Bulk acoustic wave resonator and design method thereof

Abstract

The invention relates to the technical field of bulk acoustic wave resonators, and particularly provides a bulk acoustic wave resonator and a design method thereof, and the method comprises the steps: determining the scandium doping concentration and thickness corresponding to a plurality of piezoelectric layers according to a target effective electromechanical coupling coefficient and a target resonator frequency, determining an electrode material and corresponding acoustic impedance according to the target loss performance; for each piezoelectric layer, acoustic parameters, piezoelectric coupling parameters and static capacitance parameters are calculated according to the corresponding scandium doping concentration and thickness, and the acoustic parameters comprise acoustic impedance; calculating the interface impedance of the adjacent layer structures according to the acoustic impedance of the adjacent layer structures; inputting all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode material and all the interface impedance into a Mason model to complete the design of the bulk acoustic wave resonator; according to the method, the Mason model can comprehensively consider the influence of the physical parameter difference of a plurality of piezoelectric layers on the bulk acoustic wave resonator and the interfacial effect between the layer structures.

Description

Technical Field

[0001] The present application relates to the technical field of bulk acoustic wave resonators. Specifically, it relates to a bulk acoustic wave resonator and a design method thereof. Background Art

[0002] In the technical field of bulk acoustic wave resonators, the Mason model based on a single-layer uniform piezoelectric medium is usually used for the design of bulk acoustic wave resonators. That is, the design method of bulk acoustic wave resonators in the related art can only design bulk acoustic wave resonators including a single piezoelectric layer. Therefore, there is a problem in the related art that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers by using the Mason model because the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator cannot be characterized. And because the interface effect between each layer structure in the bulk acoustic wave resonator is not considered in the related bulk acoustic wave resonator design method, and the interface effect is associated with the resonance frequency of the bulk acoustic wave resonator, there is also a problem in the related art that the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effect between each layer structure in the bulk acoustic wave resonator.

[0003] In view of the above problems, there is currently no effective technical solution. It should be noted that the above information disclosed in this part is only used to understand the background of the inventive concept of the present invention, and therefore may include information that does not constitute the prior art. Summary of the Invention

[0004] The purpose of the present application is to provide a bulk acoustic wave resonator and a design method thereof, which can effectively solve the problems that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers by using the Mason model because the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator cannot be characterized, and that the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effect between each layer structure in the bulk acoustic wave resonator.

[0005] In a first aspect, the present application provides a design method of a bulk acoustic wave resonator, which includes the following steps: S1. Determine the scandium doping concentration and thickness corresponding to multiple piezoelectric layers according to the target effective electromechanical coupling coefficient and the target resonator frequency, and determine the electrode material and its corresponding acoustic impedance according to the target loss performance; S2. For each piezoelectric layer, calculate the acoustic parameters, piezoelectric coupling parameters and static capacitance parameters according to its corresponding scandium doping concentration and / or thickness, and the acoustic parameters include acoustic impedance; S3. Calculate the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures; S4. Input all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode material, and all the interface impedances into the Mason model to complete the design of the bulk acoustic wave resonator.

[0006] A method for designing a bulk acoustic wave resonator provided by this application can calculate the physical parameters of each piezoelectric layer by calculating the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters of each piezoelectric layer based on the target effective electromechanical coupling coefficient and the target resonator frequency, and can quantify the interface effect by calculating the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures. Since this application inputs all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode material, and all the interface impedances into the Mason model, this application can enable the Mason model to comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effect between each layer structure, thereby effectively solving the problems that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers using the Mason model due to the inability to characterize the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effect between each layer structure in the bulk acoustic wave resonator.

[0007] Optionally, step S1 includes: S11. Determine the scandium doping concentration corresponding to multiple piezoelectric layers according to the target effective electromechanical coupling coefficient, and the calibrated electromechanical coupling coefficient corresponding to at least one scandium doping concentration is less than the target effective electromechanical coupling coefficient and the calibrated electromechanical coupling coefficient of at least one piezoelectric layer is greater than the target effective electromechanical coupling coefficient; S12. Calculate the acoustic impedance corresponding to each piezoelectric layer according to the scandium doping concentration, and then calculate the interface correction term according to the acoustic impedance of adjacent piezoelectric layers; S13. Determine the thickness ratio of the piezoelectric layers according to the target effective electromechanical coupling coefficient, the calibrated electromechanical coupling coefficients corresponding to all the piezoelectric layers, and all the interface correction terms; S14. Determine the thickness of each piezoelectric layer according to the target resonator frequency and the thickness ratio.

[0008] Since this technical solution introduces an interface correction term when determining the thickness of each piezoelectric layer, that is, this technical solution is equivalent to correcting the interface effect generated due to different acoustic impedances between adjacent piezoelectric layers when determining the thickness of each piezoelectric layer, so this technical solution can effectively avoid the situation that the interface effect is generated due to different acoustic impedances between adjacent piezoelectric layers, and there is a difference between the actual effective electromechanical coupling coefficient and the target effective electromechanical coupling coefficient of the finally designed bulk acoustic wave resonator, thereby effectively improving the design accuracy of the bulk acoustic wave resonator design method.

[0009] Optionally, step S12 includes: S121. For each piezoelectric layer, calculate the material sound velocity, material density, and piezoelectric stress constant according to the scandium doping concentration, and then calculate the acoustic impedance of the piezoelectric layer according to the material sound velocity and material density; S122. Calculate the interface correction term according to the acoustic impedance and piezoelectric stress constant of adjacent piezoelectric layers.

[0010] Optionally, the calculation formula of the material sound velocity is shown in Equation (1): (1); Wherein, represents the material sound velocity of the piezoelectric layer with a scandium doping concentration of x, and x represents the scandium doping concentration; The calculation formula of the material density is shown in Equation (2): (2); Wherein, represents the material density of the piezoelectric layer with a scandium doping concentration of x; The calculation formula of the acoustic impedance of the piezoelectric layer is shown in Equation (3): (3); Wherein, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x; The calculation formula of the piezoelectric stress constant is shown in Equation (4): (4); Wherein, represents the piezoelectric stress constant of the piezoelectric layer with a scandium doping concentration of x, represents the piezoelectric stress constant of aluminum nitride, and α, β, and are all pre-calibrated fitting parameters; The calculation formula of the interface correction term is shown in Equation (5): (5); Wherein, represents the interface correction term, Z k represents the acoustic impedance corresponding to one of the adjacent piezoelectric layers, Z l represents the acoustic impedance corresponding to the other piezoelectric layer in the adjacent piezoelectric layers, e 33_k represents Z k The piezoelectric stress constant of the corresponding piezoelectric layer, e 33_l represents Z l The piezoelectric stress constant of the corresponding piezoelectric layer.

[0011] Optionally, the acoustic parameters further include phase accumulation, acoustic wave amplitude modulation, acoustic wave reflection, and wave number.

[0012] Optionally, the calculation formula for phase accumulation is shown in Equation (6): (6); where A represents phase accumulation, m represents the wave number, and d represents the thickness of the piezoelectric layer; The calculation formula for the wave number is shown in Equation (7): (7); where m represents the wave number, π represents pi, f represents the target resonator frequency, represents the sound velocity of the piezoelectric layer with a scandium doping concentration of x; The calculation formula for acoustic wave amplitude modulation is shown in Equation (8): B (8); where B represents acoustic wave amplitude modulation, j represents the imaginary unit, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x; The calculation formula for acoustic wave reflection is shown in Equation (9): (9); where C represents acoustic wave reflection.

[0013] Optionally, the piezoelectric coupling parameters include electric field stress coupling, induced charge density, and nonlinear polarization effect.

[0014] Optionally, the calculation formula for electric field stress coupling is shown in Equation (10): (10); where E and G together represent electric field stress coupling, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x, represents the piezoelectric stress constant of the piezoelectric layer with a scandium doping concentration of x, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, m represents the wave number, π represents pi, f represents the target resonator frequency, and d represents the thickness of the piezoelectric layer; The calculation formula for the dielectric constant is shown in Equation (11): (11); where, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, represents the dielectric constant of aluminum nitride, and both δ and η are pre-calibrated fitting parameters; The calculation formula for induced charge density is shown in Equation (12): (12); where F represents induced charge density; The calculation formula for the nonlinear polarization effect is shown in Equation (13): (13); Among them, H represents the nonlinear polarization effect.

[0015] Optionally, the calculation formula for the static capacitance parameter is shown in Equation (14): (14); Among them, I and J together represent the static capacitance parameter, j represents the imaginary number, π represents the pi, f represents the target resonator frequency, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, m represents the wave number, and d represents the thickness of the piezoelectric layer.

[0016] In a second aspect, the present application also provides a bulk acoustic wave resonator, which is designed by the method for designing a bulk acoustic wave resonator provided in the first aspect above.

[0017] The bulk acoustic wave resonator provided by the present application is designed by the method for designing a bulk acoustic wave resonator. This design method can calculate the physical parameters of each piezoelectric layer by calculating the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters of each piezoelectric layer based on the target effective electromechanical coupling coefficient and the target resonator frequency, and can quantify the interface effect by calculating the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures. Since the present application inputs all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, the electrode material, and all interface impedances into the Mason model, the present application can enable the Mason model to comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effect between each layer structure, thereby effectively solving the problems that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers by using the Mason model due to the inability to characterize the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effect between each layer structure in the bulk acoustic wave resonator.

[0018] As can be seen from the above, a bulk acoustic wave resonator and its design method provided by the present application can calculate the physical parameters of each piezoelectric layer by calculating the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters of each piezoelectric layer based on the target effective electromechanical coupling coefficient and the target resonator frequency, and can quantify the interface effect by calculating the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures. Since the present application inputs all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials, and all interface impedances into the Mason model, the present application can enable the Mason model to comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effect between each layer structure, thereby effectively solving the problems that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers using the Mason model due to the inability to characterize the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effect between each layer structure in the bulk acoustic wave resonator. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flowchart of a method for designing a bulk acoustic wave resonator provided by an embodiment of the present application.

[0020] Figure 2 It is a schematic diagram of the Mason model provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and illustrated herein can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application claimed, but merely represents selected embodiments of the present application. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative efforts fall within the scope of protection of the present application.

[0022] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of the present application, the terms "first", "second", etc. are only used for descriptive distinction and cannot be understood as indicating or implying relative importance.

[0023] In the first aspect, as Figure 1 and Figure 2As shown, the present application provides a method for designing a bulk acoustic wave resonator, which includes the following steps: S1. Determine the scandium doping concentration and thickness corresponding to multiple piezoelectric layers according to the target effective electromechanical coupling coefficient and the target resonator frequency, and determine the electrode material and its corresponding acoustic impedance according to the target loss performance; S2. For each piezoelectric layer, calculate the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters according to its corresponding scandium doping concentration and / or thickness, and the acoustic parameters include acoustic impedance; S3. Calculate the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures; S4. Input all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode material, and all the interface impedances into the Mason model to complete the design of the bulk acoustic wave resonator.

[0024] Among them, a design method of a bulk acoustic wave resonator provided by this embodiment can design a bulk acoustic wave resonator including multiple piezoelectric layers. It should be understood that the materials of different piezoelectric layers are different. For example, when the number of piezoelectric layers is two, the material of one piezoelectric layer is aluminum nitride, and the material of the other piezoelectric layer is scandium-doped aluminum nitride. Another example is that when the number of piezoelectric layers is multiple, the material of one piezoelectric layer is aluminum nitride, and the materials of other piezoelectric layers are all scandium-doped aluminum nitride, and the scandium doping concentrations of different scandium-doped aluminum nitrides are different. The target effective electromechanical coupling coefficient in step S1 is the effective electromechanical coupling coefficient of the target bulk acoustic wave resonator (the finally designed bulk acoustic wave resonator), the target resonator frequency in step S1 is the resonant frequency of the target bulk acoustic wave resonator, and the target loss performance in step S1 is the loss performance of the target bulk acoustic wave resonator. The target resonator frequency and the target loss performance of this embodiment are preferably parameters designed in advance according to product requirements. Since the effective electromechanical coupling coefficient of a bulk acoustic wave resonator is related to the scandium doping concentration and the thickness ratio of the piezoelectric layers, and the target resonator frequency of the bulk acoustic wave resonator is related to the total thickness of all piezoelectric layers, step S1 can first determine the scandium doping concentration and the thickness ratio of the piezoelectric layers corresponding to multiple piezoelectric layers according to the target effective electromechanical coupling coefficient and the target resonator frequency, then determine the total thickness of the piezoelectric layers according to the target resonator frequency, and finally determine the thickness of each piezoelectric layer according to the total thickness of the piezoelectric layers and the thickness ratio, so as to realize determining the scandium doping concentration and thickness corresponding to multiple piezoelectric layers according to the target effective electromechanical coupling coefficient and the target resonator frequency. Since the loss performance of a bulk acoustic wave resonator is related to the electrode materials (the materials of the top electrode and the bottom electrode), step S1 can determine the electrode materials according to the target loss performance. And since there is no doping in the electrode materials, that is, the acoustic impedance corresponding to each electrode material is a fixed value, step S1 can obtain the acoustic impedance corresponding to the electrode materials determined by the target loss performance by querying a pre-constructed mapping relationship table of electrode materials and acoustic impedance according to the electrode materials determined by the target loss performance. It should be understood that the number of piezoelectric layers is a pre-designed value, and those skilled in the art can change the number of piezoelectric layers included in the bulk acoustic wave resonator according to actual needs. Preferably, the bulk acoustic wave resonator of this embodiment further includes a protective layer, and the relevant parameters such as the acoustic impedance of the protective layer are preset values.

[0025] Step S2 can calculate the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters according to the scandium doping concentration and / or thickness corresponding to each piezoelectric layer by using existing piezoelectric layer physical parameter calculation algorithms or piezoelectric layer physical parameter calculation models, that is, step S2 is equivalent to calculating the physical parameters of each piezoelectric layer respectively.

[0026] Since the interfacial effect occurs on the layer structure in contact with each other, and the magnitude of the interfacial impedance can reflect the influence degree of the interfacial effect, that is, this embodiment is equivalent to quantifying the interfacial effect by using the interfacial impedance, and the interfacial impedance is associated with the acoustic impedance of the adjacent layer structure (the layer structure in contact with each other), so step S3 can calculate the interfacial impedance of the adjacent layer structure according to the acoustic impedance of the adjacent layer structure. It should be understood that this embodiment can more accurately reflect the propagation characteristics of sound waves in the multi-layer structure by introducing the interfacial impedance.

[0027] Since step S4 inputs all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials and all interfacial impedances into the Mason model, step S4 is equivalent to expanding and improving the existing Mason model, so that the Mason model can comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interfacial effect between each layer structure.

[0028] A method for designing a bulk acoustic wave resonator provided by the present application can calculate the physical parameters of each piezoelectric layer by calculating the acoustic parameters, piezoelectric coupling parameters and static capacitance parameters of each piezoelectric layer based on the target effective electromechanical coupling coefficient and the target resonator frequency, and quantify the interfacial effect by calculating the interfacial impedance of the adjacent layer structure according to the acoustic impedance of the adjacent layer structure. Since the present application inputs all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials and all interfacial impedances into the Mason model, the present application can enable the Mason model to comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interfacial effect between each layer structure, thereby effectively solving the problems that it is impossible to use the Mason model to design a bulk acoustic wave resonator including multiple piezoelectric layers due to the inability to characterize the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interfacial effect between each layer structure in the bulk acoustic wave resonator, that is, the present application can effectively improve the design accuracy of the bulk acoustic wave resonator design method.

[0029] In some preferred embodiments, step S1 includes: S11. Determine the scandium doping concentration corresponding to multiple piezoelectric layers according to the target effective electromechanical coupling coefficient, and the calibrated electromechanical coupling coefficient corresponding to at least one scandium doping concentration is less than the target effective electromechanical coupling coefficient and the calibrated electromechanical coupling coefficient of at least one piezoelectric layer is greater than the target effective electromechanical coupling coefficient; S12. Calculate the acoustic impedance corresponding to each piezoelectric layer according to the scandium doping concentration, and then calculate the interface correction term according to the acoustic impedance of the adjacent piezoelectric layers; S13. Determine the thickness ratio of the piezoelectric layers according to the target effective electromechanical coupling coefficient, the calibrated electromechanical coupling coefficients corresponding to all piezoelectric layers, and all interface correction terms; S14. Determine the thickness of each piezoelectric layer according to the target resonator frequency and the thickness ratio.

[0030] The calibrated electromechanical coupling coefficient of this embodiment is the pre-calibrated effective electromechanical coupling coefficient. The working principle of step S11 is as follows: Under the limitation of the doping process, the accuracy of the scandium doping concentration is limited. For example, the existing doping process can only prepare scandium-doped aluminum nitride with a scandium doping concentration of 10% or 20%, but cannot prepare scandium-doped aluminum nitride with a doping concentration of 12%. Since the effective electromechanical coupling coefficient corresponding to the piezoelectric layer is associated with the scandium doping concentration, that is, in this embodiment, it may be impossible to directly prepare scandium-doped aluminum nitride that meets the requirements of the target effective electromechanical coupling coefficient based on the existing doping process. Therefore, step S11 needs to make the calibrated electromechanical coupling coefficient corresponding to at least one scandium doping concentration less than the target effective electromechanical coupling coefficient and make the calibrated electromechanical coupling coefficient of at least one piezoelectric layer greater than the target effective electromechanical coupling coefficient so that the effective electromechanical coupling coefficient of the finally obtained bulk acoustic wave resonator can meet the target effective electromechanical coupling coefficient. It should be understood that if the number of piezoelectric layers is more than two, the calibrated electromechanical coupling coefficients corresponding to the scandium doping concentrations of the remaining piezoelectric layers can be greater than or less than the target effective electromechanical coupling coefficient. Step S12 can calculate the acoustic impedance corresponding to each piezoelectric layer according to the scandium doping concentration using the existing acoustic impedance calculation algorithm. Step S12 can calculate the interface correction term of the piezoelectric layer according to the acoustic impedance of adjacent piezoelectric layers using the existing interface correction term calculation algorithm. This interface correction term can correct the interface effect generated due to different acoustic impedances between adjacent piezoelectric layers, so that the subsequent design of the bulk acoustic wave resonator can more accurately consider the mutual influence between layer structures. Since the effective electromechanical coupling coefficient of the bulk acoustic wave resonator is associated with the scandium doping concentration of the piezoelectric layer and the thickness ratio of piezoelectric layers with different scandium doping concentrations, and the target effective electromechanical coupling coefficient, calibrated electromechanical coupling coefficient, and interface correction term in step S13 are all determined values, step S13 can adjust the actual effective electromechanical coupling coefficient of the bulk acoustic wave resonator to the target effective electromechanical coupling coefficient by changing the thickness ratio of the piezoelectric layer, and determine the thickness ratio of the piezoelectric layer at this time as the final thickness ratio of the piezoelectric layer. The principle of step S14 for determining the thickness of each piezoelectric layer according to the target resonator frequency and thickness ratio is the same as the principle of step S1 for determining the thickness of each piezoelectric layer above, and will not be elaborated in detail here. Since this embodiment introduces an interface correction term when determining the thickness of each piezoelectric layer, that is, this embodiment is equivalent to correcting the interface effect generated due to different acoustic impedances between adjacent piezoelectric layers when determining the thickness of each piezoelectric layer. Therefore, this embodiment can effectively avoid the situation where the interface effect is generated due to different acoustic impedances between adjacent piezoelectric layers, and the actual effective electromechanical coupling coefficient of the finally designed bulk acoustic wave resonator is different from the target effective electromechanical coupling coefficient, thereby effectively improving the design accuracy of the bulk acoustic wave resonator design method.It should be understood that in this embodiment, the calibrated electromechanical coupling coefficient can be obtained by querying a pre-constructed mapping relationship table of doping concentration and effective electromechanical coupling coefficient according to the scandium doping concentration. In this embodiment, the calibrated electromechanical coupling coefficient can also be calculated according to the scandium doping concentration by using Equation (15). Specifically, Equation (15) is: (15); where represents the calibrated electromechanical coupling coefficient, represents the square of the piezoelectric stress constant of the piezoelectric layer with a scandium doping concentration of x. The piezoelectric stress constant of the piezoelectric layer with a scandium doping concentration of x is calculated by Equation (4), represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x under constant strain, represents the elastic stiffness constant (preset value). The target effective electromechanical coupling coefficient of this embodiment needs to satisfy the relationship shown in Equation (16). Equation (16) is: (16); where represents the target effective electromechanical coupling coefficient, represents the calibrated electromechanical coupling coefficient corresponding to the i-th piezoelectric layer, d i represents the thickness corresponding to the i-th piezoelectric layer, represents the interface correction term.

[0031] In some preferred embodiments, step S12 includes: S121. For each piezoelectric layer, calculate the material sound velocity, material density, and piezoelectric stress constant according to the scandium doping concentration, and then calculate the acoustic impedance of this piezoelectric layer according to the material sound velocity and material density; S122. Calculate the interface correction term according to the acoustic impedance and piezoelectric stress constant of adjacent piezoelectric layers.

[0032] Since the material sound velocity, material density, and piezoelectric stress constant of the piezoelectric layer are all related to the scandium doping concentration of the piezoelectric layer, step S121 can calculate the material sound velocity, material density, and piezoelectric stress constant according to the scandium doping concentration, and then calculate the acoustic impedance according to the material sound velocity and material density.

[0033] In some preferred embodiments, the calculation formula of the material sound velocity is as shown in Equation (1): (1); where represents the material sound velocity of the piezoelectric layer with a scandium doping concentration of x, and x represents the scandium doping concentration; The calculation formula of the material density is as shown in Equation (2): (2); where represents the material density of the piezoelectric layer with a scandium doping concentration of x; The calculation formula for the acoustic impedance of the piezoelectric layer is shown in Equation (3): (3); Wherein, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x; The calculation formula for the piezoelectric stress constant is shown in Equation (4): (4); Wherein, represents the piezoelectric stress constant of the piezoelectric layer with a scandium doping concentration of x, represents the piezoelectric stress constant of aluminum nitride, and α, β, and are all pre-calibrated fitting parameters; The calculation formula for the interface correction term is shown in Equation (5): (5); Wherein, represents the interface correction term, Z k represents the acoustic impedance corresponding to one of the adjacent piezoelectric layers, Z l represents the acoustic impedance corresponding to the other piezoelectric layer in the adjacent piezoelectric layers, e 33_k represents Z k corresponding to the piezoelectric stress constant of the piezoelectric layer, e 33_l represents Z l corresponding to the piezoelectric stress constant of the piezoelectric layer.

[0034] It should be understood that the piezoelectric stress constant of aluminum nitride in this embodiment is a preset value, and Z k and Z l in this embodiment are calculated from Equation (3).

[0035] In some preferred embodiments, the acoustic parameters further include phase accumulation, acoustic wave amplitude modulation, acoustic wave reflection, and wave number. The phase accumulation in this embodiment can characterize the phase change of the acoustic wave after passing through the piezoelectric layer. The acoustic wave amplitude modulation in this embodiment can reflect the modulation of the acoustic wave amplitude by the acoustic impedance of the piezoelectric layer. The acoustic wave reflection in this embodiment can reflect the acoustic wave reflection caused by the difference in acoustic impedance between different interfaces. The wave number in this embodiment can characterize the spatial frequency characteristics of the acoustic wave.

[0036] In some preferred embodiments, the calculation formula for phase accumulation is shown in Equation (6): (6); Wherein, A represents phase accumulation, m represents wave number, and d represents the thickness of the piezoelectric layer; The calculation formula for wave number is shown in Equation (7): (7); Wherein, m represents the wave number, π represents the pi, and f represents the target resonator frequency. represents the sound velocity of the piezoelectric layer with a scandium doping concentration of x; The calculation formula for acoustic wave amplitude modulation is shown in Equation (8): B (8); Wherein, B represents the acoustic wave amplitude modulation, j represents the imaginary number, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x; The calculation formula for acoustic wave reflection is shown in Equation (9): (9); Wherein, C represents the acoustic wave reflection.

[0037] It should be understood that the sound velocity of the piezoelectric layer with a scandium doping concentration of x in this embodiment is calculated by Equation (1).

[0038] In some preferred embodiments, the piezoelectric coupling parameters include electric field stress coupling, induced charge density, and nonlinear polarization effect. The electric field stress coupling in this embodiment can reflect the interaction between the electric field and mechanical stress in the piezoelectric material. The induced charge density in this embodiment can reflect the amount of charge generated in the piezoelectric material when it is subjected to mechanical stress. The nonlinear polarization effect in this embodiment can reflect the nonlinear characteristics of the piezoelectric material under high electric fields. This embodiment can make the Mason model more comprehensively and accurately describe the physical properties of the piezoelectric layer by incorporating the electric field stress coupling, induced charge density, and nonlinear polarization effect into the calculation of the piezoelectric coupling parameters, thereby improving the accuracy and reliability of the design of the bulk acoustic wave resonator.

[0039] In some preferred embodiments, the calculation formula for electric field stress coupling is shown in Equation (10): (10); Wherein, E and G together represent the electric field stress coupling, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x, represents the piezoelectric stress constant of the piezoelectric layer with a scandium doping concentration of x, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, m represents the wave number, π represents the pi, f represents the target resonator frequency, and d represents the thickness of the piezoelectric layer; The calculation formula for the dielectric constant is shown in Equation (11): (11); Wherein, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, represents the dielectric constant of aluminum nitride, and both δ and η are pre-calibrated fitting parameters; The calculation formula for the induced charge density is shown in Equation (12): (12); where F represents the induced charge density; The calculation formula for the non - linear polarization effect is shown in Equation (13): (13); where H represents the non - linear polarization effect.

[0040] In some preferred embodiments, the calculation formula for the static capacitance parameter is shown in Equation (14): (14); where I and J together represent the static capacitance parameter, j represents the imaginary number, π represents the pi, f represents the target resonator frequency, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, m represents the wave number, and d represents the thickness of the piezoelectric layer.

[0041] In some preferred embodiments, step S3 includes: S31. Calculating the reflection coefficient of each interface according to the acoustic impedance of the adjacent layer structure corresponding to the interface; S32. For each interface, calculating the interface impedance corresponding to each interface according to the reflection coefficient, the preset interface transition layer thickness, and the material wavelength of the corresponding adjacent layer structure, so as to calculate the interface impedance of the adjacent layer structure.

[0042] The interface of this embodiment can reflect the contact surface of the adjacent layer structures. Each interface corresponds to two adjacent layer structures. Specifically, the calculation formula of step S31 is shown in Equation (17): (17); where Γ represents the reflection coefficient of the interface, Z j and Z i represent the acoustic impedance of the adjacent layer structures corresponding to the interface. The calculation formula of step S32 is shown in Equation (18): (18); where R bi represents the interface impedance of the i - th interface, k represents a pre - calibrated fitting parameter, Γ i represents the reflection coefficient of the i - th interface, d b represents the preset interface transition layer thickness, λ k and λ l represent the material wavelengths of the adjacent layer structures corresponding to the i - th interface.

[0043] As can be seen from the above, a method for designing a bulk acoustic wave resonator provided by the present application can calculate the physical parameters of each piezoelectric layer by calculating the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters of each piezoelectric layer based on the target effective electromechanical coupling coefficient and the target resonator frequency, and can quantify the interface effect by calculating the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures. Since all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode material, and all the interface impedances are input into the Mason model in the present application, the present application enables the Mason model to comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effects between each layer structure, thereby effectively solving the problems that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers using the Mason model due to the inability to characterize the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effects between each layer structure in the bulk acoustic wave resonator.

[0044] In a second aspect, the present application further provides a bulk acoustic wave resonator, which is designed by the method for designing a bulk acoustic wave resonator provided in the first aspect above.

[0045] A bulk acoustic wave resonator provided by the present application is designed by the method for designing a bulk acoustic wave resonator provided in the first aspect above. The principle of the bulk acoustic wave resonator provided in this embodiment is the same as that of the method for designing a bulk acoustic wave resonator provided in the first aspect above, and will not be elaborated in detail here.

[0046] As can be seen from the above, a bulk acoustic wave resonator and a design method thereof provided by the present application can calculate the physical parameters of each piezoelectric layer by calculating the acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters of each piezoelectric layer based on the target effective electromechanical coupling coefficient and the target resonator frequency, and can quantify the interface effect by calculating the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures. Since all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode material, and all the interface impedances are input into the Mason model in the present application, the present application enables the Mason model to comprehensively consider the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effects between each layer structure, thereby effectively solving the problems that it is impossible to design a bulk acoustic wave resonator including multiple piezoelectric layers using the Mason model due to the inability to characterize the influence of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the error between the predicted resonance frequency and the actual resonance frequency of the bulk acoustic wave resonator is too large due to the lack of consideration of the interface effects between each layer structure in the bulk acoustic wave resonator.

[0047] In the embodiments provided in the present application, it should be understood that, in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations.

[0048] The above are only the embodiments of the present application and are not intended to limit the protection scope of the present application. For those skilled in the art, the present application may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for designing a bulk acoustic wave resonator, characterized in that: The BAW resonator design method comprises the following steps: S1. Determine the scandium doping concentration and thickness corresponding to the plurality of piezoelectric layers according to the target effective electromechanical coupling coefficient and the target resonator frequency, and determine the electrode material and its corresponding acoustic impedance according to the target loss performance; S2. For each of the piezoelectric layers, calculating acoustic parameters, piezoelectric coupling parameters and static capacitance parameters according to the corresponding scandium doping concentration and / or thickness thereof, wherein the acoustic parameters include acoustic impedance; S3, calculating the interface impedance of the adjacent layer structure according to the acoustic impedance of the adjacent layer structure; S4. Input all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode materials and all the interface impedances into the Mason model to complete the BAW resonator design.

2. The method for designing a bulk acoustic wave resonator according to claim 1, characterized in that: Step S1 includes: S11, determining scandium doping concentrations corresponding to a plurality of piezoelectric layers according to a target effective electromechanical coupling coefficient, wherein a calibrated electromechanical coupling coefficient corresponding to at least one of the scandium doping concentrations is smaller than the target effective electromechanical coupling coefficient and a calibrated electromechanical coupling coefficient of at least one of the piezoelectric layers is larger than the target effective electromechanical coupling coefficient; S12, calculating the acoustic impedance corresponding to each of the piezoelectric layers according to the scandium doping concentration, and then calculating the interface correction term according to the acoustic impedance of the adjacent piezoelectric layers; S13, determining the thickness ratio of the piezoelectric layer according to the target effective electromechanical coupling coefficient, the calibrated electromechanical coupling coefficients corresponding to all the piezoelectric layers, and all the interface correction terms; S14, determining the thickness of each piezoelectric layer according to the target resonator frequency and the thickness ratio.

3. The method for designing a bulk acoustic wave resonator according to claim 2, characterized in that: Step S12 includes: S121, for each of the piezoelectric layers, calculating the material sound velocity, material density and piezoelectric stress constant according to the scandium doping concentration, and then calculating the acoustic impedance of the piezoelectric layer according to the material sound velocity and the material density; S122. Calculate the interface correction term based on the acoustic impedance and piezoelectric stress constant of the adjacent piezoelectric layers.

4. The method for designing a bulk acoustic wave resonator according to claim 3, characterized in that: The calculation formula of the sound velocity of the material is shown as follows: ； in, represents the material acoustic velocity of the piezoelectric layer with a scandium doping concentration of x, where x represents the scandium doping concentration; The calculation formula of the material density is shown as follows: ； in, represents the material density of the piezoelectric layer with scandium doping concentration x; The calculation formula of the acoustic impedance of the piezoelectric layer is as follows: ； in, represents the acoustic impedance of the piezoelectric layer with scandium doping concentration x; The calculation formula of the piezoelectric stress constant is shown as follows: ； in, represents the piezoelectric stress constant of the piezoelectric layer with scandium doping concentration x, represents the piezoelectric stress constants of aluminum nitride, α, β and All are pre-calibrated fitting parameters; The calculation formula of the interface correction term is as follows: ； in, Indicates the interface correction item, Z k represents the acoustic impedance of one of the adjacent piezoelectric layers, Z l represents the acoustic impedance of the other piezoelectric layer in the adjacent piezoelectric layer, e 33_k Represents Z k The corresponding piezoelectric stress constant of the piezoelectric layer, e 33_l Represents Z l The corresponding piezoelectric stress constant of the piezoelectric layer.

5. The method for designing a bulk acoustic wave resonator according to claim 1, characterized in that: The acoustic parameters also include phase accumulation, acoustic wave amplitude modulation, acoustic wave reflection and wave number.

6. The method for designing a bulk acoustic wave resonator according to claim 5, characterized in that: The calculation formula of the phase accumulation is shown as follows: ； Where A represents phase accumulation, m represents wave number, and d represents the thickness of the piezoelectric layer; The calculation formula of the wave number is shown as follows: ； Where m represents the wave number, π represents the circumference of a circle, and f represents the target resonator frequency. represents the material acoustic velocity of the piezoelectric layer with scandium doping concentration x; The calculation formula of the sound wave amplitude adjustment is shown as follows: B ； Among them, B represents the sound wave amplitude adjustment, j represents the imaginary number, represents the acoustic impedance of the piezoelectric layer with a scandium doping concentration of x; The calculation formula of the sound wave reflection is shown as follows: ； Wherein, C represents the sound wave reflection.

7. The method for designing a bulk acoustic wave resonator according to claim 1, characterized in that: The piezoelectric coupling parameters include electric field stress coupling, induced charge density and nonlinear polarization effect.

8. The method for designing a bulk acoustic wave resonator according to claim 7, characterized in that: The calculation formula of the electric field stress coupling is shown as follows: ； Among them, E and G together represent the electric field stress coupling, represents the acoustic impedance of the piezoelectric layer with scandium doping concentration x, represents the piezoelectric stress constant of the piezoelectric layer with scandium doping concentration x, represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, m represents the wave number, π represents the circumference of a circle, f represents the target resonator frequency, and d represents the thickness of the piezoelectric layer; The calculation formula of the dielectric constant is shown as follows: ； in, represents the dielectric constant of the piezoelectric layer with scandium doping concentration x, represents the dielectric constant of aluminum nitride, δ and η are pre-calibrated fitting parameters; The calculation formula of the induced charge density is shown as follows: ； Where, F represents the induced charge density; The calculation formula of the nonlinear polarization effect is shown as follows: ； Where H represents the nonlinear polarization effect.

9. The method for designing a bulk acoustic wave resonator according to claim 1, characterized in that: The calculation formula of the static capacitance parameter is shown as follows: ； Where I and J together represent the static capacitance parameter, j represents an imaginary number, π represents pi, and f represents the target resonator frequency. represents the dielectric constant of the piezoelectric layer with a scandium doping concentration of x, m represents the wave number, and d represents the thickness of the piezoelectric layer.

10. A bulk acoustic wave resonator, characterized in that: The BAW resonator is designed by the BAW resonator design method according to any one of claims 1 to 9.

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