A bulk acoustic wave resonator and a design method thereof

Abstract

The present application relates to the technical field of bulk acoustic wave resonators, and specifically provides a bulk acoustic wave resonator and a design method thereof, the method comprising the steps of: 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, and determining the electrode material and its corresponding acoustic impedance according to a target loss performance; for each piezoelectric layer, calculating the acoustic parameters, piezoelectric coupling parameters and static capacitance parameters according to its corresponding scandium doping concentration and thickness, the acoustic parameters including the acoustic impedance; calculating the interface impedance of adjacent layer structures according to the acoustic impedance of adjacent layer structures; inputting all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials and all interface impedances into a Mason model to complete the bulk acoustic wave resonator design; the method 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 the various layer structures.

Description

Technical Field

[0001] The present application relates to the technical field of bulk acoustic wave resonators, and in particular 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 to design bulk acoustic wave resonators. That is, the bulk acoustic wave resonator design method of the related art can only design a bulk acoustic wave resonator including a single piezoelectric layer. Therefore, the related art has a problem that the Mason model cannot be used 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. Moreover, since the related bulk acoustic wave resonator design method does not consider the interface effect between the various layer structures in the bulk acoustic wave resonator, and the interface effect is related to the resonant frequency of the bulk acoustic wave resonator, the related art also has a problem that the error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator is too large due to the failure to consider the interface effect between the various layer structures in the bulk acoustic wave resonator.

[0003] There is no effective technical solution to the above problems. It should be noted that the above information disclosed in this section is only used to understand the background of the present invention, and therefore may contain information that does not constitute 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 problem that a bulk acoustic wave resonator including multiple piezoelectric layers cannot be designed 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 problem that the error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator is too large due to the failure to consider the interface effect between the various layer structures in the bulk acoustic wave resonator.

[0005] In a first aspect, the present application provides a bulk acoustic wave resonator design method, which comprises the following steps:

[0006] S1. Determine the scandium doping concentration and thickness corresponding to the 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;

[0007] S2. For each piezoelectric layer, calculate acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters according to its corresponding scandium doping concentration and / or thickness, where the acoustic parameters include acoustic impedance;

[0008] S3. calculating the interface impedance of the adjacent layer structure based on the acoustic impedance of the adjacent layer structure;

[0009] S4. Input all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials, and all interface impedances into the Mason model to complete the BAW resonator design.

[0010] The present application provides a method for designing a bulk acoustic wave resonator, which 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 interface effect by calculating the interface impedance of adjacent layer structures based on the acoustic impedance of the 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 enables the Mason model to comprehensively consider the impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effects between the various layer structures, thereby effectively solving the problem that a bulk acoustic wave resonator including multiple piezoelectric layers cannot be designed using the Mason model due to the inability to characterize the impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the problem that the error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator is too large due to the failure to consider the interface effects between the various layer structures in the bulk acoustic wave resonator.

[0011] Optionally, step S1 includes:

[0012] S11, determining scandium doping concentrations corresponding to the plurality of piezoelectric layers according to a target effective electromechanical coupling coefficient, wherein a calibrated electromechanical coupling coefficient corresponding to at least one scandium doping concentration is smaller than the target effective electromechanical coupling coefficient and a calibrated electromechanical coupling coefficient of at least one piezoelectric layer is larger than the target effective electromechanical coupling coefficient;

[0013] S12, calculating the acoustic impedance corresponding to each piezoelectric layer according to the scandium doping concentration, and then calculating the interface correction term according to the acoustic impedance of the adjacent piezoelectric layer;

[0014] 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 piezoelectric layers, and all interface correction terms;

[0015] S14. Determine the thickness of each piezoelectric layer according to the target resonator frequency and thickness ratio.

[0016] 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 caused by the different acoustic impedances between adjacent piezoelectric layers when determining the thickness of each piezoelectric layer, this technical solution can effectively avoid the interface effect caused by the different acoustic impedances between adjacent piezoelectric layers, and the situation where the actual effective electromechanical coupling coefficient of the bulk acoustic wave resonator finally designed differs from the target effective electromechanical coupling coefficient, thereby effectively improving the design accuracy of the bulk acoustic wave resonator design method.

[0017] Optionally, step S12 includes:

[0018] 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;

[0019] S122. Calculate an interface correction term based on the acoustic impedance and piezoelectric stress constant of adjacent piezoelectric layers.

[0020] Optionally, the calculation formula for the material sound velocity is shown in formula (1):

[0021] (1);

[0022] in, represents the material sound velocity of the piezoelectric layer with a scandium doping concentration of x, where x represents the scandium doping concentration;

[0023] The calculation formula of material density is shown in formula (2):

[0024] (2);

[0025] in, represents the material density of the piezoelectric layer with scandium doping concentration x;

[0026] The calculation formula of the acoustic impedance of the piezoelectric layer is shown in formula (3):

[0027] (3);

[0028] in, represents the acoustic impedance of the piezoelectric layer with scandium doping concentration x;

[0029] The calculation formula of the piezoelectric stress constant is shown in formula (4):

[0030] (4);

[0031] 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;

[0032] The calculation formula of the interface correction term is shown in formula (5):

[0033] (5);

[0034] in, Indicates 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.

[0035] Optionally, the acoustic parameters further include phase accumulation, acoustic wave amplitude modulation, acoustic wave reflection and wave number.

[0036] Optionally, the calculation formula for phase accumulation is shown in formula (6):

[0037] (6);

[0038] Where A represents the phase accumulation, m represents the wave number, and d represents the thickness of the piezoelectric layer;

[0039] The calculation formula of wave number is shown in formula (7):

[0040] (7);

[0041] 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;

[0042] The calculation formula for the acoustic wave amplitude adjustment is shown in formula (8):

[0043] B (8);

[0044] 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;

[0045] The calculation formula for sound wave reflection is shown in formula (9):

[0046] (9);

[0047] Where C represents the sound wave reflection.

[0048] Optionally, the piezoelectric coupling parameters include electric field stress coupling, induced charge density and nonlinear polarization effect.

[0049] Optionally, the calculation formula for electric field stress coupling is shown in formula (10):

[0050] (10);

[0051] 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 the circle, f represents the target resonator frequency, and d represents the thickness of the piezoelectric layer;

[0052] The calculation formula of the dielectric constant is shown in formula (11):

[0053] (11);

[0054] 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;

[0055] The calculation formula of induced charge density is shown in formula (12):

[0056] (12);

[0057] Where F represents the induced charge density;

[0058] The calculation formula for the nonlinear polarization effect is shown in formula (13):

[0059] (13);

[0060] Where H represents the nonlinear polarization effect.

[0061] Optionally, the calculation formula of the static capacitance parameter is shown in formula (14):

[0062] (14);

[0063] 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.

[0064] In a second aspect, the present application further provides a bulk acoustic wave resonator, which is designed by the bulk acoustic wave resonator design method provided in the first aspect.

[0065] The present application provides a bulk acoustic wave resonator designed by a bulk acoustic wave resonator design method. The 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 a target effective electromechanical coupling coefficient and a target resonator frequency, and quantify the interface effect by calculating the interface impedance of adjacent layer structures based on the acoustic impedance of the 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 a Mason model, the present application enables the Mason model to comprehensively consider the impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effects between the various layer structures, thereby effectively solving the problem of being unable to use the Mason model to design a bulk acoustic wave resonator including multiple piezoelectric layers due to the inability to characterize the impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the problem of excessive error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator due to the failure to consider the interface effects between the various layer structures in the bulk acoustic wave resonator.

[0066] From the above, it can be seen that the present application provides a bulk acoustic wave resonator and a design method thereof, which 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 interface effect by calculating the interface 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 interface impedances into the Mason model, 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 the various layer structures, thereby effectively solving the problem that a bulk acoustic wave resonator including multiple piezoelectric layers cannot be designed 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 problem that the error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator is too large due to the failure to consider the interface effects between the various layer structures in the bulk acoustic wave resonator. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A flow chart of a bulk acoustic wave resonator design method provided in an embodiment of the present application.

[0068] Figure 2 Schematic diagram of the Mason model provided in the embodiments of the present application. DETAILED DESCRIPTION

[0069] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the 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 of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work fall within the scope of protection of the present application.

[0070] It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and should not be understood as indicating or implying relative importance.

[0071] First, as Figure 1 and Figure 2 As shown, the present application provides a bulk acoustic wave resonator design method, which includes the following steps:

[0072] S1. Determine the scandium doping concentration and thickness corresponding to the 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;

[0073] S2. For each piezoelectric layer, calculate acoustic parameters, piezoelectric coupling parameters, and static capacitance parameters according to its corresponding scandium doping concentration and / or thickness, where the acoustic parameters include acoustic impedance;

[0074] S3. calculating the interface impedance of the adjacent layer structure based on the acoustic impedance of the adjacent layer structure;

[0075] S4. Input all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials, and all interface impedances into the Mason model to complete the BAW resonator design.

[0076] Among them, the bulk acoustic wave resonator design method provided in 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 there are two piezoelectric layers, the material of one piezoelectric layer is aluminum nitride, and the material of the other piezoelectric layer is scandium-doped aluminum nitride. For another example, when there are multiple piezoelectric layers, the material of one piezoelectric layer is aluminum nitride, and the materials of the other piezoelectric layers are all scandium-doped aluminum nitride, and the scandium doping concentrations of the different scandium-doped aluminum nitrides are different. The target effective electromechanical coupling coefficient of step S1 is the effective electromechanical coupling coefficient of the target bulk acoustic wave resonator (the bulk acoustic wave resonator ultimately designed), the target resonator frequency of step S1 is the resonant frequency of the target bulk acoustic wave resonator, and the target loss performance of step S1 is the loss performance of the target bulk acoustic wave resonator. The target resonator frequency and target loss performance of this embodiment are preferably parameters pre-designed according to product requirements. Since the effective electromechanical coupling coefficient of a BAW resonator is associated with the scandium doping concentration of the piezoelectric layers and the thickness ratio of the piezoelectric layers, and the target resonator frequency of the BAW resonator is associated with the total thickness of all piezoelectric layers, step S1 can first determine the scandium doping concentration and thickness ratio corresponding to the multiple piezoelectric layers based on the target effective electromechanical coupling coefficient and the target resonator frequency, then determine the total thickness of the piezoelectric layers based on the target resonator frequency, and finally determine the thickness of each piezoelectric layer based on the total thickness of the piezoelectric layers and the thickness ratio of the piezoelectric layers, thereby determining the scandium doping concentration and thickness corresponding to the multiple piezoelectric layers based on the target effective electromechanical coupling coefficient and the target resonator frequency. Since the loss performance of a BAW resonator is associated with the electrode material (the material of the top and bottom electrodes), step S1 can determine the electrode material based on the target loss performance. Since the electrode material is not doped, 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 material determined by the target loss performance by querying a pre-established mapping table between electrode materials and acoustic impedances based on the electrode material 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 may vary the number of piezoelectric layers included in the BAW resonator based on actual needs. Preferably, the BAW resonator of this embodiment also includes a protective layer, and the acoustic impedance and other related parameters of the protective layer are preset values.

[0077] Step S2 can use the existing piezoelectric layer physical parameter calculation algorithm or piezoelectric layer physical parameter calculation model to 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, that is, step S2 is equivalent to calculating the physical parameters of each piezoelectric layer separately.

[0078] Because the interface effect occurs in contacting layer structures, and the magnitude of the interface impedance can reflect the degree of the interface effect, this embodiment is equivalent to quantifying the interface effect using the interface impedance. The interface impedance is associated with the acoustic impedance of the adjacent layer structure (the contacting layer structure). Therefore, step S3 can calculate the interface impedance of the adjacent layer structure based on 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 multilayer structure by introducing the interface impedance.

[0079] Since step S4 inputs all acoustic parameters, all static capacitance parameters, all piezoelectric coupling parameters, electrode materials, and all interface 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 impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effects between the various layer structures.

[0080] The present application provides a bulk acoustic wave resonator design method that 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 a target effective electromechanical coupling coefficient and a target resonator frequency, and quantify the interface effect by calculating the interface impedance of adjacent layer structures based on the acoustic impedance of the 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 a Mason model, the present application enables the Mason model to comprehensively consider the impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator and the interface effects between the various layer structures, thereby effectively solving the problem of being unable to use the Mason model to design a bulk acoustic wave resonator including multiple piezoelectric layers due to the inability to characterize the impact of the physical parameter differences of multiple piezoelectric layers on the bulk acoustic wave resonator, and the problem of excessive error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator due to not considering the interface effects between the various layer structures 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.

[0081] In some preferred embodiments, step S1 includes:

[0082] S11, determining scandium doping concentrations corresponding to the plurality of piezoelectric layers according to a target effective electromechanical coupling coefficient, wherein a calibrated electromechanical coupling coefficient corresponding to at least one scandium doping concentration is smaller than the target effective electromechanical coupling coefficient and a calibrated electromechanical coupling coefficient of at least one piezoelectric layer is larger than the target effective electromechanical coupling coefficient;

[0083] S12, calculating the acoustic impedance corresponding to each piezoelectric layer according to the scandium doping concentration, and then calculating the interface correction term according to the acoustic impedance of the adjacent piezoelectric layer;

[0084] 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 piezoelectric layers, and all interface correction terms;

[0085] S14. Determine the thickness of each piezoelectric layer according to the target resonator frequency and thickness ratio.

[0086] The calibrated electromechanical coupling coefficient of this embodiment is a pre-calibrated effective electromechanical coupling coefficient. The working principle of step S11 is: 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 related to the scandium doping concentration, it may be impossible to directly prepare scandium-doped aluminum nitride that meets the target effective electromechanical coupling coefficient requirement based on the existing doping process. Aluminum, 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 final BAW resonator can meet the target effective electromechanical coupling coefficient. It should be understood that if the number of piezoelectric layers is two or more, the calibrated electromechanical coupling coefficient corresponding to the scandium doping concentration of the remaining piezoelectric layers can be greater than the target effective electromechanical coupling coefficient or less than the target effective electromechanical coupling coefficient. Step S12 can use the existing acoustic impedance calculation algorithm to calculate the acoustic impedance corresponding to each piezoelectric layer according to the scandium doping concentration. Step S12 can use the existing interface correction term calculation algorithm to calculate the interface correction term of the piezoelectric layer according to the acoustic impedance of the adjacent piezoelectric layers. The interface correction term can correct the interface effect between the adjacent piezoelectric layers due to the different acoustic impedances, so that the subsequent BAW resonator design can more accurately consider the mutual influence between the layer structures. Since the effective electromechanical coupling coefficient of the BAW resonator is related to the scandium doping concentration of the piezoelectric layer and the thickness ratio of the 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 fixed values, step S13 can adjust the actual effective electromechanical coupling coefficient of the BAW resonator to the target effective electromechanical coupling coefficient by changing the thickness ratio of the piezoelectric layers, and determine the thickness ratio of the piezoelectric layers at this time as the final thickness ratio of the piezoelectric layers. The principle of determining the thickness of each piezoelectric layer based on the target resonator frequency and thickness ratio in step S14 is the same as the principle of determining the thickness of each piezoelectric layer in step S1 above, and will not be discussed 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 caused by the different acoustic impedances between adjacent piezoelectric layers when determining the thickness of each piezoelectric layer, this embodiment can effectively avoid the interface effect caused by the different acoustic impedances between adjacent piezoelectric layers, and the situation where the actual effective electromechanical coupling coefficient of the BAW resonator finally designed differs from the target effective electromechanical coupling coefficient, thereby effectively improving the design accuracy of the BAW resonator design method.It should be understood that this embodiment can obtain the calibrated electromechanical coupling coefficient by querying a pre-constructed mapping relationship table of doping concentration and effective electromechanical coupling coefficient according to the scandium doping concentration. This embodiment can also use formula (15) to calculate the calibrated electromechanical coupling coefficient according to the scandium doping concentration. Specifically, formula (15) is: (15); among them, 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 formula (4), represents the dielectric constant of the piezoelectric layer with scandium doping concentration 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 formula (16), which is: (16); among them, 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, Indicates interface correction items.

[0087] In some preferred embodiments, step S12 includes:

[0088] 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;

[0089] S122. Calculate an interface correction term based on the acoustic impedance and piezoelectric stress constant of adjacent piezoelectric layers.

[0090] 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 based on the material sound velocity and material density.

[0091] In some preferred embodiments, the calculation formula of the material sound velocity is shown in formula (1):

[0092] (1);

[0093] in, represents the material sound velocity of the piezoelectric layer with a scandium doping concentration of x, where x represents the scandium doping concentration;

[0094] The calculation formula of material density is shown in formula (2):

[0095] (2);

[0096] in, represents the material density of the piezoelectric layer with scandium doping concentration x;

[0097] The calculation formula of the acoustic impedance of the piezoelectric layer is shown in formula (3):

[0098] (3);

[0099] in, represents the acoustic impedance of the piezoelectric layer with scandium doping concentration x;

[0100] The calculation formula of the piezoelectric stress constant is shown in formula (4):

[0101] (4);

[0102] 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;

[0103] The calculation formula of the interface correction term is shown in formula (5):

[0104] (5);

[0105] in, Indicates 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.

[0106] It should be understood that the piezoelectric stress constant of the aluminum nitride of this embodiment is a preset value. k and Z l Calculated by formula (3).

[0107] In some preferred embodiments, the acoustic parameters further include phase accumulation, acoustic wave amplitude adjustment, acoustic wave reflection, and wave number. Phase accumulation in this embodiment can characterize the phase change of the acoustic wave after passing through the piezoelectric layer, acoustic wave amplitude adjustment in this embodiment can reflect the adjustment of the acoustic impedance of the piezoelectric layer to the acoustic wave amplitude, acoustic wave reflection in this embodiment can reflect the acoustic wave reflection caused by the difference in acoustic impedance of different interface components, and wave number in this embodiment can characterize the spatial frequency characteristics of the acoustic wave.

[0108] In some preferred embodiments, the calculation formula of phase accumulation is shown in formula (6):

[0109] (6);

[0110] Where A represents the phase accumulation, m represents the wave number, and d represents the thickness of the piezoelectric layer;

[0111] The calculation formula of wave number is shown in formula (7):

[0112] (7);

[0113] 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;

[0114] The calculation formula for the acoustic wave amplitude adjustment is shown in formula (8):

[0115] B (8);

[0116] 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;

[0117] The calculation formula for sound wave reflection is shown in formula (9):

[0118] (9);

[0119] Where C represents the sound wave reflection.

[0120] It should be understood that the material sound velocity of the piezoelectric layer with a scandium doping concentration of x in this embodiment is calculated by formula (1).

[0121] 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 of this embodiment can reflect the interaction between the electric field and mechanical stress in the piezoelectric material, the induced charge density of this embodiment can reflect the amount of charge generated by the piezoelectric material when subjected to mechanical stress, and the nonlinear polarization effect of this embodiment can reflect the nonlinear characteristics of the piezoelectric material under high electric fields. This embodiment can enable the Mason model to more comprehensively and accurately describe the physical properties of the piezoelectric layer by incorporating 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 bulk acoustic wave resonator design.

[0122] In some preferred embodiments, the calculation formula of electric field stress coupling is shown in formula (10):

[0123] (10);

[0124] 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 the circle, f represents the target resonator frequency, and d represents the thickness of the piezoelectric layer;

[0125] The calculation formula of the dielectric constant is shown in formula (11):

[0126] (11);

[0127] 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;

[0128] The calculation formula of induced charge density is shown in formula (12):

[0129] (12);

[0130] Where F represents the induced charge density;

[0131] The calculation formula for the nonlinear polarization effect is shown in formula (13):

[0132] (13);

[0133] Where H represents the nonlinear polarization effect.

[0134] In some preferred embodiments, the calculation formula of the static capacitance parameter is shown in formula (14):

[0135] (14);

[0136] 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.

[0137] In some preferred embodiments, step S3 includes:

[0138] S31, calculating the reflection coefficient of each interface according to the acoustic impedance of the adjacent layer structure corresponding to the interface;

[0139] S32. For each interface, calculate 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.

[0140] The interface of this embodiment can reflect the contact surface of adjacent layer structures. Each interface corresponds to two adjacent layer structures. Specifically, the calculation formula of step S31 is shown in formula (17):

[0141] (17);

[0142] Where Γ represents the reflection coefficient of the interface, Z j and Z i represents the acoustic impedance of the adjacent layer structure corresponding to the interface. The calculation formula of step S32 is shown in formula (18):

[0143] (18);

[0144] Among them, R bi represents the interface impedance of the i-th interface, k represents the pre-calibrated fitting parameter, Γ i represents the reflection coefficient of the i-th interface, d b Indicates the preset interface transition layer thickness, λ k and λ l represents the material wavelength of the adjacent layer structure corresponding to the i-th interface.

[0145] From the above, it can be seen that the present application provides a bulk acoustic wave resonator design method, which 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 interface effect by calculating the interface 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 interface impedances into the Mason model, 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 the various layer structures, thereby effectively solving the problem that a bulk acoustic wave resonator including multiple piezoelectric layers cannot be designed 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 problem that the error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator is too large due to the failure to consider the interface effects between the various layer structures in the bulk acoustic wave resonator.

[0146] In a second aspect, the present application further provides a bulk acoustic wave resonator, which is designed by the bulk acoustic wave resonator design method provided in the first aspect.

[0147] The bulk acoustic wave resonator provided in the present application is designed by the bulk acoustic wave resonator design method provided in the first aspect above. The principle of the bulk acoustic wave resonator provided in this embodiment is the same as the principle of the bulk acoustic wave resonator design method provided in the first aspect above, and will not be discussed in detail here.

[0148] From the above, it can be seen that the present application provides a bulk acoustic wave resonator and a design method thereof, which 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 interface effect by calculating the interface 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 interface impedances into the Mason model, 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 the various layer structures, thereby effectively solving the problem that a bulk acoustic wave resonator including multiple piezoelectric layers cannot be designed 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 problem that the error between the predicted resonant frequency and the actual resonant frequency of the bulk acoustic wave resonator is too large due to the failure to consider the interface effects between the various layer structures in the bulk acoustic wave resonator.

[0149] In the embodiments provided in the present application, it should be understood that, in this document, relational terms such as first and second, etc., are merely 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.

[0150] The above description is merely an embodiment of the present application and is not intended to limit the scope of protection of the present application. For those skilled in the art, various modifications and variations of the present application are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A method for designing a bulk acoustic wave resonator, characterized in that: The bulk acoustic wave resonator design method comprises the following steps: S1. Determining scandium doping concentrations and thicknesses corresponding to the plurality of piezoelectric layers based on a target effective electromechanical coupling coefficient and a target resonator frequency, and determining electrode materials and their corresponding acoustic impedances based on a target loss performance, where the target loss performance is the loss performance of a target bulk acoustic wave resonator; S2. For each of the piezoelectric layers, calculate 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 based on the acoustic impedance of the adjacent layer structure; S4, all the acoustic parameters, all the static capacitance parameters, all the piezoelectric coupling parameters, the electrode materials and all the interface impedances are input into the Mason model to complete the BAW resonator design; 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 an interface correction term according to the acoustic impedance of 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. Determine the thickness of each piezoelectric layer according to the target resonator frequency and the thickness ratio.

2. The method for designing a bulk acoustic wave resonator according to claim 1, wherein: 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 the material density; S122. Calculate an interface correction term based on the acoustic impedance and piezoelectric stress constant of adjacent piezoelectric layers.

3. The method for designing a bulk acoustic wave resonator according to claim 2, wherein: The calculation formula of the sound velocity of the material is shown as follows: ； in, represents the material sound 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 below: ； 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 shown below: ； in, represents the acoustic impedance of the piezoelectric layer with scandium doping concentration x; The calculation formula of the piezoelectric stress constant is shown below: ； 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 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.

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

5. The method for designing a bulk acoustic wave resonator according to claim 4, wherein: The calculation formula of the phase accumulation is shown below: ； Where A represents the phase accumulation, m represents the wave number, and d represents the thickness of the piezoelectric layer; The calculation formula of the wave number is shown below: ； 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 below: 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 below: ； Where C represents the sound wave reflection.

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

7. The method for designing a bulk acoustic wave resonator according to claim 6, wherein: 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 the 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 below: ； 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 below: ； Where F represents the induced charge density; The calculation formula of the nonlinear polarization effect is shown below: ； Where H represents the nonlinear polarization effect.

8. The method for designing a bulk acoustic wave resonator according to claim 1, wherein: The calculation formula of the static capacitance parameter is shown below: ； 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.

9. 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 8.

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