Research on piezoelectric simulation characteristics based on ALN piezoelectric thin film structure

AlN piezoelectric thin films possess exceptional performance and find extensive applications in the fields of underwater acoustic communication and hydroacoustic sensing. To enhance the output voltage values of AlN piezoelectric thin films and optimize their structure, comprehensive simulations and analyses were carried out by using COMSOL on both circular and square film configurations. These investigations specifically focused on examining the impact of dimensional variations on resonance frequency and output voltage, as well as exploring the relationship between vibration frequency and output voltage. The findings revealed that by employing an appropriate cavity radius, increasing the thickness of the thin film can effectively enhance the output voltage. However, if the thickness surpasses 1.5 μm, the output voltage will gradually decline. Notably, the square film exhibited a significantly higher output voltage measurement of 2158 pm compared to the circular film.


Introduction
Aluminum Nitride (AlN) is a remarkable piezoelectric material extensively employed in MEMS (Microelectromechanical Systems) technology.Possessing desirable properties such as piezoelectricity, dielectricity, gas-sensing capabilities, and chemical stability, AlN-based piezoelectric thin films exhibit high sensitivity and low noise in the reception and transmission of acoustic waves in acoustic transducer sensors.Their exceptional underwater stability enables prolonged operation underwater, thus greatly contributing to the advancement of underwater acoustic communication and hydroacoustic sensing [1] .
Currently, AlN piezoelectric thin films have attracted extensive research attention both domestically and internationally.Many research institutions and universities worldwide are actively exploring synthesis methods [2] , performance tuning [3] , and applications of AlN piezoelectric thin films in various fields.The current research status in China also demonstrates the importance and promising prospects of AlN piezoelectric thin films.Chinese scholars have successfully prepared high-quality AlN thin films using self-developed techniques such as RF magnetron sputtering, molecular beam epitaxy, and low-temperature growth [4][5][6] .They have conducted in-depth studies in the fields of acoustic devices [7] , biosensors [8] , and energy harvesters [9] , among others.In recent years, Chinese research teams have also conducted systematic research on doping modification, micro-nano fabrication processes [10] , and device packaging of AlN films to meet the demands of different application areas.For instance, in 2016, researchers like Xu studied an SOI-based AlN MEMS ultra-low-frequency (10-100 Hz) hydroacoustic sensor [11] , while in 2021, Wu's team designed a novel honeycomb-structured MEMS hydroacoustic sensor based on AlN [12] .
As an example, we used COMSOL software to simulate the AlN piezoelectric thin films and analyze the influence of factors such as film thickness, cavity radius, and resonant frequency on the output voltage of the device.We compared the simulation results of circular and square-shaped structures in terms of output voltage.

Principle of piezoelectric thin films
Piezoelectric thin films operate based on the direct piezoelectric effect.When they are exposed to sound signals, the sound pressure acts as a mechanical load on the surface of the piezoelectric material, causing deformation.This deformation leads to polarization within the material, resulting in the generation of induced charges with opposite polarity on the top and bottom surfaces.When the external force is removed, the material returns to its charged state.The interaction between the electrical and mechanical aspects of the piezoelectric effect can be described by the piezoelectric equation.For a cylindrical piezoelectric material, the relationship between the charge density (known as the piezoelectric displacement) per unit area and the applied forces on the crystal surface can be expressed as follows: where Q represents the charge amount, A represents the area under force, and d represents the piezoelectric coefficient.
The simplified model of aluminum nitride (AlN) piezoelectric thin film is shown in Figure 1.From top to bottom, there are the top electrode, piezoelectric thin film, bottom electrode, device layer, and buried oxide layer returning to an uncharged state.The electrical and mechanical interactions in the piezoelectric effect are supported by the support layer (including the cavity).

Equivalent mechanical models
For the convenience of studying the vibration process of the thin film, the equivalent mechanical model of the piezoelectric thin film can be represented by a spring-damping-mass model, as shown in Figure 2. The piezoelectric material is represented by a spring, and the presence of frictional force is represented by a damper.When the sound pressure signal is transmitted to the surface of the piezoelectric thin film, assuming that the mass block generates a displacement x, its dynamic equation can be expressed as: where F is the external force, m is the equivalent mass, c is the equivalent damping coefficient, k is the equivalent spring stiffness, and x is the displacement.Furthermore, by substituting the expression for the undamped resonant frequency (represented as 0  ) and the expression for the dimensionless damping ratio (represented as  ) into the equation, we can obtain the following equations: This thin film has a relatively high resonant frequency, so the first two terms on the right side of the equation can be neglected.Combining the above equations, we can simplify it to: where Q is the charge, A is the force area on the piezoelectric material, Q A is the area of the piezoelectric material on the upper and lower surfaces, and d is the piezoelectric coefficient corresponding to the crystal direction of the thin film.The equation indicates that the accumulated surface charge on the film is directly proportional to the applied force magnitude.

Equivalent electrical model
The electrical characteristics of piezoelectric thin films can be represented by an equivalent circuit model, as shown in Figure 3 The admittance expressions in this model are: The series resonance frequency and parallel resonance frequency are:

Impact of cavity radius on frequency characteristics
The size of the cavity radius determines the magnitude of the vibrating displacement of the piezoelectric thin film.When subjected to the same sound pressure level, a larger radius film will have a larger vibrating displacement compared to a smaller radius film.By utilizing Comsol's parameter scanning function, the cavity radius of the film can be scanned to study its relationship with the resonant frequency, as shown in

Thickness on frequency characteristics and voltage
The thickness of the AIN film affects its piezoelectric properties, thereby influencing the output performance of the hydrophone.When the piezoelectric film is thicker, internal stresses increase, leading to a decrease in the quality of the piezoelectric film.On the other hand, when the piezoelectric film is too thin, the induced charge is reduced.Both excessive thickness and thinness will affect the performance of the hydrophone.Therefore, this study conducts a parameter scan of the thickness of the AIN film to investigate the relationship between the output voltage of the hydrophone and the thickness of the AIN film, as shown in Figure 5.The maximum output voltage is achieved when the AIN  .Consequently, the thickness of the AIN film in this study is set to 1.5 m  .

Figure 5.
Curve relationship between film output voltage and film thickness.

Comparison and simulation analysis of vibration modes
The simulation calculation of the vibration modes is performed for the established circular/square piezoelectric film simulation models.The simulation results for the first to fourth modes are shown in Figures 6 and 7.The resonant frequencies of the circular film for the first to fourth mechanical vibrational modes are 688.7 kHz, 1428.6 kHz, 1429.5 kHz, and 2366.6 kHz, respectively.The resonant frequencies of the square film for the first to fourth modes are 609.9kHz, 1241.2 kHz, 1243.3 kHz, and 1851.7 kHz, respectively.For both designs, the first mode of vibration mainly occurs along the z-axis direction, with the largest average surface displacement.This vibration mode is relatively simple and allows for better testing performance, making it the preferred vibration mode.On the other hand, other vibration modes with asymmetric film configurations tend to exhibit nonlinear output when receiving sound signals.By comparing the first mode vibration patterns of the two designs, the latter has a flatter response curve, lower resonant frequency, easier initiation of vibration, and a relatively larger overall displacement of the vibrating film.

Variation of output voltage and vibration amplitude with vibration frequency
During the simulation process, the external load resistance was set to 12 kΩ, and the damping ratio of the piezoelectric film was set to 0.001.The frequency range of the sinusoidal excitation set from 100 kHz to 1300 kHz.The curve relationship between the output voltage and the amplitude (in the zdirection) of the piezoelectric film concerning the vibration frequency within the set frequency range was obtained, as shown in Figures 8 and 9.The output voltage and the amplitude of the piezoelectric film initially increase and then decrease with the increase in vibration frequency.In both figures, when the vibration frequency reaches 600 kHz and 700 kHz, the maximum displacement of the film is 1456 pm and 2158.5 pm, respectively.At these frequencies, the output voltage also reaches its maximum values of 348 mV and 1078.5 mV, respectively.Additionally, it can be observed from the figure that when the external excitation frequency reaches the first resonant frequency of the device, both sides of the vibration amplitude show a symmetric decrease trend.Based on the analysis of the excitation frequency, when discussing the influence of the structural dimensions of the external film on the output voltage, the square film has a lower response frequency and higher sensitivity in terms of vibrational displacement.Therefore, the square film is preferred.

Conclusion
The equivalent models of the AlN piezoelectric film and the system were established, and the factors (cavity radius, film thickness, and vibration frequency) that affect the output voltage of the piezoelectric film were studied.
• The following conclusions were found: the resonant frequency gradually decreases as the cavity radius increases, with the resonant frequencies of the square film generally being lower than those of the circular film.
• When the film thickness is below 1.5 m  , the output voltage increases with increasing thickness, while the opposite is observed when the thickness exceeds 1.5 m  .The output voltage of the square film is generally higher than that of the circular film.• When the excitation frequency reaches a certain resonant frequency, the output voltage and vibration amplitude of the device reach their maximum values, and the square film outperforms the circular film in these aspects.These analysis results provide references for improving the performance of piezoelectric films and serve as a basis for future research on AlN piezoelectric films in underwater acoustic sensing and related fields.

Figure 4 .
As the radius increases, the resonant frequency of the piezoelectric film decreases.Since underwater detection primarily focuses on low-frequency sound signals, the resonant frequency should be designed to be as close to the low-frequency range as possible to enhance the response to low-frequency signals.The cavity radius should be maximized accordingly.However, if the film radius is too large, issues such as collapse and fracture can occur, resulting in device damage.Therefore, this study designs a circular vibrating membrane with a radius of 200 m  and a square vibrating membrane with a side length of 400 m  .

Figure 4 .
Figure 4. Curve relationship between film resonance frequency and cavity radius impact of film.

Figure 6 .
Figure 6.The first four vibration modes of circular piezoelectric films.

Figure 7 .
Figure 7.The first four vibration modes of square piezoelectric films.

Figure 8 .
Figure 8. Frequency response of circular film output voltage and amplitude.

Figure 9 .
Figure 9. Frequency response of square film output voltage and amplitude.

Table . 1
Therefore, a geometric structure of the piezoelectric thin film is established in COMSOL software.The specific size parameters of the material are shown in Table1.Material parameters of piezoelectric films.