromechanical resonators may be arranged. 
     A method for manufacturing an electromechanical resonator according to the sixth embodiment of the invention is shown in  FIG. 12A to 12F . The manufacturing method may be implemented by the same process as that in the first embodiment shown in  FIGS. 2A to 2D  only except that a different photo mask is used for patterning an oscillator, so that the corresponding description is omitted. The sixth embodiment differs from the first embodiment in that beams of a trapezoidal section  121 ,  123  are formed instead of the beam of a triangular section  109  shown in the third embodiment. 
     Seventh Embodiment 
       FIG. 13  shows an electromechanical resonator according to the seventh embodiment of the invention.  FIG. 14  is a cross-sectional view for explaining a method for manufacturing the electromechanical resonator according to the seventh embodiment. 
     While a beam of a triangular section is used as an oscillator and a gap is formed on a slanting surface in the first to fourth embodiments, the side faces of the oscillators  153 ,  155 ,  157  are perpendicular to the substrate surface and the end face of the fixed electrode  151  is made into a tapered section for a region where a broad gap is to be formed in this embodiment. Except for the above difference, the electromechanical resonator provided in this embodiment is the same as that of the sixth embodiment. 
     In this embodiment, an electromechanical resonator is shown where a groove  171  is formed on a polycrystalline silicon layer (conductor layer)  151  which is formed on the silicon substrate  101  via a first insulating film  103  to form oscillators of a rectangular section  153 ,  155 ,  157 . To arrange a fixed electrode  151  that is optimum for the resonance frequency of the resonator with respect to these oscillators, an electrode using an inclination having gaps of a broad width and a narrow width. 
     A method for manufacturing the electromechanical resonator according to the seventh embodiment is shown in  FIG. 14A to 14E . In  FIG. 14A , same as the first embodiment, an SOI substrate is used as a starting material and the groove  171  is formed on the polycrystalline silicon layer  151  to form a first protective film  173  made of silicon nitride. 
     Next, as shown in  FIG. 14B , the polycrystalline silicon layer (conductive layer)  175  as an oscillator is deposited and a surface layer is removed by way of etching-back. 
     After that, as shown in  FIG. 14C , a second protective film  177  composed of a silicon nitride film is formed and patterned through photolithography. 
     Etching is made using the second protective film  177  as a mask. In this process, a positive tapered cross-sectional shape is formed. This is readily attained for example by a process of ion beam etching (IBE) or crystal anisotropy etching ( FIG. 14D ). 
     Finally, the first protective film  173  and the first insulating film  103  are removed to separate the oscillator  153  from the substrate  101 . 
     In this way, an electromechanical resonator including a first region  163  of a narrow gap width and a second region  161  of a broad gap width is formed. 
     The first and second protective films used in this example are of any material as an etching mask and are not limited to an insulating material. In case the first protective film  173  is not removed but left as a dielectric gap, a dielectric film of a desired dielectric constant should be used. 
     Eighth Embodiment 
     The eighth embodiment of the invention will be described. While the plural different resonator portions are arranged on the substrate in the sixth embodiment, a fixed electrode has a thickness larger than that of an oscillator constituting a resonator in a similar structure in this embodiment. 
       FIGS. 15A to 15D  are cross-sectional views for explaining a method for manufacturing an electromechanical resonator according to the eighth embodiment. 
       FIG. 15D  is an as-built drawing of the electromechanical resonator including plural electromechanical resonators having different resonance frequencies on a single substrate. A numeral  121  represents a first oscillator having a beam of a trapezoidal section. A numeral  123  represents a second oscillator of a large-sized rectangular shape. Fixed electrodes  107  are formed in the same layer. The gap formed between the second oscillator  123  and the fixed electrode  107  has a constant width. The gap formed between the first oscillator  121  and the fixed electrode  107  includes a first region having a constant gap width and a second region having a broad gap width, same as the first embodiment. In the second region, a region where the gap between the oscillator  121  and the electrode  107  is broader. 
     With this configuration, the first oscillator  121  and the second oscillator  123  are excited in different vibration modes and have different resonance frequencies. It is thus possible to readily provide an electromechanical resonator supporting a plurality of frequencies. 
     While two resonators having different resonance frequencies are arranged side by side in this embodiment, the overlap region of a constant gap width occurring between a fixed electrode and an oscillator formed in the same layer can be arbitrarily changed, so that three or more electromechanical resonators may be arranged. 
     A method for manufacturing an electromechanical resonator according to the eighth embodiment of the invention is shown in  FIG. 15A to 15D . The manufacturing method may be implemented by the same process as that in the first embodiment shown in  FIGS. 2A to 2D  only except that a different photo mask is used for patterning an oscillator, so that the corresponding description is omitted. The eighth embodiment differs from the first embodiment in that beams of a trapezoidal section  121 ,  123  are formed instead of the beam of a triangular section  109  shown in the first embodiment. 
     Ninth Embodiment 
       FIG. 16  shows an electromechanical resonator according to the ninth embodiment of the invention.  FIGS. 17A to 17E  are cross-sectional views for explaining a method for manufacturing an electromechanical resonator according to the ninth embodiment. 
     While the thickness of the fixed electrode  107  is approximately equal to that of an oscillator in the first embodiment, the thickness of the fixed electrode  107  is smaller than that of an oscillator in the electromechanical resonator according to this embodiment. 
     As shown in  FIG. 16 , the electromechanical resonator according to this embodiment includes a resonator portion which has fixed electrodes  107  and an oscillator  109  formed separately from the fixed electrodes  107  with gaps. The electromechanical resonator includes a first region with a gap of a constant width from the fixed electrode  107  in the direction of the thickness of the oscillator, with the thickness of the fixed electrode  107  being smaller than that of the oscillator  109 , and a second region large enough for the capacitance between the fixed electrode and the oscillator to be negligible since a fixed electrode being absent. The oscillator  109  forms a beam-shaped body of a triangular section. The fixed electrodes  107  are arranged up to a predetermined height of the two side faces of this oscillator, a portion of the oscillator  109  is an air gap including a portion where the fixed electrodes  107  are not opposed to each other. To be precise, the air gap includes a gap  111  having a broad width and a gap  113  of a narrow width. Between the oscillator  109  and the fixed electrode  107 , a maximum electrostatic force is generated in the gap  113  of a narrow width. The electrostatic force exerted between capacitors is proportional to the square of the width of the gap. Almost no electrostatic force is generated in a gap  111  having a broad width and a small driving force is obtained. 
       FIGS. 17A to 17E  show a method for manufacturing a resonator structure according to the ninth embodiment of the invention. 
     First, an SOI substrate, in which a monocrystalline silicon thin film is formed on a surface of a silicon substrate serving as a material substrate  101  via a silicon oxide layer serving as a first insulating film  103 , is prepared. 
     Next, a mask pattern is formed by way of photolithography. Anisotropic etching is performed using the mask pattern, and an oscillator  109  in which a beam-shaped body of a triangular section having a slanted side face (with an inclination angle of 54.7 degrees) is formed. The silicon oxide film serving as the second insulating film  105  is formed on an upper layer of the oscillator  109 . 
     As shown in  FIG. 17A , a doped polycrystalline silicon layer as a fixed electrode  107  is formed on the second insulating film  105  by way of the CVD method. The depressurized CVD method or the like is desirably used in order to form a flat film on a stepped portion. 
     As shown in  FIG. 17B , a resist R is applied to a doped polycrystalline silicon layer as a fixed electrode  107 . 
     As shown in  FIG. 17C , the resist is removed to a predetermined depth by way of the resist etching-back method so as to cause the doped polycrystalline silicon layer as a fixed electrode  107  to be exposed only at the apex of the surface of the oscillator. 
     Next, as shown in  FIG. 17D , the doped polycrystalline silicon layer is removed by using the resist R as a mask. 
     Finally, as shown in  FIG. 17D , the second insulating film  105  to be exposed is removed by etching to form a gap and remove the first insulating film  103 , thus forming an electromechanical resonator. 
     In this way, it is possible to form the electromechanical resonator shown in  FIG. 16  with good workability. 
     In the ninth embodiment, the fixed electrode  107  is formed via the first insulating film  103  as a post on a substrate. The thickness of the fixed electrode opposed to the oscillator  109  is reduced and the fixed electrode is formed along the side wall of the oscillator to form an electrostatic generation area having a desired width. 
     Since the thickness of the fixed electrode is thinner than that of the oscillator, the strength is decreased, but the opposed area is easily determined by changing the mask. 
     The invention provides an electromechanical resonator supporting a plurality of resonance frequencies and including input and output terminals with high mechanical strength that can be formed in the same layer. The electromechanical resonator provides a compact design and reduces manufacturing costs by way of simplified processes, so that is applicable to communication devices including portable terminals.