Wafer-level experimental study of residual stress in AlN-based bimorph piezoelectric micromachined ultrasonic transducer

Recently, some researches using AlN-based piezoelectric micromachined ultrasonic transducer (pMUT) opened up novel applications such as photoacoustic imager [1, 2], fingerprint sensor [3], and rangefinder [4]. These applications are taking advantage of c-axis textured AlN-based pMUT to achieve high reception sensitivity and low power consumption. AlN material has also a great potential for monolithic complementary metal oxide semiconductor (CMOS) integration due to relatively small process temperature (<400 °C) compared to PZT [5]. Recent work include curved pMUT [6], multiple electrode pMUT [7] and so-called zero-bending pMUT [8] that demonstrate significant improvement of pMUT performances. Bimorph pMUT made of two AlN layers are particularly promising [9]. In this case, the multi-electrodes scheme allowed by the bimorph structure may be used to differentially drive or sense the pMUT, improving by up to a factor 4 the performance of the device, what somehow balance the relatively low piezoelectric properties of AlN compared to PZT. Yet, bimorph pMUT architecture is expected to be particularly sensitive to residual stress in AlN material since most of the membrane is made of AlN.

It is well known that residual stress detrimentally affects pMUT performance such as resonant frequency, sensitivity, and bandwidth and may cause device failure because of initial buckling [8, 10], especially when the membrane thickness is small so that the pMUT diaphragm cannot be considered as a plate. Many researches cover how residual stress impacts individual pMUT performance [11–13] and it is alleged that the effects of residual stress hamper the commercialization of these devices [8], much probably because of the residual stress distribution over the wafer. Yet, few works focuses on the resulting distribution of performance over the whole wafer [14].

Due to the importance of the residual stresses, many characterization tools have been employed to analyze the stress of thin films such as examination of curvature [15], x-ray diffraction (XRD) techniques [16], coherent gradation sensing (CGS) [17], Raman spectra [18] and microstructures [19]. Among those techniques, curvature-based stress analysis are broadly used tool for thin film due to its convenience. The conventional Stoney's formula is valid if stress is constant over the whole surface of the wafer, i.e. if the wafer curvature is uniform, which is often assumed. There were several studies to extend Stoney's formula to more realistic cases [20–22]. Among others, [21] proposed a pointwise stress analysis by relaxing equi-biaxial stress assumption and adding non-local term in Stoney's equation.

We propose here a study that covers the different sides of the issue at stake, including both material characterization and device characterization at the wafer level, in the specific case of bimorph AlN-based pMUT designed for low-frequency applications (50–250 kHz range). The characterization of the resonant frequency of pMUT devices over a wafer provides a first estimation of membrane tension dispersion through FEM simulation. In parallel, the stress variation is estimated by curvature measurements of a similar reference wafer combined with a non-local Stoney's equation. The comparison of the two approaches provide a good basis to discuss stress variation over the wafer and its impact on pMUT characteristics.

The pMUT design and process flow is described in part II. Characterization results using laser Doppler vibrometer and the determination of membrane tension distribution are presented in part III. Stress variation is calculated by curvature measurements in part IV. The impact on pMUT performances is discussed in terms of resonant frequency, sensitivity and robustness to technological variations in part V.

Figure 1 shows the schematic view of the AlN-based bimorph pMUT, similar to what is presented in ref. [9]. Three radius pMUT have been designed, set to 260, 420, and 750 μm to target resonant frequency in the 50–250 kHz range for air-borne applications. The bimorph pMUT is made of two 800 nm-thick AlN layers sandwiched between three 200 nm-thick Molybdenum (Mo) layers. While the bottom and top Mo layers are patterned to form outer annular and inner circular electrodes, the middle electrode is not patterned at the diaphragm level and works as a ground electrode. The radius of inner electrode are chosen to 60% of radius, which is expected to be optimal coverage for clamped circular pMUT [23]. When an AC bias is applied to one of the bottom or top electrode, the induced stress within the corresponding AlN layer causes the bending of the pMUT and subsequent acoustic waves in the surrounding medium.

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The process flow is described in the figure 2. The fabrication of bimorph pMUT starts with a thermal oxidation of a 1 μm-thick SiO₂ on the 8'' silicon wafer (figure 2(a)), which aims at reducing parasitic capacitance between bottom electrode and bulk. Then, a 20 nm-thick AlN seed layer is deposited (figure 2(b)). AlN is deposited by reactive pulsed DC magnetron sputtering of an Al target in an argon—nitrogen plasma. A RF bias is applied to the chuck to control the average stress value. The deposition tool is fitted with a planar rotating magnetron, as well as with a rotating substrate holder to improve the thickness homogeneity of the AlN film. However, we did not evidence a noticeable influence of the rotation speed of the magnetron on the film stress homogeneity. The first Molybdenum (Mo)/AlN stack is deposited by sputtering on the seed layer (figures 2(c)–(d)) followed by the second Mo/AlN/Mo stack (figures 2(e)–(g)). After each deposition process, electrodes were patterned using reactive ion etching (RIE). Top AlN layer is deposited with slightly different chuck bias conditions so that top and bottom AlN layers exhibit similar stress, using standard Stoney formula to roughly estimate the stress of each layer. To address each electrode in the device, etching of the AlN layers was conducted to form via towards the different electrodes, followed by the deposition and patterning of a SiN passivation layer (200 nm) (figure 2(g)). Then, a 1-μm thick silicon dioxide layer is deposited by plasma enhanced chemical vapor deposition (PECVD) and gold under-bump metallic layer (Ti/Ni/Au: 200/500/100 nm) are deposited to form a bonding pad to electronics (figures 2(h)–(i)). Lastly, pMUT is released by backside deep reactive ion etching (DRIE) of silicon and removal of the SiO₂ layer (figure 2(j)).

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Optical pictures of the three pMUT types are shown in figure 3. Due to footing effect of DRIE process, the three radius targeted at 260, 420 and 750 μm are broadened to 278, 440 and 773 μm, respectively.

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The pMUT were characterized using a probe station equipped with a laser Doppler vibrometer (Polytech inc., USA). In this work, we focus on stress issues and do not try to benefit from the multi-electrode scheme: the displacement at the center of pMUT was measured in air by applying an actuation voltage of 0.5V between the internal bottom electrode and middle grounded electrode while other electrodes are floating. The displacement of pMUT with different radius are presented in frequency domain in figure 4, focusing on the first mode. The pMUTs exhibit a resonance in the 50–150 kHz range, depending on the radius of diaphragm and the tension of the membrane, what will be discussed later in the paper. The drive sensitivity ranges from 78 nm/V for the largest diaphragm to 216 nm V⁻¹ for the smallest diaphragm. The results are well fitted with a second order harmonic oscillator model described by:

$$\begin{eqnarray}&&H(j\omega )=\displaystyle \frac{G}{{\omega }_{0}^{2}-{\omega }^{2}+j\tfrac{{\omega }_{0}\omega }{Q}}\end{eqnarray} \tag{ 1 }$$

Where G is the gain, Q is the quality factor and ω₀ is the natural angular frequency, which is very close to the resonant angular frequency for these devices.

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The transmitting sensitivity at resonance at the membrane center is directly read on the experimental plots and corresponds to

$$\begin{eqnarray}&&{S}_{res}\approx \displaystyle \frac{G\cdot Q}{{\omega }_{0}^{2}}\end{eqnarray} \tag{ 2 }$$

The measurements have been reproduced on different devices along a wafer's diameter. The dispersion of the resonant frequency is shown on figure 5. For the sake of clarity, each device is accounted for by its relative distance to the wafer center. Due to the particular configuration of the layout mask, some area of the wafer such as wafer center does not present any devices. It appears that the resonant frequency dramatically depends on the location of the device on the wafer, showing higher values on the center and smaller values on the edge. This dependency can be explained by many factors, among which radius and residual stress variation over the wafer are the most probable one. Yet, our calculations show that a frequency change of typically 107% would be explained by a radius variation of 33% which is far above what has been observed. We therefore conclude that the resonant frequency dispersion was mostly caused by non-uniform residual stress.

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We use some modelling tools to quantitatively assess the overall plate tension of the different devices from these measurements. First, we use a basic analytical solution, plotted using continuous line on figure 6 [24]. Second, we use a 2D axisymmetric COMSOL model that includes all the layers of the diaphragm except the 20 nm thick AlN seed layer. The plate tension is the relevant physical parameter but models require stress values, assessed from previous experiments and summed up in table 1. At this step, one cannot attribute any change in tension to one layer in particular, hence we played only with the stress of the top AlN layer by convenience. We checked that the results did not depend on how the stress are distributed within the stack. The overall tension was calculated using:

$$\begin{eqnarray}&&T=\displaystyle \displaystyle \sum _{i}{\sigma }_{i}{h}_{i}\end{eqnarray} \tag{ 3 }$$

where, σ_i : residual stress of layer I; h_i $:$ thickness of layer i

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A good agreement is shown between analytical tool and FEM simulation. As a result, we used this model to link the resonant frequency distribution to tension variation. We conclude that tension spread from 100 to 800 N m⁻¹ over the wafer, which reflects some stress variation in one or more layers of the stack.

To get relevant information about the residual stress of each layer of the diaphragm, a stress analysis is performed on a reference wafer, which is fabricated with the same process conditions as pMUT wafer except patterning steps and final release. Before and after each deposition stage, the deformation of wafer is measured by interferometry, from which a curvature profile and then a stress profile are calculated. We assume that such stress measured on an unpatterned wafer is similar to that of the patterned wafer, i.e. that stress is not locally released because of the patterning step, which seems to be a reasonable assumption for such large patterns [25]. We also assume that the stress of a layer is not impacted by the following technological steps.

Figure 7 shows the wafer deformation after deposition of the first 800-nm thick AlN layer. This deformation map clearly presents an axisymmetric pattern. Therefore, we focus on 1D measurements along two orthogonal diameters of the wafer thereafter referenced as 'x' and 'y' that provide relevant information with less time consumption and efforts. We use the following equation derived from [22] to determine the stress from the curvature measurement:

$$\begin{eqnarray}&&{\sigma }_{xx,yy}^{{f}_{(i)}}=\displaystyle \frac{{E}_{s}{h}_{s}^{2}}{6\left(1-{v}_{s}\right){h}_{f}^{i}}\,\left({\rm{\Delta }}{k}_{xx,yy}^{(i)}+\displaystyle \frac{1-{v}_{s}}{1+{v}_{s}}\left({\rm{\Delta }}{k}_{xx,yy}^{(i)}-\overline{{\rm{\Delta }}{k}_{xx,yy}^{(i)}}\right)\right)\end{eqnarray} \tag{ 4 }$$

Where, ${E}_{S}:$ young's modulus of substrate, ${h}_{s}:$ thickness of substrate, ${h}_{f}:$ thickness of thin film, ${v}_{s}:$ Poisson's ratio of substrate, ${\rm{\Delta }}{k}_{xx,yy}^{(i)}:$ ${k}_{xx,yy}^{(i)}-{k}_{xx,yy}^{(i-1)}$ curvature of ${i}^{th}$ layer in x- and y-axis for Cartesian, , $\overline{{\rm{\Delta }}{k}_{xx,yy}^{(i)}}:$ mean of ${k}_{xx,yy}^{(i)}-{k}_{xx,yy}^{(i-1)}.$

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Figure 8 presents the stress of the different layers. The residual stresses of the three Mo layers (figure 10(a)) are significantly different. The mean values are −158, 284 and 553 MPa for bottom, middle and top electrode, respectively. By comparing stress in x- and y-axis, one may deduce that bottom electrode presents a higher stress at the center than at the edge, while middle and top electrodes might exhibit a more flat profile. The stress of the AlN layers shown in figure 8(b) presents a very good reproductibility between x- and y-axis and between first and second AlN layers, with a particular hat-shape that spread overs 750 MPa. The right/left symmetry observed for the different profiles, as well as the small discrepancy between the x- and y-direction, confirm the axisymmetric distribution of the residual stress of the AlN layers. These axisymmetry is most probably explained by equipment features, as exposed by some equipement suppliers [26, 27]. SiN layer (figure 8(c)) exhibits a more flat profile that spreads over 100 MPa with a mean value of −120 MPa, with no correlation between x and y diameter. That stresses out that the variations observed for the other layers, especially the AlN layers, do reflect the material properties. These measurements have been reproduced several times and the main trends highlighted here are confirmed.

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Figure 9 presents the overall plate tension along a diameter of the wafer, calculated through the resonant frequency as described in part III (scattered points) and from stress obtained by curvatures measurements (continuous line). The results arising from the three pMUTs type are merged on a single figure and are consistent. The two independent methods reveal similar tension profile shape, with a maximum at the wafer center and a minimum at half radius. Yet, the stress analysis from pMUT and bow of wafer presents a significant mismatch up to 500 N m⁻¹ similar to what is observed in ref. [20]. This difference may be due to our Stoney-based approaches that relies on several assumption such as uniform thickness of film and substrate, homogeneity, equivalent biaxial stress and infinitesimal displacement. Nevertheless, we conclude that the resonant frequency variation is caused by the AlN stress variation presented in figure 8.

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The performance of pMUT have been analyzed as a function of membrane tension. Figure 10(a) presents the sensitivity of pMUTs with radius of 278, 440 and 773 μm at the fundamental resonant frequency, when AC voltage is only applied to inner bottom electrode. The measured data were fitted to equation (2) introduced in part III, used as a guide for the eye to interpret the main trend of the results. The frequency range offered by each pMUT type is large and cover respectively 150–325 kHz, 75–225 kHz and 50–125 kHz, due to the stress distribution of the AlN layers evidenced in this paper. Our experiments show that small pMUT with low tension may be preferred to large pMUT to obtain good sensitivity. To decrease tension is efficient to improve sensitivity as plotted in figure 10(b), yet this makes the membrane very fragile if not buckled [8]. One may also play with thickness to target low frequency and better sensitivity but this approach is limited by technological considerations since piezoelectric properties of AlN are expected to be poor at small thickness below 500 nm [28]. Figures 10(c)–(d) presents gain and quality factor of the different pMUT devices. Gain does not depend on tension, what means that piezoelectric coefficients are not affected by stress. The quality factor shows a downward trend, what partially explain why sensitivity decreased when tension is increased. The coupling coefficient was extracted from some impedance measurements (not shown) and is typically of 3.5%, 1.9% and 0.3% for pMUT with radius of 278, 440, and 773 μm and a mechanical tension of 180 N m⁻¹, 100 N m⁻¹ and 50 N m⁻¹, respectively.

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As one may have expected, the important AlN stress distribution from −250 to 500 MPa on a wafer is noteworthy and result in a important distribution of pMUT performance over the wafer. We believe that such dispersion is very common even if it not pointed out. Since stress does not strongly affect piezoelectric coefficients, AlN-based devices without mobile part are probably slightly impacted. The development of devices such as bulk acoustic wave resonator may have circumvented stress-related issues. On the contrary, pMUT devices are sensitive to material stress, in particular low frequency devices for which the resonant frequency is strongly affected by the overall plate tension. Bimorph pMUT are even more impacted because of the two AlN layers. For such devices, AlN stress distribution could be overcome by technological improvement of deposition tools [26, 27] since the stress is strongly dependent on deposition parameters, as reported in [29]. The resonance of a single pMUT may also be tuned by the use of a DC bias [30].

In this paper, AlN-based bimorph pMUTs with radius of 278, 440, and 773 μm have been fabricated and characterized at the wafer level. pMUT gain, natural frequency and quality factor have been assessed experimentally. A large distribution of performance is observed for natural frequency and quality factor, which is attributed to the variation of AlN stress over the wafer. The study shows that small pMUT with radius of 278 μm and a mechanical tension of 100 N m⁻¹ provide good performance and are not buckled. This is confirmed by a study on a reference unpatterned wafer, where the stress of each layer is determined using a non-local Stoney's formula. This advocates for technological tools with better AlN stress control that would also benefit to other AlN-based devices such as microphones.