Method and system for analyzing vibration characteristics of FBAR mass sensor

Abstract

The invention provides an FBAR mass sensor vibration characteristic analysis method. The method comprises the following steps: simplifying a piezoelectric linear equation set; according to the displacement solution hypothesis and the potential solution of the pure shear state, the resonant frequency of the device in the pure shear state and the wave number of sound waves in each physical layer are solved; setting a new displacement solution according to a thickness stretching and thickness shearing coupling condition closer to an actual working condition, and establishing an increment relationship between a wave number and a pure shearing wave number in the state; updating the specific form of the displacement solution of each physical layer according to the result of the previous step, and obtaining a frequency control matrix equation by combining the boundary condition and the continuity condition; and performing mathematical processing simplification on the matrix equation to obtain a partial differential equation capable of representing the displacement in the water surface of the sensor, and solving to obtain the vibration mode of the sensor. According to the embodiment, the analysis efficiency can be greatly improved under the condition that enough precision is guaranteed, and theoretical support is provided for homogenization optimization design of vibration displacement of the FBAR micro-mass sensor.

Description

Technical Field

[0001] The present invention relates to the technical field of piezoelectric acoustic wave devices, and in particular to a method and system for analyzing vibration characteristics of an FBAR mass sensor. Background Art

[0002] In recent years, environmental monitoring, clinical diagnosis, process control and anti-terrorism have put forward more and more urgent demands for miniaturized, intelligent and high-performance sensor devices. In addition to high sensitivity in theory, sensor devices designed and manufactured based on film bulk acoustic resonator (FBAR) have many advantages such as fast response speed, small size, easy integration and array, and have broad application prospects.

[0003] FBAR devices generally use longitudinal wave mode or shear wave mode. Generally speaking, the longitudinal wave mode has the highest cutoff frequency, which makes longitudinal wave mode FBAR widely used in RF devices such as filters, duplexers, and oscillators in modern communication systems. Since the energy dissipated into the liquid by the shear mode vibration is much less than that of the longitudinal wave form in a liquid environment, the FBAR working in the shear vibration mode has become a hot topic in the research of FBAR sensors. The main structure of the piezoelectric oscillation stack of the film bulk acoustic wave resonator is usually composed of a piezoelectric film and a support layer between electrodes. The commonly used materials of the piezoelectric film are zinc oxide (ZnO), aluminum nitride (AlN), lithium niobate (LiNbO3) and other compounds with piezoelectric effect. Similar to the situation that the vibration mode of a quartz crystal resonator depends on the wafer cut type, piezoelectric films with different c-axis orientations will cause different vibration modes excited by FBAR. Taking zinc oxide film as an example, when the c-axis angle is 42° or 90°, a pure thickness shear mode can be excited in theory.

[0004] FBAR sensors are considered to be the continuation and development of the quartz crystal microbalance (QCM). Tiersten and other scholars have used the methods in QCM to derive two-dimensional scalar differential equations suitable for early FBAR devices. However, with the advancement of MEMS and other technologies, the early scalar differential equations have the following main problems: in the early equations, since the thickness of the electrode layer is much smaller than that of the piezoelectric layer, the electrode layer is ignored, and only the piezoelectric layer and the support layer are regarded as the sound wave propagation layer; in the early equations, the influence of electrical boundary conditions is not considered, which is bound to cause errors.

[0005] The circular electrode is the most widely used electrode form in existing FBAR devices. The physical properties of zinc oxide piezoelectric film with a c-axis of 90° are anisotropic, which leads to different propagation and attenuation speeds of sound waves in different directions. From the energy distribution point of view, the vibration energy decays to zero at different speeds from the center of the electrode to the surrounding areas, and its cloud shape is quite different from the circular electrode itself. When the target molecules or micelles are adsorbed on the FBAR surface, due to the uneven distribution of vibration energy, different adsorption positions will lead to different or fluctuating responses, which is one of the obstacles to achieving high-precision sensing. On the other hand, most of the existing FBAR sensor designs ignore the current situation of uneven energy distribution, which limits the detection precision and accuracy.

[0006] The microstructure of FBAR plays a huge role in improving its performance, among which the frame structure is the most important microstructure. There are two types of frame structures: raised frame and recessed frame. The first one was proposed and implemented by Japanese engineer Kaitila in 2003. Existing studies have shown that the raised structure can increase the impedance mismatch between the FBAR transverse sound wave energy and the air interface, enhance reflection, and reduce the leakage of sound energy. Summary of the invention

[0007] The present invention provides an analysis method and system for the vibration characteristics of FBAR mass sensors, improves the original two-dimensional scalar differential equation to make it more consistent with the structural characteristics of modern FBAR devices, greatly improves the analysis efficiency while ensuring sufficient accuracy, and provides theoretical support for the uniform optimization design of the vibration displacement of FBAR micro-mass sensors.

[0008] This specification discloses a method for analyzing vibration characteristics of a FBAR mass sensor, comprising:

[0009] S1. Simplified elastic mechanics equations of piezoelectric film layer for zinc oxide film at c-axis level;

[0010] S2. Based on the elastic mechanics equations, according to the displacement solution assumption and potential solution of the pure shear state, the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer are solved;

[0011] S3, based on the resonant frequency and the wave number of the acoustic wave in each physical layer, a new displacement solution is set according to the coupling of thickness stretching and thickness shear, and an incremental relationship between the wave number in this state and the pure shear wave number is established;

[0012] S4. According to the incremental relationship between the wave number and the pure shear wave number, the specific form, simultaneous boundary conditions and continuity conditions of the displacement solutions of each physical layer are updated to obtain the frequency control matrix equation;

[0013] S5. The frequency control matrix equation is mathematically processed and simplified to obtain a partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the partial differential equation.

[0014] In this specification, in S1:

[0015] For an arbitrary piezoelectric elastic body, it satisfies the governing equation:

[0016]

[0017] The constitutive equation is:

[0018] T 11 =c 11 u 1,1 +c 12 u 1,2 +c 13 u 3,3 +c 14 (u 2,3 +u 3,2 )+e 11 φ ,1 ,

[0019] T 22 =c 12 u 1,1 +c 22 u 2,2 +c 23 u 3,3 +c 24 (u 2,3 +u 3,2 )+e 12 φ ,1 ,

[0020] T 33 =c 13 u 1,1 +c 23 u 2,2 +c 33 u 3,3 +c 34 (u 2,3 +u 3,2 )+e 13 φ ,1 ,

[0021] T 23 =c 14 u 1,1 +c 24 u 2,2 +c 34 u 3,3 +c 44 (u 2,3 +u 3,2)+e 14 φ ,1 ,

[0022] T 13 =c 55 (in 3,1 +in 1,3 )+c 56 (in 1,2 +in 2,1 )+e 25 φ ,2 +e 35 φ ,3 ,

[0023] T 12 =c 56 (in 3,1 +in 1,3 )+c 66 (in 1,2 +in 2,1 )+e 26 φ ,2 +e 36 φ ,3 ,

[0024] D1=e 11 in 1,1 +e 12 in 2,2 +e 13 in 3,3 +e 14 (in 2,3 +in 3,2 )-ε 11 φ ,1 ,

[0025] D2=e 25 (in 3,1 +in 1,3 )+e 26 (in 1,2 +in 2,1 )-ε 22 φ ,2 -ε 23 φ ,3 ,

[0026] D3=e 35 (in 3,1 +in 1,3 )+e 36 (in 1,2 +in 2,1 )-ε 23 φ ,2 -ε 33 φ ,3 .;

[0027] Where T is the stress tensor, ρ is the density, u is the displacement, D is the electric displacement, c is the elastic constant, φ is the electric potential, e is the piezoelectric constant, ε is the dielectric constant, the comma in the subscript of the equation represents the derivative of the coordinates that follow it, and the double dot symbol on the displacement u represents the second-order derivative with respect to time.

[0028] In this specification, in S1:

[0029] The piezoelectric film is zinc oxide with a c-axis horizontal to provide a pure thickness shear vibration mode;

[0030] Ignore the in-plane electric displacement components D1 and D2;

[0031] Ignore the changes of electric potential φ and electric displacement D along the x1-x2 plane (or horizontal plane);

[0032] Considering the piezoelectric material as a weak coupling material, the coupling with the thickness direction u3 is ignored;

[0033] Ignore high-order small quantities u 3,11 、u 3,22 、u 3,12 and the field variables in the x2 direction.

[0034] After the above processing, the elastic mechanics equations of the piezoelectric film layer are simplified to:

[0035]

[0036] Wherein, the superscript f represents the piezoelectric film layer, In this specification, S2 includes:

[0037] S21. Under pure shear state, the potential solution of the short circuit on the upper surface of the piezoelectric film is:

[0038]

[0039] The potential solution of the open circuit on the upper surface of the piezoelectric film is:

[0040]

[0041] The above two potential solutions are applicable to the electrode-covered area and the electrode-free area respectively; S22, the equation of motion and the constitutive equation of each layer are:

[0042]

[0043] The continuity and boundary conditions are:

[0044]

[0045] Where φ=0 and D3=0 are applicable to the piezoelectric film surface electrical short circuit and electrical open circuit states, or electrode covered and electrode-free states, respectively;

[0046] S23. Under pure shear condition, the displacement is assumed to be:

[0047]

[0048] S24. Substituting the displacement assumption into the equation of motion, the wave number of each layer can be obtained:

[0049]

[0050] S25. Based on the simultaneous boundary conditions, potential solution, displacement solution, and motion and control equations, the frequency control matrix equation under pure shear state is derived as follows:

[0051]

[0052] in,

[0053]

[0054]

[0055] In the above expressions, the subscripts f, d, g, and s represent the piezoelectric film layer, the upper electrode layer, the lower electrode layer, and the silicon support layer, respectively.

[0056] In this specification, S3 includes:

[0057] S31. Considering the coupling of thickness tensile mode, the displacement follows:

[0058]

[0059] According to the elastic mechanics equations, there are two wave number solutions η for each layer f1 and η f2 , and they correspond to a set of displacement amplitude ratios:

[0060]

[0061] in,

[0062]

[0063] S32. Establish the wave number relationship between coupled vibration and pure shear state:

[0064]

[0065] In this specification, the wave number increment and frequency satisfy:

[0066]

[0067] in,

[0068] In this manual, ω is deleted. 2 , the relationship between each increment satisfies:

[0069] δ d =K d ξ 2 +L d ν 2 +μ d δ f ;

[0070] in,

[0071]

[0072] In this specification, S4 includes:

[0073] S41. According to the incremental relationship between the wave number and the pure shear wave number, the displacement solution is updated as:

[0074]

[0075] S42. According to the displacement solution, control equations and boundary conditions, the frequency control matrix equation considering the thickness stretching and thickness shear coupling vibration is:

[0076]

[0077] in,

[0078]

[0079] In this specification, S5 includes:

[0080] S51. In order to make the frequency control matrix equation have a non-trivial solution, the determinant corresponding to the coefficient matrix should be 0, that is:

[0081]

[0082] In the determinant of the above formula, ignore the third and higher terms about ξ in the coefficient matrix of the frequency control matrix equation;

[0083] S52, combined with the wave number relationship between coupled vibration and pure shear state, N 21 、N 24 、N 41 、N 44 Expand the process to:

[0084]

[0085] in,

[0086]

[0087] S53, for N 12 、N 13 、N 32 、N 33 , the wave numbers in them are all taken as the wave numbers in pure shear mode;

[0088] S54, remember L = N 13 N 32 -N 12 N 33 , the expression in S51 is transformed into:

[0089] W 2 +LQδ f +LR1ξ 2 +LR2ν 2 =0;

[0090] Combining the relationship between wave number increment and frequency, we get:

[0091]

[0092] in,

[0093]

[0094] Combined with the displacement solution, the above formula can also be written as:

[0095]

[0096] This specification also discloses a vibration characteristic analysis system of an FBAR mass sensor, which is used to implement the vibration characteristic analysis method of an FBAR mass sensor described in any one of the above. The vibration characteristic analysis system of an FBAR mass sensor comprises:

[0097] Simplification module, used to simplify the elastic mechanics equations of the piezoelectric film layer for the zinc oxide film at the c-axis level;

[0098] A solution module, used for solving the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer based on the elastic mechanics equations and according to the displacement solution assumption and potential solution in the pure shear state;

[0099] A relationship building module, for setting a new displacement solution according to the coupling of thickness stretching and thickness shear based on the resonant frequency and the wave number of the acoustic wave in each physical layer, and establishing an incremental relationship between the wave number in this state and the pure shear wave number;

[0100] An equation determination module is used to update the specific form, simultaneous boundary conditions and continuity conditions of the displacement solutions of each physical layer according to the incremental relationship between the wave number and the pure shear wave number, and obtain the frequency control matrix equation;

[0101] The analysis module is used to simplify the frequency control matrix equation by mathematical processing to obtain the partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the partial differential equation.

[0102] The embodiments of this specification can at least achieve the following beneficial effects:

[0103] The present invention improves the original two-dimensional scalar differential equation to make it more consistent with the structural characteristics of modern FBAR devices, greatly improves the analysis efficiency while ensuring sufficient accuracy, and provides theoretical support for the uniform optimization design of vibration displacement of FBAR micro-mass sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0105] Figure 1 It is a schematic diagram of the analysis method of the vibration characteristics of the FBAR mass sensor involved in the present invention.

[0106] Figure 2 It is a front view schematic diagram of the FBAR sensor involved in the present invention.

[0107] Figure 3 It is a top view schematic diagram of the FBAR sensor involved in the present invention.

[0108] Figure 4 It is a schematic diagram of the first-order thickness shear mode vibration shape of a common frameless circular electrode obtained in combination with COMSOL software involved in the present invention.

[0109] Figure 5 It is a schematic diagram of the first-order thickness shear mode vibration shape of the elliptical frame structure obtained in combination with COMSOL software involved in the present invention.

[0110] Figure 6 It is a schematic diagram of the change of the mass frequency response of the FBAR sensor with the load adsorption position under the two electrode structures involved in the present invention. DETAILED DESCRIPTION

[0111] In the following, only some exemplary embodiments are briefly described. As those skilled in the art will appreciate, the described embodiments may be modified in various ways without departing from the spirit or scope of the embodiments of the present invention. Therefore, the drawings and descriptions are considered to be exemplary and non-restrictive in nature.

[0112] The disclosure below provides many different embodiments or examples to implement different structures of the embodiments of the present invention. In order to simplify the disclosure of the embodiments of the present invention, the parts and settings of specific examples are described below. Of course, they are only examples, and the purpose is not to limit the embodiments of the present invention. In addition, the embodiments of the present invention can repeat reference numbers and / or reference letters in different examples, and this repetition is for the purpose of simplification and clarity, which itself does not indicate the relationship between the various embodiments and / or settings discussed.

[0113] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0114] like Figure 1 As shown, this embodiment provides a method for analyzing vibration characteristics of a FBAR mass sensor, including:

[0115] S1. Simplified elastic mechanics equations of piezoelectric film layer for zinc oxide film at c-axis level;

[0116] S2. Based on the elastic mechanics equations, according to the displacement solution assumption and potential solution of the pure shear state, the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer are solved;

[0117] S3, based on the resonant frequency and the wave number of the acoustic wave in each physical layer, a new displacement solution is set according to the coupling of thickness stretching and thickness shear, and an incremental relationship between the wave number in this state and the pure shear wave number is established;

[0118] S4. According to the incremental relationship between the wave number and the pure shear wave number, the specific form, simultaneous boundary conditions and continuity conditions of the displacement solutions of each physical layer are updated to obtain the frequency control matrix equation;

[0119] S5. The frequency control matrix equation is mathematically processed and simplified to obtain a partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the partial differential equation.

[0120] This embodiment provides a system for analyzing vibration characteristics of an FBAR mass sensor, which is used to implement any one of the above-mentioned methods for analyzing vibration characteristics of an FBAR mass sensor. The system for analyzing vibration characteristics of an FBAR mass sensor includes:

[0121] Simplification module, used to simplify the elastic mechanics equations of the piezoelectric film layer for the zinc oxide film at the c-axis level;

[0122] A solution module, used for solving the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer based on the elastic mechanics equations and according to the displacement solution assumption and potential solution in the pure shear state;

[0123] A relationship building module, for setting a new displacement solution according to the coupling of thickness stretching and thickness shear based on the resonant frequency and the wave number of the acoustic wave in each physical layer, and establishing an incremental relationship between the wave number in this state and the pure shear wave number;

[0124] An equation determination module is used to update the specific form, simultaneous boundary conditions and continuity conditions of the displacement solutions of each physical layer according to the incremental relationship between the wave number and the pure shear wave number, and obtain the frequency control matrix equation;

[0125] The analysis module is used to simplify the frequency control matrix equation by mathematical processing to obtain the partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the partial differential equation.

[0126] The technical concept of the present invention is as follows:

[0127] The present invention can quickly analyze the vibration mode of the FBAR micro-mass sensor with thickness shear as the working mode, and the specific method includes:

[0128] S1, simplified piezoelectric equations for zinc oxide thin film at the c-axis level;

[0129] S2. Based on the displacement solution assumption and potential solution of the pure shear state, the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer are solved;

[0130] S3, setting a new displacement solution according to the coupling of thickness stretching and thickness shear, and establishing the incremental relationship between the wave number in this state and the pure shear wave number;

[0131] S4. Update the specific form of the displacement solution of each physical layer according to the results of the previous steps, combine the boundary conditions and the continuity conditions, and obtain the frequency control matrix equation;

[0132] S5. The matrix equation is processed to obtain a partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the equation.

[0133] For Figure 2 and Figure 3 In the implementation object shown, step S1 is further as follows:

[0134] S11. For an arbitrary piezoelectric elastic body, it satisfies the governing equation:

[0135]

[0136] The constitutive equation is:

[0137] T 11 = c 11 u 1,1 + c 12 u 1,2 + c 13 u 3,3 + c 14 (u 2,3 + u 3,2 ) + e 11 φ ,1 ,

[0138] T 22 = c 12 u 1,1 + c 22 u 2,2 + c 23 u 3,3 + c 24 (u 2,3 + u 3,2 ) + e 12 φ ,1 ,

[0139] T 33 = c 13 u 1,1 + c 23 u 2,2 + c 33 u 3,3 + c 34 (u 2,3 + u 3,2 ) + e 13 φ ,1 ,

[0140] T 23 = c 14 u 1,1 + c 24 u 2,2 + c 34 u 3,3 + c 44 (u 2,3 + u 3,2 ) + e 14 φ ,1 ,

[0141] T 13 = c 55 (u 3,1 + u 1,3 ) + c 56 (u 1,2 + u2,1 )+e 25 φ ,2 +e 35 φ ,3 ,

[0142] T 12 =c 56 (u 3,1 +u 1,3 )+c 66 (u 1,2 +u 2,1 )+e 26 φ ,2 +e 36 φ ,3 ,

[0143] D1=e 11 u 1,1 +e 12 u 2,2 +e 13 u 3,3 +e 14 (u 2,3 +u 3,2 )-ε 11 φ ,1 ,

[0144] D2=e 25 (u 3,1 +u 1,3 )+e 26 (u 1,2 +u 2,1 )-ε 22 φ ,2 -ε 23 φ ,3 ,

[0145] D3=e 35 (u 3,1 +u 1,3 )+e 36 (u 1,2 +u 2,1 )-ε 23 φ ,2 -ε 33 φ ,3 .;

[0146] Where T is the stress tensor, ρ is the density, u is the displacement, D is the electric displacement, c is the elastic constant, φ is the electric potential, e is the piezoelectric constant, ε is the dielectric constant, the comma in the subscript of the equation represents the derivative of the coordinates following it, and the double dot symbol on the displacement u represents the second-order derivative with respect to time;

[0147] The specific material parameter matrix is ​​as follows:

[0148] Elastic constant matrix:

[0149]

[0150] Piezoelectric constant matrix:

[0151]

[0152] Dielectric constant matrix:

[0153]

[0154] The above is the form of the material parameter matrix, and the following is an explanation of the stress, electric displacement, and displacement components.

[0155] Stress Tensor:

[0156]

[0157] The first numerical subscript of each stress component represents the orientation of the surface on which the component acts, and the second numerical index represents the direction in which the stress component acts, such as T 11 represents the stress component acting parallel to the x2-x3 plane and pointing in the x1 direction. And according to the mutual shear stress, T 12 =T 21 , T 13 =T 31 , T 23 =T 32 ;

[0158] D1, D2, D3 and u1, u2, u3 represent the electric displacement and the components of the displacement along the x1, x2, x3 directions respectively.

[0159] S12, ignore the in-plane electric displacement components D1 and D2; ignore the dependence of the potential φ and the electric displacement D on the in-plane x1 and x2; consider the piezoelectric material as a weak coupling material and ignore the coupling with the thickness direction u3; ignore the high-order small quantities u 3,11 、u 3,22 、u 3,12 and the field variables in the x2 direction.

[0160] S13. After the above processing, the main equation of the piezoelectric film layer is simplified to:

[0161]

[0162] Wherein, the superscript f represents the piezoelectric film layer,

[0163] The upper electrode and the lower electrode are both metal films, and the material of the support layer is single crystal silicon or other physical support layers, which satisfy the control equation and the constitutive equation:

[0164]

[0165] Figure 2 and Figure 3 The continuity conditions between the layered structures of the implementation object shown are:

[0166]

[0167] Where T is the stress tensor, h f is the thickness of the lower electrode, h d is the thickness of the upper electrode, h d In different regions, h has different values. g is the thickness of the lower electrode, h s is the thickness of the support layer.

[0168] For Figure 2 and Figure 3 In the implementation object shown, step S2 is further as follows:

[0169] S21, pure shear state, according to D i,i =0, the potential solution of the short circuit on the piezoelectric film is:

[0170]

[0171] The potential solution of the open circuit on the upper surface of the piezoelectric film is:

[0172]

[0173] The above two potential solutions are applicable to the covered electrode region and the electrode-free region respectively;

[0174] S22, the motion equations and constitutive equations of each layer are:

[0175]

[0176] The continuity and boundary conditions are:

[0177]

[0178] Where φ=0 and D3=0 are respectively applicable to the piezoelectric film surface electrical short circuit and electrical open circuit state, or electrode covered and electrode-free state; because it is a pure shear state, only the shear stress T is considered. 31 With displacement u1, T 33 and u3 is 0.

[0179] S23. Under pure shear condition, the displacement is assumed to be:

[0180]

[0181] S24. Substituting the displacement assumption into the equation of motion, the wave number of each layer can be obtained:

[0182]

[0183] S25, combined with boundary conditions, potential solution, displacement solution, motion and control equations, the frequency control equation under pure shear state is derived as follows:

[0184]

[0185] in,

[0186]

[0187]

[0188] In the above expressions, the subscripts f, d, g, and s represent the piezoelectric film layer, the upper electrode layer, the lower electrode layer, and the silicon support layer, respectively. In order for the control equation to have a non-trivial solution, the determinant of the corresponding coefficient matrix should be 0, from which the resonant frequency and wave number of each layer under pure shear short circuit or open circuit conditions can be obtained.

[0189] For Figure 2 and Figure 3 In the implementation object shown, step S3 is further as follows:

[0190] S31. Considering the coupling between the thickness tensile mode and the thickness shear mode, the displacement follows:

[0191]

[0192] According to the simplified equations in S13, there are two wave number solutions η for each layer f1 and η f2 , and they correspond to a set of displacement amplitude ratios:

[0193]

[0194] in,

[0195]

[0196] S32. Establish the wave number relationship between coupled vibration and pure shear state:

[0197]

[0198] Furthermore, according to the above equations in this section and the simplified equations in S13, the wave number increment and frequency satisfy:

[0199]

[0200] in,

[0201]

[0202] Furthermore, by eliminating ω from the above formula 2 , the relationship between each increment satisfies:

[0203] δ d =K d ξ 2 +L d ν 2 +μ d δ f ;

[0204] in,

[0205]

[0206] For Figure 2 and Figure 3 In the implementation object shown, step S4 is further as follows:

[0207] S41, the displacement solution is updated according to the above steps:

[0208]

[0209] S42. Further, according to the displacement solution, control equation and boundary conditions, the frequency control equation considering the thickness stretching and thickness shear coupling vibration is:

[0210]

[0211] in,

[0212]

[0213] For Figure 2 and Figure 3 In the implementation object shown, step S5 is further as follows:

[0214] S51. In order to make the frequency control equation have a non-trivial solution, the determinant corresponding to the coefficient matrix should be 0, that is

[0215]

[0216] In the determinant of the above formula, the third-order and above terms about ξ in the coefficient matrix of the frequency control equation shown in S42 are ignored;

[0217] S52, further, combined with the wave number relationship between coupled vibration and pure shear state established in S32, N 21 、N 24 、N 41 、N 44 Expand the process to:

[0218]

[0219] in,

[0220]

[0221] S53, for N 12 、N 13 、N 32 、N 33 , the wave numbers among them are taken as the wave numbers in pure shear mode;

[0222] S54, remember L = N 13 N 32 -N 12 N 33 , the expression in S51 is transformed into:

[0223] W 2 +LQδ f +LR1ξ 2 +LR2ν 2 =0;

[0224] Combining the relationship between the wave number increment of S32 and the frequency, we get:

[0225]

[0226] in,

[0227]

[0228] Combined with the displacement solution shown in S41, the above formula can also be written as:

[0229]

[0230] Among them, M1 and M2 are the coefficients of partial differential equations, u1 is the principal displacement in the piezoelectric film surface, ω s is the pure first-order thickness shear resonance frequency corresponding to each different thickness area. The above parameters are different in electrode areas with different thicknesses, and their values ​​are only related to the thickness of the upper electrode in each area.

[0231] The specific implementation process of the method of the present invention is described in detail above. By constructing a solution code, only relevant structural parameters need to be input to quickly calculate the relevant coefficients, and then determine the two-dimensional scalar differential equation that can characterize the dispersion relationship of different areas on the surface of the FBAR sensor. Furthermore, using the finite element solution method of commercial software, such as the PDE module of COMSOL, the obtained partial differential equation can be quickly solved to obtain information such as the vibration mode and vibration frequency of the sensor.

[0232] The present invention is not limited to the specific details of the above-mentioned embodiments. Within the technical concept of the present invention, the technical solution of the present invention can be transformed with equivalent ideas, and these transformations should all fall within the protection scope of the present invention.

[0233] Test example

[0234] Figure 2 and Figure 3 The present invention shows a FBAR sensor with an elliptical frame structure, wherein Figure 2 is the front view, Figure 3 The FBAR is free at both ends, and the horizontal cross-section is circular. It is described by the Cartesian coordinate system, and the directions of the x1, x2 and x3 axes are as follows: Figure 2 and Figure 3 As shown, the polarization direction of the piezoelectric film, i.e., the c-axis, is along the positive direction of the x1 axis.

[0235] The thickness of the zinc oxide piezoelectric film is 15 microns, the thickness of the lower electrode is 1 micron, the thickness of the inner circular part of the upper electrode is 1 micron, the thickness of the outer frame part is 1.3 microns, the thickness of the supporting layer is 5 microns, the diameter of the inner circular part of the upper electrode is 60 microns, the major axis of the ellipse is 69 microns, the minor semi-axis is 65.6 microns, and the overall diameter of the FBAR is 120 microns.

[0236] Parameters of the equation of the circular electrode on the upper surface: M1 = 5.61336, M2 = 1.83553, ω s =2.59878.

[0237] The equation parameters of the upper surface frame are: M1 = 5.59785, M2 = 1.83598, ω s =2.57813.

[0238] The equation parameters of the upper surface without electrode: M1 = 5.61596, M2 = 1.84779, ω s =2.74742.

[0239] The present invention analyzes and studies the vibration characteristics of FBAR with and without frame structure:

[0240] Specifically, according to the obtained equation and COMSOL's PDE module, Figure 4 and Figure 5 The vibration mode diagrams of FBAR in the first-order thickness shear mode with and without the elliptical frame structure are shown, as well as the resonance frequency obtained by solving the equation. The presence of the elliptical frame structure significantly changes the distribution of vibration energy in the piezoelectric oscillator stack. Figure 4It is shown that for the anisotropic piezoelectric film at the c-axis level, directly using conventional circular electrodes will result in obvious uneven vibration. Its energy distribution is roughly elliptical, with the major semi-axis in the x1 direction and the minor semi-axis in the x2 direction. It weakens at different rates from the center of the electrode to the surrounding areas and quickly decays to zero near the edge of the circular electrode. Figure 5 It shows that the vibration energy of the device tends to be evenly distributed after the introduction of the elliptical frame structure.

[0241] On the basis of the above, Figure 6 Specifically, the mass frequency response of the FBAR sensor under two electrode structures is shown as the load is adsorbed. The |Δf| is the frequency shift and the load mass Δm = R m ·ρ f h f ·Δs, in this test example, R m Take 0.01, ρ f is the density of the piezoelectric film, h f is the thickness of the piezoelectric film, Δs is the contact area and is taken as the radius r s The loading position changes from the center of the electrode along the positive direction of x1. It can be seen that the frequency response stability of the FBAR sensor is greatly enhanced under the elliptical frame structure of the present invention.

[0242] Based on the concept of the present invention, the experimental example shows the positive effect of the elliptical frame microstructure on the uniform distribution of vibration energy, and the role of the frame microstructure in improving the stability of the sensor frequency response. This provides a new idea for controlling the distribution of vibration energy inside FBAR, which is of great significance to the design of FBAR sensors.

[0243] The above-described embodiments are used to illustrate the present invention, not to limit the present invention, so changes in the exemplified values ​​or replacement of equivalent elements should still fall within the scope of the present invention.

[0244] From the above detailed description, it can be understood by those skilled in the art that the present invention can indeed achieve the aforementioned objectives and is in compliance with the provisions of the Patent Law.

[0245] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic creative concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. It should be pointed out that any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

[0246] It should be noted that the above description of the relevant process is only for example and explanation, and does not limit the scope of application of this specification. For those skilled in the art, various modifications and changes can be made to the process under the guidance of this specification. However, these modifications and changes are still within the scope of this specification.

[0247] The basic concepts have been described above. Obviously, for those of ordinary skill in the art who have read this application, the above invention disclosure is only for example and does not constitute a limitation of this application. Although not explicitly stated here, those of ordinary skill in the art may make various modifications, improvements and amendments to this application. Such modifications, improvements and amendments are suggested in this application, so such modifications, improvements and amendments still belong to the spirit and scope of the exemplary embodiments of this application.

[0248] At the same time, the present application uses specific words to describe the embodiments of the present application. For example, "one embodiment", "an embodiment", and / or "some embodiments" refer to a certain feature, structure or characteristic related to at least one embodiment of the present application. Therefore, it should be emphasized and noted that "one embodiment" or "an embodiment" or "an alternative embodiment" mentioned twice or more in different positions in this specification does not necessarily refer to the same embodiment. In addition, some features, structures or characteristics in one or more embodiments of the present application can be appropriately combined.

[0249] In addition, it will be appreciated by those skilled in the art that various aspects of the present application may be illustrated and described by a number of patentable categories or situations, including any new and useful combination of processes, machines, products or substances, or any new and useful improvements thereto. Therefore, various aspects of the present application may be implemented entirely by hardware, entirely by software (including firmware, resident software, microcode, etc.), or by a combination of hardware and software. The above hardware or software may all be referred to as "units", "modules" or "systems". In addition, various aspects of the present application may take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0250] In addition, unless explicitly stated in the claims, the order of the processing elements and sequences described in this application, the use of alphanumeric characters, or the use of other names are not intended to limit the order of the processes and methods of this application. Although the above disclosure discusses some invention embodiments that are currently considered useful through various examples, it should be understood that such details are only for illustrative purposes, and the attached claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that are consistent with the essence and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a pure software solution, for example, installation on an existing server or mobile device.

[0251] Similarly, it should be noted that in order to simplify the description disclosed in this application and thus help understand one or more embodiments of the invention, in the above description of the embodiments of the application, multiple features are sometimes combined into one embodiment, figure or description thereof. However, this method of the application should not be interpreted as reflecting the intention that the claimed object requires more features than those explicitly stated in each claim. On the contrary, the subject of the invention should have fewer features than the above single embodiment.

Claims

1. A method for analyzing vibration characteristics of a FBAR mass sensor, characterized in that: include: S1. Simplified elastic mechanics equations of piezoelectric film layer for zinc oxide film at c-axis level; S2. Based on the elastic mechanics equations, according to the displacement solution assumption and potential solution of the pure shear state, the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer are solved; S3, based on the resonant frequency and the wave number of the acoustic wave in each physical layer, a new displacement solution is set according to the coupling of thickness stretching and thickness shear, and an incremental relationship between the wave number in this state and the pure shear wave number is established; S4. According to the incremental relationship between the wave number and the pure shear wave number, the specific form, simultaneous boundary conditions and continuity conditions of the displacement solutions of each physical layer are updated to obtain the frequency control matrix equation; S5. The frequency control matrix equation is mathematically processed and simplified to obtain a partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the partial differential equation.

2. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 1, characterized in that: In S1: For an arbitrary piezoelectric elastic body, it satisfies the governing equation: and 11 u 1,11 +(and 26 +and 12 )u 2,12 +(and 13 +and 35 )u 3,13 +(and 14 +and 36 )u 2,13 + (and 14 +e 25 )u 3,12 +(and 25 +e 36 )u 1,23 +e 26 the 1,22 +e 35 the 1,33 -ε 11 φ ,11 - e 22 f ,22 -2e 23 f ,23 -e 33 f ,33 =0.; The constitutive equation is: T 11 =c 11 u 1,1 +c 12 u 1,2 +c 13 u 3,3 +c 14 (u 2,3 +u 3,2 )+e 11 φ ,1 , T 22 =c 12 u 1,1 +c 22 u 2,2 +c 23 u 3,3 +c 24 (u 2,3 +u 3,2 )+e 12 φ ,1 , T 33 =c 13 u 1,1 +c 23 u 2,2 +c 33 u 3,3 +c 34 (u 2,3 +u 3,2 )+e 13 φ ,1 , T 23 =c 14 u 1,1 +c 24 u 2,2 +c 34 u 3,3 +c 44 (u 2,3 +u 3,2 )+e 14 φ ,1 , T 13 =c 55 (in 3,1 +in 1,3 )+c 56 (in 1,2 +in 2,1 )+e 25 φ ,2 +e 35 φ ,3 , T 12 =c 56 (in 3,1 +in 1,3 )+c 66 (in 1,2 +in 2,1 )+e 26 φ ,2 +e 36 φ ,3 , D1=e 11 in 1,1 +e 12 in 2,2 +e 13 in 3,3 +e 14 (in 2,3 +in 3,2 )-ε 11 φ ,1 , D2=e 25 (in 3,1 +in 1,3 )+e 26 (in 1,2 +in 2,1 )-ε 22 φ ,2 -ε 23 φ ,3 , D3=e 35 (u 3,1 +u 1,3 )+e 36 (u 1,2 +u 2,1 )-e 23 f ,2 -e 33 f ,3 .; Where T is the stress tensor, ρ is the density, u is the displacement, D is the electric displacement, c is the elastic constant, φ is the electric potential, e is the piezoelectric constant, ε is the dielectric constant, the comma in the parameter subscript represents the derivative of the coordinates behind it, and the double dot symbol on the displacement u represents the second-order derivative with respect to time; the specific material parameter matrix is ​​as follows: Elastic constant matrix: Piezoelectric constant matrix: Dielectric constant matrix: Above is the shape of the material parameter matrix; Stress Tensor: The first numerical subscript of each stress component represents the orientation of the surface on which the component acts, and the second numerical index represents the direction in which the stress component acts. 11 represents the stress component acting parallel to the x2-x3 plane and pointing in the direction of x1, and according to the mutual equality of shear stress, T 12 =T 21 , T 13 =T 31 , T 23 =T 32 ; D1, D2, D3 and u1, u2, u3 represent the electric displacement and the components of displacement along the x1, x2, x3 directions respectively.

3. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 2, characterized in that: In S1: The piezoelectric film is zinc oxide with a c-axis horizontal to provide a pure thickness shear vibration mode; Ignore the in-plane electric displacement components D1 and D2; Ignore the changes of electric potential φ and electric displacement D along the x1-x2 plane; Considering the piezoelectric material as a weak coupling material, the coupling with the thickness direction u3 is ignored; Ignore high-order small quantities u 3,11 、u 3,22 、u 3,12 and the field variables in the x2 direction; After the above processing, the elastic mechanics equations of the piezoelectric film layer are simplified to: D3=e 35 you 1,3 -e 33 f,3.; Wherein, the superscript f represents the piezoelectric film layer, 4. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 3, wherein S2 include: S21. Under pure shear state, the potential solution of the short circuit on the upper surface of the piezoelectric film is: The potential solution of the open circuit on the upper surface of the piezoelectric film is: The above two potential solutions are applicable to the covered electrode region and the electrode-free region respectively; S22, the motion equations and constitutive equations of each layer are: The continuity and boundary conditions are: Where φ=0 and D3=0 are applicable to the piezoelectric film surface electrical short circuit and electrical open circuit states, or electrode covered and electrode-free states, respectively; S23. Under pure shear condition, the displacement is assumed to be: S24. Substituting the displacement assumption into the equation of motion, the wave number of each layer can be obtained: S25. Based on the simultaneous boundary conditions, potential solution, displacement solution, and motion and control equations, the frequency control matrix equation under pure shear state is derived as follows: in, In the above expressions, the subscripts f, d, g, and s represent the piezoelectric film layer, the upper electrode layer, the lower electrode layer, and the silicon support layer, respectively.

5. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 4, wherein S3 include: S31. Considering the coupling of thickness tensile mode, the displacement follows: According to the elastic mechanics equations, there are two wave number solutions for each layer: and And they correspond to a set of displacement amplitude ratios: in, S32. Establish the wave number relationship between coupled vibration and pure shear state:

6. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 5, characterized in that: The wave number increment and frequency satisfy: in, 7. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 6, characterized in that: Eliminate ω 2 , the relationship between each increment satisfies: d d =K d x 2 +L d n 2 +m d d f ; in, 8. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 7, wherein S4 include: S41. According to the incremental relationship between the wave number and the pure shear wave number, the displacement solution is updated as: S42. According to the displacement solution, control equations and boundary conditions, the frequency control matrix equation considering the thickness stretching and thickness shear coupling vibration is: in, 9. The method for analyzing vibration characteristics of a FBAR mass sensor according to claim 8, wherein S5 include: S51. In order to make the frequency control matrix equation have a non-trivial solution, the determinant corresponding to the coefficient matrix should be 0, that is: In the determinant of the above formula, ignore the third-order and above terms about ξ in the coefficient matrix of the frequency-controlled matrix equation; S52, combined with the wave number relationship between coupled vibration and pure shear state, N 21 、N 24 、N 41 、N 44 Expand the process to: N 21 N 44 -N 24 N 41 =U+Qδ f +R1ξ 2 +R2ν 2 ; in, S53, for N 12 、N 13 、N 32 、N 33 , the wave numbers in them are all taken as the wave numbers in pure shear mode; S54, remember L = N 13 N 32 -N 12 N 33 , the expression in S51 is transformed into: Wξ 2 +LQδ f +LR1ξ 2 +LR2ν 2 =0; Combining the relationship between wave number increment and frequency, we get: in, Combined with the displacement solution, the above formula can also be written as:

10. An analysis system for vibration characteristics of a FBAR mass sensor, characterized in that: A method for analyzing vibration characteristics of an FBAR mass sensor according to any one of claims 1 to 9, wherein the analysis system for vibration characteristics of the FBAR mass sensor comprises: Simplification module, used to simplify the elastic mechanics equations of the piezoelectric film layer for the zinc oxide film at the c-axis level; A solution module, for solving the resonant frequency of the device in the pure shear state and the wave number of the acoustic wave in each physical layer based on the elastic mechanics equations and according to the displacement solution assumption and potential solution in the pure shear state; A relationship building module, for setting a new displacement solution according to the coupling of thickness stretching and thickness shear based on the resonant frequency and the wave number of the acoustic wave in each physical layer, and establishing an incremental relationship between the wave number in this state and the pure shear wave number; The equation determination module is used to update the specific form, simultaneous boundary conditions and continuity conditions of the displacement solutions of each physical layer according to the incremental relationship between the wave number and the pure shear wave number, and obtain the frequency control matrix equation; the analysis module is used to simplify the frequency control matrix equation by mathematical processing to obtain the partial differential equation that can characterize the displacement distribution of the sensor on the water surface. The vibration mode of the sensor in the horizontal plane can be obtained by solving the partial differential equation.

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