CN114964356B - Aluminum nitride film parameter extraction method - Google Patents
Aluminum nitride film parameter extraction method Download PDFInfo
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- CN114964356B CN114964356B CN202210384332.9A CN202210384332A CN114964356B CN 114964356 B CN114964356 B CN 114964356B CN 202210384332 A CN202210384332 A CN 202210384332A CN 114964356 B CN114964356 B CN 114964356B
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- PMHQVHHXPFUNSP-UHFFFAOYSA-M copper(1+);methylsulfanylmethane;bromide Chemical compound Br[Cu].CSC PMHQVHHXPFUNSP-UHFFFAOYSA-M 0.000 title claims abstract description 126
- 238000000605 extraction Methods 0.000 title claims abstract description 65
- 239000000463 material Substances 0.000 claims abstract description 69
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- 229910044991 metal oxide Inorganic materials 0.000 description 4
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- 239000004065 semiconductor Substances 0.000 description 4
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- PIGFYZPCRLYGLF-UHFFFAOYSA-N Aluminum nitride Chemical compound [Al]#N PIGFYZPCRLYGLF-UHFFFAOYSA-N 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 230000007123 defense Effects 0.000 description 2
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Abstract
The invention provides an aluminum nitride film parameter extraction method, relates to the technical field of material parameter extraction, and can accurately extract the material coefficient of an aluminum nitride film. According to the embodiment of the invention, the method for extracting the parameters of the aluminum nitride film comprises the following steps: extracting a component based on manufacturing parameters of the aluminum nitride film to be tested; measuring the impedance spectrum of the parameter extraction assembly, and calculating to obtain the dielectric constant of the aluminum nitride film to be detected in the parameter extraction assembly according to the impedance spectrum; measuring an attribute parameter of the parameter extraction assembly, and calculating a piezoelectric coefficient and an elastic coefficient of the aluminum nitride film to be measured according to the attribute parameter; and integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be tested to obtain the material parameters of the aluminum nitride film to be tested. In the method provided by the embodiment of the invention, various material coefficients of the aluminum nitride film are extracted separately, so that the accumulated error can be reduced, and the extraction precision is improved.
Description
Technical Field
The invention relates to the technical field of material parameter extraction, in particular to an aluminum nitride material coefficient.
Background
In recent years, attention has been paid to aluminum nitride (AlN) thin films because of their excellent dielectric constant, being capable of being deposited at low temperature, being compatible with complementary metal oxide semiconductor (Complementary Metal Oxide Semiconductor, CMOS) processes, and the like, and resonators and filters using AlN thin films as piezoelectric materials are widely used in fields of biomedical science, national defense, military, environmental detection, mobile communication, and the like, wherein the material coefficients of AlN thin films are critical to the design and mass production of these devices, and the material coefficients of AlN thin films include piezoelectric coefficients, elastic coefficients, and dielectric constants.
However, in the case where a large error is commonly found in the related art for extracting the material coefficient of the AlN thin film, the device produced will also have a large error. In addition, as the size of the device is reduced, the size of the AlN film is reduced, and the material coefficient matrix of the AlN film is changed greatly along with the change of the size and the adopted growth process, so that errors are more likely to occur. Therefore, there is an urgent need in the scientific and industrial fields for a method capable of precisely extracting the material coefficient of an AlN film.
Disclosure of Invention
The present invention aims to solve at least one of the technical problems existing in the prior art. Therefore, the invention provides the aluminum nitride film parameter extraction method which can accurately extract the material coefficient of the aluminum nitride film.
According to the embodiment of the invention, the method for extracting the parameters of the aluminum nitride film comprises the following steps:
extracting a component based on manufacturing parameters of the aluminum nitride film to be tested;
measuring the impedance spectrum of the parameter extraction component, and calculating to obtain the dielectric constant of the aluminum nitride film to be detected in the parameter extraction component according to the impedance spectrum;
measuring attribute parameters of the parameter extraction assembly, and calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the attribute parameters;
and integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be detected to obtain the material parameters of the aluminum nitride film to be detected.
The aluminum nitride film parameter extraction method provided by the embodiment of the invention has at least the following beneficial effects:
extracting parameters of an aluminum nitride film to be detected, firstly manufacturing a parameter extraction component based on the aluminum nitride film to be detected, and then measuring impedance spectrum and attribute parameters of the parameter extraction component. And then, calculating according to the impedance spectrum to obtain the dielectric constant of the aluminum nitride film to be detected in the parameter extraction assembly, and calculating according to the attribute parameters to obtain the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be detected in the parameter extraction assembly. And finally, integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be tested to obtain the material parameters of the aluminum nitride film to be tested. In the method provided by the embodiment of the invention, various material coefficients of the aluminum nitride film are extracted separately, so that accumulated errors can be reduced, and the extraction precision is relatively high.
Optionally, according to some embodiments of the present invention, the parameter extraction component includes a transverse bulk acoustic resonator, a longitudinal bulk acoustic resonator, a radial bulk acoustic resonator, a thickness shear bulk acoustic resonator, and a lamb wave resonator, and the parameter extraction component is fabricated based on an aluminum nitride film to be measured, including:
and manufacturing the transverse bulk acoustic wave resonator, the longitudinal bulk acoustic wave resonator, the radial bulk acoustic wave resonator, the thickness-cut bulk acoustic wave resonator and the lamb wave resonator based on the aluminum nitride film to be tested.
Optionally, according to some embodiments of the invention, the calculating the dielectric constant of the aluminum nitride film to be measured in the parameter extraction component according to the impedance spectrum includes:
obtaining the detuning capacitance of the lamb wave resonator according to the impedance spectrum
Detuning capacitance of the lamb wave resonatorSubstituting the plate capacitance equation +.>Determining dielectric constant->Wherein S is the area of the capacitor electrode plate, d is the distance between the electrode plates, epsilon 0 Is vacuum dielectric constant;
the dielectric constant is setThe detuning capacitance->Substitution formula->Determining dielectric constant->Therein N, W, t e And lambda is the interdigital logarithm, aperture width, thickness and lamb of the lamb wave resonator, respectivelyWavelength of the wave.
Optionally, according to some embodiments of the present invention, the attribute parameters include a resonant frequency and an antiresonant frequency of the parameter extraction component, and a density, a length, and a thickness of the aluminum nitride film to be measured, and the measuring the attribute parameters of the parameter extraction component, and calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the attribute parameters includes:
obtaining the resonant frequency f of the parameter extraction component according to the impedance spectrum r Anti-resonant frequency f a Detecting the density rho, the length L and the thickness t of the aluminum nitride film to be detected;
according to the formulaCalculating the electromechanical coupling coefficient k of the transverse bulk acoustic wave resonator 31 ；
Let said k 31 Said f r Said f a Substituting p and L into formulaObtaining the elasticity coefficient->Piezoelectric coefficient d 31 ；
According to the formulaCalculating to obtain the electromechanical coupling coefficient k of the longitudinal bulk acoustic wave resonator t ；
Let said k t Said f r Said f a Substituting p and t into formula Obtaining the elasticity coefficient->Piezoelectric coefficient d 33 ；
According to the first-order resonant frequency of the radial bulk acoustic wave resonatorAnd second order resonance frequency->Determining the Poisson ratio sigma of the aluminum nitride film to be tested;
let the poisson ratio sigma, theSubstitution formula->Calculating to obtain elasticity coefficient->
According to the formulaCalculating to obtain the electromechanical coupling coefficient k of the thickness shear bulk acoustic wave resonator 15 ；
Let said k 15 Said f r Said f a Substituting p and t into formulaObtaining the elasticity coefficient->Piezoelectric coefficient d 15 。
Optionally, according to some embodiments of the present invention, the calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the attribute parameter further includes:
will be spentF is as follows r Substituting the λ into the formula v=f r Lambda, obtaining the actual measurement wave velocity v in the lamb wave resonator;
the elastic coefficient is setSaid elastic coefficient->Said elastic coefficient->Said elastic coefficient->The piezoelectric coefficient d 15 Said piezoelectric coefficient d 33 Said piezoelectric coefficient d 31 Said dielectric constant->The dielectric constant->Substituting the piezoelectric equation, maxwell equation and elastic dynamics equation of the lamb wave resonator to obtain a wave velocity calculated value v 0 ；
Calculating the wave velocity v 0 Comparing the measured wave velocity v with the measured wave velocity v to obtain a wave velocity difference value;
when the wave velocity difference value is smaller than or equal to a preset error value, obtaining a calculated value v of the wave velocity 0 Corresponding elastic coefficient
Alternatively, according to some embodiments of the present invention, when the wave velocity value is greater than the preset error value, the calculated value v of the wave velocity is adjusted according to the wave velocity value 0 Corresponding elastic coefficient
The adjusted elastic coefficientAnd updating the wave velocity calculated value by using a piezoelectric equation, a Maxwell equation and an elastic dynamics equation of the lamb wave resonator.
Alternatively, according to some embodiments of the invention, the elastic modulusSaid elastic coefficient->Said elastic coefficient->Said elastic coefficient->Said elastic coefficient->Integrating to generate an elastic coefficient matrix in the material parameters>Wherein i represents a stress direction and j represents a strain direction;
the piezoelectric coefficient d 15 Said piezoelectric coefficient d 33 Said piezoelectric coefficient d 31 Integrating to generate piezoelectric strain coefficient matrix in the material parametersWherein m represents the electric field direction;
the dielectric constant is setThe dielectric constant->Integrating to generate a dielectric constant matrix in the material parameters>Where n represents the direction of electrical displacement.
Optionally, according to some embodiments of the invention, the method further comprises:
and establishing finite element analysis simulation according to the material parameters to obtain a de-electrode mass load effect coefficient gamma, wherein the gamma is used for eliminating the influence of the electrode mass load effect.
Optionally, according to some embodiments of the present invention, after integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured to obtain the material parameters of the aluminum nitride film to be measured, the method further includes:
recording and extracting the turns of the material parameters;
when the rotation of extracting the material parameters is less than the preset times, re-measuring the impedance spectrum of the parameter extracting component, and updating the detuned capacitance of the parameter extracting component;
calculating the updated dielectric constant according to the updated detuned capacitance;
re-measuring the attribute parameters of the parameter extraction assembly, and updating the piezoelectric coefficient and the elastic coefficient according to the re-measured attribute parameters;
integrating the updated dielectric constant, the updated piezoelectric coefficient and the updated elastic coefficient to obtain the updated material parameter;
and establishing finite element analysis simulation according to the updated material parameters to obtain a de-electrode mass load effect coefficient gamma, wherein the gamma is used for eliminating the influence of the electrode mass load effect.
Optionally, according to some embodiments of the invention, the method further comprises:
manufacturing a pure pad device excluding a resonator, and measuring a reflection coefficient of the pure pad device;
obtaining the equivalent resistance and the equivalent capacitance of the pure pad device according to the reflection coefficient;
and calculating the scattering parameter according to the equivalent resistance and the equivalent capacitance, wherein the scattering parameter is used for de-embedding a bonding pad carrying the parameter extraction component.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic flow chart of a method for extracting parameters of an aluminum nitride film according to an embodiment of the invention;
fig. 2 is a schematic diagram of constituent elements of a parameter extraction component according to an embodiment of the present invention.
FIG. 3 is a schematic flow chart of another method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention;
FIG. 4 is a schematic flow chart of another method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention;
FIG. 5 is a flow chart of another method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a lamb wave resonator according to an embodiment of the present invention;
FIG. 7 is a flowchart of another method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention;
FIG. 8 is a flowchart of another method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention;
FIG. 9 is a flowchart of another method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention;
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
In the description of the present invention, a number means one or more, a number means two or more, and greater than, less than, exceeding, etc. are understood to not include the present number, and above, below, within, etc. are understood to include the present number. The description of the first and second is for the purpose of distinguishing between technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, it should be understood that the direction or positional relationship indicated with respect to the description of the orientation, such as up, down, left, right, front, rear, etc., is based on the direction or positional relationship shown in the drawings, is merely for convenience of describing the present invention and simplifying the description, and does not indicate or imply that the apparatus or element to be referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention.
In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
In the description of the present invention, unless explicitly defined otherwise, terms such as arrangement, installation, connection, etc. should be construed broadly and the specific meaning of the terms in the present invention can be reasonably determined by those skilled in the art in combination with the specific contents of the technical scheme. In addition, the following identification of specific steps does not represent a limitation on the order of steps and execution logic, and the order of execution and logic between steps should be understood and inferred by reference to the corresponding illustrative expressions.
In recent years, attention has been paid to aluminum nitride (AlN) thin films because of their excellent dielectric constant, being capable of being deposited at low temperature, being compatible with complementary metal oxide semiconductor (Complementary Metal Oxide Semiconductor, CMOS) processes, and the like, and resonators and filters using AlN thin films as piezoelectric materials are widely used in fields of biomedical science, national defense, military, environmental detection, mobile communication, and the like, wherein the material coefficients of AlN thin films are critical to the design and mass production of these devices, and the material coefficients of AlN thin films include piezoelectric coefficients, elastic coefficients, and dielectric constants.
However, on the one hand, the material coefficient matrix of the existing AlN film has a large error, resulting in a produced device error even as high as step S30%. On the other hand, as the device size is reduced, the size of the AlN thin film used is also reduced, and the material coefficient matrix is also changed greatly along with the change of the size and the adopted growth process (Epitaxy Growth Technology). Therefore, there is a great need in the scientific and industrial fields for a reliable and standard method for accurately extracting the material coefficient matrix of the AlN film, and the method should have universality and repeatability to adapt to AlN films of different thicknesses grown under different process conditions.
The present invention aims to solve at least one of the technical problems existing in the prior art. Therefore, the invention provides the aluminum nitride film parameter extraction method which can accurately extract the material coefficient of the aluminum nitride film.
Further description will be made below with reference to the accompanying drawings.
Referring to fig. 1, the method for extracting parameters of an aluminum nitride film according to an embodiment of the present invention includes:
step S101, manufacturing a parameter extraction component based on an aluminum nitride film to be detected;
it should be understood that the parameter extraction component is a component manufactured by measuring and calculating the parameters of the aluminum nitride film material, and is used for providing a measurement basis for obtaining the parameters of the aluminum nitride film material. In some embodiments of the present invention, the parameter extraction components include, but are not limited to, transverse bulk acoustic wave resonators, longitudinal bulk acoustic wave resonators, radial bulk acoustic wave resonators, thickness shear bulk acoustic wave resonators, and lamb wave resonators.
Step S102, measuring the impedance spectrum of the parameter extraction assembly, and calculating to obtain the dielectric constant of the aluminum nitride film to be detected in the parameter extraction assembly according to the impedance spectrum;
step S103, measuring attribute parameters of the parameter extraction assembly, and calculating to obtain a piezoelectric coefficient and an elastic coefficient of the aluminum nitride film to be measured according to the attribute parameters;
it should be noted that, the attribute parameters are basic parameters based on the self attribute of the parameter extraction component, including the resonant frequency, anti-resonant frequency, and the density, length, and thickness of the aluminum nitride film to be measured in the parameter extraction component.
And step S104, integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be tested to obtain the material parameters of the aluminum nitride film to be tested.
It should be noted that AlN in the aluminum nitride film to be measured is a wurtzite structure crystal, belongs to a hexagonal system, and includes main material parameters: elasticity coefficient, piezoelectric coefficient and dielectric constant, wherein the elasticity coefficient includes elasticity compliance coefficientElastic stiffness coefficient->The piezoelectric coefficient includes a piezoelectric strain coefficient d mj Coefficient of piezoelectric stress e mi The dielectric constants include the dielectric constants +.A.A dielectric constant obtained under mechanical free measurement conditions with stress T=0>Strain s=0Dielectric constant under mechanical clamping measurement conditions +.>i. j, m, n represent stress, strain, electric field and electric displacement direction respectively; the superscripts E and D in the elastic coefficients represent the electrical short-circuit and electrical open-circuit measurement conditions of electrical displacement d=0, respectively, of the electric field strength e=0.
In some embodiments of the present invention, the material parameters of the aluminum nitride film are expressed according to the following equation:
elastic compliance coefficient among elastic coefficientsElastic stiffness coefficient->
Piezoelectric strain coefficient among piezoelectric coefficientsPiezoelectric stress coefficient->
Dielectric constant among dielectric constantsDielectric constant->
Since the material coefficients of AlN can be converted from each other by the above equation, in some embodiments of the present invention, the material parameters required to be extracted from the aluminum nitride film to be measured include the following ten: coefficient of elasticityPiezoelectric coefficient d 31 、d 33 、d 15 And dielectric constant->
Extracting parameters of an aluminum nitride film to be detected, firstly manufacturing a parameter extraction component based on the aluminum nitride film to be detected, and then measuring impedance spectrum and attribute parameters of the parameter extraction component. And then, calculating according to the impedance spectrum to obtain the dielectric constant of the aluminum nitride film to be detected in the parameter extraction assembly, and calculating according to the attribute parameters to obtain the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be detected in the parameter extraction assembly. And finally, integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be tested to obtain the material parameters of the aluminum nitride film to be tested. In the method provided by the embodiment of the invention, various material coefficients of the aluminum nitride film are extracted separately, so that accumulated errors can be reduced, and the extraction precision is relatively high.
According to some embodiments of the present invention, an extraction component for manufacturing parameters based on an aluminum nitride film to be measured includes:
and manufacturing a transverse bulk acoustic wave resonator, a longitudinal bulk acoustic wave resonator, a radial bulk acoustic wave resonator, a thickness shear bulk acoustic wave resonator and a lamb wave resonator based on the aluminum nitride film to be tested.
According to some embodiments of the present invention, the present invention contemplates a parameter extraction assembly as shown in fig. 2, the parameter extraction assembly comprising the following elements:
the transverse bulk acoustic wave resonator is shown in fig. 2 (a), and comprises an A1 electrode 211, a transverse film to be measured 212 and an A2 electrode 213;
the longitudinal bulk acoustic wave resonator is shown in fig. 2 (B), and comprises a B1 electrode 221, a longitudinal film to be measured 222, and a B2 electrode 223;
the radial bulk acoustic resonator is shown in fig. 2 (C), and comprises a C1 electrode 231, a radial film to be measured 232 and a C2 electrode 233;
the thickness shear bulk acoustic wave resonator is shown in fig. 2 (D), and comprises a D1 electrode 241, a D2 electrode 242 and a thickness shear film 243 to be measured;
the Lamb (Lamb) wave resonator is shown in fig. 2 (E) and comprises an E1 electrode 251, a Lamb wave film 252 to be measured, and an E2 electrode 253.
All the five resonators are in a suspension state, and support and electrode introduction are performed through aluminum nitride films to be detected at two sides, namely a transverse film to be detected 212, a longitudinal film to be detected 222, a radial film to be detected 232, a thickness shear film to be detected 243 and a lamb wave film to be detected 252 shown in fig. 2. It should be noted that, the use of the aluminum nitride film to be tested for support and the introduction of the electrode can reduce the influence of clamping of the substrate on the resonance mode. It should be appreciated that the processing of the five resonators described above is not complex and the fabrication of the device can be accomplished by several deposition, patterning and etching processes. It should be noted that the dimensions of the resonator body and the support anchors may affect the accuracy of the measurement to some extent, and in actual measurement, the appropriate dimensions may be selected by simulation.
Referring to fig. 3, in step S102, the dielectric constant of the aluminum nitride film to be measured in the parameter extraction assembly is calculated according to the impedance spectrum, which includes:
step S301, obtaining the detuning capacitance of the lamb wave resonator according to the impedance spectrum
Step S302, substituting the detuned capacitance of the lamb wave resonator into a plate capacitance equation, and calculating to obtain the dielectric constant.
In some embodiments of the present invention, the specific calculation process for deriving the dielectric constant from the detuned capacitance of the lamb wave resonator includes:
detuning capacitance of lamb wave resonatorSubstituting the plate capacitance equation +.>Determination of dielectric constantWherein S is the area of the capacitor electrode plate, d is the distance between the electrode plates, epsilon 0 Is vacuum dielectric constant;
will dielectric constantDetuned capacitor->Substitution formula->Determining dielectric constant->Therein N, W, t e And lambda are the interdigital logarithm of the lamb wave resonator, the aperture width, the thickness, and the wavelength of the lamb wave, respectively.
It should be emphasized that the dielectric constant of the aluminum nitride film to be testedAnd dielectric constant->Obtained by the calculation process in the above steps S301 to S302.
Referring to fig. 4, according to some embodiments of the present invention, the attribute parameters include a resonant frequency, an anti-resonant frequency of the parameter extraction component, and a density, a length, and a thickness of the aluminum nitride film to be measured, and the step S103 of measuring the attribute parameters of the parameter extraction component, and calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the attribute parameters includes:
step S401, obtaining the resonance frequency f of the parameter extraction assembly according to the impedance spectrum r Anti-resonant frequency f a Detecting the density rho, the length L and the thickness t of the aluminum nitride film to be detected;
step S402, according to the resonant frequency f r Anti-resonant frequency f a And calculating the density rho, the length L and the thickness t of the aluminum nitride film to be measured to obtain the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured.
In some embodiments of the present invention, the specific calculation process for calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured includes:
according to the formulaCalculating to obtain electromechanical coupling coefficient k of transverse bulk acoustic wave resonator 31 ；
Will k 31 、f r 、f a Substitution of ρ and L into the formulaObtaining the elasticity coefficient->Piezoelectric coefficient d 31 ；
According to the formulaCalculating to obtain electromechanical coupling coefficient k of longitudinal bulk acoustic wave resonator t ；
Will k t 、f r 、f a Substitution of ρ and t into the formulaObtaining the elasticity coefficient->Piezoelectric coefficient d 33 ；
According to the first-order resonant frequency of the radial bulk acoustic wave resonatorAnd second order resonance frequency->Determining the Poisson ratio sigma of the aluminum nitride film to be tested;
poisson's ratio sigma,Substitution formula->Calculating to obtain elasticity coefficient->
According to the formulaCalculating to obtain electromechanical coupling coefficient k of thickness shear bulk acoustic wave resonator 15 ；
Will k 15 、f r 、f a Substitution of ρ and t into the formulaObtaining the elasticity coefficient->Piezoelectric coefficient d 15 。
It should be emphasized that the elastic coefficient of the aluminum nitride film to be measuredPiezoelectric coefficient d 31 Elasticity coefficient->Piezoelectric coefficient d 33 Elasticity coefficient->Elastic coefficient->Piezoelectric coefficient d 15 Obtained by the calculation process in the above steps S401 to S402.
Referring to fig. 5, in step S103, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured are calculated according to the attribute parameters according to some embodiments of the present invention, and further includes:
step S501, extracting the resonant frequency f of the component according to the parameters r Lamb waveThe wavelength lambda is calculated to obtain the actual measurement wave velocity v in the lamb wave resonator;
specifically, in some embodiments of the invention will be f r Lambda is substituted into formula v=f r Lambda, obtaining the actual wave velocity v in the lamb wave resonator;
step S502, substituting the elasticity coefficient and the piezoelectric coefficient into the piezoelectric equation, maxwell equation and elastic dynamics equation of the lamb wave resonator to calculate the wave velocity calculated value v 0 ；
In particular, in some embodiments of the invention the coefficient of elasticity is to beElastic coefficient->Elastic coefficient->Elastic coefficient->Piezoelectric coefficient d 15 Piezoelectric coefficient d 33 Piezoelectric coefficient d 31 Dielectric constant->Dielectric constant->Substituting piezoelectric equation, maxwell equation and elastic dynamics equation of lamb wave resonator to obtain wave velocity calculated value v 0 . In some embodiments of the invention, the wave velocity calculation v 0 The calculation process of (1) comprises:
referring to the lamb wave resonator model shown in FIG. 6, the lamb wave particle displacement u is assumed h And electric field E m The method comprises the following steps:
wherein u is h 、E m 、A h 、B m Respectively representing the particle displacement and the electric field and the amplitude of the particle displacement and the electric field; beta, k and omega are lamb wave edges x respectively 3 The directional attenuation factor, wavenumber and angular frequency due to its particle displacement u h And electric field E m Can be mutually converted, so that the two have the same attenuation factor beta;
by particle displacement u h Equation solving for Strain equation S j And sum with electric field E m The equations are brought together into the following piezoelectric equation, maxwell's equation and elastohydrodynamic equation, and then combined with the zero stress boundary condition T 3 ＝T 4 ＝T 5 =0 and electrical boundary condition E 1 Equal, D 3 Equality to obtain the above S 0 The velocity equation of the mode lamb wave includes the specific equation:
piezoelectric equation:maxwell's equations: />Elastic kinetic equation: />Wherein T is i 、S j 、E m 、D n Respectively represent stress, strain, electric field and electric displacement, mu 0 Is vacuum permeability.
Step S503, calculating the wave velocity v 0 Comparing with the actually measured wave velocity v to obtain a wave velocity difference value;
step S504, when the wave velocity difference is smaller than or equal to the preset error value, obtaining the calculated value v of the wave velocity 0 Corresponding elastic coefficient
It should be noted that the above calculation process requires presetting an elastic coefficientAnd then->Substituting the calculated wave velocity value obtained by calculating the piezoelectric equation, maxwell equation and elastic dynamics equation in the step S502, further obtaining a wave velocity difference value according to the difference between the obtained wave velocity calculated value and the actually measured wave velocity v, and if the wave velocity difference value is smaller than or equal to the preset error value, meaning the elastic coefficient ++>The difference from the desired elasticity coefficient value is within the tolerance of the error, so that the corresponding elasticity coefficient can be set>The elastic coefficient is regarded as the required value +.>
In addition, in some embodiments of the present invention, when the wave velocity difference is greater than the preset error value, the calculated value v of the wave velocity is adjusted according to the wave velocity difference 0 Corresponding elastic coefficientThen the adjusted elastic coefficient +.>The piezoelectric equation, maxwell equation and elastic dynamics equation of the lamb wave resonator are updated, the wave velocity calculated value is recalculated, and the wave velocity difference value is obtained until the wave velocity difference value is smaller than or equal to the preset error value, and the calculated value v of the wave velocity is obtained 0 Corresponding elastic coefficient/>It will be appreciated that the adjustment of the spring constant +.>The process of (1) is equivalent to the adjustment of the independent variable of the equation until the calculation result of the equation meets the condition, namely, until the wave velocity difference value is smaller than or equal to the preset error value, the corresponding independent variable, namely, the elasticity coefficient ∈ ->Can be regarded as the elasticity coefficient to be calculated>It should be appreciated that the preset error value may be determined according to actual conditions.
It should be emphasized that the elastic coefficient of the aluminum nitride film to be measuredObtained by the calculation process in the above steps S501 to S504.
According to some embodiments of the invention, the dielectric constant of the aluminum nitride film to be testedAnd dielectric constant->Can be obtained by the calculation process in the above steps S301 to S302; elastic coefficient of aluminum nitride film to be measured +.>Piezoelectric coefficient d 31 Elasticity coefficient->Piezoelectric coefficient d 33 Elasticity coefficient->Elastic coefficient->Piezoelectric coefficient d 15 Can be obtained by the calculation process in the above steps S401 to S402; elastic coefficient of aluminum nitride film to be measured +.>The calculation can be performed by the calculation procedures in steps S501 to S504. Thus, referring to fig. 7:
step S701, the elastic coefficient is calculatedElastic coefficient->Elastic coefficient->Elastic coefficient->Elastic coefficient->Integrating to generate elastic coefficient matrix in material parameters>Wherein i represents a stress direction and j represents a strain direction;
step S702, piezoelectric coefficient d 15 Piezoelectric coefficient d 33 Piezoelectric coefficient d 31 Integrating to generate piezoelectric strain coefficient matrix in material parametersWherein m represents the electric field direction;
step S703 of setting the dielectric constantDielectric constant->Integrating to generate dielectric constant matrix in material parameters>Where n represents the direction of electrical displacement.
According to some embodiments of the invention, the method for extracting parameters of the aluminum nitride film further comprises:
and establishing finite element analysis simulation according to the material parameters to obtain a de-electrode mass load effect coefficient gamma which is used for eliminating the influence of the electrode mass load effect.
It should be noted that, according to the basic principle of the piezoelectric mass sensor, the following equation can be obtained:
wherein f 0 And f is the frequency when there is no electrode and there is an electrode, respectively; n, ρ e 、t top/left 、t bot/right 、ρ p 、t p The constants associated with the vibration modes, the mass of the electrodes, the upper/left electrode thickness, the lower/right electrode thickness, the piezoelectric material density and thickness, respectively.
It can be seen that for a resonator of fixed structure and vibration mode, f 0 And f there is a constant relationship γ. Therefore, the invention establishes finite element analysis (Finite Element Analysis, FEA) simulation to obtain gamma by using the material parameters of the aluminum nitride monocrystal to eliminate errors caused by electrode mass loading effect.
Referring to fig. 8, according to some embodiments of the present invention, after integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured to obtain the material parameters of the aluminum nitride film to be measured, the method further includes:
step S801, recording the turn of extracting material parameters;
step S802, when the rotation of extracting the material parameters is less than the preset times, re-measuring the impedance spectrum of the parameter extracting component, and updating the detuning capacitance of the parameter extracting component;
step S803, calculating to obtain an updated dielectric constant according to the updated detuned capacitance;
step S804, re-measuring the attribute parameters of the parameter extraction assembly, and updating the piezoelectric coefficient and the elastic coefficient according to the re-measured attribute parameters;
step S805, integrating the updated dielectric constant, piezoelectric coefficient and elastic coefficient to obtain updated material parameters;
step S806, establishing finite element analysis simulation according to the updated material parameters to obtain an electrode mass load effect removing coefficient gamma, wherein the gamma is used for eliminating the influence of the electrode mass load effect.
It should be noted that, in the above method, the FEA simulation is established using the material constant of the aluminum nitride single crystal to obtain the electromechanical coupling coefficient compensation factor α and the photoelectrode mass loading effect coefficient γ of the thickness shear mode, and the material coefficient of the aluminum nitride thin film is generally smaller than that of the aluminum nitride single crystal, so that an error is caused to some extent. To reduce this error, some embodiments of the present invention will reestablish FEA simulation with the first extracted aluminum nitride film material coefficients and repeat the extraction step once (i.e., the second iteration of the extraction step), the second extracted aluminum nitride film material coefficients will have a higher accuracy. It will be appreciated that the more iterations of the extraction step, the less errors the simulation causes. It should be appreciated that the preset number of times may be determined according to the actual situation.
Referring to fig. 9, according to some embodiments of the present invention, the aluminum nitride film parameter extraction method further includes:
step S901, manufacturing a pure pad device excluding a resonator, and measuring a reflection coefficient of the pure pad device;
step S902, obtaining the equivalent resistance and the equivalent capacitance of the pure pad device according to the reflection coefficient;
in step S903, a scattering parameter is calculated according to the equivalent resistance and the equivalent capacitance, and the scattering parameter is used for de-embedding the bonding pad carrying the parameter extraction component.
It should be noted that, a pure pad (without resonator) device is fabricated, and according to the MBVD (Modified Butterworth-Van Dyke) model, since the pad does not resonate in the vibration frequency band of the resonator, it can be described by a simple model in which an equivalent resistor R and an equivalent capacitor C are connected in series. By measuring the reflection coefficient Γ of the device, the equivalent resistance R and the equivalent capacitance C can be calculated by the following formula, and thus the S parameter of the bonding pad can be calculated. The equation for the reflection coefficient Γ has the form:
wherein Z and Z 0 Representing the impedance and characteristic impedance, respectively, of a pure pad device.
And then the reflection coefficient of the resonator can be calculated through the following equation, so that the de-embedding of the bonding pad is completed.
Wherein Γ is total And Γ r Representing the total reflection coefficient of the bonding pad and the resonator and the reflection coefficient of the resonator itself respectively; s is S 11 、S 12 、S 21 、S 22 Is the four scattering (S) parameters of a pure pad device.
While the preferred embodiment of the present invention has been described in detail, the present invention is not limited to the above embodiments, and those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit and scope of the present invention, and these equivalent modifications or substitutions are included in the scope of the present invention as defined in the appended claims.
Claims (8)
1. The aluminum nitride film parameter extraction method is characterized by comprising the following steps of:
extracting a component based on manufacturing parameters of the aluminum nitride film to be tested; wherein the parameter extraction component comprises a lamb wave resonator;
measuring an impedance spectrum of the parameter extraction component;
calculating to obtain the dielectric constant of the aluminum nitride film to be measured according to the impedance spectrum; the dielectric constant of the aluminum nitride film to be measured is obtained by calculation according to the impedance spectrum, and specifically comprises the following steps:
obtaining the detuning capacitance of the lamb wave resonator according to the impedance spectrum；
Detuning capacitance of the lamb wave resonatorSubstituting the plate capacitance equation +.>Determination of dielectric constantWherein S is the area of the capacitor plate, d is the plate spacing +.>Is vacuum dielectric constant;
the dielectric constant is setSaid detuned capacitance->Substitution formula->Determine the dielectric constant +.>Wherein->、/>And->The interdigital logarithm, the aperture width, the thickness and the wavelength of the lamb wave resonator are respectively;
measuring attribute parameters of the parameter extraction assembly, and calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the attribute parameters; the parameter extraction component further comprises a transverse bulk acoustic wave resonator, a longitudinal bulk acoustic wave resonator, a radial bulk acoustic wave resonator and a thickness shear bulk acoustic wave resonator, and the attribute parameters comprise the resonance frequency and anti-resonance frequency of the parameter extraction component and the density, the length and the thickness of the aluminum nitride film to be detected;
and obtaining the material parameters of the aluminum nitride film to be tested according to the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be tested.
2. The method according to claim 1, wherein measuring the property parameter of the parameter extraction component and calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the property parameter comprises:
obtaining the resonant frequency of the parameter extraction component according to the impedance spectrumAnti-resonant frequency->And detecting the density +.>Length->Thickness->；
According to the formulaCalculating to obtain electromechanical coupling coefficient of the transverse bulk acoustic wave resonator>；
The saidSaid->Said->Said->And said->Substitution formula->、/>Obtaining elasticity coefficient->Piezoelectric coefficient->；
According to the formulaCalculating to obtain electromechanical coupling coefficient of the longitudinal bulk acoustic wave resonator>；
The saidSaid->Said->Said->And said->Substitution formula->、/>、、/>Obtaining elasticity coefficient->Piezoelectric coefficient->；
According to the first-order resonant frequency of the radial bulk acoustic wave resonatorAnd second order resonance frequency->Is used for determining the Poisson's ratio of the aluminum nitride film to be tested>；
The Poisson ratio is setSaid->Substitution formula->Calculating to obtain elasticity coefficient->；
According to the formulaCalculating to obtain the electromechanical coupling coefficient of the thickness shear bulk acoustic wave resonator>；
The saidSaid->Said->Said->And said->Substitution formula->、/>Obtaining elasticity coefficient->Piezoelectric coefficient->。
3. The method according to claim 2, wherein the calculating the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be measured according to the attribute parameter further comprises:
the saidSaid->Substitution formula->Obtaining a measured wave velocity in the lamb wave resonator>；
The elastic coefficient is setSaid elastic coefficient->Said elastic systemCount->Said elastic coefficient->Said piezoelectric coefficient->Said piezoelectric coefficient->Said piezoelectric coefficient->Said dielectric constant->Said dielectric constant->Substituting the piezoelectric equation, maxwell equation and elastic dynamics equation of the lamb wave resonator to obtain a wave velocity calculation value +.>；
Calculating the wave velocityAnd the measured wave velocity +.>Comparing to obtain a wave velocity difference value;
when the wave velocity difference value is smaller than or equal to a preset error value, obtaining a calculated value of the wave velocityCorresponding elastic coefficient->。
4. A method according to claim 3, characterized in that the method further comprises:
when the wave velocity difference value is larger than the preset error value, adjusting a preset elastic coefficient according to the wave velocity difference value；
The adjusted preset elastic coefficientSubstituting the piezoelectric equation, the maxwell equation and the elastic dynamics equation of the lamb wave resonator, and updating the wave velocity calculated value.
5. A method according to claim 3, wherein integrating the dielectric constant, piezoelectric coefficient and elastic coefficient of the aluminum nitride film to be measured to obtain the material parameters of the aluminum nitride film to be measured comprises:
the elastic coefficient is setSaid elastic coefficient->Said elastic coefficient->Said elastic coefficient->Said coefficient of elasticityIntegrating to generate an elastic coefficient matrix in the material parameters>Wherein->Indicating stress direction,/->Indicating the strain direction;
the piezoelectric coefficient is setSaid piezoelectric coefficient->Said piezoelectric coefficient->Integration is carried out to generate a piezoelectric strain coefficient matrix in the material parameters>Wherein->Indicating the direction of the electric field;
the dielectric constant is setSaid dielectric constant->Integrating to generate dielectric constant matrix in the material parametersWherein->Indicating the direction of the electrical displacement.
6. The method according to any one of claims 1 to 5, further comprising:
establishing finite element analysis simulation according to the material parameters to obtain a de-electrode mass load effect coefficient。
7. The method according to any one of claims 1 to 5, wherein the method further comprises, after integrating the dielectric constant, the piezoelectric coefficient and the elastic coefficient of the aluminum nitride film to be tested to obtain the material parameters of the aluminum nitride film to be tested:
recording and extracting the turns of the material parameters;
when the number of times of extracting the material parameter is less than a preset number of times, performing the measuring of the impedance spectrum of the parameter extracting component to update the material parameter;
establishing finite element analysis simulation according to the updated material parameters to obtain a de-electrode mass load effect coefficient。
8. The method according to any one of claims 1 to 5, further comprising:
manufacturing a pure bonding pad device which does not comprise the parameter extraction component, and measuring the reflection coefficient of the pure bonding pad device;
obtaining the equivalent resistance and the equivalent capacitance of the pure pad device according to the reflection coefficient;
and calculating scattering parameters according to the equivalent resistance and the equivalent capacitance, wherein the scattering parameters are used for de-embedding a bonding pad carrying the parameter extraction component.
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