DUT samples based on AlN and ASN piezoelectric layered structures.
The theory of external loading influence on acoustic parameters of piezoelectric five-layered structure as “Al/(001) AlN/Mo/(001) diamond/Me” has been developed. Oscillations in diamond-based high-overtone bulk acoustic resonators (HBARs) have been investigated in terms of 3D FEM simulation. Peculiarities of technology of aluminum-scandium nitride (ASN) films have been discussed. Composition Al0.8Sc0.2N was obtained to create the diamond-based HBAR and SAW resonator. Application of ASN films has resulted in a drastic increasing an electromechanical coupling up to 2.5 times in comparison with aluminum nitride. Development of ASN technology in a way of producing a number of compositions with the better piezoelectric properties has a clear prospective. SAW resonator based on “Al IDT/(001) AlN/(001) diamond” structure has been investigated in the band 400–1500 MHz. The highest-quality factor Q ≈ 1050 was observed for the Sezawa mode at 1412 MHz. Method of measuring HBAR’s parameters within 4–400 K at 0.5–5 GHz has been developed. Results on temperature dependence of diamond’s Q-factor at relatively low frequencies were quite different in comparison with the ones at the frequencies up to 5 GHz. Difference could be explained in terms of changing mechanism of acoustic attenuation from Akhiezer’s type to the Landau-Rumer’s one at higher frequencies in diamond.
- aluminum nitride
- aluminum-scandium nitride
- diamond-based HBAR
- diamond-based SAW resonator
- acoustoelectronic sensor
Thin piezoelectric films (TPF) are the important components of many electronic sandwich devices due to its compatibility with the planar technology and comparatively low cost. Combination of effective TPF with non-piezoelectric substrate possessing the good acoustic properties allows obtaining the new micro devices especially in UHF bands. The matter is that the known single-crystalline piezoelectric materials as quartz, lithium niobate, tantalate, langasite, and langatate do not own a set of useful properties such as high electromechanical coupling, thermostable cuts, and good acoustic properties joined within a given crystal. Additionally, an enhancement of operational frequencies up to several GHz for bulk acoustic wave (BAW) resonators requires the thinning of crystal plates to the thickness close to several microns which seems really impossible because a lot of defects will be arisen. So, producing the best quality piezoelectric films compatible with any substrate materials is one of the main tasks of modern piezoelectric technology.
Since the end of the twentieth century, the zinc oxide (ZnO) and aluminum nitride (AlN) polycrystalline films with the wurtzite structure were widely used in such acoustoelectronic devices as composite resonators, filters, duplexers, etc. [1, 2]. It seems that the aluminum nitride has a more preferable combination of required qualities due to high dielectric properties as well as good temperature stability up to 1000 °C. First, in 2009 the authors  have found an enhancement of piezoelectric response in aluminum-scandium nitride (ASN) Al1-
High-overtone bulk acoustic resonator (HBAR) differs from conventional piezoelectric resonators due to their small size and high-quality factor
Naturally, thin piezoelectric films are widely used as the important elements in acoustoelectronic devices on surface acoustic waves (SAW), such as SAW delay lines, resonators, filters, and sensors. For example, in Ref.  the one-port SAW resonator, based on the layered structure AlN/polycrystalline diamond/Si and excited on the resonant frequency ~1.35 GHz, has been described. SAW filter at the frequency band ~6.3 GHz based on the structure SiO
A main aim of this paper was defined by the necessity in describing the modern trends in application of thin piezoelectric films as active elements in microwave acoustoelectronic composite devices, including the choice and development of the new effective piezoelectric materials compatible with single-crystalline diamond substrates.
2. Theory of the thin-film loading influence on the acoustic parameters of diamond-based piezoelectric layered structure
An effective application of multilayered piezoelectric structure as a prototype of specialized acoustoelectronic sensor device should be based on the theory of the influence of an external loading on its acoustic parameters.
Propagation of the small amplitude acoustic waves of a piezoelectric crystal could be described basically by the equations of electrostatics and the equations of state of a piezoelectric medium written in coordinate form :
where ρ0 is the density of a crystal, is the vector of dynamic elastic displacements, is the tensor of thermodynamic stresses, is the vector of electrical induction, is the tensor of small deformations, , , and are second-order elastic, piezoelectric, and clamped dielectric constants, respectively. The comma after the subscript denotes a spatial derivative, and coordinate Latin indices vary from 1 to 3. Here and further, the rule of summation over repeated indices will be used. For elastic displacements and the electric potential in the form of small-amplitude plane monochromatic waves, the system of equations was written in the form of the well-known Green-Christoffel equations, which must be solved for each layered medium to be used:
where is the wave vector; is the unit vector of wave propagation; ω and
one can obtain a matrix of boundary conditions, and the vanishing of its determinant allows obtaining the equations for determining the parameters of elastic wave propagation. In Eq. (4) a superscript
At the assumption that the lower layer is sufficiently thick (semi-infinite), i.e., the thickness of a layer should be much greater than the length of the elastic wave, in which case the last equation in Eq. (3) cannot be taken into account, i.e., the presence of a free lower boundary will be ignored. It is also necessary to require that the condition ensuring the attenuation of the elastic wave into the depth of a substrate should be satisfied. Thus, the boundary conditions (Eq. (3)) describing the elastic wave propagation in the “layer-substrate” structure will have the form.
Here, the digital superscripts 1 and 2 denote the layer and the substrate, respectively; and
In modern acoustoelectronics, accurate information about the mechanical parameters of thin layers of new materials and thin mono- and polycrystalline films used to create microwave acoustic resonators, filters, and sensors should be of great importance. Previously proposed and used in a number of experiments, the original method of resonance acoustic microwave spectroscopy has opened a possibility of measuring these parameters . The essence of such method was based on the investigated film that was included into a content of an acoustic composite microwave resonator changing its acoustic parameters (Figure 1). Connection with the external electrical circuit was carried out by the TFPT. In the case of thin films, the last one should be deposited on a sufficiently thick substrate made of a material with low acoustic losses. Information on the attenuation coefficient and sound velocity in the film were found from the comparison of the measured total losses and the positions of the resonant peaks without the film and after its deposition.
To solve the problems of acoustic microwave spectroscopy, it is necessary to introduce a system of boundary conditions for the PLS according to Figure 1. For elastic displacements in the form of a plane sinusoidal wave, one can be written as
where the subscript
Assuming that the electrodes were consisted of isotropic metals, the piezoelectric layer had the crystalline symmetry as 6
(1) Stress tensor should have the zero normal components at the interface “top electrode-vacuum” in the form
(2) Normal components of the stress tensor and displacement vectors should be equal to appropriate values taken at the interface “top electrode-piezoelectric film” as follows:
In Eq. (9) the following notations are introduced:
(3) Normal components of the stress tensor and displacement vectors should be equal to appropriate values taken at the interface “piezoelectric film-bottom electrode” as follows:
In Eq. (10) the following notations are introduced:
(4) Normal components of the stress tensor and displacement vectors should be equal to appropriate values taken at the interface “bottom electrode-substrate” as follows:
In Eq. (11) the following notations are introduced:
(5) Normal components of the stress tensor and displacement vectors should be equal to appropriate values taken at the interface “substrate-the layer to be investigated” as follows:
In Eq. (12) the following notations are introduced:
(6) Normal components of the stress tensor should be equal to appropriate values taken at the “the layer to be investigated-vacuum” as follows:
Boundary conditions (Eq. (8)–(13)) form a system of equations as 10×10 dimensions, the solution of which makes it possible to determine the amplitudes of the elastic waves in all the layers and the PLS frequency characteristics. Note that the part of the boundary condition matrix as 7×7 dimensions allows to obtain the so-called form factor of HBAR including into calculation a traveling acoustic wave only, i.e., without taking into account the lower boundary of the crystalline substrate (12) and (13). Additionally, when Eq. (12) was taken into account, as a result appropriate boundary condition matrix as 8×8 dimensions can be formed, and the HBAR’s form factor can be calculated including the influence of a bottom boundary of a substrate.
In order to study the influence of the fifth layer on the PLS acoustic parameters, a required own software “Modeling of the processes of resonant acoustic spectroscopy in multilayered structures” based on the above theory has been developed . An estimation of the influence of metal film deposition as a fifth layer on the change of the overtone resonant frequency of diamond-based PLS “Al/(001) AlN/Mo/(001) diamond/Al (Mo)” is presented in Figure 2. In calculations the thickness of Al or Mo films was varied within 0–1300 nm. As one can see, the metal deposition leads to the decrease of resonant frequency with the thickness increasing both the metals. But on the curve associated with Al influence, the sharp variation of resonant frequency in the vicinity of 400–600 nm takes place on the contrary with the linearly proportional dependence of resonant frequency on the thickness of Mo film. This can be explained by the quite different acoustic impedances
3. 3D simulation of acoustic wave propagation in multilayered piezoelectric structure
Earlier [13, 14], we have successfully applied the 2D FEM simulation in order to obtain a quite complex pattern of dispersive dependences of phase velocities of plate Lamb waves observing visualization of the fields of elastic displacements belonging to a lot of acoustic modes with a number of eigenfrequencies. Besides of Lamb waves, the BAW and SAW modes of Rayleigh type were found. But the statement of the task in 2D approximation did not allow obtaining the results on the SH modes.
In the 3D FEM simulation as a model, the PLS “Al/(001) AlN/Mo/(001) diamond” has been investigated by the software COMSOL Multiphysics. Boundary conditions on the top and bottom surfaces of a model sample were chosen as the free ones, and on all the vertical surfaces as the symmetrical ones. Width×length×thickness (in microns) of diamond substrate and AlN film were 1000×1000×392 and 400×400×0.624, respectively. Thicknesses (in nm) of Al and Mo films were taken as 164 and 169, respectively. All the dimensions of a model sample were close to appropriate ones in the experimental sample. In Figure 3, the results on the second overtone of longitudinal bulk acoustic wave in the PLS investigated are presented as 2D and 3D images. Note that the calculated data on resonant frequency (in MHz) as 44.72 obtained in 2D approximation (Figure 3a) are in close accordance with the similar as 44.75 (Figure 3b) in 3D approximation.
In Figure 4, an example of the data on the elastic displacement patterns arising for the SH-type waves in the PLS “Al/(001) AlN/Mo/(001) diamond” is presented in 3D image. SH waves are dispersive and deeply penetrating into a substrate. As a consequence, SH wave velocities should be strongly depended on the operational frequency. Such dependences for a number of first dispersive branches within the frequency band 10–50 MHz are presented in Figure 5 in comparison with theory data. As one can see, a good agreement between the model and theory was obtained.
In Figure 6 an example of the elastic displacement patterns arising for the Rayleigh-type waves in the PLS “Al/(001) AlN/Mo/(001) diamond” is presented in 2D and 3D image. As one can calculate, the SAW wave lengths in a diamond were both equal to 200 microns in 2D and 3D approximation, and the SAW phase velocities were equal to 10,922 and 11,014 m/s, respectively. One can speak about a reasonable agreement between the results of two models.
4. Aluminum nitride and aluminum-scandium nitride film preparation: sample characterization
In our microwave experiments, a lot of devices under test (DUT) operating the BAW or SAW propagation in PLS were required (Figure 7). As one can see, it was necessary to fabricate the multilayered piezoelectric structures involving the TFPT and diamond substrate (Figure 7a
The IIa type synthetic diamond single crystals grown by HPHT method at the Technological Institute for Superhard and Novel Carbon Materials were used as substrates for producing in all the DUTs investigated. Such crystals have the good dielectric properties and a low content of nitrogen impurity. All the substrates with the orientation of the main surfaces (100), (110), and (111) were double side polished up to roughness
Metal electrodes, aluminum nitride or aluminum-scandium nitride piezoelectric films, were deposited by magnetron sputtering equipment AJA ORION 8. Process of aluminum-scandium nitride synthesis in comparison with that for AlN was differed by the application of additional Sc target, so the Al and Sc targets were in work simultaneously. One can see from the available experimental data  that a significant increase in piezoelectric module
A preferred choice of Mo as a bottom electrode was explained by a good accordance between acoustical impedances of diamond substrate and Mo. Aluminum chosen as a material of top electrode can be described as the metal with good conductance and low density. The last property is useful because the deposition of top electrode should be influenced on PLS properties as less as possible. Electrode structures with a specified topology were deposited using photolithography process by the Heidelberg μPG 101 equipment. Explosive photolithography process was necessary to form a specified AlN or ASN film topology. Increasing an accuracy of IDT manufacturing and other electrode structures was connected with an understanding of the physical and chemical features of photolithography process in application to the small-sized substrates. Since the deposition of Al electrodes in the PLS investigated was performed on the surface of AlN or ASN piezoelectric films, it should be taken into account that their surfaces had a distinctive relief defined by triangular pyramid tops of crystallites, so that the roughness of such surfaces can be about 20–30 nm. Deposited Al films should overlap these irregularities. The thickness of deposed metal films was varied within 150–200 nm for the top electrode and 150–200 nm for the bottom one.
5. Microwave investigation tools and measurement methods
Method of low-temperature (LT) microwave studies of PLS acoustic properties was developed on the vector network analyzer E5071C-2 K5 (300 kHz–20 GHz), the probe station M150, the automated low-temperature system for measuring material properties Quantum Design Physical Property Measurement System EverCool II (4–400 K), and the nonstandard LT adapter (Figure 9).
To carry out the microwave measurements with HBARs as experimental samples, due to a weak level of the useful signal against the noise, and to obtain the correct quantitative value of the impedance, it must calibrate the whole measuring circuit consisting of a probe, a microwave cable, and a vector network analyzer. Typically, this procedure is performed near the room temperature at the probe station using a special calibration plate. However, for cryogenic temperatures, the use of a probe station was impossible. We have developed the LT measuring adapter that made possible to measure the complex reflection coefficient of microwave signal obtained by HBAR conjugated with the possibility of calibration procedure starting from cryogenic temperatures up to 400 K.
Since all measurements were carried out using a reflected signal, a single-port connection scheme with open-short-load calibration options was selected for measurement and calibration. The calibration elements corresponding to these options were located on the operational disk made of corundum ceramics with contact pads from Au/Pt/Ti produced by the photolithography method. Connection of a measured sample to the contact pads on the operational disk was done by adhering with a silver paste SPI 5001-AB Silver Paint, resistant to both low and high temperatures. At the same time, two measured samples could be placed on the operational disk. Control measurements on the same sample, carried out at room temperature by M150 probe station or using a low-temperature measuring adapter, were in a good agreement.
The method for measuring the sound phase velocity in a substrate was based on the determination of the HBAR’s eigenfrequencies taking into account the frequency and temperature dependences of the complex reflection coefficient in the composite resonator. Then, the complex impedance of the measuring circuit along with the sample was calculated with the help of vector analyzer software in accordance with the relation:
Required impedance was determined by Eq. (15) where the value was experimentally determined at the frequency outside the resonance one of the given overtones. Taking the values by the vector analyzer software, the frequency dependence of HBAR’s loaded quality factor
To determine an absolute value of the BAW phase velocity in the substrate, two different methods were used. Common to both methods was that the antiresonance frequencies
The second method determining the phase velocity in a substrate was based on the relation obtained taking into account the results (Ref. ) about the relation for Δ
where the corresponding density and thickness of layers or substrate should be inserted in accordance with the order in the “Al/(001) AlN/Mo/(100) diamond” PLS (see Figure 7a). In practice, a quantity Δ
6. Microwave acoustic properties of diamond-based HBARs and SAW resonators utilizing aluminum nitride and aluminum-scandium nitride piezoelectric films
Detailed study of microwave acoustic properties of diamond-based HBARs realized by aluminum nitride and aluminum-scandium nitride piezoelectric films has been fulfilled by a set of samples 1, 2, and 3 (Table 1). For example, in Figure 10 one can see the view of the HBAR’s sample 3 based on PLS “Al/(001) ASN/Mo/(100) diamond.” On the diamond substrate, two independent HBARs designated as 1a and 1b and differing the effective resonant areas as 20,000 and 5000 square microns, respectively, are located. Topology of the top and bottom electrodes was especially developed to be convenient for an investigation of temperature dependences of HBAR’s acoustic parameters within a wide range from 4 up to 400 K.
|Sample||Piezoelectric layered structure||Thickness (in microns) of|
|Diamond substrate||Piezoelectric film||Top electrode||Bottom electrode|
|1||Al/(001) AlN/Mo/(100) diamond||299||1.04||0.200||0.150|
|2||Al/(001) ASN/Mo/(100) diamond||488||1.125||0.140||0.160|
|3||Al/(001) ASN/Mo/(100) diamond||501||1.125||0.140||0.160|
|4||Al/(001) AlN/Mo/(100) diamond||180||2.790||0.107||0.135|
|5||Al/(001) AlN/Mo/(111) diamond||497||2.790||0.107||0.135|
|6||Al/(001) AlN/Mo/(110) diamond||1274||2.790||0.107||0.135|
|7||Al/(001) AlN/Mo/(100) diamond||482||0.970||0.105||0.176|
|8||Al/(001) AlN/Mo/(100) diamond||1107||0.970||0.105||0.176|
|9||Al IDT/(001) AlN/(001) diamond|
Results on microwave quality factor
In order to calculate the square of EMCC, , at a given frequency ω
Then, close to the frequency of the first half-wave resonance of TFPT called
It is interesting to compare the AlN and ASN piezoelectric properties taking into account such electromechanical coupling coefficient as the quantity which is defined for the thickness-extensional mode of a conventional piezoelectric resonator and can be calculated taking into account the piezoelectric, elastic, and dielectric properties of a piezoelectric material:
Following to , the relation between and can be written in the form.
where the corresponding density and thickness of layers or substrate are the same as in Eq. (21). Data on values obtained for the samples 1–3 were summarized in Table 2. For of true comparison of results, the samples with the close dimensions and shape of TFPT have to be chosen. So, the samples 1 and 2 based on ASN piezoelectric film were obtained in the same process. Then, the overtones with close resonant frequencies have been selected. Note that studied HBARs based on PLSs differing the material of piezoelectric films and substrate thickness demonstrate the close magnitudes of quality factor
|1||Al/(001) AlN/Mo/(100) diamond||3550||0.82||1.34||3.7|
|2||Al/(001) ASN/Mo/(100) diamond||3500||3.0||8.85||9.4|
|3||Al/(001) ASN/Mo/(100) diamond||3500||2.81||7.82||8.8|
As a main result, one can emphasize that the application of aluminum-scandium nitride as piezoelectric material leads to a drastic increase of both the effective and EMCCs up to 2.5 times. Other things being equal, the ASN-based acoustoelectronic devices will have the prospective advantages.
As a DUT sample 9 (see Table 1), the SAW resonator based on PLS “Al IDT/(001) AlN/(001) diamond” was investigated in the frequency band from 400 up to 1500 MHz at the SAW propagation in the  direction on the (001) crystalline cut of diamond. Scheme of a single-port SAW resonator was presented in Figure 7b. Distance between the nearest electrodes of IDT and MSR was taken as
The square of the EMCC concerned with surface acoustic waves was calculated by a conventional relation as.
7. Investigation of temperature dependences of acoustic parameters in diamond-based piezoelectric layered structures
In a way described in
where in those calculations the diamond’s density at room temperature ρ= 3516 kg/m3 was taken, and
Qualitatively, the temperature changes in the elastic modulus correspond to the conventional variation of elastic properties in a lot of solid states. One can emphasize on the existence of two temperature regions at which a clearly distinctive behavior of elastic properties as well as quality factor was observed: firstly, a weak dependence in the low-temperature region, which corresponds to the “freezing out” of the acoustic phonons and, secondly, a well-formed dependence close to linearly proportional one in the relatively high-temperature region, where, according to Planck’s law, a lot of acoustic phonons will be excited (Figure 16
Research of the temperature dependence of HBAR parameters was performed with using a set of samples which were different in crystallographic orientations of diamond substrate, a thickness of films of aluminum nitride and aluminum-scandium nitride, an electrode topology, etc. The choice of a given piezoelectric film thickness was mainly associated with the TFPT peculiarities: if it is desirable to get a more TFPT effectiveness at low frequencies, it should necessarily deposit a higher thickness. So, in a way to obtain the results at the frequency band below 1 GHz, the appropriate TFPTs were based on AlN films with the thickness up to 2.79 microns (see Table 1, samples 4–6). Besides it, the choice of an operational frequency should be agreed with the frequency bands where the maximal
It should be emphasized that an evident general conclusion, such as the results obtained at relatively low frequencies below 1.1 GHz, was quite different in comparison with ones measured at the frequencies up to 5 GHz. Such behavior was observed for all the samples regardless the substrate’s orientation. Really, observing the
Theory of the influence of an external loading on the acoustic parameters of piezoelectric five-layered structure as “Al/(001) AlN/Mo/(001) diamond/Me” has been derived. Approach how to obtain the boundary conditions can be spread on the more complicated multilayered structures too. On the base of that theory, the own software “Modeling of the processes of resonant acoustic spectroscopy in multilayered structures” has been developed. Study of the influence of metal film deposition as the fifth layer on the change of the overtone resonant frequency of diamond-based PLS “Al/(001) AlN/Mo/(001) diamond/Me” (Me = Al, Mo) has been fulfilled. It has been obtained that metal film deposition leads to the decrease of resonant frequency with the thickness increasing both the metals.
HBAR based on the PLS “Al/(001) AlN/Mo/(001) diamond” has been investigated in terms of 3D FEM simulation by the software COMSOL Multiphysics. Boundary conditions on the top and bottom surfaces of a model sample were chosen as the free ones, and on all the vertical surfaces as the symmetrical ones. All the dimensions of a model sample were close to appropriate ones in the experimental sample. Besides Lamb waves the BAW and SAW modes of Rayleigh and SH type were found. It has been shown that the calculated data on HBAR’s resonant frequency in 2D approximation were in close accordance with the similar obtained in 3D approximation. Elastic displacement patterns arising for the SH-type waves in the PLS “Al/(001) AlN/Mo/(001) diamond” were obtained in 3D image. Dispersive dependences of SH-type wave velocities on a frequency for a number of the first dispersive SH-branches have been calculated. Comparison of the data obtained by 3D FEM simulation with the theory and 2D FEM results has been demonstrated a good agreement between a model and theory. Visualization of elastic displacement fields associated with the SAW of Rayleigh type has been realized, and calculated phase velocity of the SAW propagating in a given direction on the (001) diamond surface was quite the same as known data.
Peculiarities of the technology of aluminum nitride and aluminum-scandium nitride piezoelectric films have been discussed. The Al0.8Sc0.2N composition was obtained to create the microwave BAW and SAW test devices as diamond-based HBAR and SAW resonator. By the X-ray diffraction pattern, it has been proven that the crystallites of ASN film had a preferred orientation (00⋅2) and the full width at half maximum for that reflection was 0.24°. This shows on a good quality texture of axial type along the sixfold axis of the wurtzite-type structure. Data obtained will be used for the future development of ASN film technology in a way of producing a number of compositions with the better piezoelectric properties.
Detailed study of microwave acoustic properties of diamond-based HBARs realized by aluminum nitride and aluminum-scandium nitride piezoelectric films has been fulfilled by a set of the samples. Topology of the top and bottom electrodes as well as piezoelectric film areas was especially developed to be convenient for an investigation of temperature dependences of HBAR’s acoustic parameters within a wide range from 4 up to 400 K. Investigated HBARs based on PLSs differing the material of piezoelectric films and substrate thickness have demonstrated the close magnitudes of quality factor
Single-port SAW resonator based on PLS “Al IDT/(001) AlN/(001) diamond” has been investigated in the frequency band from 400 up to 1500 MHz at the SAW propagation in the  direction on the (001) crystalline cut of diamond. Highest
Method of HBAR microwave studies of temperature dependences of such acoustic properties as BAW phase velocity and quality factor in the temperature region 4–400 K and frequency band 0.5–5 GHz has been developed. A general conclusion should be emphasized that the results on the temperature dependence of diamond’s
This work was supported by a grant of the Russian Science Foundation (project 16-12-10293).