# Modeling and Optimization of a Novel ScAlN-Based MEMS Scanning Mirror with Large Static and Dynamic Two-Axis Tilting Angles

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

_{DC}and ±36.2°@180 V

_{DC}, respectively, and the dynamic tilting angles increases linearly with the driving voltage. Device B with a 10 mm-length square mirror provides the accessible tilting angles of ±36.0°@200 V

_{DC}and ±35.9°@180 V

_{DC}for horizontal and diagonal actuations, respectively. In the dynamic actuation regime, the orthogonal and diagonal tilting angles at 10 Hz are ±8.1°/V

_{pp}and ±8.9°/V

_{pp}, respectively. This work confirmed that the Union Jack-shaped arrangement of trapezoidal actuators is a promising option for designing powerful optical devices.

## 1. Introduction

_{x}Ti

_{1−x}O

_{3}(PZT) piezoelectric material to meet the requirements in laser projection and detection applications. For instance, Baran et al. developed a 1.4 mm-wide PZT thin-film actuation scanning mirror with the combination of mechanical amplification, exhibiting an optical scan angle of 38.5° at 24 V with the resonant frequency of 40 kHz [4]. Chen et al. presents a MEMS thin-PZT cantilever driven micro-lens actuator capable of delivering a large out-of-plane displacement of 145 μm at 22 V driving voltage, with a resonant frequency of 2 kHz [16]. Although commonly used PZT-type micromirrors exhibit large deflection due to high piezoelectric coefficients, the high permittivity resulting in low energy conversion efficiency, large temperature coefficient, low Curie point, hysteresis behavior, challengeable patterning process and poor compatibility with the mainstream complementary metal-oxide-semiconductor (CMOS) and/or MEMS process greatly limits its wide use in the MEMS area [4,20,21,22,23,24].

_{DC}[11,26,27], in addition to the aforementioned inherent superiorities in AlN-based micromirrors. Although only a handful of ScAlN-based micromirrors have been created with the improvement of piezoelectric coefficient ${e}_{31,f}$ [11,28,29,30], almost all of them have a limited mirror plate with the aperture size of less than 1 mm. Generally, the large aperture size and mass of a MEMS scanning mirror limits the possibility of achieving a larger scanning angle and a higher operation frequency unless the actuation moment is high enough [9]. Up to now, to overcome the aforementioned limitations of PZT-, AlN- and ScAlN-based micromirrors, a MEMS scanning mirror with two-dimensional static and/or dynamic tilting angles of greater than ±15° in the centimeter range is desired and being pursued for laser projection applications [11,31]. In addition to improving the fabricate uniformity with low residual stress, raising the piezoelectric coefficient of ScAlN material and deploying multiple ScAlN layers, one of the most pressing areas of research needed to significantly promote MEMS mirror technology lies primarily in pushing novel advanced designs.

## 2. Electromechanical Design of ScAlN-Based Piezoelectric Micro-Electro-Mechanical Systems (MEMS) Mirror

#### 2.1. MEMS Mirror Structure

_{x}Al

_{1−x}N material as the actuator with Sc content up to x = 0.50. As illustrated in Figure 1, the architecture of the MEMS mirror (Device A) is composed of a square reflection mirror plate and eight trapezoidal Sc

_{x}Al

_{1−x}N-based piezoelectric microcantilevers (PMs) sandwiched between a 200 nm top electrode (TE) and a 200 nm bottom electrode (BE), which are connected to a silicon-on-insulator (SOI) substrate having a 10-μm-thick device layer. Both the insulating SiO

_{2}layer and Sc

_{x}Al

_{1−x}N film have the thickness of 1 μm. The mirror plate is coated with 150 nm Au thin film to increase the reflective coefficient of the reflector. To explore a much larger mechanical tilting angle than ±15° within 150 V DC voltage, eight PMs are arranged as Union Jack-shaped actuators and four S-shaped meandering springs are adopted to connect the actuators and the mirror plate (referring to Figure 1c). Such spring design can not only avoid high stress concentrations in the corners, but also leverage its rotation transformation to enlarge the tilting angle of the MEMS mirror. Benefiting from this MEMS mirror design, good mode separation without crosstalk is more easily achieved when operating at dynamic resonance mode, especially at multiple resonance modes.

^{2}, a modified MEMS mirror design concept (Device B) based on Device A is presented in Figure 1b, where a square pillar is placed on the central holding platform driven by eight PM actuators to mechanically support the square mirror plate with a length of 10 mm and a thickness of 100 μm. The height of the pillar is determined by the maximum tilting angle, i.e., it must be set at above 2.4 mm to target 25° tilting angle. Note that the maximum principal stress within both devices A and B need be controlled at the level of 800 MPa to ensure no mechanical failure [4,11,33]. The geometrical parameter specifications of the proposed MEMS mirror devices A and B have been listed in Table 2.

#### 2.2. Actuation Principle

_{x}Al

_{1−x}N based PM actuators are fully deployed as bendable microcantilevers to efficiently deliver the bending forces and moments for arbitrary two-axis rotation motions of the MEMS mirror. The separate actuators design has also beneficial influence on the structure stiffness to adjust the dynamic resonance frequency of the mirror. The other advantage of such trapezoidal PM actuator design is to enlarge the effective actuation length of the microcantilever within the same device frame by fixing the actuator corners instead of their straight edges parallel to x or y axes. Based on COMSOL simulations, Figure 2 shows the mirror actuation principle for some targeted tilting angles (0°, 45°, 90° and 135°) in the cases of using only four PM actuators and all eight PM actuators. Although both two actuation cases are able to achieve arbitrary tilting angles, the eight PM actuators arrangement turns out to be more efficient from the aspect of the deflection, which can improve the output performance by about 50%.

## 3. Modeling and Analysis

_{x}Al

_{1−x}N based actuators is essential to better understand their scanning characteristics and optimize the structural parameters. The static deflection and tilting angle at the bias voltage excitations are key performance indices to represent the device sensitivity. In the following mathematical models, each actuator is approximately modeled as a multilayer microcantilever with a fixed boundary condition at one end and a roller boundary condition at the meandering spring connection end, as shown in Figure 3, where the S-shaped meandering springs are functionalized as the rotation transformer. What needs illustration before modeling is that the right-angled trapezoidal actuators in Figure 4 are in a final designed form after optimization of structural angle θ

_{0}(i.e., θ

_{0}= 45°). In addition, to simplify the calculations, it is assumed that the initial residual stress caused during the microfabrication can be ignored and the radius of curvature resulting from the applied bending force is much larger than the total thickness of the multilayer trapezoidal actuator. Each layer of the actuator is in static equilibrium and the Sc

_{x}Al

_{1−x}N piezoelectric layer has already been polarized during theoretical analysis.

#### 3.1. Analytical Model of the Static Behavior Multilayer Trapezoidal Actuator

_{i}and C

_{i}represents the Young’s modulus and flexural rigidity of the i-th layer in the multilayer actuator, respectively, and ${L}_{0}={w}_{0}+\sqrt{2}\left({w}_{1}-{w}_{2}/2\right)$ is the effective actuation length of the multilayer actuator. The effective surface area of the actuator can be obtained by integrating its width w(x) along the length direction x, which is proportional to the structural angle θ

_{0}and reaches the maximum at θ

_{0}= 45°. As a result, the flexural rigidity C

_{i}of the i-th layer has a maximum value when θ

_{0}= 45°. z

_{n}is the neutral axis position, which is calculated according to:

_{4}produced in the piezoelectric layer and one opposing moment M

_{R}associated to the torsional meandering spring. To model the deflection and bending angle of the piezoelectric actuator for the static operation case, we can firstly assume the bending angle at one spring connecting end of the piezoelectric layer is given as θ

_{A}and the angle at the other end of the torsional meandering spring is estimated as θ

_{R}under the torque M

_{R}. Therefore, the bending moment of the multilayer actuator is the difference between these two moments, given by:

_{θR}is the torsional spring constant, which is equal to the spring constant of all meandering spring segments in series.

_{0}should be optimized at 45° to obtain the best defection performance, which is highly consistent with the following simulated results. In order to derive K

_{θR}about the rotation axis with a flexural rigidity C

_{R1}of each horizontal spring segment and C

_{R2}of each vertical spring segment, it can be summarized as the following [16]:

_{A}, the rotation angle θ

_{R}of the meandering spring should meet the following relationship:

_{R}for arbitrary DC voltage excitation can be calculated and optimized by means of integration of Equations (9)–(12) according to (13), which is a function of structural parameters of the multilayer trapezoidal actuator.

#### 3.2. Analytical Model of the Dynamic Behavior Multilayer Trapezoidal Actuator

_{a}, the differential equation for bending motions of the actuator with the external load f(x,t) can be given by:

_{4}in accordance with Equation (7). The harmonic driving voltage V(t) is applied over the whole piezoelectric bending actuator, thus the resulting load f(x,t) can be defined by the Dirac delta function, written as:

_{R}(t) for a harmonic voltage excitation can be predicted.

## 4. Three-Dimensional (3D) Finite-Element Modeling (FEM) Simulation, Optimization and Discussion

_{x}Al

_{1−x}N layer with the Sc content x ranging from 0% to 50% can be approximately predicted by the following Equations (28) and (29) [27,36,37,38], while the material properties of the other layers used in the simulations are listed in Table 3. It is noted that both the mechanical damping and dielectric loss within the Sc

_{x}Al

_{1−x}N layer have been considered as 0.01 during simulations in view of actual conditions [11,26,37]. The meshing of the entire geometry has been taken by the sweep mesh with the quadrilateral source faces, as depicted in Figure 4. The number of domain elements is about 0.5 million with the maximum and average growth rates of roughly 3.4 and 1.1, respectively. The number of degrees of freedom solved for the model is about 9 million. Besides, the fixed boundaries at the lower surfaces of the silicon substrate are used for the FEM models. The relative tolerance during the simulation studies is set at 0.01 to balance the computation speed and accuracy.

#### 4.1. Structure Optimization

_{DC}voltage should be no higher than 4.0 MPa. Therefore, the first structural optimization point is the maximum principal stress within the piezoelectric MEMS mirror. Accordingly, FEM simulations at 1 V

_{DC}voltage were performed for three different meandering spring designs, as shown in Figure 5. Note that the Sc content in Sc

_{x}Al

_{1−x}N film is assumed as 41% which has been processed and tested to provide a piezoelectric coefficient ${e}_{31,f}$ of about 2.83 C/m

^{2}in several previous works of literature [27,32,37,38]. By comparing the results, it is obviously demonstrated that the S-shaped meandering springs in Figure 5b,c have less maximum principal stress than the rectangular-shaped meandering spring in Figure 5a. In addition, the maximum principal stress can be further reduced and the maximum mechanical deflection can be improved to some extent by properly decreasing the spring pitch and increasing the number of the spring turns. The S-shaped meandering spring design in Figure 5c has been adopted in all subsequent simulations.

_{R}depends critically on the structural parameters θ

_{0}, l

_{1}, w

_{0}and w

_{2}which are independent and irrelevant to each other. Thus, these four structural parameters can be optimized individually by using a control variate method with three out of four structural parameters fixed for each parametric sweep. According to the simulation results shown in Figure 6, the structural angle θ

_{0}of the multilayer trapezoidal actuator is optimized at 45° when l

_{1}= 4000 μm, w

_{0}= 940 μm and w

_{2}= 880 μm, defining the actuator as right-angled trapezoidal shape, which is highly consistent with the above theoretical analysis. Moreover, there is a peak value for both the structural parameters l

_{1}and w

_{0}. After further optimizing structural parameter w

_{2}in its range, it can be seen from Figure 6d that the static tilting angle of the MEMS mirror reaches the threshold value of 0.21145°/V

_{DC}. The optimal values of structural parameters l

_{1}, w

_{0}and w

_{2}are given in Table 2.

_{s}of the Si device layer, it is demonstrated from simulation results shown in Figure 7 that the MEMS scanning mirror will deliver a smaller mechanical tilting angle and linearly increase resonance frequencies for both piston modes and tilt modes. To obtain a more powerful Sc

_{x}Al

_{1−x}N-based scanning mirror from the perspective of structural design, deploying a thicker Sc

_{x}Al

_{1−x}N film to reduce electrical field intensity and induced stress may be an alternative approach [11]. The mechanical tilting angles and maximum principal stress of the MEMS scanning mirrors with 1 μm-thick and 2 μm-thick Sc

_{0.41}Al

_{0.59}N films are shown in Figure 7a,b. The tilting angle ratio R

_{tp}is defined as the ratio of the mirror tilting angles of two device designs with 1 μm-thick and 2 μm-thick Sc

_{0.41}Al

_{0.59}N films. The tilting angle ratio R

_{tp}increases with the thickness of the Si device layer and can be improved by about 20% when the thickness of the Si device layer is larger than 20 μm. The simulation results indicate that a 2 μm-thick Sc

_{0.41}Al

_{0.59}N based mirror can work more efficiently than a 1 μm-thick Sc

_{0.41}Al

_{0.59}N based mirror only when the thickness of the Si device layer is not less than 10 μm, because the thickness of Sc

_{0.41}Al

_{0.59}N film will make a significant impact on the total flexural rigidity of the multilayer actuator when the Si device layer is too thin, thereby affecting the mechanical deflection and tilting angle. Thus the thickness of the Sc

_{0.41}Al

_{0.59}N and Si device layers are set as 1 μm and 10 μm in all subsequent simulations, respectively.

_{x}Al

_{1−x}N film on the mechanical efficiency of the MEMS scanning mirror has also been considered. As shown in Figure 8a, both the mechanical tilting angle and maximum principal stress increases piecewise linearly with the Sc content changing from 0% to 50%. Considering the limitations that the maximum principal stress and driving DC voltage of the designed mirrors should be controlled within 800 MPa and 200 V

_{DC}[16], respectively, it is necessary to strike a better balance between them in order to achieve its full potential. The ratio of the tilting angle and maximum principal stress for Sc

_{x}Al

_{1−x}N -based mirrors with different Sc contents is defined to demonstrate the sensitivity to the material stress, as shown in Figure 8b. By analyzing the attainable tilting angle subject to the above limitations, it is suggested that the best performance of the designed mirror may be realized when the Sc content in Sc

_{x}Al

_{1−x}N film increases to 45~50%. However, according to the previously reported experiments in terms of ScAlN crystal structure and piezoelectric response [36,37,38,41], both hexagonal wurtzite and cubic rocksalt phases coexist when the Sc content is between 42% and 45% and the crystal orientation drastically decreases when the Sc content is above 45%, implying that the optimal value of the Sc content in the proposed Sc

_{x}Al

_{1−x}N-based mirrors is within range of 41~45%. Moreover, the manufacturing process for achieving the scandium concentration of higher than 42% is really challenging in the present studies. Alternatively, the Sc content of 41% is considered in all subsequent simulations to further investigate both the static and dynamic performance of the designed mirrors.

#### 4.2. Static Actuation

_{DC}with a maximum principal stress of 729.8 MPa. As a comparison, the maximum tilting angle will be limited to 36.2°@180 V

_{DC}within the maximum principal stress of 767.2 MPa for the diagonal actuation of Device A, because the maximum principal stress of 852.4 MPa at 200 V

_{DC}will irreversibly destroy the device. The tilting angle sensitivities of Device A in horizontal and diagonal actuations are 0.1856°/V

_{DC}and 0.2011°/V

_{DC}in the DC voltage range from 0 to 180 V

_{DC}, respectively. Besides, the numerical calculations for both horizontal and diagonal tilting angles of Device A have also been made in the DC driving voltage range of 0 to 200 V, offering the theoretical tilting angle sensitivities of 0.1964°/V

_{DC}and 0.2157°/V

_{DC}, respectively. The maximum relative errors between simulations and calculations are 8.4% for horizontal actuation and 10.3% for diagonal actuation at 200 V

_{DC}. The ratios of the diagonal to horizontal maximum principal stress and von Mises stress at the same DC voltage are about 117% and 140%, respectively, which may be caused by the result of two orthogonal stresses. On the other hand, the diagonal actuation can deliver a marginally higher static tilting angle sensitivity than the horizontal actuation owing to the softer torsion springs. Moreover, the static performance of Device B is also analyzed, showing very similar characteristics to Device A. The accessible tilting angles for both horizontal and diagonal actuations of Device B are 36.0°@200 V

_{DC}and 35.9°@180 V

_{DC}, respectively. The tilting angle sensitivities of Device B in horizontal and diagonal actuations are 0.1843°/V

_{DC}and 0.1999°/V

_{DC}in the DC voltage range from 0 to 180 V

_{DC}, respectively, which are only slightly smaller than those of Device A. The explanation for the angle variation between two devices can be owing to the different mirror structures, albeit with the same piezoelectric actuators. Moreover, numerical calculations for both horizontal and diagonal tilting angles of Device B have also been undertaken in the DC driving voltage range of 0 to 200 V, offering the theoretical tilting angle sensitivities of 0.1949°/V

_{DC}and 0.2141°/V

_{DC}, respectively. The maximum relative errors between simulations and calculations for Device B were 8.3% for horizontal actuation and 10.3% for diagonal actuation at 200 V

_{DC}.

_{DC}. The tilting angle sensitivities of Device A in horizontal and diagonal actuations are 0.1856°/V

_{DC}and 0.2010°/V

_{DC}, respectively, while those of Device B in horizontal and diagonal actuations are 0.1841°/V

_{DC}and 0.1996°/V

_{DC}, respectively. After comparing two different cases with and without consideration of the device weight, the tilting angle sensitivity variations of both devices are only within 0.2%, which is consistent with the above argument. The displacement and inner principal stress distribution along the length of both mirrors (A, B) are plotted in Figure 10c,d. The maximum principal stresses within both mirrors occur in the four spring connection points and the central region, respectively, which are much lower than the residual stress of some fabricated micromirrors [15,16,38,40]. Moreover, the displacement curves are almost perfectly linear, indicating that there are no noticeable mechanical deformations occurring during the tilting motions of both mirrors (A, B). Therefore, the gravity effect of the mirrors during the analysis can be ignored to simplify theoretical calculations and simulations. Table 4 compares the static performance of Devices A and B presented in this paper with other piezoelectric scanning mirrors reported in the literature [11,21,42,43,44]. It is demonstrated that the proposed devices tend to exhibit an outstanding θ·D product.

#### 4.3. Dynamic Actuation

_{x}Al

_{1−x}N film. On the other hand, the pair of PM actuators (X1, X4, Y1, Y4) and (X2, X3, Y2, Y3) can be configured with opposite AC voltage excitations to obtain the orthogonal 90°-tilt vibration modes. In addition, Devices A and B can also operate at the diagonal tilt modes when the pair of PM actuators (X1, X2, Y2, Y3) and (X3, X4, Y1, Y4) are excited by the opposite AC voltages. At 1 V

_{pp}driving voltage, the simulated displacement responses at the edge of Device A are plotted in Figure 12. This shows that the proposed scanning mirror is able to work very efficiently and powerfully, offering the piston displacement sensitivity of 509 μm/V

_{pp}at 431 Hz and the orthogonal tilt displacement sensitivities of 272 μm/V

_{pp}at 498 Hz and 8.7 μm/V

_{pp}at 1435 Hz. Moreover, the diagonal tilt displacement of 303 μm can be achieved by applying 1 V

_{pp}voltage at 498 Hz, in which case the maximum principal stress in Device A is about 426 MPa. Both the orthogonal and diagonal tilting angles increases linearly with the driving voltage, offering the tilting angle sensitivities of 28.6°/V

_{pp}and 31.3°/V

_{pp}at 498 Hz, respectively, as shown in Figure 12d.

_{pp}at 69 Hz, while the first-order orthogonal and diagonal tilting angles reach about 8.1°/V

_{pp}and 8.9°/V

_{pp}at 10 Hz, respectively. The maximum principal stress at the first-order tilt modes will be as high as 792.6 MPa when the applied AC voltage is 4.0 V

_{pp}. The resonant frequencies of both the piston and tilt modes decrease dramatically because of the larger micro-mirror mass as compared to that of Device A. The products of θ·D for Devices A and B at the first-order tilt mode is about 31.3°·mm/V

_{pp}and 88.5°·mm/V

_{pp}, respectively, which is larger than almost all of those in the literature [4,16,21,43,44,45]. Moreover, the second-order orthogonal and diagonal tilting angles of about 0.126° was obtained when an AC voltage of 1 V

_{pp}at 631 Hz was applied, while the maximum principal stress is at level of 160 MPa/V

_{pp}.

## 5. Conclusions

_{x}Al

_{1−x}N-based piezoelectric MEMS scanning mirror with a pupil size of 10 mm was explored. The novel MEMS mirror, comprised a reflection mirror plate, four S-shaped meandering springs and eight trapezoidal Sc

_{x}Al

_{1−x}N-based actuators, was proposed to achieve large static and dynamic two-axis tilting angles. The detailed theoretical modeling, simulations and comparative analysis for two different Sc

_{0.41}Al

_{0.59}N-based MEMS mirror designs were investigated prior to device fabrication. For the proposed Device A including a square mirror with a 1 mm length and 10 μm thickness, the maximal orthogonal and diagonal static tilting angles were ±36.2°@200 V

_{DC}and ±36.2°@180 V

_{DC}with the maximum principal stress of less than 767.2 MPa, respectively. In the dynamic actuation regime, the piston displacement sensitivity was 509 μm/V

_{pp}at 431 Hz, and both the first-order orthogonal and diagonal tilting angles increased linearly with the driving voltage, offering the tilt angle sensitivities of 28.6°/V

_{pp}and 31.3°/V

_{pp}at 498 Hz, respectively. In comparison, Device B including a square mirror with a 10 mm length and 100 μm thickness was able to provide the accessible tilting angles of ±36.0°@200 V

_{DC}and ±36.9°@180 V

_{DC}for horizontal and diagonal actuations, respectively. In the dynamic actuation regime, the first-order orthogonal and diagonal tilting angles of ±8.1°/V

_{pp}and ±8.9°/V

_{pp}could be obtained at 10 Hz, respectively, while the second-order tilting angles are about ±0.13°/V

_{pp}at 631 Hz. Moreover, the displacement sensitivity of Device B at the resonant piston mode was also simulated and discussed. This work has suggested from the view of FEM simulations and mathematical calculations that the right-angle trapezoidal actuators potentially possess excellent mechanical efficiency for possible optoelectronic applications thanks to the novel actuator structure design and the Union Jack-shaped arrangement.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Architectures of two Sc

_{x}Al

_{1−x}N-based micro-electro-mechanical systems (MEMS) mirrors: (

**a**) Device A, (

**b**) Device B, (

**c**) Union Jack-shaped actuators and S-shaped meandering springs.

**Figure 2.**Mirror actuation principle for (

**a**–

**d**) 0°, 45°, 90° and 135°tilting angles when only using four PM actuators; (

**e**–

**h**) 0°, 45°, 90° and 135° tilting angles when using eight PM actuators.

**Figure 3.**Simplified structural model of the trapezoidal Sc

_{x}Al

_{1−x}N based actuators: (

**a**) structure configuration of the MEMS mirror, (

**b**) top view of the PM actuator, (

**c**) design schematic of the meandering spring, (

**d**) cross-sectional view of the PM actuator, (

**e**) simplification of the MEMS mirror.

**Figure 5.**FEM simulations of material principal stress and defection in three piezoelectric MEMS mirrors with different meandering spring designs at 1 V

_{DC}driving voltage: (

**a**) rectangular-shaped spring, (

**b**,

**c**) S-shaped springs.

**Figure 6.**The dependence of the static tilting angles on the structural parameters: (

**a**) θ

_{0}, (

**b**) l

_{1}, (

**c**) w

_{0}and (

**d**) w

_{2}.

**Figure 7.**Simulation results of the MEMS scanning mirrors varying with the thickness t

_{s}of the Si device layer: (

**a**) mirror tilting angle, (

**b**) maximum principal stress, (

**c**,

**d**) resonance frequencies of different modes.

**Figure 8.**Dependence of the mechanical tilting angle and maximum principal stress on the Sc content: (

**a**) mirror tilting angle, (

**b**) angle-stress ratio.

**Figure 9.**Comparison of dependence of the tilting angle and maximum principal stress on the DC driving voltages: (

**a**,

**b**) Device A without gravity, (

**c**,

**d**) Device B without gravity.

**Figure 10.**Comparison of dependence of the maximum principal stress and tilting angle on the DC driving voltages for Devices A and B with gravity: (

**a**) maximum principal stress, (

**b**) static tilting angle, (

**c**,

**d**) displacement.

**Figure 12.**Frequency response of Device A: (

**a**) displacement at the piston mode, (

**b**) tilting angle at the 1st and 2nd orthogonal tilt modes, (

**c**) tilting angle at the diagonal tilt mode, (

**d**) tilting angle vs. applied AC voltage.

**Figure 13.**Frequency response of Device B: (

**a**,

**b**) displacement at the 1st and 2nd tilt modes, (

**c**,

**d**) tilting angle vs. applied AC voltage.

Performance | Sc_{0.41}Al_{0.59}N [11,27,32] | AlN [11,26] | PZT [11,26] |
---|---|---|---|

Material Category | Non-ferroelectric | Ferroelectric | |

Piezoelectric Coefficient, ${e}_{31,f}$ [C/m^{2}] | ~3.16 | ~1.1 | ~21 |

Relative Permittivity, ${\epsilon}_{r}$ | 16.7 | 10 | 1300 |

Figure of Merit (FoM), ${e}_{31,f}^{2}/{\epsilon}_{0}{\epsilon}_{r}$ [GPa] | 67.5 | 13.7 | 38.3 |

Highest DC Driving Voltage [V] | ±200 | ±200 | ±30 |

Directionality | Bidirectional | Unidirectional | |

CMOS compatibility | Yes | No |

Parameter | Device A | Device B |
---|---|---|

Mirror length, l_{A} or l_{B} [μm] | 1000 | 10,000 |

Thickness of the mirror plate, t_{A} or t_{B} [μm] | 10 | 100 |

Length of the pillar, l_{p} [μm] | - | 250 |

Height of the pillar, h_{p} [μm] | - | 3500 |

Length of the PM actuator, l_{1} [μm] | 4025 | |

Fixed boundary width of the PM actuator, w_{0} [μm] | 700 | |

Lower width of the PM actuator, w_{1} [μm] | 3035 | |

Upper width of the PM actuator, w_{2} [μm] | 880 | |

Length of the meandering spring, l_{m} [μm] | 370 | |

Width of the meandering spring, w_{m} [μm] | 20 | |

Spacing pitch of the meandering spring, w_{p} [μm] | 120 | |

Length of the torsion bar, l_{b} [μm] | 390 | |

Width of the torsion bar, w_{b} [μm] | 20 | |

Length of the connecting bar, l_{c} [μm] | 410 | |

Width of the connecting bar, w_{c} [μm] | 20 |

Parameter | Si | SiO_{2} | Pt | Mo | Au |
---|---|---|---|---|---|

Young’s Modulus [GPa] | 170 | 70 | 168 | 312 | 70 |

Poisson’s Ratio | 0.28 | 0.17 | 0.38 | 0.31 | 0.44 |

Density [kg/m^{3}] | 2329 | 2200 | 21,450 | 10,200 | 19,300 |

Relative Permittivity | 11.7 | 4.2 | - | - | - |

**Table 4.**Static performance comparison between the MEMS mirrors presented here and in the literature.

Piezoelectric Mirrors | Material | Mirror Size, D [mm] | Tilt Angle, θ [°/V] | Maximum Angle, θ_{max} [°] | θ·D [°·mm/V] |
---|---|---|---|---|---|

Device A | ScAlN | 1 | 0.2011 | ±36.2 @180 V | 0.201 |

Device B | ScAlN | 10 | 0.1999 | ±36.0 @180 V | 1.999 |

Ref. [11] | ScAlN | 0.8 | 0.0933 | ±14.00 @150 V | 0.075 |

Ref. [21] | AlN | 0.2 | 0.005 | ±0.15 @30 V | 0.001 |

Ref. [42] | Bulk PZT | 20 | 0.0224 | 3.14 @120 V | 0.449 |

Ref. [43] | PZT | 2 | 0.46 | 4.60 @10 V | 0.920 |

Ref. [44] | PZT | 2 | 0.3 | 5.10 @17 V | 0.600 |

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**MDPI and ACS Style**

Sun, C.; Liu, Y.; Li, B.; Su, W.; Luo, M.; Du, G.; Wu, Y. Modeling and Optimization of a Novel ScAlN-Based MEMS Scanning Mirror with Large Static and Dynamic Two-Axis Tilting Angles. *Sensors* **2021**, *21*, 5513.
https://doi.org/10.3390/s21165513

**AMA Style**

Sun C, Liu Y, Li B, Su W, Luo M, Du G, Wu Y. Modeling and Optimization of a Novel ScAlN-Based MEMS Scanning Mirror with Large Static and Dynamic Two-Axis Tilting Angles. *Sensors*. 2021; 21(16):5513.
https://doi.org/10.3390/s21165513

**Chicago/Turabian Style**

Sun, Changhe, Yufei Liu, Bolun Li, Wenqu Su, Mingzhang Luo, Guofeng Du, and Yaming Wu. 2021. "Modeling and Optimization of a Novel ScAlN-Based MEMS Scanning Mirror with Large Static and Dynamic Two-Axis Tilting Angles" *Sensors* 21, no. 16: 5513.
https://doi.org/10.3390/s21165513