The effect of FeNi-AlN layer thickness on the response of magnetic SAW sensor by FEM simulation

ABSTRACT


INTRODUCTION
Surface acoustic wave (SAW) devices have numerous applications in the fields of actuators and sensors, including the microelectromechanical systems (MEMS) actuator [1].SAW sensors have been applied in various fields, such as mechanical, biological, chemical, gas, and microfluidics, to measure physical quantities including temperature, pressure, viscosity, mass, stress, current, gas composition, magnetic field, and the spatial localization of partial discharges [2]- [9].Recently, the wireless magnetic sensors with low energy consumption are essential for developments in the field of the internet of things, autonomous vehicles and the factory of the future.Common constructions for magnetic SAW sensors usually have a magnetic sensitive materials, an intermediate layers, an electrodes and a piezoelectric substrates (magnetic sensitive materials/intermediate layers/electrodes/piezoelectric substrates).Several recent studies indicate that common magnetostrictive sensitive materials, including Ni, FeGa, FeCo, and FeNi, have been combined with quartz and LiNbO3 piezoelectric substrates to measure magnetic field intensity and current with high sensitivity [4]- [6], [10]- [17].The results show that the thickness of the magnetic materials significantly  [4], [11], [15].Notely that the simulation approach was used to optimize the design parameters of sensors, in which the electromechanical equations set are solved numerically through finding boundary conditions to satisfy the CHRISTOFFEL equation and using perturbation theory [11].In fact, it is difficult to determine the boundary conditions, and thus consequently this approach is not convenient to implement.Currently, the most popular simulation method for SAW sensors is using finite element method (FEM) through commercial software tools such as COMSOL and ANSYS.The survey shows that many studies have used FEM to simulate gas sensors, pressure sensors, magnetic field sensors, and SAW filters [6], [18]- [23].Namely, the FEM with the COMSOL tool was used to evaluate the influence of the intermediate layer on the sensor properties of the magnetic SAW sensor [16].
Thus, in this work, we used the FEM with ANSYS software to simulate the SAW-MO sensor with FeNi/IDT/AlN structures.In this SAW-MO sensor, FeNi is selected because it has good sensitivity, low nonlinearity and small hysteresis; AlN is a piezoelectric material and has a large surface wave velocity that leads to being able to achieve the high sensitivity.The thickness of the FeNi and AlN layers changed during the simulation to determine the optimal parameters for the sensor structure to achieve the highest sensitivity.
The rest of the paper is organized as follows: section 2 presents the simulation process of the paper, which is divided into smaller sections, whereby section 2.1 explains the principle and structure parameters of the sensor, while section 2.2 gives mathematical model for FEM simulation, and section 2.3 presents FEM simulation process.Section 3 shows the results and discussions of this research paper and, finally, section 4 displays the conclusive findings for this research paper.

SIMULATION PROCESS 2.1. Principle and structure parameters of the sensor
Figure 1 illustrates the SAW-MO sensor structure.The sensor comprises an AlN piezoelectric substrate, which has two sets of electrodes, namely the input (IDT-in) and output (IDT-out) electrodes.These electrodes sandwich the FeNi sensitive layer (in a delay-line form).When a voltage is applied to the IDT-in, the piezoelectric substrate generates a surface acoustic wave through the reverse piezoelectric effect, which propagates through the FeNi sensitive layer to the IDT-out, where a forward piezoelectric effect occurs and forms a voltage on the IDT-out.The interaction between the measured magnetic field intensity (H) and the FeNi magnetic sensitive layer changes the frequency of this signal (or the SAW velocity).The structural parameters of the sensor are detailed in Figure 2 and Table 1.In the simulations, the sensor has a constant length (in the  1 axis) and depth (in the  3 axis), and initially, the sensor is simulated with  = 10 μm (corresponding to the sensor with wavelength  = 40 μm.The thickness of the piezoelectric substrate (ℎ1) is 400 μm, while the thickness of the magnetic sensitive layer (ℎ3) varies to determine the optimal working point of the sensor.Subsequently, the simulation changes the thickness (h1) of the piezoelectric layer to determine the limit of the sensor's working point when the wavelength λ is constant based on the found optimal point (ℎ3).

Mathematical model for FEM simulation
In this work, we set up a mathematical model of the SAW-MO sensor in a piezoelectric material environment, representing the forward and reverse piezoelectric effects with a set of electromechanical ( 1) and (2) [24], [25].These equations involve parameters such as the elastic matrix (), piezoelectric matrix (), and dielectric constant matrix () along with stress (), strain (), electric displacement (), and electric field () (see in Table 2).We also use motion ( 3) and (4) [24] to describe particle movement in the solid, with phase velocity, particle displacement, and potential as variables. (3) Where  is the particle displacement in the solid,  is the potential, and  is the density of the piezoelectric material.Here the operators are: Combining ( 3) to ( 6) with (1), (2) and the condition  •  = 0, we can express the constitutive (7) in index form for the AlN piezoelectric material [4].
This equation involves the density, elastic coefficient, piezoelectric coefficient, mechanical displacement, and electric field of AlN, as well as indices , , , =1, 2, 3. Similarly, we have the constitutive (8) for FeNi magnetic sensitive material, which does not involve electric or displacement components [4].
The wave used in our study is the Rayleigh wave (  ), and the velocity relationship between this wave and the shear wave (  ) is described in ( 9) and ( 10) [26], [27], with anisotropy coefficient  and shear wave velocity   calculated differently for isotropic and anisotropic materials [24], [26].
We note that   is always greater than the surface acoustic wave velocity.Based on the sensor structure illustrated in Figure 2, the surface acoustic wave propagates through the delay-line element, which is coated with a magnetic sensitive layer made of FeNi with a variable thickness.Consequently, the surface acoustic wave experiences two factors.First, the mass () of the FeNi magnetic sensitive layer reduces the surface acoustic wave velocity [11], which can be calculated using (12).Second, the surface acoustic wave velocity gradually increases and approaches the shear velocity when the thickness of the FeNi sensitive layer increases [24], [26] or the AlN piezoelectric layer decreases.The mass is calculated as (11): In this simulation, the depth () and the length () of FeNi sensitive layer are constant, while its thickness (ℎ3) varies, and its density (  ) is defined as the constant  =  × .Therefore, the mass of the FeNi magnetic sensitive layer can be expressed using: Moreover, the elastic coefficients of the FeNi magnetic sensitive material layer are determined by the relationship [11].
Bulletin of Electr Eng & Inf ISSN: 2302-9285  The effect of FeNi-AlN layer thickness on the response of magnetic SAW sensor by … (Do Duy Phu) Where  is the Young's modulus defined by the E-H characteristic and the poison coefficient (  ) is equal to 0.3. is the measured magnetic field intensity.
To simulate the sensor's working response accurately, the E-H characteristic described in [11] is used to determine the sensor's working points.Specifically, as the measured magnetic field intensity () changes, it alters the young's modulus () of the magnetic sensitive material layer, which affects the propagation velocity of surface acoustic wave (  ).Combining this with the relation   /  = /0 [31], where  0 is the center frequency of the sensor, determines the frequency change of the sensor.By varying the thickness (ℎ3) of the FeNi sensitive layer at  = 0 Oe, we can establish the relationship between the center frequency and the thickness of the FeNi sensitive layer to identify the optimal working point, which maximizes the acoustic wave velocity or resonant frequency at a given thickness.Subsequently, additional simulations are performed around the optimal working point to determine the sensor's working response and draw conclusions regarding the best sensitivity of the magnetic sensor.With the optimal working point fixed, the thickness of the AlN piezoelectric layer is varied to determine the central frequency limit point of the sensor with a constant wavelength.This serves as the basis for increasing the center frequency of the sensor, which hopefully enhances the sensitivity of the sensor when working at lower measuring ranges.

FEM simulation process
To simulate the sensor's working response, we used the constitutive ( 7) and ( 8) and data from Table 2.We performed FEM simulation in the following steps: firstly, entering the physical parameters (Table 2) and declaring the structure parameters (Table 1); secondly, building the sensor structure (as shown in Figure 2), meshing and changing material layers; thirdly, applying voltage to the IDT-in and setting boundary conditions; finally, solving and reading results.The simulation process is illustrated in Figure 3.We applied a square pulse voltage of 100 V and pulse width of 10 ns to the IDT-in, then let the FEM calculation run long enough for the surface acoustic wave to propagate from IDT-in to IDT-out (about 1,500 ns), with a signal sampling period of 0.3 ns to satisfy Shannon's theorem.The output voltage was read on the IDT-out in the time domain and converted to the frequency domain using the FFT spectral density transform algorithm to determine the resonant frequency (  ) and surface acoustic wave velocity.We iteratively repeated this process to find the optimal working point by changing the FeNi sensitive layer thickness and to determine the working responses around the optimal point as the measured magnetic field intensity () changes.We also changed the AlN piezoelectric layer thickness to determine the limit point of the center frequency and the sensor's working response when the center frequency is increased, with the aim of improving the sensor's sensitivity when measuring at a lower range.

RESULTS AND DISCUSSION
The simulation results presented in Table 3, Figures 4 and 5 reveal a two-stage behavior in the characteristic.In the first stage, increasing the thickness of the FeNi magnetic sensitive layer up to 1,060 nm results in an increase in the center frequency and surface acoustic wave velocity.However, in the second stage, further increases in the thickness of the FeNi layer lead to a decrease in the center frequency and surface acoustic wave velocity.These results are consistent with the theoretical framework proposed in this study and corroborated by previous research [4], [11], [15].Table 3. Center frequency ( 0 ) and surface acoustic wave velocity (VR) at the different thickness points of the FeNi magnetic sensitive layer (h3),   =   0 , ℎ1 = 400 m and  = 40 m Based on the simulation results, we identify the optimal working point of the sensor at ℎ3 = 1,060 nm, when ℎ1 = 400 µm and  = 40 µm remain unchanged.This conclusion follows from the fact that the center frequency and surface acoustic wave velocity reach their maximum values at this thickness.To gain a clearer understanding of the process used to determine the center frequency of the sensor at different thicknesses (ℎ3) of the FeNi magnetic sensitive layer, Figure 6 displays the frequency response of the sensor at three thickness points: 1,000 nm, 1,060 nm, and 1,210 nm.We determine the center frequency of the sensor for each thickness point by identifying the resonance peak of the frequency response.
We simulated the sensor's working response at different FeNi magnetic sensitive layer thicknesses, including 1,000 nm, 1,060 nm, and 1,210 nm, around the optimal working point.The simulation results are presented in Figure 7 and Tables 4 to 6  We determined the sensor's sensitivity in two cases based on its working responses at different ℎ3 points.In the first case, the sensitivity is calculated over the full response scale of the sensor.At ℎ3 = 1,000 nm, the response range  = [0 ÷ 109] Oe, with an achieved sensitivity Sn of 8.661 kHz/Oe; at ℎ3 = 1,060 nm, the response range  = [0 ÷ 89] Oe, with an achieved sensitivity Sn of 10.287 kHz/Oe; and at ℎ3 = 1,210 nm,  7 and Figure 8.In the second case, the sensitivity is calculated on the same response scale of the sensor  = [0 ÷ 89] Oe.At ℎ3 = 1,000 nm, the achieved sensitivity Sn is 8.661 kHz/Oe; at ℎ3 = 1,060 nm, the achieved sensitivity Sn is 10.287 kHz/Oe; and at ℎ3 = 1,210 nm, the achieved sensitivity Sn is 9.375 kHz/Oe.In the second case, the sensitivity of the sensor is calculated on the same response scale of the sensor  = [0 ÷ 89] (Oe), with achieved sensitivities of 8.661 kHz/Oe at ℎ3 = 1,000 nm, 10.287 kHz/Oe at ℎ3 = 1,060 nm, and 9.375 kHz/Oe at ℎ3 = 1,210 nm.Details are shown in Table 7 and Figure 9.These results indicate that at ℎ3 = 1,060 nm, the sensor exhibits the highest surface acoustic wave velocity and center frequency, resulting in the maximum sensitivity of 10.287 kHz/Oe in both cases.Our findings are in line with previous research in [6], which shows that higher surface acoustic wave velocity or center frequency leads to greater sensitivity.Additionally, to identify the points on the response range of the sensor when the magnetic field intensity changes from 0 to 89 Oe, we examined the resonance peaks on the frequency responses, as shown in Figures 10 to 12   We conducted simulations to investigate the influence of piezoelectric substrate thickness on the central frequency limit of the sensor.The results indicate that decreasing the piezoelectric substrate thickness increases the center frequency, as shown in Figures 13 and 14.This finding is consistent with previous studies in [6], [24], [26], [27], which suggest that as the piezoelectric substrate thickness decreases, the surface acoustic wave velocity approaches the shear wave velocity.However, when the piezoelectric substrate thickness is reduced to less than one wavelength (see in Figure 14), the frequency characteristic at ℎ1 = 35 μm no longer exhibits a resonance peak, leading to the indeterminability of the center frequency, unlike points with greater thickness.This phenomenon can be explained by the fact that when voltage is to the IDT-in, the piezoelectric material undergoes deformation due to the reverse piezoelectric effect from the surface to a depth of approximately one wavelength (), as stated in [26].Thus, if the piezoelectric substrate thickness is greater than approximately one wavelength, the deformation region on the piezoelectric substrate is preserved.However, if the thickness is less than one wavelength, the deformation region is not preserved, causing the surface acoustic wave to be cut off at the lower peak, and as a result, the frequency characteristics are not preserved.
To preserve the frequency characteristics of the sensor, we can reduce the wavelength to  = 30 μm or increase the center frequency.The simulation results, which are shown in Figure 15, demonstrate that the frequency center  0 = 218.46517MHz when the wavelength is reduced to  = 30 μm.The working range of the sensor is [0 ÷ 89] Oe, as shown in Figure 10, and the highest sensitivity is achieved when the magnetic sensitive layer thickness ℎ3 is 1,060 nm.However, the sensitivity is lower in the segment from 0 to 35 Oe, as seen from the frequency shift characteristic of the sensor at ℎ3 = 1,060 nm.To increase the

Figure 1 .
Figure 1.The SAW-MO sensor structure

Figure 6 .Figure 7 .
Figure 6.Frequency response around the sensor's optimum working point

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ISSN: 2302-9285Bulletin of Electr Eng & Inf, Vol. 13, No. 1, February 2024: 167-178 176 sensitivity of this segment, we can reduce the piezoelectric substrate thickness, which also reduces the fabrication and simulation time, and increase the center frequency of the sensor.The response simulation results of the sensor are shown in Figure16.The simulation results show that the center frequency  0 = 218.46517MHz, the working range reaches from 0 to 33.1 Oe with the frequency shift of 248.21 kHz when the sensor has the parameters ℎ1 = 35 μm,  = 30 μm, and ℎ3 = 1,060 nm.On the other hand, the structure of the sensor with the parameters ℎ1 = 400 μm,  = 40 μm, and ℎ3 = 1,060 nm only gives the frequency shift of 118.79 kHz when considering the working range from 0 to 33.1 Oe.These results demonstrate that increasing the center frequency increases the sensitivity of the sensor, as shown in Table8.

Table 1 .
Structural parameters of the sensor

Table 7 .
The sensitivity () of sensor at points ℎ3 when  = 40 m and ℎ1 = 400 m