JP2007248324A - Detection sensor - Google Patents

Abstract

An object of the present invention is to provide a technique capable of increasing the sensitivity of a vibrator.
By appropriately selecting a ratio Rb / Ra between an inner diameter Rb and an outer diameter Ra of a vibrator 20, an r component (U (Ra ) Or U (Rb)), and the r component (V (Ra) or V (Rb)) of displacement in the tangential direction may be zero. When U (Ra) = 0 in the outer diameter Ra of the vibrator 20, the vibration at the outer diameter portion of the vibrator 20 is eliminated, so that the vibrator 20 is supported by the outer diameter portion by the support member 22. At this time, even if V (Ra) ≠ 0, the displacement in the tangential direction does not generate vibration at a position where sin (nθ) = 0. By holding the vibrator 20 by the support member 22 at this position, the vibrator 20 can be held without the vibration energy of the vibrator 20 being lost by the support member 22.
[Selection] Figure 2

Description

  The present invention relates to a detection sensor suitable for use in detecting the presence or absence of a substance having mass, detecting the mass of a substance, and the like.

  Advances in microfabrication technologies such as micromachine / MEMS (Micro Electro Mechanical Systems) technology have made it possible to make mechanical vibrators extremely small. As a result, the mass of the vibrator itself can be made small, so even if the mass changes due to the adhesion of extremely small substances (such as molecules or viruses) at the molecular level, the frequency and impedance characteristics fluctuate. Highly sensitive vibrators are being realized. By using such a highly sensitive vibrator, it is possible to configure a sensor or the like that can detect the presence or amount of a very small substance. In other words, because the size of the vibrator has been significantly reduced, the frequency of the vibrator has increased to the GHz level, and since Si can be used as a material, it has developed into research aimed at integration with semiconductor circuits. I am doing.

  One type of vibrator is a disk-shaped vibrator. Basic research on the mechanical vibration of disk-shaped vibrators has been conducted for a long time, and basic research on vibration modes (vibration modes) that define the vibration state of disk-shaped vibrators has already been completed. In other words, research is currently actively conducted for the purpose of applying a vibrator manufactured by micromachine / MEMS technology to an RF signal filter (see, for example, non-patent literature).

C. T.-C. Nguyen, “Vibrating RF MEMS Technology: Fuel for an Integrated Microchemical Circuit Revolution ?.” The 13th International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers `05), Korea, June 5-9, 2005

Research issues associated with the MEMS of disk-shaped vibrators include improvement of Q value for higher sensitivity, vibrator drive / detection method, characteristic control by combination of vibrators for the purpose of application to filters, etc. There are intensive studies on these.
An object of the present invention is to provide a technique capable of increasing the sensitivity of a vibrator among the technical problems as described above.

Here, in order to improve the Q value for increasing the sensitivity, it was considered that the method for holding the vibrator when using the MEMS could be improved.
The Q value, which is a parameter for evaluating the vibrator, is determined by whether the vibrator can be kept without losing vibration energy, and can be expressed by a relationship such as Expression (1).

That is, as a main cause of the loss of vibration energy of the vibrator,
1) Loss Q _air due to surrounding medium such as _air ,
2) Loss Q _TED caused by vibration and deformation of the vibrator,
3) _Loss Q _{anchor Loss} due to the holding mechanism of the vibrator,
And other loss Q _others are considered.
1) In order to reduce energy loss to the surrounding medium represented by _air, which determines the Q _air , the vibration of the vibrator is controlled so that the vibration energy of the vibrator is large but the energy transfer to the surrounding medium is not. This is dealt with by selecting fewer vibration modes. For example, a disk-shaped mechanical vibrator vibrates only in the disk in-plane direction of the vibrator (in a cylindrical coordinate, it vibrates only in the r and θ directions and does not vibrate in the Z direction), like a drum film (Z It is less likely to vibrate and move large vibrational energy to the surrounding medium.
The Q _TED of 2) is deformed by vibration of the vibrator, and adiabatic expansion or adiabatic compression occurs due to the deformation. For this reason, it is said that the adiabatic expansion region is cooled, and conversely, the region where adiabatic compression is performed becomes hot, and a temperature gradient is generated in the vibrator. In other words, this energy loss is determined by the vibration mode of the vibrator and the material of the vibrator.
Now, Q _{anchor loss of} 3) is a _loss due to the holding portion of the vibrator, and is caused by the vibration of the vibrator being transmitted to the holding portion. For example, it is considered that it is possible to eliminate energy loss by providing a holding portion in a place where the vibrator does not vibrate. However, in a normal disk-like disk-like vibrator, the most common vibrator material is a Si single crystal. As long as is used, such a condition has not been found.

  For example, the most well-known mode among the resonance modes of the disk-shaped vibrator is the wine-glass mode (2, 1). In such vibration of the disk-shaped vibrator, the radial direction displacement U (r, θ) and the tangential direction displacement V (r, θ), which are mode functions, can be expressed by the following equation (2).

In this formula (2), the Wine-Glass mode (2, 1) means that the resonance mode has the lowest frequency at n = 2, and the mode of vibration in the (2, 1) mode is Radial. In the direction, all the r components except for r = 0 of the vibrator have a finite value at r, which changes in the circumferential direction according to cos 2θ, and θ = π / 4, 3π / 4, −3π / 4. The vibration in the radial direction is eliminated at an angle of −π / 4. Such a position is called “nodal point”, and a method of holding the vibrator at the position has been proposed.
However, since this (2, 1) mode is a compound mode and there is a vibration component in the tangential direction, the r component has a finite value for all r except r = 0 even in the vibration in the tangential direction. In the circumferential direction, it changes according to sin 2θ. For this reason, at each angle of θ = π / 4, 3π / 4, -3π / 4, and −π / 4 when U (r, θ) is 0, that is, cos 2θ is 0, V (r, θ) is sin 2θ. On the other hand, since the amplitude becomes 1, -1,1, -1, the amplitude becomes maximum. That is, if a circular vibrator that vibrates in the Wine-Glass mode (2, 1) is to be held at a point where there is no radial component vibration, the circular component is held in a form that prevents the vibration of the tangential component. However, the vibrator cannot be held at a point where there is no vibration.
Therefore, as a result of intensive studies, the present inventors have come to find a technique that can eliminate both the radial component and the tangential component, unlike the above example.

  The detection sensor of the present invention thus configured detects a vibrator whose vibration characteristics change due to adhesion or adsorption of a substance having a mass, a drive unit that vibrates the vibrator, and a change in vibration in the vibrator. Thus, the vibrator has a ring shape in which the outer diameter is Ra and the inner diameter is Rb by forming an opening in the center. The displacement at the position r in the position coordinates (r, θ) when the vibrator vibrates is, as shown in the equation (3), the displacement in the radial direction is U (r), and the displacement in the tangential direction is V ( r). At this time, the vibrator is formed with an outer diameter Ra and an inner diameter Rb that substantially satisfy U (r) = 0 or V (r) = 0 when r = Ra or Rb.

  In Equation (3), A6, A7, and A8 are the outer diameter and inner diameter of the vibrator, the Young's modulus, density, and Poisson's ratio of the vibrator material, and the boundary conditions of the vibrator (in this case, the Free-Free condition). Is a constant uniquely determined according to the natural vibration mode defined by. Specifically, when A5 = 1 in equation (9) described later, A6, A7, and A8 are solutions of simultaneous linear equations of equation (9).

As described above, in the ring-shaped vibrator, vibration may not occur in the outer diameter portion or the inner diameter portion depending on the ratio of the outer diameter Ra and the inner diameter Rb. The ratio at this time varies depending on the Poisson ratio of the material forming the vibrator, the mode number n of the vibration mode when vibrating the vibrator, and the order m of the harmonic vibration.
When r = Ra in the expression (3) and U (r) = 0 or V (r) = 0 is substantially satisfied, the vibrator is supported by the outer diameter portion. In addition, when r = Rb in Equation (3) and U (r) = 0 or V (r) = 0 is substantially satisfied, the vibrator is supported by the inner diameter portion.
Furthermore, when r = Ra or Rb in Equation (3) and U (r) = 0 is substantially satisfied, the vibrator supports at a position θ where sin (nθ) = 0. In addition, when r = Ra or Rb in Expression (3) and V (r) = 0 is substantially satisfied, the vibrator is supported at a position θ where cos (nθ) = 0.
In this way, it is possible to eliminate both the radial component and the tangential component in the vibrator.
Here, in the present invention, not only the case where the condition of U (r) = 0 or V (r) = 0 is completely satisfied, but also the case where it is almost satisfied is allowed. This is because it is difficult to form a vibrator with an outer diameter Ra and an inner diameter Rb that can completely satisfy the condition of U (r) = 0 or V (r) = 0 due to manufacturing errors and the like. Further, even if the condition of U (r) = 0 or V (r) = 0 is slightly deviated, vibration may be sufficiently small in the outer diameter part or the inner diameter part.

  In such a detection sensor, a change in the vibration of the vibrator caused by the substance directly or indirectly adhering or adsorbing to the vibrator is detected, and thereby the substance is detected. In addition, the detection of the substance can detect not only the presence / absence of the substance but also the amount of the substance attached to the vibrator.

  In order to attach or adsorb a substance to the vibrator, for example, an adsorbing material that can efficiently adsorb molecules may be added to the surface of the vibrator. There are global recognition materials and selective recognition materials. A global recognition material is a polymer that adsorbs a specific molecular group, such as alcohol or ether, although the selectivity is not strong. It is also effective to increase the surface area by making these polymers into nanofibers or making them porous. Examples of highly selective recognition materials include biological materials that cause antigen-antibody reactions, acceptor-receptor combinations, probes with specific base sequences that hybridize with genes, DNA, and RNA. is there. A lipid bilayer membrane may also be used.

  In such a detection sensor, the substance to be detected can be a specific molecule or a plurality of types of molecules having specific characteristics or characteristics. Thereby, this detection sensor can be used for a gas detection sensor, an odor sensor, etc., for example. For this purpose, when a specific target molecule is a gas, a biological molecule, a living space floating molecule, a volatile molecule, etc., only a specific type of molecule is detected with high selectivity. Is desirable. In addition, by using a plurality of detection sensors with high selectivity as described above, a plurality of types of molecules can be recognized and the application range of applications can be expanded. It is also possible to detect a group of molecules having specific characteristics or a group of molecules having the same side chain, which is called global recognition. In this case, a plurality of detection sensors may be used, and molecular groups may be recognized by signal processing, processing using software, or the like based on the difference in detection ability between the plurality of detection sensors. In addition, a specific protein, enzyme, sugar chain, or the like may be detected by changing the configuration to operate in a liquid.

The detection of minute mass can also be used for bio-research such as film thickness monitoring during antibody film formation, antibody antigen reaction and protein adsorption. The detection sensor of the present invention is suitable for such applications.
The detection sensor and vibrator of the present invention can also be used for applications such as small and stable high-sensitivity home and personal gas sensors, and portable, disposable types that detect harmful substances floating in the air. It can also be used. If the sensitivity is further increased, the range of application will be further expanded, and it can be developed until “smell” can be detected and identified. It does not prevent.
Moreover, since the detection sensor of the present invention can be manufactured by the MEMS technology by using so-called Si single crystal as a structural material, it can be built in the same chip as the Si semiconductor. In that case, a very inexpensive and high-performance minute substance detection device can be obtained.

  According to the present invention, it is possible to hold a vibrator where there is no vibration component of the disk-like vibrator, and it is possible to provide a high-quality detection sensor having a high Q value.

Hereinafter, the present invention will be described in detail based on embodiments shown in the accompanying drawings.
FIG. 1 is a diagram for explaining a basic configuration of a sensor (detection sensor) 10 according to the present embodiment.
The sensor 10 shown in FIG. 1 has a disk shape, and has a circular shape, a rectangular shape, or other shape as a whole, and a vibrator 20 whose vibration frequency changes when a detection object such as a molecule having a mass is attached. A drive source 30 for vibrating the disk-shaped vibrator 20 and a detection unit 40 for detecting a change in vibration characteristics of the vibrator 20.

In the drive source 30, the vibrator 20 is vibrated using an electrostatic effect or a piezoelectric effect (piezoelectric effect) by a current generated by an external controller (not shown).
The detection unit 40 also detects vibration in the vibrator 20 by an electrostatic effect or a piezo effect and outputs it as an electrical signal. At this time, if a substance having a mass adheres to the vibrator 20, the vibration frequency of the vibrator 20 changes under the influence of the mass. By detecting the electrical vibration output from the detection unit 40, the detection unit 40 can detect whether the substance is attached to the vibrator 20 or the amount of the substance attached to the vibrator 20. It has become.

In such a sensor 10, the vibrator 20 has an opening 21 at the center thereof. And this vibrator | oscillator 20 is supported only by the support member 22 connected to the predetermined position of an outer peripheral part, and all the remaining parts are made into a free state.
Here, when the outer diameter of the vibrator 20 is Ra and the diameter of the opening 21 is Rb, the vibrator 20 has an outer diameter Ra of the vibrator 20 such that Rb / Ra substantially satisfies the following conditions. The diameter of the opening 21 (the inner diameter of the vibrator 20) Rb is preferably set.

The vibration generated in the disk-shaped vibrator 20 includes (a) a radial mode (mode that vibrates only in the radial direction (r direction)), (b) a tangential mode (a mode that vibrates only in the θ direction), and (c) compound. There are three modes (modes in which radial vibration and θ-direction vibration are combined).
The equation for determining the resonance frequency in the compound mode of the vibrator 20 is as shown in the following equation (4).

_However, a 11 _{~a 44} is as follows.

  Here, σ is the Poisson's ratio of the vibrator material, E is the Young's modulus of the vibrator material, ρ is the density of the vibrator material, and ω is the angular frequency (= 2πf).

  Now, at the two boundaries in the vibrator 20 having the opening 21, that is, the outer diameter and the inner diameter portion, because of the Free-Free condition, the residual stress in the radial direction and the residual stress in the tangential direction are eliminated. It can be seen that two boundary conditions are determined. Further, the radial direction displacement U (r, θ) and the tangential direction displacement V (r, θ), which are mode functions, can be expressed by the following equations.

  Then, the following relational expression is obtained by applying the above-described four boundary conditions to the expression (6).

  Furthermore, the equation for determining the resonance frequency in Equation (3) means that Equation (7) holds for any A5, A6, A7, and A8, and this means that the Determinant = 0 of the 4 × 4 matrix in Equation (7) is It becomes a condition. This is equation (3) that determines the resonant frequency.

  Now, the coefficients A5, A6, A7, and A8 of the equation (6), which is a mode function, are not yet determined. If this is not determined, the vibration state of the vibrator 20 is not determined. Further, since the equation (7) is established for any A5, A6, A7, and A8 under the resonance condition, the coefficients A5, A6, A7, and A8 at the time of resonance are undecided and cannot be determined as they are. However, if the matrix of the equation (7) is decomposed into a linear equation, the following equation (8) is obtained.

  From the four linear equations of the equation (8) thus determined, any three equations are taken and, as a ratio to any one of the coefficients A5, A6, A7, A8, A coefficient can be defined. For example, taking the above three equations from equation (8) and dividing them all by A5, a simultaneous linear equation such as the following equation (9) is obtained.

From this equation (9), the coefficient ratios A6 / A5, A7 / A5, A8 / A5 with A5 as the denominator can be obtained. By substituting this result into equation (6), the displacement in the radial direction and the tangential direction at the time of resonance, that is, all the mode functions can be determined. Although the above three equations are used here, they can be similarly solved using any three different equations, and four different linear equations are obtained here. All the results are the same.
In addition, since all are proportional to A5, there is essentially no change in the mode function even if A5 = 1, so that A5 = 1 again and the r component in the radial direction in each mode is U (r), Tangential. If the r component in the direction is expressed as V (r), the mode function of Expression (6) is expressed by the following Expression (10).

  Here, U (r) and V (r) are as shown in the following equation (11).

This analysis is for a circular disk-shaped vibrator 20 having an opening 21, unlike a normal disk-shaped vibrator. In this vibrator 20, U (r) and V (r) shown in Expression (11) vary greatly depending on the ratio of the outer diameter Ra and the inner diameter Rb of the vibrator 20, and the vibrator 20 outer diameter Ra and inner diameter Rb are changed. It is possible that U (r) or V (r) becomes zero when the ratio of becomes a specific value.
For example, when U (Ra) = 0 at the outer diameter Ra of the vibrator 20, vibration at the outer diameter portion of the vibrator 20 is eliminated. Therefore, the vibrator 20 is supported at the outer diameter portion by the support member 22.
At this time, even if V (Ra) ≠ 0, the displacement in the tangential direction is obtained by multiplying sin (nθ) by this, as shown in Expression (10), so sin (nθ) = 0. At the position, no vibration occurs at V (r, θ) in the equation (10). In the vibration mode of n = 1, if the vibrator 20 is held by the support member 22 at the positions of V (Ra, 0) and V (Ra, π), the vibration energy of the vibrator 20 is lost through the support member 22. There is nothing to be done.
Conversely, when V (Ra) = 0, even if U (Ra) ≠ 0, the displacement in the radial direction is obtained by multiplying this by cos (nθ), so that cos (nθ) = 0. Thus, the vibrator 20 may be held.
Here, the holding method at the outer diameter of the perforated disk-shaped vibrator 20 has been described, but even if this is held at the inner diameter, the position can be determined in the same way.

2 to 4 show the variation of the r component in each vibration mode from n = 1 to n = 3, that is, the variation of U (r) and V (r) shown in Equation (11), with the inner diameter Rb. The ratio Rb / Ra of the outer diameter Ra is shown on the horizontal axis. At this time, a Si single crystal was assumed as the material of the vibrator 20, and the Poisson's ratio was set to σ = 0.28. Further, n represents the number of vibration modes, and m represents the order of harmonic vibration.
2 to 4, the lowest resonance frequency (m = 1) to the fourth resonance frequency (m = 4) are shown in each mode, and this is expressed as (n, m) according to the normal mode expression. ing.

2 to 4, U (Ra), U (Rb), and V (Ra) except for the (2,1) mode in FIG. 3A and the (3,1) mode in FIG. ) And V (Rb) are observed to be zero at the appropriate Rb / Ra.
For example, in the (1,2) mode shown in FIG. 2B, it is shown that V (Ra) is 0 when Rb / Ra = 0.17. Accordingly, in order to design the vibrator 20 used in the (1,2) mode using a material having a Poisson's ratio of 0.28 (for example, single crystal Si), the ratio of the inner diameter Rb to the outer diameter Ra is selected to be 0.17, If the vibrator 20 is designed to be held at the inner diameter portion at the position of cos θ = 0, that is, θ = ± π / 2, the vibrator 20 can be held without affecting the resonance vibration of the vibrator 20 at all. Is possible.

  That is, in the case of the vibrator 20 used in the (1,2) mode with an outer diameter of 100 μm, when Rb / Ra = 0.17 and the diameter of the opening 21 is 17 μm, the outer diameter of the vibrator 20 The vibration in the tangential direction in the portion can be set to zero. At this time, the resonator 20 is supported at the outer diameter portion of the opening 21 at an angle of cos θ = 0, that is, at a position of θ = ± π / 2, so that the resonator does not affect the resonance vibration at all. 20 retention methods can be realized.

  By the way, in a general material, for example, a material having a Poisson's ratio of σ = 0 to σ = 0.5, when U (Ra), U (Rb), V (Ra) and V (Rb) are 0, any It is very important to investigate what happens in the case of Rb / Ra. For this reason, the combination of Rb / Ra and the Poisson's ratio σ, in which the following expression (12) holds, was examined for each mode (n = 1 to 3, m = 1 to 4) from the expression (11).

The results are shown in FIGS.

The reason that all the materials were examined by using only the Poisson's ratio as a variable is that h and k are obtained from equation (6).
k = h (2 / (1-σ)) ^1/2
When h and k are viewed as variables, these two variables are related only by the Poisson's ratio σ.

  5 to 7, the Poisson's ratio σ (vertical axis) that satisfies Expression (12) in each mode of n = 1 to 3 and m = 1 to 4 and the ratio of the inner diameter Rb and the outer diameter Ra of the vibrator 20. The relationship with Rb / Ra (horizontal axis) is shown. That is, if the Poisson's ratio of the vibrator material is known, the vibration mode and the position where the vibrator 20 is held and the ratio between the inner diameter Rb and the outer diameter Ra of the vibrator 20 can be determined from the relationship shown in FIGS. . The resonance frequency is determined by changing the vibrator 20, for example, the size, that is, the outer diameter Ra.

  As described above, by knowing the relationships in FIGS. 5 to 7 in advance, it is possible to realize a high-performance disk-shaped vibrator 20 in which vibration energy does not escape through the holding portion.

Now, the support member 22, the case of the vibrator 20 to be used to vibrate the Tangential direction, preferably to have a length _{L R} represented by the following formula (13). When the driving method using the piezo effect is adopted in the driving source 30, the vibrator 20 is used by vibrating in the tangential direction. In this case, the length of the support member 22 is expressed by the equation (13). It is preferable to make it _LR represented by these.

In the case of the vibrator 20 that is vibrated in the radial direction, the support member 22 preferably has a length L _S represented by the following formula (14).

  As described above, by appropriately selecting the ratio Rb / Ra between the inner diameter Rb and the outer diameter Ra of the vibrator 20, the r component of the radial displacement at the outer diameter part or the inner diameter part of the vibrator 20, that is, U (Ra). Alternatively, U (Rb) and the r component of displacement in the tangential direction, that is, V (Ra) or V (Rb) may be zero. By using a phenomenon peculiar to the vibrator 20 having the disc-like opening 21 as described above, it becomes possible to hold the vibrator 20 without affecting the resonance vibration of the vibrator 20 at all. A high vibrator 20 can be provided. Thereby, in the sensor 10, it becomes possible to detect an object with high sensitivity and to detect mass. Further, since the vibrator 20 can be manufactured by a MEMS technology using so-called Si single crystal as a structural material, the sensor 10 can also be built in the same chip as the Si semiconductor.

In the above description, the example of the vibrator 20 using the Si single crystal (Poisson's ratio σ = 0.28) as the vibrator material has been described. Of course, other materials can be similarly examined. The outer diameter Ra of the vibrator 20, the inner diameter Rb of the opening 21, and the support position by the support member 22 can be selected.
In addition to this, as long as it does not depart from the gist of the present invention, the configuration described in the above embodiment can be selected or changed to another configuration as appropriate.

It is a figure which shows the structure of the sensor of this Embodiment. It is a figure which shows the relationship between the ratio of the outer diameter of a disc-shaped vibrator | oscillator in a n = 1 mode, and the value of U (Ra), U (Rb), V (Ra), and V (Rb). It is a figure which shows the relationship between the ratio of the outer diameter of a disk-shaped vibrator | oscillator in a n = 2 mode, and the value of U (Ra), U (Rb), V (Ra), and V (Rb). It is a figure which shows the relationship between the ratio of the outer diameter of a disk-shaped vibrator | oscillator in a n = 3 mode, and the value of U (Ra), U (Rb), V (Ra), and V (Rb). It is a figure which shows the relationship between the ratio of the outer diameter of a disc-shaped vibrator | oscillator and internal diameter, and Poisson's ratio when Formula (12) is materialized in n = 1 mode. It is a figure which shows the relationship between the ratio of the outer diameter of a disc-shaped vibrator | oscillator and internal diameter, and Poisson's ratio when Formula (12) is materialized in n = 2 mode. It is a figure which shows the relationship between the ratio of the outer diameter of a disc-shaped vibrator | oscillator and internal diameter, and Poisson's ratio when Formula (12) is materialized in n = 3 mode.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 ... Sensor (detection sensor), 20 ... Vibrator, 21 ... Opening part, 22 ... Support member, 40 ... Detection part

Claims (7)

A disk-shaped vibrator whose vibration characteristics change due to the attachment or adsorption of a substance having a mass;
A drive unit for vibrating the vibrator;
A detection unit for detecting the substance by detecting a change in vibration in the vibrator, and
The vibrator has a ring shape in which the outer diameter is Ra and the inner diameter is Rb by forming an opening in the center.
The displacement U (r) in the radial direction and the displacement V (r) in the tangential direction represented by Expression (1) at the position r in the position coordinates (r, θ) when the vibrator vibrates are r = A detection sensor, wherein the vibrator is formed with an outer diameter Ra and an inner diameter Rb that substantially satisfy U (r) = 0 or V (r) = 0 when Ra or Rb is set.

  In the formula (1), when r = Ra, if U (r) = 0 or V (r) = 0 is substantially satisfied, the vibrator is supported by an outer diameter portion. Item 2. The detection sensor according to Item 1.   The vibrator is supported by an inner diameter portion when substantially satisfying U (r) = 0 or V (r) = 0 when r = Rb in the formula (1). The detection sensor according to 1.   In the formula (1), when r = Ra or Rb and U (r) = 0 is substantially satisfied, the vibrator is supported at a position θ where sin (nθ) = 0. The detection sensor according to claim 2 or 3.   In the formula (1), when r = Ra or Rb and V (r) = 0 is substantially satisfied, the vibrator is supported at a position θ where cos (nθ) = 0. The detection sensor according to claim 2 or 3.   The detection sensor according to claim 1, wherein the detection unit detects an amount of the substance attached to the vibrator.   The detection sensor according to claim 1, wherein the substance is a specific molecule or a plurality of types of molecules having specific characteristics or characteristics.

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