Compensation of the Stress Gradient in Physical Vapor Deposited Al1−xScxN Films for Microelectromechanical Systems with Low Out-of-Plane Bending

Thin film through-thickness stress gradients produce out-of-plane bending in released microelectromechanical systems (MEMS) structures. We study the stress and stress gradient of Al0.68Sc0.32N thin films deposited directly on Si. We show that Al0.68Sc0.32N cantilever structures realized in films with low average film stress have significant out-of-plane bending when the Al1−xScxN material is deposited under constant sputtering conditions. We demonstrate a method where the total process gas flow is varied during the deposition to compensate for the native through-thickness stress gradient in sputtered Al1−xScxN thin films. This method is utilized to reduce the out-of-plane bending of 200 µm long, 500 nm thick Al0.68Sc0.32N MEMS cantilevers from greater than 128 µm to less than 3 µm.


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 (Al 1−x Sc x N) films deposited using Molecular Beam Epitaxy (MBE) or metal-organic Chemical Vapor Deposition (MOCVD) demonstrate exceptional film quality and high electromechanical coupling (k t 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 Al 1−x Sc x N Lamb wave resonators at super high frequencies directly on Silicon with acoustic velocities of 14,000 m/s and k t 2 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 c-axis orientation, could be sputter-deposited on Si with a controlled average film stress ranging from −458 to 287 MPa, by controlling N 2 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 2 flow within the 20-30 sccm range during the deposition of Al 0.68 Sc 0.32 N. Furthermore, we demonstrate the utility of this method by fabricating Al 0.68 Sc 0.32 N MEMS cantilevers with low out-of-plane bending.
Al 1−x Sc x N 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 Al 1−x Sc x N 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 Al 1−x Sc x N materials are to be utilized in sensing and energy harvesting applications it is imperative to achieve low through-thickness stress gradient for the Al 1−x Sc x N film and low out-of-plane bending for the MEMS structures implemented with the Al 1−x Sc x N film.

Average Film Stress Measurement
Once released from a substrate, as is common in MEMS processing, films will relax their built-in stress, which can lead to undesired deformation and/or buckling. Thus, knowing the stress in each layer of a MEMS process is vitally important. The average film stress is computed by measuring the wafer's radius of curvature with a profilometer and subsequently using the Stoney equation [3,14,20,26,27]. To separate the various components leading to bending of the substrate, the radius of curvature is measured both before, R 0 , and after, R, the deposition of each film, allowing the built-in stress of each layer, T f,BI , [3,14,20,26,27] in a process to be isolated where Y s , v s and t s are the Young's Modulus, Poisson's ratio, and thickness of the substrate respectively, and t f is the thickness of the film.

Relationship between the Total Process Gas Flow and the Resulting Film Stress
Knisely [14] introduced a model describing the power law relation between the RF substrate bias and the resulting AlN film stress. For a fixed Sc alloy this power law equation can be adapted to instead describe the total Al 1-x Sc x N films stress T ave as a function of N 2 process gas flow where α is determined from the slope of the stress versus N 2 gas flow, F N 2 is the N 2 gas flow in the chamber, and β and γ are empirical fits based on the deposition parameters and environment. Similar to Knisely [14] we implement a film that utilizes multiple layers deposited under different sputtering gas conditions where the average film stress of each layer is used to compensate for the through-thickness stress gradient. Where Knisely [14] utilizes a different RF substrate bias to control the stress of each AlN layer, we utilize a different N 2 flow to control the stress of each Al 0.68 Sc 0.32 N layer. The layer film stress, t f , based on the thickness and N 2 flow of the layer is derived from integrating the average film stress [14] and is given by where F N 2 is the constant flow applied to the layer and t is the thickness of the layer. Equation (3) can be used to calculate the layer stresses needed to compensate for the through-thickness stress gradient within the film. The stress gradient is calculated from the average stress measurements taken from different wafers deposited using identical deposition process parameters and at varying AlScN thicknesses. Equation (3) is then used to interpolate between the experimental measurements of films with different thicknesses to find the through-thickness stress gradient.

Experimentation Details
The average stress through the thickness of the film is evaluated using the methods described in Section 2.1. The slope of the stress versus F N 2 curve, α, is determined using a linear fit to the measured stress data. The local stress of each individual layer required to compensate for the through-thickness stress gradient is calculated using Equation (3). Cantilevers with a width of 50 µm and a length of 200 µm are realized in 500 nm thick Al 0.68 Sc 0.32 N films with out-of-plane displacements measured from the difference between the anchor and beam tip heights. The Al 1−x Sc x N cantilever fabrication is shown in Figure 1 and begins with deposition of Al 0.68 Sc 0.32 N on 100 mm p-type (100) Si wafers in an Evatec CLUSTERLINE ® 200 II Physical Vapor Deposition System in steps (a) and (b). Table 1 summarizes the DC reactive co-sputtering parameters used to deposit the Al 0.68 Sc 0.32 N films. The Al 1−x Sc x N films are deposited on a 15 nm thick AlN seed layer and a 35 nm thick gradient seed layer (Al 1→0.68 Sc 0→0.32 N) where the Sc alloying ratio is linearly varied through the thickness from 0 to 32%. This seed and gradient layer was previously demonstrated to suppress anomalously oriented grains while maintaining crystal quality [3]. The crystal quality characterized in a previous study using the full width half maximum (FWHM) of a rocking curve omega-scan showed a FWHM of 2.18 • with the seed layer and 2.23 • without the seed layer for films of 500 nm total (film plus seed) thickness. In step (c) Plasma Enhanced Chemical Vapor Deposition (PECVD) Silicon Nitride (SiN) is deposited and patterned using CF 4 reactive ion etching (RIE) to form a hard mask for Al 1−x Sc x N etching. In step (d) aqueous Potassium Hydroxide (KOH in 45% H 2 O) at 45 • C for 100 s is used to etch the Al 1−x Sc x N and define the cantilever dimensions with SiN protecting the Al 1−x Sc x N film where etching is undesired. Finally, in step (e) the SiN hard mask is stripped using CF 4 RIE and the Al 1−x Sc x N cantilevers are released from the substrate using isotropic XeF 2 dry etching. After release, the cantilever out-of-plane deflection is measured using a VHX-5000 Digital Microscope Multiscan.

Through-Thickness Stress Gradients in Sputtered Al1−xScxN films
During film growth, stresses due to lattice mismatch, intrinsic strains and microstructure produces tensile and compressive stresses. The average stress of a sputtered Al1−xScxN film is strongly correlated to the value of the chamber pressure during deposition [3]. At 25 sccm process gas flow, the sputtering chamber will be at a near constant pressure of 1.09 × 10 −3 mbar. At 25 sccm pure N2 flow, when Al0.68Sc0.32N is deposited to a final thickness of 500 nm, the average stress within the film will be approximately 137 MPa. The average film stress vs. thickness for Al0.68Sc0.32N films deposited under 25 sccm pure N2 flow using the process conditions in Table 1 is provided in Figure 2a. The average film stress is a strong function of the final film thickness due to the through-thickness stress gradient of the films. The through-thickness stress gradient can be modeled using Equation (2) in conjunction with the data in in Figure 2a where α is 41.12, β is 6.6522, and γ is 0.2194. α is determined using a linear fit of the measured average stress versus flow data shown in Figure 2b. In Figure 2a, the stress starts highly compressive and becomes more tensile as the thickness of the film increases. At lower film thicknesses, the microstructure of the film continuously changes and the grain size increases with increasing film thickness. As the thickness increases, the columnar growth of the film is more stable

Through-Thickness Stress Gradients in Sputtered Al 1−x Sc x N films
During film growth, stresses due to lattice mismatch, intrinsic strains and microstructure produces tensile and compressive stresses. The average stress of a sputtered Al 1−x Sc x N film is strongly correlated to the value of the chamber pressure during deposition [3]. At 25 sccm process gas flow, the sputtering chamber will be at a near constant pressure of 1.09 × 10 −3 mbar. At 25 sccm pure N 2 flow, when Al 0.68 Sc 0.32 N is deposited to a final thickness of 500 nm, the average stress within the film will be approximately 137 MPa. The average film stress vs. thickness for Al 0.68 Sc 0.32 N films deposited under 25 sccm pure N 2 flow using the process conditions in Table 1 is provided in Figure 2a. The average film stress is a strong function of the final film thickness due to the through-thickness stress gradient of the films. The through-thickness stress gradient can be modeled using Equation (2) in conjunction with the data in in Figure 2a where α is 41.12, β is 6.6522, and γ is 0.2194. α is determined using a linear fit of the measured average stress versus flow data shown in Figure 2b. In Figure 2a, the stress starts highly compressive and becomes more tensile as the thickness of the film increases. At lower film thicknesses, the microstructure of the film continuously changes and the grain size increases with increasing film thickness. As the thickness increases, the columnar growth of the film is more stable causing the throughthickness stress gradient to reduce and the average film stress to asymptote towards a constant value with further increases in thickness. These trends are clearly observable in Figure 2a.
causing the through-thickness stress gradient to reduce and the average film stress to asymptote towards a constant value with further increases in thickness. These trends are clearly observable in Figure 2a.

Out-of-Plane Cantilever Deflection in Uncompensated Al1−xScxN Materials
Low average stress (membranes) and low through-thickness stress gradient (cantilevers) are critical for realizing high yield MEMS structures with low out-of-plane bending. The multilayer stress and stress gradient compensation approach reported in this paper can be utilized to simultaneously achieve low average stress and low through-thickness stress gradient. Table 2 provides a summary of the various flow conditions and the resulting stress and out-of-plane cantilever deflections. While low average stress is achievable in all films, only a multi-layer Al1−xScxN achieves the low through-thickness stress gradient required to realize cantilevers with low out-of-plane bending. The compressive-to-tensile stress gradient through the Al1−xScxN film thickness results in a high degree of out-ofplane bending in uncompensated Al1−xScxN films. A Z-axis microscope is used to measure the tip deflection with the anchor as the z = 0 reference. Figure 3 provides SEM images of the high out-of-plane bending in Al0.68Sc0.32N cantilevers deposited with a constant flow of 25 sccm.

Out-of-Plane Cantilever Deflection in Uncompensated Al 1−x Sc x N Materials
Low average stress (membranes) and low through-thickness stress gradient (cantilevers) are critical for realizing high yield MEMS structures with low out-of-plane bending. The multilayer stress and stress gradient compensation approach reported in this paper can be utilized to simultaneously achieve low average stress and low through-thickness stress gradient. Table 2 provides a summary of the various flow conditions and the resulting stress and out-of-plane cantilever deflections. While low average stress is achievable in all films, only a multi-layer Al 1−x Sc x N achieves the low through-thickness stress gradient required to realize cantilevers with low out-of-plane bending. The compressive-to-tensile stress gradient through the Al 1−x Sc x N film thickness results in a high degree of out-of-plane bending in uncompensated Al 1−x Sc x N films. A Z-axis microscope is used to measure the tip deflection with the anchor as the z = 0 reference. Figure 3 provides SEM images of the high out-of-plane bending in Al 0.68 Sc 0.32 N cantilevers deposited with a constant flow of 25 sccm.       Figure 4 shows top view SEM images of cantilevers fabricated from Al 0.68 Sc 0.32 N films from across a 100 mm wafer demonstrating that the residual stress gradient within the film not only induces bending but also generates twisting and rotations within released structures. The center of the wafer produces structures with minimal twisting while the edge of the wafer produces significant twisting depending on the location of the die. The twisting is due to the interaction of the through-thickness stress gradient with the radial variation of the average stress across the 100 mm diameter wafer and is consistent with previous studies [3] which exhibit more compressive average stresses at the wafer edge and more tensile average stresses near the wafer center. If no stress compensation is established, depending on the performance requirements for a MEMS device, the location of the die on the wafer and the orientation of the released structures can lead to differences in out-of-plane bending and twisting.
Micromachines 2022, 13, x FOR PEER REVIEW 8 of 13 Figure 4 shows top view SEM images of cantilevers fabricated from Al0.68Sc0.32N films from across a 100 mm wafer demonstrating that the residual stress gradient within the film not only induces bending but also generates twisting and rotations within released structures. The center of the wafer produces structures with minimal twisting while the edge of the wafer produces significant twisting depending on the location of the die. The twisting is due to the interaction of the through-thickness stress gradient with the radial variation of the average stress across the 100 mm diameter wafer and is consistent with previous studies [3] which exhibit more compressive average stresses at the wafer edge and more tensile average stresses near the wafer center. If no stress compensation is established, depending on the performance requirements for a MEMS device, the location of the die on the wafer and the orientation of the released structures can lead to differences in out-of-plane bending and twisting.

Stress Gradient Compensated Al1−xScxN Films and Cantilevers
The through-thickness stress gradient is the primary source of out-of-plane bending in released Al1−xScxN structures. To find the additional flow needed to compensate the stress gradient, Equation (3) is used to estimate the local stress. At 25 sccm N2 flow, the local stress within the first 15 nm after the seed layer has been deposited is approximated to be −424 MPa using Equation (3). At 500 nm, the local stress is 276 MPa. A compensating 424 MPa in the initial layers, −276 MPa at the top of the film, and the appropriate opposing stress gradient is required to compensate for the through-thickness stress gradient. Using Figure 2b, at 20 and 30 sccm N2 flow, a 500 nm Al1−xScxN film will yield an average stress

Stress Gradient Compensated Al 1−x Sc x N Films and Cantilevers
The through-thickness stress gradient is the primary source of out-of-plane bending in released Al 1−x Sc x N structures. To find the additional flow needed to compensate the stress gradient, Equation (3) is used to estimate the local stress. At 25 sccm N 2 flow, the local stress within the first 15 nm after the seed layer has been deposited is approximated to be −424 MPa using Equation (3). At 500 nm, the local stress is 276 MPa. A compensating 424 MPa in the initial layers, −276 MPa at the top of the film, and the appropriate opposing stress gradient is required to compensate for the through-thickness stress gradient. Using Figure 2b, at 20 and 30 sccm N 2 flow, a 500 nm Al 1−x Sc x N film will yield an average stress of −450 and 317 MPa, respectively. We utilized Equation (3) to design a 2-layer stack deposited at 30 sccm (lower) and 20 sccm (upper) to compensate for the through-thickness stress gradient. Figure 5 provides an SEM image of a 2-layer Al 1−x Sc x N material where the N 2 flow is varied between layers to suppress the stress gradient and the resulting out-ofplane bending in cantilevers. Here, 30 sccm N 2 flow is utilized during the deposition of the AlN seed, Al 1−x Sc x N gradient layer, and the lower 225 nm of the bulk film while 20 sccm N 2 flow is utilized when depositing the upper 225 nm of the film stack. The approach successfully compensates for the through-thickness stress gradient and reduces the out-ofplane cantilever bending in the center of the wafer from 109 µm for the uncompensated materials to less than 3 µm for cantilevers realized in the stress gradient compensated 2-layer material.
Micromachines 2022, 13, x FOR PEER REVIEW 9 of 13 of −450 and 317 MPa, respectively. We utilized Equation (3) to design a 2-layer stack deposited at 30 sccm (lower) and 20 sccm (upper) to compensate for the through-thickness stress gradient. Figure 5 provides an SEM image of a 2-layer Al1−xScxN material where the N2 flow is varied between layers to suppress the stress gradient and the resulting out-ofplane bending in cantilevers. Here, 30 sccm N2 flow is utilized during the deposition of the AlN seed, Al1−xScxN gradient layer, and the lower 225 nm of the bulk film while 20 sccm N2 flow is utilized when depositing the upper 225 nm of the film stack. The approach successfully compensates for the through-thickness stress gradient and reduces the outof-plane cantilever bending in the center of the wafer from 109 µm for the uncompensated materials to less than 3 µm for cantilevers realized in the stress gradient compensated 2layer material. Figure 6b displays a 5-layer Al0.68Sc0.32N stack used to compensate for the throughthickness stress gradient. Since lower flows produce more compressive films while higher flows produce more tensile films, a layer stack is utilized where for each consecutive 100 nm layer, an additional 2.5 sccm of flow provides a tensile-to-compressive transition to cancel the original compressive-to-tensile stress gradient through the thickness. For the 5layer material the N2 flow is varied over the range from 30 to 20 sccm to yield a low average stress in addition to a low through-thickness stress gradient. After release, the cantilevers remain consistently flat, as shown in Figure 6a 1, 2, and 3 positions, respectively. The 1, 2, and 3 structures exhibited the same behavior and deflection as those directly across from them, namely cantilevers 5, 6, and 7. Table 2 compares the average wafer stress and cantilever tip deflection for the uncompensated and stress gradient compensated Al0.68Sc0.32N materials. The out-of-plane cantilever displacement for the 5-layer, low stress material at position 2 is reduced by more than 14-fold for the center die and 19-fold for the east die 35 mm from the wafer center. Overall, substantial reductions in out-of-plane tip displacement are observed for all cantilevers fabricated in the stress gradient compensated films. The 5-layer film does not have an AlN/gradient seed layer and possess a higher tip deflection than the 2-layer  [3] to suppress AOGs and two equal thickness layers with different N 2 process gas flows designed to compensate for the native through-thickness stress gradient. Figure 6b displays a 5-layer Al 0.68 Sc 0.32 N stack used to compensate for the throughthickness stress gradient. Since lower flows produce more compressive films while higher flows produce more tensile films, a layer stack is utilized where for each consecutive 100 nm layer, an additional 2.5 sccm of flow provides a tensile-to-compressive transition to cancel the original compressive-to-tensile stress gradient through the thickness. For the 5-layer material the N 2 flow is varied over the range from 30 to 20 sccm to yield a low average stress in addition to a low through-thickness stress gradient. After release, the cantilevers remain consistently flat, as shown in Figures 6a and 7, especially when compared to the cantilevers formed in the uncompensated films. The cantilevers in Figures 4-7 use the same naming conventions depicted in Figure 3a,b. In Figure 6a the maximum tip deflection is approximately 5.8 +/− 0.4 µm, −7.6 +/− 0.4 µm, and −4.0 +/− 0.4 µm when measured from the 1, 2, and 3 positions, respectively. The 1, 2, and 3 structures exhibited the same behavior and deflection as those directly across from them, namely cantilevers 5, 6, and 7. Table 2 compares the average wafer stress and cantilever tip deflection for the uncompensated and stress gradient compensated Al 0.68 Sc 0.32 N materials. The out-of-plane cantilever displacement for the 5-layer, low stress material at position 2 is reduced by more than 14-fold for the center die and 19-fold for the east die 35 mm from the wafer center. Overall, substantial reductions in out-of-plane tip displacement are observed for all cantilevers fabricated in the stress gradient compensated films. The 5-layer film does not have an AlN/gradient seed layer and possess a higher tip deflection than the 2-layer film with seed layer. This is because the gradient in the N 2 process gas flow was designed using the data from Figure 2 where all the films have the seed layer. Table 3 confirms the precise control of the tip deflection by varying the range of N 2 gas flow for a 2-layer material stack. The range of gas flows controls the stress gradient while the mean N 2 gas flow controls the average stress within the film. In Table 3 film with seed layer. This is because the gradient in the N2 process gas flow was designed using the data from Figure 2 where all the films have the seed layer. Table 3 confirms the precise control of the tip deflection by varying the range of N2 gas flow for a 2-layer material stack. The range of gas flows controls the stress gradient while the mean N2 gas flow controls the average stress within the film. In Table 3, a 2.5 sccm increase of the range from 27.5-22.5 sccm to 30-22.5 sccm reduces the deflection 2-fold.

Discussion of Stress Gradient Cancellation Trends
This work provides, for the first-time, methods to individually control the stress and stress gradient in Al 1−x Sc x N films while maintaining film quality. Figure 8 shows the out-of-plane displacement along the length of the cantilever for the uncompensated and 2-layer compensated Al 0.68 Sc 0.32 N materials while Table 3 summarizes the out-of-plane tip displacement. The compensated cantilever tip bending confirms that the radius of curvature can be controlled in the released Al 1−x Sc x N structures. The multilayer gas gradient method can be utilized to simultaneously and independently control both the average stress, via the average N 2 flow, and through-thickness stress gradient, via the through-thickness variation of the N 2 flow, in Al 1−x Sc x N thin films. Previously reported methods to control Al 1−x Sc x N average film stress do not provide control of the through-thickness stress gradients within the film. While the previous RF substrate bias method reported by Knisley [14] achieved independent control of stress and through-thickness stress gradient in AlN films and demonstrated reduced radius of curvature and tip displacement in AlN cantilevers, use of an RF substrate bias is less suitable for Al 1−x Sc x N. Addition of an RF substrate bias results in more compressive film stress and is a good technique for stress control of AlN where the films are highly tensile without an RF substrate bias [14]. Al 0.68 Sc 0.32 N, by contrast, is highly compressive when deposited at the low process pressures that suppress formation of anomalously oriented grains (AOGs) without using an RF substrate bias [3]. Thus, addition of an RF substrate bias to an Al 0.68 Sc 0.32 N growth will require even higher process pressures to achieve near-neutral average film stress, and under such process conditions a large number of AOGs would be expected.

Conclusions
This study reports methods to fabricate Al0.68Sc0.32N films and cantilevers with low average stress and with low through-thickness stress gradients. Al1−xScxN films were optimized to control stress for N2 flows between 20 to 30 sccm. The average stress within the

Conclusions
This study reports methods to fabricate Al 0.68 Sc 0.32 N films and cantilevers with low average stress and with low through-thickness stress gradients. Al 1−x Sc x N films were optimized to control stress for N 2 flows between 20 to 30 sccm. The average stress within the films ranged from 78.6 MPa to 349.6 MPa. The out-of-plane tip deflection for 100 µm long cantilevers fabricated in 500 nm thick Al 0.68 Sc 0.32 N films was reduced from >109 µm for films without stress gradient compensation to less than 3 µm and 8 µm for 2-and 5-layer compensated film stacks for dies studied in the wafer center. The resulting deposition parameters provide methods to control stress and through-thickness stress gradients in highly Sc alloyed AlN materials and are promising for next-generation MEMS devices.