**1. Introduction**

Micromirrors as scanning devices are reported intensively in literature with different electromechanical transducer principles. They are mostly classified into the electrostatic, electrothermal, electromagnetic, and piezoelectric micromirrors [1–5]. The piezoelectric transducer principle offers the advantages of high deflections at moderate excitation voltages and high dynamic ranges. Furthermore, a high degree of miniaturization and the monolithic integration of actuators and sensor elements is possible. In addition to the commonly used transducer material, lead zirconate titanate (PZT), piezoelectric AlN, and AlScN thin films can alternatively be used as piezoelectric transducers for actuation. Since 2018, several AlN and AlScN-based micromirrors have been presented. Shao et al. [6] presented the first AlN-based micromirror. The microsystem with a 0.2 <sup>×</sup> 0.2 mm<sup>2</sup> mirror plate area and L-shaped bending actuators reached a resonant scan angle of 4◦ at 5 V and 63.3 kHz. Since then, further publications on AlN-based micromirrors have followed. Since June 2019, our preliminary work [7,8] includes resonantly operated 1D micromirrors with a 600 nm AlN film, a mirror plate length of 0.8 mm, and a chip size of 2 <sup>×</sup> 3 mm<sup>2</sup> . Large scan angles of up to 137.9◦ at 20 V and 3.4 kHz were reached in air. In October 2020, two 2D micromirror designs with a footprint of 2 <sup>×</sup> 2 mm<sup>2</sup> and mirror plate diameter of 0.7 mm were developed to realize Lissajous and spiral scan trajectories [9]. For the Lissajous scanning design, a scan angle of 92.4◦ at 12,060 Hz and 123.9◦ at 13,145 Hz was reached at 50 V for the x- and y-axis, respectively. The spiral scanning design reached

**Citation:** Stoeckel, C.; Meinel, K.; Melzer, M.; Žukauskaite, A.; ˙ Zimmermann, S.; Forke, R.; Hiller, K.; Kuhn, H. Static High Voltage Actuation of Piezoelectric AlN and AlScN Based Scanning Micromirrors. *Micromachines* **2022**, *13*, 625. https:// doi.org/10.3390/mi13040625

Academic Editor: Huikai Xie

Received: 8 March 2022 Accepted: 7 April 2022 Published: 15 April 2022

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a scan angle of 91.2◦ at 13,834 Hz and 50 V. In 2021, a 2D circular-scanning AlN-based mircomirror with a large aperture of 7 mm for laser material processing was published by Senger et al. [10]. In air, a scan angle of 5◦ is reached at 40 V and 1265 Hz. Due to the application, no large deflection angles were specified. In order to achieve higher deflections with larger mirror apertures, vacuum packaging is often used in literature. A wobbling mode AlN-scanner for automotive applications was published in October 2019 by Pensala et al. [11]. The microsystem with an aperture of 4 mm and 6.75 <sup>×</sup> 6.75 <sup>×</sup> 2 mm<sup>3</sup> chip size reached a scan angle of 30◦ at 1 V and 1.6 kHz by the implementation of a vacuum package. In 2020, Senger et al. [12] also presented a vacuum-packaged AlN-based micromirror with a 5.5 mm aperture. A Lissajous scan pattern with 50◦ × 20◦ scan angle was realized.

The previously mentioned micromirrors are exclusively driven in resonance to achieve sufficiently large tilt angles. Resonance frequency deviations, caused by variations of the ambient conditions like mechanical vibration and temperature change or heating due to light losses during laser irradiation, lead to a change of the tilt angle and, finally, result in errors in image formation and reconstruction [4,13]. Therefore, a static or quasi-static working mode has many advantages in regards of the electronics and drivers. In March 2019, Gu-Stoppel et al. presented an AlScN-based quasi-static micromirror with mirror plate diameter of 0.8 mm [14]. The mirror plate is mounted onto a pillar, which is deflected by four actuators hidden beneath. A high static scan angle of 50◦ at 150 VDC was achieved by this novel construction. The challenge with this concept is a complex manufacturing process, which includes different wafer bonding processes for the micromirror assembly.

In this work, the static deflection and high voltage performance of the Design 1 MOEMS in [8] is investigated. Additionally, a technology is developed using a 2 µm Al0.68Sc0.32N with high thickness as transducer material for a direct comparison of the performance of the MOEMS with higher piezoelectric coefficient. Furthermore, the design is optimized for a chip size with twice the length and width of MOEMS (Design 2) to identify the performance gain for different chip footprints and further increase the deflection. By reducing the silicon spring width in relation to previous designs, the stiffness is decreased, targeting a high deflection per voltage.

### **2. Design**

In Figure <sup>1</sup> the schematics of the fabricated Al(Sc)N micromirrors with 2 <sup>×</sup> 3 mm<sup>2</sup> and <sup>4</sup> <sup>×</sup> 6 mm<sup>2</sup> footprint are shown. In Table 1 the mirrors parameter are shown. The mirror plate is connected with two actuators by four L-shaped springs. The design and FEA of the <sup>2</sup> <sup>×</sup> 3 mm<sup>2</sup> MOEMS is shown by Meinel et al. [8]. The MOEMS design and FEA process for optimization of the leverage effect is described by Meinel et al. [7] previously. In this publication, the static deflections of the MOEMS are calculated analytically. The parameters for the analytical calculation are given in Table 1. The actuators are described in a quarter symmetrical model of the MOEMS (Figure 2). The piezoelectric unimorphs are divided into two separate actuators in parallel. The actuator has the length *l* and the width *w*. Both actuators have a free displacement ξ<sup>0</sup> and a blocking force *F*0.

$$\xi\_0 = -3 \cdot \frac{d\_{31} \cdot l^2}{t\_p^2} \cdot \frac{AB \cdot (B+1)}{D} \cdot V \tag{1}$$

$$F\_0 = -\frac{3}{4} \cdot t\_p \cdot E\_p \cdot d\_{31} \cdot \frac{AB \cdot (B+1)}{AB+1} \cdot \left(\frac{w\_1}{l\_1} + \frac{w\_2}{l\_2}\right) \cdot n \cdot V \tag{2}$$

$$A = \frac{E\_S}{E\_p};\ B = \frac{t\_S}{t\_p};\ D = A^2 \cdot \mathcal{B}^4 + 2A \cdot \left(2\mathcal{B} + 3\mathcal{B}^2 + 2\mathcal{B}^3\right) + 1\tag{3}$$

The free displacement is defined by the deflection of the longest actuator in the system. The blocking force is a sum of all four actuators *n* of the system. The actuator force in relation to the displacement at the leverage arm ξ*<sup>p</sup>* can be described as *F<sup>p</sup>* ξ*p* :

$$F\_p\left(\xi\_p\right) = -\frac{F\_0}{\mathfrak{f}\_0} \cdot \xi\_p + F\_0 \tag{4}$$

The microsystem has a resonance frequency as a result of the systems stiffness *C* and mass *m*. The mass is approximated as the mirror plate mass only. The stiffness is calculated by the resonance frequency *f* of the system. The force in relation to the stiffness and the deflection at the center of the mass ξ*<sup>m</sup>* can be described as *Fc*(ξ*m*).

$$F\_{\mathfrak{C}}(\xi\_{\mathfrak{m}}) = \mathbb{C} \cdot \xi\_{\mathfrak{m}} = 4\pi^2 \cdot f^2 \cdot m \cdot \xi\_{\mathfrak{m}} \tag{5}$$

**Table 1.** Comparison of the parameter of the micromirror designs and transducer materials.


<sup>1</sup> Symbolism according to Figures 1 and 2.

The relation between ξ*<sup>m</sup>* and ξ*<sup>p</sup>* is defined by the leverage arm distance to the center *b<sup>p</sup>* and the distance to the area center *bm*:

$$
\mathfrak{E}\_m = \frac{b\_m}{b\_p} \cdot \mathfrak{E}\_p \tag{6}
$$

The momentum of the actuators and the systems stiffness are in an equilibrium:

$$\mathbf{M}\_p = \mathbf{M}\_m \tag{7}$$

$$F\_p \cdot b\_p = F\_c \cdot b\_m \tag{8}$$

$$\left(-\frac{F\_0}{\mathfrak{F}\_0} \cdot \mathfrak{E}\_p + F\_0\right) \cdot b\_p = \left.\mathbb{C} \cdot \frac{b\_m}{b\_p} \cdot \mathfrak{E}\_p \cdot b\_m\right.\tag{9}$$

**Figure 1.** Schematic of the presented micromirror designs.

**Figure 2.** Quarter symmetrical model of the MOEMS: (**a**) Design 1; and (**b**) Design 2.

The deflection at the leverage arm position in relation to the leverage arm distance to the center of the MOEMS can be calculated with this equilibrium of the momentum:

$$\mathfrak{E}\_p(b\_p) = \frac{F\_0}{\frac{F\_0}{\xi\_0} - \frac{b\_m^2}{b\_p^2} \cdot \mathbb{C}} \tag{10}$$

The deflection at the edge of the mirror plate *ξ<sup>e</sup>* in relation to the lever arm position *b<sup>p</sup>* is given by Equation (11).

$$\xi\_{\varepsilon}(b\_{p}) = \frac{F\_{0}}{\frac{F\_{0}}{\xi\_{0}} + \frac{b\_{m}^{2}}{b\_{p}^{2}} \cdot \mathcal{C}} \cdot \frac{b\_{m}}{b\_{p}} \cdot \frac{\frac{\varepsilon}{2}}{b\_{m}} = \frac{F\_{0}}{\frac{F\_{0}}{\xi\_{0}} + \frac{b\_{m}^{2}}{b\_{p}^{2}} \cdot \mathcal{C}} \cdot \frac{e}{\mathcal{D}b\_{p}}\,. \tag{11}$$

= ிబ ಷబ

మ

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(10)

(11)

It should be noticed, that a LDV-based measurement of the deflection will not be done at the exact edge of the mirror plate, due to irregular reflections of the light. The measurement of the mirrors deflection in this paper is done in a distance to the mirror edge of approximately 50 µm. Additionally, the analytic equations do not include losses of the elastic energy, or mechanical stress and strain in the torsion springs. measurement of the mirrors deflection in this paper is done in a distance to the mirror edge of approximately 50 µm. Additionally, the analytic equations do not include losses of the elastic energy, or mechanical stress and strain in the torsion springs. In Figure 3 the mirror plate deflection is shown in relation to the lever arm distance to the center. An optimum lever arm length can be identified, depending on the systems

ሺሻ = ிబ ಷబ బ ି ್ మ ್ <sup>మ</sup> ∙

The deflection at the edge of the mirror plate in relation to the lever arm position

*Micromachines* **2022**, *13*, x 6 of 15

൫൯ = ிబ ಷబ

మ

∙ ∙ మ 

is given by Equation (11).

In Figure 3 the mirror plate deflection is shown in relation to the lever arm distance to the center. An optimum lever arm length can be identified, depending on the systems mass and stiffness as well as the blocking force and free deflection of the actuators. The parameter of silicon height, piezoelectric charge coefficient, and resonance frequency are estimated within a 10% limit of variation. For Design 1 with AlN as transducer and a 40 µm lever arm distance the calculated deflection is in the range of 65 nm/V to 116 nm/V. Using Al0.68Sc0.32N and Design 1 increases the deflection up to 143 nm/V to 241 nm/V. Design 2 has a lever arm distance to the center of 80 µm. For this design and Al0.68Sc0.32N a deflection of 563 nm/V to 959 nm/V is calculated. mass and stiffness as well as the blocking force and free deflection of the actuators. The parameter of silicon height, piezoelectric charge coefficient, and resonance frequency are estimated within a 10% limit of variation. For Design 1 with AlN as transducer and a 40 µm lever arm distance the calculated deflection is in the range of 65 nm/V to 116 nm/V. Using Al0.68Sc0.32N and Design 1 increases the deflection up to 143 nm/V to 241 nm/V. Design 2 has a lever arm distance to the center of 80 µm. For this design and Al0.68Sc0.32N a deflection of 563 nm/V to 959 nm/V is calculated.

**Figure 3.** The static mirror plate deflection (mechanical tilt angle) per voltage in relation to the lever arm distance to the center is given for different designs and transducer materials. The parameter substrate height, piezoelectric charge coefficient, and resonance frequency are estimated with a 10% limit of variation. Therefore, an upper and lower limit of the approximated variation to the mechanical tilt angle is given. **Figure 3.** The static mirror plate deflection (mechanical tilt angle) per voltage in relation to the lever arm distance to the center is given for different designs and transducer materials. The parameter substrate height, piezoelectric charge coefficient, and resonance frequency are estimated with a 10% limit of variation. Therefore, an upper and lower limit of the approximated variation to the mechanical tilt angle is given.

#### . **3. Fabrication**

The wafers with AlN and Al0.68Sc0.32N piezoelectric layers are processed with an identical process flow and process parameters, except for the deposition and etching of the piezoelectric material. Figure 4 illustrates the device fabrication process flow. The microsystem fabrication is based on 150 mm SOI technology with 575 µm thick handle wafer and 20 µm device-silicon thickness. First, a 1 µm thermal oxide is grown by oxidation. LPCVD silicon nitride with a layer thickness of 100 nm is used as an isolation layer due to its selectivity against HF wet etching processes. The piezoelectric layer stack starts with a seed layer of 100 nm platinum. For a better adhesion with the substrate, a 20 nm titanium film is used. The Pt is deposited in <111> orientation to minimize the elastic energy to a <0002> Al(Sc)N crystal. A 600 nm AlN or 2000 nm Al0.68Sc0.32N, respectively, and a 100 nm PECVD SiO<sup>2</sup> layer are deposited as piezoelectric material. Table 1 summarizes the PVD deposition conditions for the AlN and Al0.68Sc0.32N layer. DC magnetron process with an Al target (double ring magnetron target 120 mm and 123–236 mm, purity 5N5) in 100% nitrogen atmosphere is used for AlN. In the case of Al0.68Sc0.32N, co-sputtering

from 5N5 Al and 4N pure Sc targets in pulsed DC mode in 100% nitrogen atmosphere is used at combined power of 1000 W. AlScN growth optimization, as well as structural and compositional analysis are discussed elsewhere [15,16].

**Figure 4.** Fabrication process flow: (**a**) Initial layer stack; (**b**) AlN wet etching; (**c**) Pt structuring; (**d**) Dry etching of silicon nitride and wet etching of silicon oxide, aluminum deposition; (**e**) backside structuring by DRIE; and (**f**) dry etching of device silicon.

The adhesion of photoresists during the AlN wet etch process is not sufficient. Therefore, a 100 nm SiO<sup>2</sup> is the hard mask material for the patterning process. AlN and Al0.68Sc0.32N wet etching is done with 85% phosphoric acid solution (H3PO4) at 80 ◦C (Figure 4b). The etch rate of AlN is 1.4 nm/s. The Al0.68Sc0.32N has a etch rate of 6.7 nm/s. Test wafer with Al0.86Sc0.14N have etch rates of 4.2 nm/s. This indicates a correlation of higher etch rates and higher Scandium ratios in the piezoelectric transducer.

The platinum and titanium are structured via tungsten hard mask by a dry etch process (Figure 4c) which is monitored with an optical emission spectrometer. By analyzing the species in the plasma, an etch stop can be defined as soon as the Ti/Pt is etched and the dry etching of the silicon nitride starts. In Figure 4d, the silicon nitride is patterned by RIE and the silicon oxide is wet etched. This enables an aluminum deposition on a smooth silicon surface. The 800 nm aluminum layer serves as reflective layer on the mirror plate and as upper electrode for excitation of the piezoelectric actuators. After wet etching of the aluminum layer, the handle wafer silicon is structured by DRIE using the buried SiO<sup>2</sup> of the initial SOI wafer as etch stop (Figure 4e).

By variation of the exposure parameters in the lithography as well as the DRIE parameters, a side wall shift of the silicon springs can be done to reduce the systems stiffness. This process can be done by using different resists, exposure times, or another DRIE process recipe. For the wafer with AlN this side wall shift is about 0.85 µm at each sidewall. This results in a change of the spring with from a = 5 µm to a0 = 3.3 µm. For the wafer with Al0.68Sc0.32N a side wall shift of 1.35 µm is used. The lower stiffness should result in higher deflection per voltage and further increase the MOEMS performance compared to systems with high resonance frequency.
