Enhancing AlN PMUTs’ Acoustic Responsivity within a MEMS-on-CMOS Process

In this paper, guidelines for the optimization of piezoelectrical micromachined ultrasound transducers (PMUTs) monolithically integrated over a CMOS technology are developed. Higher acoustic pressure is produced by PMUTs with a thin layer of AlN piezoelectrical material and Si3N4 as a passive layer, as is studied here with finite element modeling (FEM) simulations and experimental characterization. Due to the thin layers used, parameters such as residual stress become relevant as they produce a buckled structure. It has been reported that the buckling of the membrane due to residual stress, in general, reduces the coupling factor and consequently degrades the efficiency of the acoustic pressure production. In this paper, we show that this buckling can be beneficial and that the fabricated PMUTs exhibit enhanced performance depending on the placement of the electrodes. This behavior was demonstrated experimentally and through FEM. The acoustic characterization of the fabricated PMUTs shows the enhancement of the PMUT performance as a transmitter (with 5 kPa V−1 surface pressure for a single PMUT) and as a receiver (12.5 V MPa−1) in comparison with previously reported devices using the same MEMS-on-CMOS technology as well as state-of-the-art devices.


Introduction
Currently, there is a growing demand for miniaturized devices capable of producing and sensing ultrasonic signals in a very efficient manner. There is a broad range of applications that use ultrasonics due to its non-invasive approach and small size including: minimally invasive intravascular medical imaging [1], ultrasonic powering of miniaturized implantable medical devices for in vivo and in situ physiological monitoring [2,3], systems for selective neural stimulation with an ultrasound signal [4], and fingerprints for biometric identification [5]. Some of these applications demand compact, minute systems. Piezoelectrical micromachined ultrasound transducers (PMUTs), based on out-of-plane micrometric flexural membranes are devices that can meet these requirements, thus replacing bulky piezoceramics that are difficult to compact, and result in low yield of the fabricated devices due to fabrication complexity. PMUTs composed of a multilayer laminate structure where at least one layer is made of a piezoelectric material, benefit from the robust fabrication processes used in MEMS technology, and provide high yields and scalable designs [6][7][8][9]. Moreover, PMUTs monolithically fabricated over pre-processed CMOS wafers enhance the obtention of very compact systems, are highly programmable if required and exhibit a high fabrication yield. Despite these benefits, some constraints due to the poor compatibility of PMUTs with the CMOS process, can limit the performance of ultrasonic signal processing. In addition, the CMOS process is limited to technologies that allow electrical contact from its last metal layer to the MEMS device within a specific post-process. Up until now, most of the reported PMUTs over CMOS are based on two-wafer bonding processes, in which the wafer with the PMUT (either AlN or PZT) is bonded to a CMOS wafer with analog front-end circuitry [10][11][12][13]. Despite the feasibility of this approach, the complexity of the bonding process and the limitations of the achievable fill factor impose some limitations. So far, we have already presented a system with AlN PMUTs monolithically integrated with a dedicated analog front-end circuitry for a single-pixel ultrasonic transducer [14,15]. Although we have demonstrated the viability and workability of this approach, in this paper we develop some guidelines for the optimization of the PMUTs over the CMOS and compare the results with previous ones.
The paper is divided into four sections. Section 2 presents the main parameters for the optimization of the acoustic pressure output and mechanical simulations to determine the optimal parameters of the PMUT layers. Section 3 is dedicated to the experimental electrical and acoustic characterization of the PMUTs to establish the device's performance. In Section 4, a discussion and a comparison with the state-of-the-art PMUTs are provided.

Materials and Methods: Optimization of PMUT Transducer
PMUTs can act as acoustic transmitters and acoustic receivers. If an electrical field is applied at both sides of the membrane, a transverse stress due to the inverse piezoelectrical effect at the piezoelectrical layer is produced and bending of the membrane out-of-plane is achieved, thus producing acoustic output pressure in the media (transmitter). If an input acoustic field is applied to the membrane, it will be bent and produce a transverse stress on the piezoelectrical layer; consequently, some electrical field is produced at the sides of the membrane due to the direct piezoelectrical effect of the piezoelectrical layer (receiver). For efficient production of the acoustic or electrical signal as a transmitter or a receiver, the membrane should be excited in its first out-of-plane flexural resonant mode, which relates the dimensions, layers, and materials of the PMUT with the desired resonant frequency [16]. In this paper we focus on PMUTs working in a liquid environment in the MHz range.
To optimize the size and thickness of PMUT devices (maximum acoustic pressure output as a transducer and maximum electrical signal as a receiver), it is convenient to define a cost function or figure of merit to be optimized. For this purpose, we have defined a figure of merit (FoM) as the product of the generated output acoustic pressure, P, and generated voltage at the PMUTs electrodes, V r . This FoM should be maximized to enhance the PMUT's performance. Both parameters, P and V r , are analyzed below.
The axial pressure amplitude at a distance z, P(z), in the far field region (z > R 0 , being R 0 , Rayleigh distance = S/λ, where S is the PMUT surface and λ is the wavelength of the acoustic signal in the propagation media, λ = c/f 0 , f 0 = resonance frequency, c = sound speed) is given by Equation (1), where P 0 is the pressure at the surface of the PMUT [16]. This pressure P 0 is proportional to the membrane velocity, u 0 = 2πd 0 f 0 (where d 0 is the membrane displacement) and the acoustic impedance of the media, Z 0 = ρ med c (where ρ med is the mass density of the acoustic media).
According to Equation (1), high resonance frequencies and large membrane displacements will benefit the acoustic pressure output of equal sized PMUTs. The membrane displacement for a PMUT is directly related to the elastic constant, k m , of the structure and the electro-mechanical coupling factor, η (as shown in Equation (2), where V in is the actuation voltage applied between the top and bottom electrodes). Thin structures will produce larger displacement at the expense of resonating with smaller frequency because these structures will have smaller elastic constants. Analogously, when an acoustic pressure, P a , is applied over the PMUT membrane, the output voltage between the top and bottom electrodes of the membrane, V r , will be proportional to the membrane displacement, d r (where r refers to receiver) according to Equation (3). In both cases it is necessary to compute the electro-mechanical coupling factor, η (Equation (4)) [16], which will quantify the conversion efficiency between the applied or received voltage and the membrane displacement. Because the PMUT is resonating, the dynamic displacement of the membrane, d = Q × d 0 should be used, where Q is the resonator quality factor. Both displacements, static and dynamic, will be in the same range due to the high damping in the liquid environment, which reduces the Q factor to values between 1 and 3, as will be shown in the Experimental section, and it is also reported in [17].
V r = d r k m /η = P a S/η η = 0.5e 31,f z p I piezo (4) In Equation (4), e 31,f is the transverse effective piezoelectrical coefficient of the piezoelectrical layer, z p is the distance from the mid-plane of the piezoelectric layer to the neutral axis, which depends on the multilayer lattice structure and I piezo is an integral that depends on the mode shape and electrode size, which equals 5.73 for an optimized inner electrode in a square membrane [18].
The resonance frequency, f 01 , Equation (5), in a multilayered membrane depends on the resonance mode, λ 01 2 = 35.99 for the first out-of-plane flexural mode in square-shaped membranes [19], the membrane side, a, the flexural rigidity, D, given in Equation (6) and on the mass per unit area or surface density, µ, Equation (7). Although the membrane resonance frequency will depend linearly on the thickness, and inversely on the square of the size of the membrane, it is difficult to analyze the dependence of the resonance frequency on thickness variations in multilayered membranes with different physical properties (i.e., plate modulus, E 11 , and mass density, ρ) [16].
where h n = h n − Z NA , is the distance from the top of the n-th layer to the neutral axis, Z NA and h n is the relative height between the bottom device and the top of the n-th layer.
where t n is the thickness of the n-th material layer. Due to the complexity of the multilayer laminate structure for analytical computation of the above equations, finite element models (FEM) were used to evaluate the performance of the PMUT parameters of interest: displacement, d 0 ; frequency, f 0 ; membrane velocity u o and output voltage, V r ; and the defined figure of merit, FoM = P * V r .
In the MEMS-on-CMOS technology considered [20,21], the PMUT is composed of four layers of different materials: AlN for the piezoelectrical layer, Si 3 N 4 as the elastic layer, and Al for the top and bottom electrodes. Figure 1 shows the schematic cross section of the PMUT with two top electrodes: an inner or central electrode (CENT) and outer or ring electrode (RING), and one bottom electrode (BOT).
In a first approximation, an axisymmetric model of a circular PMUT was assumed and mechanic-acoustic simulations were done by means of the COMSOL finite element software. The thickness of the Si 3 N 4 passive layer as well as the AlN piezoelectrical layer was swept from 1 to 2 µm and 0.5 to 1.5 µm, respectively, to obtain an enhanced acoustic performance in an equal-sized PMUT. The physical parameters for each of the PMUT's layers used in the model are listed in Table 1. In the simulations, the PMUT was immersed in a liquid medium, in this case FC-70, in accordance with the experimental characterization discussed in the next sections.  In Figure 2, the resonance frequency and normalized displacement as a function of the piezoelectrical layer thickness is shown (with a passive layer of Si 3 N 4 with a thickness of 1.5 µm). As expected, thinner membranes produce larger displacements at the expense of lower resonant frequencies. In fact, resonance frequency is linearly dependent on the membrane thicknesses as is inferred from Equation (5) [22]. The dependence of resonance frequency and normalized displacement (in terms of applied voltage) as a function of the AlN and Si 3 N 4 layer thicknesses are shown in Figure 3. This figure shows that the variation in the displacement is greater than a factor of ×77 (from 34 nm V −1 at minimum thicknesses to 0.44 nm V −1 at maximum thicknesses) while the variation in frequency does not change by more than a factor of ×3.3 (from 3.14 MHz at the maximum thicknesses to 0.95 MHz at the minimum). Accordingly, it is expected that the output pressure is maximum with the minimum thickness since the sound pressure depends on the normalized displacement and the square frequency (see Equation (1)).
On the other hand, we are also interested in the PMUT as a receiver, thus we also simulated the normalized output voltage at the central top electrode when an acoustic pressure is applied on the PMUT surface ( Figure 4). In all these simulations, the size of the top central electrode was optimized to have the maximum out-of-plane membrane displacement [18], and it was fixed for all the thicknesses. As shown in Figure 4, a maximum terminal voltage was generated at an AlN thickness close to 0.8 µm and Si 3 N 4 thickness of 1 µm (black curve).
Once the main parameters involved in the PMUT performance as transmitter and receiver have been obtained, the figure of merit can be computed. For this computation we assumed that the acoustic pressure is proportional to d 0 × f 2 , considering equal sized PMUTs according to Equation (1). In Figure 4b, the computed FoM = d 0 × f 2 × V r defines an optimal point with an AlN thickness close to 0.6 µm and with a Si 3 N 4 thickness of 1 µm.   Once the optimal thicknesses for the piezoelectrical layer, AlN, and the passive layer, Si 3 N 4 were defined, a theoretical comparison of the PMUT static behavior as a transmitter considering the two top electrodes was done. Figure 5 shows the comparison between two piezoelectrical layer thicknesses with a fixed passive layer thickness (Si 3 N 4 , 1.5 µm) in terms of normalized displacement as a function of the inner electrode side. Excitation of the membrane with the inner or the outer electrode achieves different deflections of the membrane because the outer electrode width is reduced from the optimal one, to incorporate the required gap between the inner and outer electrodes (2 µm) and the distance between the cavity and metal layer according to the technological rules for the PMUT fabrication (see schematic of the PMUT layout in the inset in Figure 5). From this static displacement, the displacement achieved with the 0.6 µm AlN was almost three times larger than with a thicker 1.3 µm AlN thickness, as expected. Finally, to predict more realistic PMUT behaviors, 3D COMSOL simulations considering all the geometric layout and material's layer thicknesses for the PMUT were performed. Figure 5b shows good agreement between the theoretical values computed for both electrodes: there is no difference between the theoretical and simulation results for the static displacement when the actuation is made using the outer electrodes and with a small difference with the inner electrode. From Figure 5b, it is also clear that bigger displacements are obtained with inner electrode actuation, with this difference being higher in the 0.6 µm AlN PMUT (yellow area). The main PMUT characteristics in liquid for the different proposed thicknesses are quantified in Table 2.
Several conclusions can be extracted from the results shown in Table 2. Thinner passive layers enhance the performance as a sensor but slightly decrease the output achievable pressure, mainly due to the decrease in the resonance frequency (note that the output pressure depends quadratically on the frequency according to Equation (1)). Despite the decrease in the output pressure, the FoM (considering both transmitting and receiving PMUT system) is higher for thinner PMUTs. Moreover, the performance of thicker PMUTs (i.e., 1.3 µm AlN + 1.5 µm Si 3 N 4 , was also simulated, obtaining: f = 2.48 MHz, d = 450 pm V −1 , V r = 1.34 V MPa −1 (normalized voltage at inner electrode), corresponding to a FoM less than 3.71 Hz 2 m kPa −1 ), which is a factor of ×2.2 lower than that reported in the first column of Table 2, which clearly highlights the benefits of using thinner piezoelectrical layers.

PMUTs Fabrication and Electrical Characterization
According to the optimized piezoelectrical layer thickness (0.6 µm AlN), a set of PMUTs with three Si 3 N 4 thicknesses (1 µm, 1.25 µm and 1.5 µm) were fabricated using the MEMS-on-CMOS SilTerra technology. The results were compared with a previously fabricated PMUT with a 1.3 µm AlN piezoelectric material [18]. The MEMS-on-CMOS process from Silterra [20,21], basically consists of: (a) deposition and patterning of an stack of Al metal electrodes (top and bottom) and a physical vapor deposited AlN layer on top of the last CMOS layer; (b) releasing of the membrane through pre-defined holes around the PMUT structure; and (c) deposition of the Si 3 N 4 elastic layer deposited with a low temperature plasma-enhanced chemical vapor deposition (PECVD) process, which allows the holes to be sealed for liquid operation.
Next, the electrical characterization in air was performed and compared with COM-SOL and the analytical expression of the resonance frequency. Figure 6 corresponds to the experimental frequency response for the PMUT with 0.6 µm AlN and 1.25 µm Si 3 N 4 thicknessess, an optical image is shown as an inset in the characterization set-up (Figure 6a).
From Figure 6b, an effective electromechanical coupling factor, k eff 2 = 1.14% was computed according to Equation (8) [23,24], between the inner and outer electrodes where f s = 4.866 MHz (resonance) and f p = 4.894 MHz (antiresonance or parallel resonance). In Table 3, the resonance frequencies for the three squared PMUTs are shown together with those computed by Equation (5), and the FEM simulated ones, and show a good match.

Acoustic Characterization
The PMUTs were characterized as an acoustic transmitter and receiver in a liquid environment (FC-70, sound speed c = 689 m s −1 and mass density, ρ = 1940 kg m −3 ). As transmitters, the PMUTs were driven by four cycles of a 22V pp harmonic signal generated by the signal generator (Keysight 81150A, Sunnyvale, CA, USA). Both top electrodes (inner and outer) were independently polarized for a complete characterization with the bottom electrode grounded. The acoustic pressure was measured with a commercial hydrophone from ONDA, Sunnyvale, CA, USA (HNC-1500) and displayed on an oscilloscope (Keysight DSOX3054A, Sunnyvale, CA, USA). Frequency and hydrophone micrometric positioning over the PMUT were manually tuned to maximize the receiving signal. Note that for liquid operation, the added mass loading effect should be considered [25], which will lower the resonance frequency from the 4-5 MHz found in air to the 1-2 MHz range as expected from the results shown in Figure 3.
The signals received by the hydrophone exciting the PMUT with 0.6 µm AlN and 1.25 µm Si 3 N 4 thicknessess at 1.6 MHz are shown in Figure 7. Unexpectedly, driving the inner electrode (Figure 7a) produces lower amplitude signals than driving the outer electrode (Figure 7b). FEM simulations from the previous section predicted the contrary as the size of the electrodes are complementary and were chosen to maximize the movement. This behavior can be attributed to the additional curvature produced on the PMUT surface by the residual stress from the piezoelectric, passive layer and electrodes during the fabrication. The physical characterization of the surface profiles of the PMUTs using a surface profilometer confirmed that thinner membranes are more prone to bending ( Figure 8) [26,27]. The maximum central height for the 0.6 µm AlN and 1.25 µm Si 3 N 4 thicknessess was 1 µm (see Figure 8) while the same feature decreased to 200 nm in the case of 1.3 µm AlN and 1.5 µm Si 3 N 4 . Several FEM simulations were done with samesized membranes with two top electrodes and two different curvatures (maximum central heights of 1 µm and 400 nm). Figure 9 shows the simulated displacements, which are higher when the outer electrode is driven in both cases and with higher movement when the central height is bigger, which is in line with the obtained voltage amplitudes shown in Figure 7. Table 4 summarizes the performance of the fabricated PMUTs. The output pressure was measured at 2 mm using the HNC-0200 ONDA hydrophone considering its sensitivity at the operation frequency and under the same voltage driving conditions (four cycles and 22 Vpp). From the normalized acoustic pressure in respect to applied voltage, the normalized surface pressure (P 0 = P × distance/R 0 , where R 0 is the Rayleigh distance already defined) can be calculated. This normalized surface pressure is an important parameter for the assessment of the performance of the presented PMUTs as transmitters and allows the comparison with the state-of-the-art PMUTs, as will be discussed in Section 4. As expected, thinner PMUTs with 0.6 µm AlN result in higher surface pressure, being almost a factor of 2 in comparison with the thicknesses used in previous works using the same technology. In addition, the influence on the achieved surface pressure is weakly related to the Si 3 N 4 layer thicknesses.    The PMUTs devices were also characterized as sensors using a commercial ultrasound transducer (OPTEL) at a 3 mm distance in the liquid environment. The transducer was excited with four cycles at the central resonance frequency of each of the PMUTs, with four cycles and 22 V pp . The generated signal in the outer electrode directly acquired by the oscilloscope is shown in Figure 10 for the case of a 0.6 µm AlN and 1.25 µm Si 3 N 4 PMUT. The same measurements under the same conditions were done for all the PMUTs to complete the comparison (Table 4, Received voltage column). The amplitudes decrease for thicker piezoelectric layers, with a weak dependence in respect to the thickness of the passive layer as was already seen in the simulations. Finally, the FoM was computed in this table, and demonstrated better performance for the thin PMUTs as was already predicted by the FEM simulations.

Discussion and Conclusions
As was shown in the previous sections, the presented PMUTs with reduced thicknesses for the piezoelectrical and elastic layer, achieve better performance as transmitters as well as receivers in comparison to PMUTs of equal size with the same technology but larger thicknesses. In this section, we compare the PMUTs' performance with several recently published papers on PMUTs. For convenience, the receiving sensitivity will be used. The receiving sensitivity is computed considering the calibration of the used ultrasound transducer at distances of 3 mm and 2 MHz [18].
A summary is given in Table 5. In comparing the same technological process, which follows a MEMS-on-CMOS process and exactly the same PMUT layout [18], the presented PMUTs exhibit bigger transmission and receiving sensitivities, with an overall x4 enhancement factor. This enhancement was also demonstrated in comparison with other PMUTs based on AlN, either with CMOS compatible processes [28] for the fabrication of PMUTs together with CMOS circuitry or with non-CMOS compatible processes [5] in which complex bonding between PMUT devices and CMOS circuitry are required. On the other hand, the presented PMUTs offer lesser performance in comparison with PZT devices [29] as transmitters, due to the high piezoelectrical constant of this material [6]. Despite this, the FoM is only a factor of ×1.8 smaller, which can be overcome by considering the compactness of the system due to the monolithic integration with the CMOS circuitry in our process. Note also that only simulated results are given for the receiver sensitivity in the case in [29]. In summary, the thinner PMUT with 0.6 µm AlN thickness and 1 µm Si 3 N 4 thicknesses presented in this work, demonstrates higher acoustic pressure production along with higher receiver sensitivity, and enhances the applicability of PMUTs on CMOS for ultrasound systems that need to be miniaturized. a Clampled-clamped square PMUT (same layout as presented here). b Estimated according to the data provided in [29] and considering ST = P × distance/R 0 = 27 kPa V −1 if experimental data are used (extracted from [29]: Pressure = 8 kPa/30 V = 0.3 kPa V −1 , distance = 5 mm, and R 0 = (80 µm) 2 /λ = 55.6 µm where λ = c/f = 1500 m s −1 /13 MHz = 115 µm). c Value obtained together with the custom CMOS ASIC [5]. d In reception 10 V pC −1 charge amplifier was used [28]. e PZFlex simulations [29]. Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.