**1. Introduction**

Microelectromechanical System (MEMS) structures are utilized to form cantilevers for sensors [1,2], resonators [3], and piezoelectric energy harvesters [4]. In piezoelectric energy harvesters [4] and micro-accelerometers [5], the properties of the cantilevers and their geometric limits directly impact device performance. The amount of deformation in cantilever beams and other structures depends on the growth technique utilized and material selection.

Aluminum Nitride (AlN) is a piezoelectric material commonly selected for the fabrication of vibrating MEMS structures. In 2009, it was determined that alloying AlN with scandium (Sc) can increase the piezoelectric coefficients by 500% [6]. AlN and Aluminum Scandium Nitride (Al1−xScxN) films deposited using Molecular Beam Epitaxy (MBE) or metal-organic Chemical Vapor Deposition (MOCVD) demonstrate exceptional film quality and high electromechanical coupling (k<sup>t</sup> 2 ) but require processing at high temperature [7,8] and exhibit challenges due to stress gradients in the epi layers and complications in the releasing of structures at the end of the fabrication process [8]. For example, Park et al. [8] developed MBE Al1−xScxN Lamb wave resonators at super high frequencies directly on Silicon with acoustic velocities of 14,000 m/s and k<sup>t</sup> <sup>2</sup> of 7.2%, but compressive film stresses produced buckling in the released films [9].

Sputtering is a Physical Vapor Deposition (PVD) method used to produce semiconformal films of controlled thickness with high deposition rates at low substrate temperatures for realizing MEMS devices. During sputter deposition, ions accelerate and bombard a target removing atoms to be deposited on the wafer. There are numerous collisions that

**Citation:** Beaucejour, R.; D'Agati, M.; Kalyan, K.; Olsson, R.H., III Compensation of the Stress Gradient in Physical Vapor Deposited Al1−xScxN Films for Microelectromechanical Systems with Low Out-of-Plane Bending. *Micromachines* **2022**, *13*, 1169. https://doi.org/10.3390/mi13081169

Academic Editor: Nam-Trung Nguyen

Received: 2 June 2022 Accepted: 21 July 2022 Published: 24 July 2022

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impact the mean free path of atoms and which control coverage on all surfaces. These processes also introduce stresses within the resulting film [10,11]. Reush et al. grew 001 polycrystalline AlN films using reactive RF magnetron sputtering directly on Silicon [7]. During growth, differences in grain size induced forces between grains at the grain boundaries. The increase in grain size with increasing thickness produced an intrinsic stress gradient through the thickness caused by zone T growth [12] and self-shadowing [6,13]. Knisely et al. determined that stress gradients in AlN film growth were a result of film growth stress, nucleation, and coalescence [14]. Knisely [14] further demonstrated a method to control both the stress and through-thickness stress gradient in AlN thin films using radio frequency (RF) substrate bias power modeled using a power law function. Introduction and further increases in RF substrate bias power during the sputtering of AlN based materials results in films with more compressive stress [14]. For Al1−xScxN films with high Sc substitution for Al, the resulting average film stress is often compressive [3,15] without the introduction of an RF substrate bias, especially when optimizing for low anomalously oriented grain (AOG) growth. Thus, it may not be possible to utilize RF substrate bias to simultaneously optimize for low average film stress and low through-thickness stress gradient in highly Sc alloyed AlN thin films.

Several stress and stress control techniques have been produced for MEMS devices. Pulskamp et al. mitigated the stress and stress gradient in sol-gel Lead Zirconium Titanate (PZT) multi-layer MEMS devices by altering the silane flow rates, annealing the top layer Platinum (Pt), and adjusting the film thickness [16]. For the 0.5 µm devices, a Titanium/Platinum 651 MPa (Ti/Pt) adhesive layer produced a stress of 35 MPa in the PZT with displacements of −250 µm [16]. Characterizing the released structures with analytical modeling and controlling process variability during growth further characterized the stress within these films [16]. Devices such as RF switches, accelerometers, and optical mirrors are very sensitive to the stress and stress gradient [9,17]. Sedky et al. developed these MEMS devices with p-type Silicon Germanium (SixGe1−x) using low pressure chemical vapor deposition (LPCVD) [17]. The stress was optimized by modifying the Se concentration from 40% to 90%, tuning the pressure from 650 mtorr to 800 mtorr, and controlling the deposition temperature to be between 400 and 450 ◦C. The stress gradient was reduced with a laser annealing technique which reduced stress from 125 MPa to 25 MPa and deflections from 118 µm to 5 µm [17]. Zhu determined the stress was caused by variations in film growth resulting in uneven grains and nonuniform boundaries [18]. When Aluminum Nitride (AlN) and Ruthenium (Ru) is sputtered to fabricate MEMS resonators, a folded beam design was used to limit deflection [18]. Mulloni et al. used similar clamped-clamped and single-clamped cantilever designs for Gold microstructure using electrodepositing [19]. The clamped-clamped released structures were more sensitive to stress variations than the single-clamped design [19]. Depending on the desired bending, the release temperature was reduced to limit stress which increased fabrication time [19]. These methods including temperature control, thickness variation, process control, laser annealing, design alterations, and pressure tuning show promise in reducing stress and stress gradients in other material systems.

Previous studies have explored methods using total N<sup>2</sup> process gas flow to control average Al1−xScxN film stress [3,20,21]. These studies show that total process gas flow and the process gas mixture have a significant impact on the crystallinity, defects, and stress of sputter-deposited Al1−xScxN films [3,20,21]. Al1−xScxN films with a high degree of crystallinity and few defects require long mean free path and thus low process pressures. Sputtering Al1−xScxN at low process pressure in a pure N<sup>2</sup> environment improves caxis orientation and decreases surface roughness [3]. Increases in N<sup>2</sup> flow increases ion scattering, reduces ion mean free path (MFP) and increases average film stress [20–22]. A method to suppress the stress gradients which produce out-of-plane bending while holding Sc concentration constant, maintaining film quality, and minimizing average stress has not been established for Al1−xScxN thin film materials. We previously demonstrated that 500 nm thick Al0.68Sc0.32N materials, free of AOGs, with low surface roughness and strong

c-axis orientation, could be sputter-deposited on Si with a controlled average film stress ranging from −458 to 287 MPa, by controlling N<sup>2</sup> flow between 20–30 sccm [3]. Here we provide a novel method that demonstrates both low average film stress and low throughthickness film stress gradient simultaneously by varying the N<sup>2</sup> flow within the 20–30 sccm range during the deposition of Al0.68Sc0.32N. Furthermore, we demonstrate the utility of this method by fabricating Al0.68Sc0.32N MEMS cantilevers with low out-of-plane bending.

Al1−xScxN with high Sc alloying is a promising piezoelectric material for MEMS radio frequency (RF) filtering [3], energy harvesting [4], and sensing [23,24] devices because of its demonstrated high figure of merit [2] for each of these application areas. Piezoelectric RF bulk acoustic wave (BAW) resonator filters can often be implemented as anchored plates with extremely high out-of-plane bending stiffness. Such an implementation allows the realization of high-performance BAW resonators and filters using Al1−xScxN materials with high through-thickness stress gradient [3]. By contrast, high performance energy harvesters [4] and piezoelectric sensors [24,25] often require implementations using compliant cantilever [24] and clamped-guided beams [25] with low out-of-plane bending stiffness. In these devices, large film through-thickness stress gradients and the resulting out-of-plane bending can cause a significant degradation of the on-axis sensitivity and a corresponding increase in the cross-axis sensitivity. In addition, high out-of-plane bending complicates wafer level packaging (WLP) of MEMS devices because the packaging cavity must be able to accommodate the out-of-plane bending displacement. Therefore, if high performance Al1−xScxN materials are to be utilized in sensing and energy harvesting applications it is imperative to achieve low through-thickness stress gradient for the Al1−xScxN film and low out-of-plane bending for the MEMS structures implemented with the Al1−xScxN film.
