JP2007175577A - Mems vibrator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a MEMS vibrator in which the insertion loss is diminished by keeping a resistance component of the MEMS vibrator to a minimum. <P>SOLUTION: The MEMS vibrator has a lower electrode 10 as a first electrode plate, a vibration body 12, as a second electrode plate, which has a gap g for the electrode 10 to be oppositely positioned, a supporting beam 14 extended from a side of the vibration body 12, a power supplying circuit 16 as a power supplying means for applying an alternating power of the same phase to the lower electrode 10 and the vibration body 12, and an output circuit 18 as a detection means for obtaining a power output corresponding to the electrostatic capacity between the lower electrode 10 and the vibration body 12, wherein the resistance component is kept to the minimum by adjusting the dimension of the vibration body 12. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a MEMS vibrator.

  MEMS (Micro Electro Mechanical System) is one of micromachine technologies, and refers to technologies and products that make microelectron mechanical systems of micron (or nano) order. A semiconductor chip is planar because a silicon thin film is stacked on a silicon substrate to make an electronic circuit, but while using the same semiconductor technology, MEMS cuts silicon like machining, micron-sized leaf springs and mirrors, rotating Make an axis. These are three-dimensional and the parts are movable.

  As a field in which MEMS is attracting attention, a communication field, particularly a mobile phone is cited. In addition to LSIs, cellular phones incorporate many components such as filters, antenna switches, and transmission / reception switches. As the number of multibands using Bluetooth (registered trademark) and wireless LAN increases, passive components such as an antenna changeover switch and a band changeover switch increase. In order to reduce the size and power consumption, it is most efficient to reduce these points by putting these parts on one chip. Further, since the wiring is shortened and mechanically operated, no signal noise is introduced, and a performance improvement such as realizing a filter having a loss 10 times or more that of individual components is expected. Since silicon is used, it can be integrated with a system LSI, packaged, or bonded together.

  In general, a device using the MEMS technology is driven without wasting energy by driving using a resonance motion. For example, sensor applications such as an acceleration sensor, a temperature sensor, and a humidity sensor sense a change (physical quantity) by detecting a change in resonance frequency. The MEMS vibrator is used as an oscillator by stably resonating at a resonance frequency. The shapes of these (sensors and vibrators) are determined by the target characteristics and frequency. The shape is roughly classified into three types: a beam structure, a comb structure, and a disk structure. Moreover, there are two vibration methods, and it is known that they are bending motion and telescopic motion (for example, refer nonpatent literature 1).

S. Lee and C.L. T. T. et al. -C. Nguyen, “Mechanically-coupled micromechanical arrays for improved phase noise,” Proceedings, IEEE Int. Ultrasonics, Ferroelectrics, and Frequency Control 50th Anniv. Joint Conf. Montreal, Canada, Aug. 24-27, 2004, pp. 280-286

  What is common to all three types of structures is that the resistance component of the MEMS vibrator (when considered as an equivalent circuit) is large. A large resistance component means a large insertion loss (loss ratio of output signal to input signal). A device with a small insertion loss is desired.

  An object of the present invention is to provide a MEMS vibrator having a small insertion loss by minimizing the resistance component of the MEMS vibrator.

  (1) A MEMS vibrator according to the present invention includes a first electrode plate, a second electrode plate disposed opposite to the first electrode plate with a gap, and the first electrode plate. A support beam extending from the side surface of the substrate, power supply means for applying in-phase AC power to the first electrode plate and the second electrode plate, the first electrode plate and the second electrode plate Detecting means for obtaining an output corresponding to the capacitance between the electrode plate and the electrode plate. The dimension of the second electrode plate is adjusted, and the following equation is established to make the resistance component the lowest.

但し、ｌは前記第２の電極板の長さ（μｍ）；ｇは前記第１の電極板と前記第２の電極板との空隙（ｎｍ）；Ｅは前記第２の電極板のヤング率（ＧＰａ）；ｔは前記第２の電極板の厚み（ｎｍ）；ε₀は前記第２の電極板の誘電率（Ｆ／ｍ）；Ｖ_DCは前記第２の電極板にかかるＤＣバイアス電圧（Ｖ）：である。本発明によれば、第２の電極板の寸法を調整することにより、第２の電極板が第１の電極板と接触することなくＭＥＭＳ振動子の抵抗成分が最も低くなるように第２の電極板の形状の寸法を調整できる（具体的には長さを最適な値にすることにより抵抗成分を下げる）。したがって、上記の設計方法を用いることでＭＥＭＳ振動子の抵抗成分を下げられ、抵抗成分が下がることによって振動子として用いたとき素子の挿入損失の小さいＭＥＭＳ振動子ができる。

Where l is the length of the second electrode plate (μm); g is the gap (nm) between the first electrode plate and the second electrode plate; E is the Young's modulus of the second electrode plate (GPa); t is the thickness (nm) of the second electrode plate; ε ₀ is the dielectric constant (F / m) of the second electrode plate; _VDC is the DC bias voltage applied to the second electrode plate (V): According to the present invention, by adjusting the dimensions of the second electrode plate, the second electrode plate does not come into contact with the first electrode plate so that the resistance component of the MEMS vibrator is minimized. The shape dimension of the electrode plate can be adjusted (specifically, the resistance component is lowered by setting the length to an optimum value). Therefore, by using the above-described design method, the resistance component of the MEMS vibrator can be lowered, and a MEMS vibrator having a small insertion loss of an element when used as a vibrator can be obtained by reducing the resistance component.

  (2) In this MEMS vibrator, the drive unit may have a cantilever structure. This makes the structure easier to process. Further, it can be driven at a lower voltage than the both-end support structure.

  Embodiments to which the present invention is applied will be described below with reference to the drawings.

  FIG. 1 is a diagram showing a cantilever structure of a MEMS vibrator according to an embodiment of the present invention. FIG. 2 is a diagram showing an equivalent circuit of the MEMS vibrator according to the embodiment of the present invention. As shown in FIG. 1, the MEMS vibrator according to the present embodiment includes a lower electrode 10 as a first electrode plate, a vibrating body 12 as a second electrode plate, a support beam 14, and power supply means. Power supply circuit 16 and an output circuit 18 as detection means.

  The MEMS vibrator according to this embodiment has, as a basic configuration, a lower electrode 10 formed on the surface of a substrate (not shown) and a rectangular shape that is opposed to the lower electrode 10 with a gap g. And the vibrating body 12.

The lower electrode 10 is formed on a plane of a substrate (not shown), that is, on a surface having at least an insulating property. The lower electrode 10 is formed on an upper surface of an insulating layer made of silicon oxide (SiO ₂ ), for example, on the surface of a silicon substrate. The lower electrode 10 can be formed of, for example, a polycrystalline silicon film or a metal film such as aluminum (Al). As the substrate (not shown), for example, a substrate in which an insulating film is formed on a semiconductor substrate such as silicon (Si) or gallium arsenide (GaAs), or an insulating substrate such as a quartz substrate or a glass substrate is used.

  The vibrating body 12 is disposed to face the lower electrode 10 with a gap g. The vibrating body 12 adjusts the dimension of the vibrating body 12 and makes the resistance component the lowest by satisfying the following equation.

但し、ｌは振動体１２の長さ（μｍ）；ｇは下部電極１０と振動体１２との空隙（ｎｍ）；Ｅは振動体１２のヤング率（ＧＰａ）；ｔは振動体１２の厚み（ｎｍ）；ε₀は振動体１２の誘電率（Ｆ／ｍ）；Ｖ_DCは振動体１２にかかるＤＣバイアス電圧（Ｖ）：である。振動体１２は、支持梁１４で一体に支持されている。振動体１２は、例えば、多結晶シリコン膜、アルミニウム（Ａｌ）などの金属膜にて形成することができる。

Where l is the length (μm) of the vibrating body 12; g is the gap (nm) between the lower electrode 10 and the vibrating body 12; E is the Young's modulus (GPa) of the vibrating body 12; t is the thickness of the vibrating body 12 ( nm); ε ₀ is a dielectric constant (F / m) of the vibrating body 12; _VDC is a DC bias voltage (V) applied to the vibrating body 12; The vibrating body 12 is integrally supported by the support beam 14. The vibrating body 12 can be formed of a metal film such as a polycrystalline silicon film or aluminum (Al), for example.

  The support beam 14 extends from the side surface of the vibrating body 12. The support beam 14 may have a cantilever (cantilever) structure. This makes the structure easier to process. Further, it can be driven at a lower voltage than the both-end support structure.

The power feeding circuit 16 applies in-phase AC power to the lower electrode 10 and the vibrating body 12. The power supply circuit 16 is provided with an AC power source V _AC and a supply line 26 that connects the _AC power source V _AC and an electrode layer (not shown) formed on the lower electrode 10. The power supply circuit 16 is monolithically configured inside the substrate, but may be configured separately from the substrate, or may form only a wiring structure for supplying AC power from the outside.

The output circuit 18 obtains an output corresponding to the capacitance between the lower electrode 10 and the vibrating body 12. The output circuit 18 obtains an output signal (detection signal) corresponding to the stretching vibration of the vibrating body 12 from the electrode layer 24 on the lower surface of the support beam 14 via the output line 20. The output circuit 18 is composed of a DC bias voltage V _DC and the inductance L _t which is connected between the output potential of the output line 20, the output potential and the connected capacitance C _t between the ground potential Yes.

  A support portion 22 connected to the substrate is formed at the end of the support beam 14, and a gap g is provided between the lower electrode 10 and the lower portion of the vibration body 12, and the vertical direction (the thickness t direction of the vibration body 12) In FIG. 1, it is a shape capable of stretching vibration in the vertical direction). An electrode layer 24 is formed on the lower surface of the vibrating body 12 and the support beam 14, and is connected to the output circuit 18 via the output line 20.

The MEMS vibrator of the present embodiment has a structure that detects and outputs a change in capacitance generated between the vibrating body 12 and the lower electrode 10 when the vibrating body 12 bends and vibrates in the vertical direction. The capacitance is inversely proportional to the square of the gap g between the vibrating body 12 and the lower electrode 10 facing each other, and is proportional to the electrode crossing area A. In addition, vibration in a mode in which the vibration body 12 and the lower electrode 10 are bent in a vertical direction in a plane is generated, and the distance of the gap g is changed according to the stretching vibration, whereby the vibration body 12 and the lower electrode are changed. The capacitance between 10 increases and decreases. Increase or decrease of the capacitance is outputted to the output terminal t ₂ as an output current i _O generated in the output circuit 18. Further, the bending vibration of the vibrating body 12 is a vertical vibration accompanied by a change in the shape of the rectangular vibrating body 12, and is caused by an electrostatic force between the vibrating body 12 and the lower electrode 10. In this vibration mode, the vibrating body 12 has a natural vibration frequency determined by its planar shape, thickness, density of constituent materials, and elastic characteristics (for example, Young's modulus, Poisson's ratio, etc.).

In the MEMS vibrator according to the present embodiment, as shown in FIG. 2, the resonance phenomenon of the MEMS vibrator can be replaced with an equivalent circuit. That is, between the input terminal t ₁ and the output terminal t ₂ , a series circuit of a resistor R _X , an inductance L _X, and a capacitor C _X constituting a resonance system and a parasitic capacitance C ₀ due to a gap between input and output electrodes are inserted in parallel. Is done.

The operation of the MEMS vibrator according to the present embodiment is as follows. As shown in FIG. 1, a required DC bias voltage V _DC is applied to the vibrating body 12. The AC power source V _AC is input to the lower electrode 10 through the input terminal t ₁ . When the AC power supply V _AC of target frequency is input, an electrostatic force generated between the vibrator 12 and the lower electrode 10, the vibrating body 12 in the secondary vibration mode resonates. The output current i _O of target frequency from the supporting beams 14 at the resonance of the vibrating body 12 through the output terminal t ₂ is output. When the signal of the other frequency is input without resonance vibrator 12, the signal is not output from the output terminal t _2.

As shown in FIG. 2, when the MEMS vibrator is considered as an equivalent circuit, a resistance value R _X as a resistance component can be expressed by Equation 3.

但し、Ｖ_ACは交流電圧（Ｖ）；ｉは抵抗値Ｒ_Xを流れる電流（μＡ）：である。

Where V _AC is an alternating voltage (V); i is a current (μA) flowing through the resistance value R _X :

From Non-Patent Document 1, the output current i _O (see FIG. 1) output from the MEMS vibrator can be expressed by Equation 4.

但し、Ｖ_DCはＤＣバイアス電圧（Ｖ）；δＣ／δｘは空隙ｇの変位あたりの容量変化；δｘ／δｔは振動体１２が駆動しているときの速度変化；ω₀は角周波数（＝２πｆ）：である。

Where _VDC is a DC bias voltage (V); δC / δx is a capacity change per displacement of the gap g; δx / δt is a speed change when the vibrating body 12 is driven; ω ₀ is an angular frequency (= 2πf) ):

  δC / δx is a change in capacity per displacement of the gap g, and can be expressed by Equation 5.

但し、ε₀は前記第１の電極板の誘電率（Ｆ／ｍ）；Ａは下部電極１０−振動体１２の電極交差面積；ｇ₀は前記第１の電極板と前記第２の電極板との初期空隙（ｎｍ）：である。

Where ε ₀ is the dielectric constant (F / m) of the first electrode plate; A is the electrode crossing area of the lower electrode 10 and the vibrating body 12; g ₀ is the first electrode plate and the second electrode plate. And initial gap (nm):

The entire resistance component of the MEMS vibrator is only the resistance value R _X because it is resonant when the inductance L _X and the impedance C _{X of the} capacitor are equal (ωL = 1 / ωC). By substituting Equations 4 and 5 into Equation 3, the resistance value R _X can be expressed by Equation 6.

但し、ｋ_rは振動体１２のばね定数（Ｎ／ｍｍ）；ω₀（＝２πｆ）は角周波数；Ｑは振動体１２のＱ値；Ｖ_DCはＤＣバイアス電圧（Ｖ）；ｇは下部電極１０−振動体１２間の空隙（ｎｍ）；ε₀は振動体１２の誘電率（Ｆ／ｍ）；Ａは下部電極１０−振動体１２の電極交差面積：である。

Where k _r is the spring constant (N / mm) of the vibrating body 12; ω ₀ (= 2πf) is the angular frequency; Q is the Q value of the vibrating body 12; V _DC is the DC bias voltage (V); 10 is a gap (nm) between the vibrating body 12; ε ₀ is a dielectric constant (F / m) of the vibrating body 12, and A is an electrode crossing area of the lower electrode 10 and the vibrating body 12.

As a method of decreasing the resistance value R _X , 1. The gap g between the lower electrode 10 and the vibrating body 12 is narrowed (the gap g is reduced). 2. The voltage applied to the vibrating body 12 is increased (DC bias voltage V _DC is increased). 3. A plurality of vibrators are simultaneously driven at the same frequency (resistors are arranged in parallel). Can be considered. Among these, 3. This method is effective as a method for reducing the resistance value without changing the shapes of the vibrating body and the electrode.

FIG. 3 is a diagram illustrating a case where (A) a plurality of driving units are driven at the same frequency and (B) the frequency is shifted by 0.01% in the MEMS vibrator. However, as shown in FIG. 3, it is difficult to realize a plurality of vibrators simultaneously driven at the same frequency because a highly accurate process is required. On the other hand, And 2. The method of 3. Unlike the method of reducing the resistance value of the MEMS vibrator alone, the gap g and the DC bias voltage _VDC are increased, so that the lower electrode 10 and the vibrator 12 are easily brought into contact with each other (Pull-in). There's a problem. Therefore, if the relationship between the applied voltage and the shape can be clarified, the optimum shape of the MEMS vibrator can be designed, and the resistance value R _X of the MEMS vibrator can be minimized.

FIG. 1 shows a basic structure of a longitudinal bending vibration type cantilever. As shown in FIG. 1, there are five elements that affect the resistance value R _X: width w, length l, thickness t, electrode crossing area A, and gap g. Although FIG. 1 shows a structure that moves in the vertical direction as an example, the structure that moves in the horizontal direction is not different from the vertical movement.

FIG. 4 is a diagram showing the relationship between the resistance value and the length of the MEMS vibrator according to the embodiment of the present invention. (Void 100 nm, beam thickness 100 nm, beam width 1 μm, applied voltage 20 V) FIG. 4 shows the relationship between resistance value R _X and beam length when the gap is 100 nm, beam width 1 μm, and beam thickness 1 μm. As shown in FIG. 4, the resistance value R _X initially decreases as the beam length increases, but the resistance value R _X increases from a certain length in inverse proportion to the beam length. This is because the longer the beam, the less rigid the needle and the smaller the applied voltage. Therefore, it can be seen that the resistance of the MEMS vibrator is minimized when the length, width w, and thickness t of a specific beam are provided.

Consider the maximum displacement of the MEMS vibrator in a static state. When the spring constant of the MEMS vibrator is set to k, the restoring force F _{S of the} spring can be expressed by Equation 7.

また、ＭＥＭＳ振動子は静電引力Ｆ_elで駆動される。静電引力Ｆ_elはバネの復元力Ｆ_sと反対方向に働くので符号はバネの復元力Ｆ_sに対して逆（ここでは負）になり数８として表すことができる。

Further, the MEMS vibrator is driven by an electrostatic attractive force _Fel . The electrostatic attractive force F _el the code so acts in a direction opposite to the restoring force F _s of the spring can be expressed as the number becomes 8 (negative in this case) opposite to that restoring force F _s of the spring.

但し、Ｖ_DCは前記第１の電極板にかかるＤＣバイアス電圧（Ｖ）；ε₀は前記第１の電極板の誘電率（Ｆ／ｍ）；Ａは下部電極１０−振動体１２の電極交差面積；ｇは前記第１の電極板と前記第２の電極板との空隙（ｎｍ）：である。

Where _VDC is a DC bias voltage (V) applied to the first electrode plate; ε ₀ is a dielectric constant (F / m) of the first electrode plate; A is an electrode intersection of the lower electrode 10 and the vibrating body 12 Area; g is a gap (nm) between the first electrode plate and the second electrode plate.

Next, consider the case where the MEMS vibrator is displaced to the maximum. Here, the initial capacity is assumed to be 3 μm. The state of maximum displacement is 1. 1. Give as much DC bias voltage V _DC as possible. Restoring force of the spring F _s and the electrostatic attractive force F _el is equal. For example, consider the displacement when the voltage V1 is applied to the DC bias voltage V _DC (the electrostatic attractive force F _el 1 at this time). Then, it becomes like FIG.

FIG. 5 is a diagram showing the relationship between the restoring force F _s of the spring and the electrostatic attractive force F _el 1 when the voltage V1 is applied to the DC bias voltage V _DC of the MEMS vibrator according to the embodiment of the present invention. A black spot 28 shown in FIG. 5 is a place where the restoring force F _{s of the} spring and the electrostatic attractive force F _el 1 are balanced. Beyond that, the spring restoring force F _s is larger, so there is no displacement. Next, consider a case where a voltage (V2 <V3 <V4) greater than V1 is applied. The results are shown in FIG.

FIG. 6 is a diagram showing the relationship between the restoring force F _s of the spring and the electrostatic attractive force when each voltage is applied to the MEMS vibrator according to the embodiment of the present invention. As shown in FIG. 6, when the voltage V3 is applied to the DC bias voltage V _DC (when the electrostatic attractive force F _el 3), it is found that the maximum displacement 30 is the maximum displacement. When given a voltage V4 to the DC bias voltage V _DC (electrostatic attraction F _el 4) is vibrator 12 immediately for electrostatic attraction is greater than the restoring force F _s of the spring is attracted to the lower electrode 10. From this, the relationship of maximum displacement is 1. 1. When the slope of the electrostatic attractive force F _el (differentiated from Equation 8) and the slope of the spring restoring force F _s (differentiated from Equation 7) are equal. It can be seen that the electrostatic attractive force F _el and the spring restoring force F _s are equal to each other. When this is expressed as an equation, it can be expressed by equation (9).

数９を計算すると数１０が求まる。

When Equation 9 is calculated, Equation 10 is obtained.

数１０の関係式を解くと、数１１が求まる。

When the relational expression of Expression 10 is solved, Expression 11 is obtained.

以上のことから最大変位は初期空隙ｇ₀から１ｇ₀／３変位したところであることがわかる。よって、数７、数８に最大変位量ｘ＝１ｇ／３を代入するとＤＣバイアス電圧Ｖ_DCの最大電圧が数１２で求まる。

Maximum displacement is found to be the place from the initial gap g ₀ and 1 g _0/3 displaced from the above. Therefore, when the maximum displacement amount x = 1 g / 3 is substituted into Equations 7 and 8, the maximum voltage of the DC bias voltage V _DC is obtained by Equation 12.

片持ち梁のばね定数ｋ_rは、数１３で表すことができる。

The spring constant k _r of the cantilever can be represented by the number 13.

但し、Ｅは振動体１２のヤング率；ｔは前記第１の電極板の厚み（μｍ）；ｗは前記第１の電極板の幅（μｍ）；ｌは前記第１の電極板の長さ（μｍ）：である。厚みｔが厚く、幅ｗが広いとばね定数は大きく、長さｌが長いとばね定数は小さくなる。

Where E is the Young's modulus of the vibrator 12, t is the thickness (μm) of the first electrode plate, w is the width (μm) of the first electrode plate, and l is the length of the first electrode plate. (Μm): When the thickness t is thick and the width w is wide, the spring constant is large, and when the length l is long, the spring constant is small.

  Therefore, the relationship between the applied voltage and the shape of the cantilever can be expressed by Equation 14.

数１４からＤＣバイアス電圧Ｖ_DCが大きいほど抵抗値Ｒ_Xは小さくなることがわかる。しかし、加電圧は構成する回路によって決定され制限があり、ＭＥＭＳ振動子はプロセスによって空隙ｇと厚みに制限がある。よって実際には振動体１２の長さｌのみが設計によって決定できる値になる。

It can be seen from Equation 14 that the resistance value R _X decreases as the DC bias voltage V _DC increases. However, the applied voltage is determined and limited by a circuit to be configured, and the MEMS vibrator is limited in the gap g and thickness depending on the process. Therefore, only the length l of the vibrating body 12 is actually a value that can be determined by design.

  From the above, Equation 14 can be expressed by Equation 15 when the length l of the vibrating body 12 is summarized.

数１５からＭＥＭＳ振動子の抵抗成分は、与えられるＤＣバイアス電圧Ｖ_DCに依存する。ＤＣバイアス電圧Ｖ_DCは、ＭＥＭＳ振動子に電荷を貯める（チャージする）のに必要であり、大きいほど駆動（振幅）に対して流れる電流が大きくなり抵抗値Ｒ_Xが下がる。つまり数１５より求められる振動体１２の長さｌがＭＥＭＳ振動子の抵抗値Ｒ_Xを最小にする値になる。

From Equation 15, the resistance component of the MEMS vibrator depends on the applied DC bias voltage V _DC . The DC bias voltage V _DC is necessary for storing (charging) electric charges in the MEMS vibrator, and as the DC bias voltage V _DC increases, the current flowing with respect to driving (amplitude) increases and the resistance value R _X decreases. That is, the length 1 of the vibrating body 12 obtained from Equation 15 is a value that minimizes the resistance value R _X of the MEMS vibrator.

FIG. 7 is a diagram showing a combination of shapes (V _DC = 20 V, E = 160 GPa) that minimizes the resistance value R _{X of the} MEMS vibrator according to the embodiment of the present invention. FIG. 7 using Equation 15 shows, as an example, the result of obtaining the length l of each vibrating body when the gap g is changed from 100 nm to 1 μm and the vibrating body thickness t is changed from 100 nm to 50 μm at a voltage of 20V.

According to this embodiment, it is possible to reduce the resistance value R _X of the MEMS resonator. When used as a vibrator (or transmitter) by decreasing the resistance value R _X, the insertion loss of the element (loss ratio of the output signal with respect to the input signal) is reduced, and a vibrator or transmitter with low current consumption can be obtained. . Further, the shape in which the resistance value R _{X of the} MEMS vibrator is lowest without contacting the lower electrode 10 and the vibrating body 12 (specifically, the resistance value is obtained by setting the length l of the vibrating body 12 to an optimum value). _Rx is reduced).

The applied voltage applied to the MEMS vibrator has a limit value depending on the circuit to be configured. Further, the MEMS shape is also limited in the gap g between the lower electrode 10 and the vibrating body 12 and the thickness t of the vibrating body 12 depending on the process. Therefore, the resistance value R _X of the MEMS vibrator can be lowered by optimally designing the length l of the vibrating body 12 that can be changed only by design. Therefore, the resistance value R _X of the MEMS vibrator can be lowered by using the above design method. Insertion loss of the device when used as oscillators (or oscillator) by the resistance R _X decreases (loss ratio of output signal to input signal) is reduced, it is less transducer or transmitter current consumption .

  In addition, since it is the above structures, the MEMS vibrator | oscillator of this embodiment can be manufactured by a normal semiconductor process including the vibrating body 12. FIG.

  In addition, this invention is not limited to embodiment mentioned above, A various deformation | transformation is possible. For example, the present invention includes configurations that are substantially the same as the configurations described in the embodiments (for example, configurations that have the same functions, methods, and results, or configurations that have the same purposes and results). In addition, the invention includes a configuration in which a non-essential part of the configuration described in the embodiment is replaced. In addition, the present invention includes a configuration that exhibits the same operational effects as the configuration described in the embodiment or a configuration that can achieve the same object. Further, the invention includes a configuration in which a known technique is added to the configuration described in the embodiment. Furthermore, the present invention includes contents that exclude any of the technical matters described in the embodiments in a limited manner. Or this invention includes the content which excluded the well-known technique limitedly from embodiment mentioned above.

It is a figure which shows the cantilever structure of the MEMS vibrator | oscillator which concerns on embodiment of this invention. It is a figure which shows the equivalent circuit of the MEMS vibrator | oscillator which concerns on embodiment of this invention. In a MEMS vibrator, (A) When a plurality of drive parts are driven at the same frequency, (B) It is a figure showing a case where a frequency has shifted 0.01%. It is the figure which showed the relationship between resistance value and length of the MEMS vibrator | oscillator which concerns on embodiment of this invention. It is a diagram showing the relationship between the restoring force F _s and the electrostatic attractive force F _el 1 of the spring when given a voltage V1 to the DC bias voltage V _DC of the MEMS resonator according to the embodiment of the present invention. It is a diagram showing the relationship between the restoring force F _s and the electrostatic attractive force of the spring when given the voltages of MEMS resonator according to the embodiment of the present invention. The combination of shape resistance R _X of the MEMS resonator according to the embodiment of the present invention is minimized _{(V DC = 20V, E =} 160GPa) is a diagram showing a.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 ... Lower electrode 12 ... Vibrating body 14 ... Supporting beam 16 ... Feeding circuit 18 ... Output circuit 20 ... Output line 22 ... Support part 24 ... Electrode layer 26 ... Supply line 28 ... Black spot 30 ... Maximum displacement.

Claims (2)

A first electrode plate;
A second electrode plate disposed opposite to the first electrode plate with a gap;
A support beam extending from a side surface of the second electrode plate;
Power supply means for applying in-phase AC power to the first electrode plate and the second electrode plate;
Detecting means for obtaining an output corresponding to a capacitance between the first electrode plate and the second electrode plate;
Including
A MEMS vibrator that adjusts the dimension of the second electrode plate and minimizes the resistance component by satisfying the following expression.

Where l is the length of the second electrode plate (μm); g is the gap (nm) between the first electrode plate and the second electrode plate; E is the Young's modulus of the second electrode plate (GPa); t is the thickness (nm) of the second electrode plate; ε ₀ is the dielectric constant (F / m) of the second electrode plate; _VDC is the DC bias voltage applied to the second electrode plate (V): The MEMS vibrator according to claim 1,
The supporting beam is a MEMS vibrator having a cantilever structure.

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