*5.1. Frequency Response and Small Signal Actuation*

In Figure 6a,b the FRFs are depicted in logarithmic scaling. The amplitude is measured for a range of six decades. Due to the high deflection in resonance, the LDV sensor sensitivity is low. Therefore, there is a significant noise for low amplitudes. The measurement values are given in Table 2. A motion scan image of exemplary micromirrors of Design 1 and Design 2 in torsional mode is shown in Figure 7.

An analytical calculation is shown to describe the static deflection of the 1D MOEMS. For a MOEMS with AlN and Design 1 a static deflection of 65 nm/V up to 116 nm/V is calculated. The measured deflection is 61.1 nm/V. One reason for the smaller deflection in the manufactured system can be the loss of elastic energy in the torsion spring with a high stiffness, which is not modeled by the analytical formulas. The measured MOEMS deflection with Design 1 and Al0.68Sc0.32N is 157.6 nm/V. The measured deflection is within the calculated deflection range of 143 nm/V to 241 nm/V. For Design 2 with Al0.68Sc0.32N as piezoelectric transducer, the modeled deflection of 563 nm/V to 959 nm/V matches with the measurement result of 667.3 nm/V.

For Design 1, the AlN MOEMS has a resonance frequency of 3444 Hz. For the same design, the resonance frequency of the Al0.68Sc0.32N MOEMS is 1819 Hz. The side wall shift of the silicon results in a decrease of the resonance frequency and, therefore, in a

lower stiffness of the system. The resonant mechanical tilt angle of the AlN based MOEMS (Design 1) is 2.8◦ at 1 MV/m. For the Al0.68Sc0.32N MOEMS an angle of 11.9◦ at 1 MV/m is measured. The deflection in relation to the electric field is increased by a factor of 4. sensor sensitivity is low. Therefore, there is a significant noise for low amplitudes. The measurement values are given in Table 2. A motion scan image of exemplary micromirrors of Design 1 and Design 2 in torsional mode is shown in Figure 7.

*Micromachines* **2022**, *13*, x 9 of 15

**Figure 6.** Frequency resonance functions of the presented micromirrors: (**a**) Mirror deflection per voltage; and (**b**) Mirror deflection per electric field. **Figure 6.** Frequency resonance functions of the presented micromirrors: (**a**) Mirror deflection per voltage; and (**b**) Mirror deflection per electric field.



<sup>1</sup> Parameters are medium values over five samples.

**Figure 7.** Motion scan images of exemplary micromirrors recorded by Laser-Doppler-Vibrometry: (**a**) Design 1; and (**b**) Design 2. **Figure 7.** Motion scan images of exemplary micromirrors recorded by Laser-Doppler-Vibrometry: (**a**) Design 1; and (**b**) Design 2.

An analytical calculation is shown to describe the static deflection of the 1D MOEMS. For a MOEMS with AlN and Design 1 a static deflection of 65 nm/V up to 116 nm/V is calculated. The measured deflection is 61.1 nm/V. One reason for the smaller deflection in the manufactured system can be the loss of elastic energy in the torsion spring with a high stiffness, which is not modeled by the analytical formulas. The measured MOEMS deflection with Design 1 and Al0.68Sc0.32N is 157.6 nm/V. The measured deflection is within the Due to the larger chip area and actuator length and width of Design 2, the deflection is increased to 35.6◦ per MV/m in resonance. The resonance frequency for the MOEMS with Design 2 is 2121 Hz. In total, the resonant deflection from a MOEMS with AlN and Design 1 compared to Al0.68Sc0.32N with Design 2 increased from 2.8◦ to 35.6◦ per 1 MV/m. This is a factor of 12.

#### calculated deflection range of 143 nm/V to 241 nm/V. For Design 2 with Al0.68Sc0.32N as *5.2. Static High Voltage Actuation*

piezoelectric transducer, the modeled deflection of 563 nm/V to 959 nm/V matches with the measurement result of 667.3 nm/V. For Design 1, the AlN MOEMS has a resonance frequency of 3444 Hz. For the same design, the resonance frequency of the Al0.68Sc0.32N MOEMS is 1819 Hz. The side wall shift of the silicon results in a decrease of the resonance frequency and, therefore, in a lower stiffness of the system. The resonant mechanical tilt angle of the AlN based MOEMS (De-In this section, the scanning characteristics of three selected micromirror samples in torsional mode for voltages of up to 400 V are shown. 400 V is the maximum voltage of the power supply in the setup. Due to limitations in the measurement setup, deflections up to 15◦ mechanical deflection can be measured. In Table 3 and Figure 8 the static mechanical deflections of the systems are shown.


measured. The deflection in relation to the electric field is increased by a factor of 4. Due to the larger chip area and actuator length and width of Design 2, the deflection **Table 3.** Comparison of the static mechanical tilt angles of the several micromirror designs and piezoelectric transducer technologies.

sign 1) is 2.8° at 1 MV/m. For the Al0.68Sc0.32N MOEMS an angle of 11.9° at 1 MV/m is

ure 9). Up to 400 V actuation voltage is used for the samples with Al0.68Sc0.32N. The reason <sup>1</sup> Limit of measurement setup.

is the high electric field for the 600 nm thin AlN layers compared to the 2 µm thick Al0.68Sc0.32N. Electric breakthroughs are observed for AlN chips at voltages higher than 200 V (Figure 9). Up to 400 V actuation voltage is used for the samples with Al0.68Sc0.32N. The reason is the high electric field for the 600 nm thin AlN layers compared to the 2 µm thick Al0.68Sc0.32N.

For Design 1 the maximum deflection is 9.6◦ at 400 V with Al0.68Sc0.32N as piezoelectric transducer. AlN-based chips show deflections up to 4.1◦ at 200 V. By comparing the deflection of the MOEMS in relation of the electric field, the use of 2 µm Al0.68Sc0.32N and lower system stiffness increased the static deflection by a factor of approximately 4. It can be assumed that the high piezoelectric coefficient of the Al0.68Sc0.32N is one major reason

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piezoelectric transducer technologies.

Mech. tilt angle (°)

1 Limit of measurement setup.

**Table 3.** Comparison of the static mechanical tilt angles of the several micromirror designs and

**Static Parameters Design 1 Design 1 Design 2** 

 At 100 V 2.1 2.1 6.3 At 200 V 4.1 4.3 12.5 At 400 V — 9.6 — 1 At 50 MV/m 0.6 2.1 6.3 At 100 MV/m 1.2 4.3 12.5 At 200 MV/m 2.5 9.6 — 1 Maximum mech. tilt angle (°) 4.1 (at 200 V) 9.6 (at 400 V) 13.9 1 (at 220 V)

for the larger deflection. In addition, the lower stiffness of the Al0.68Sc0.32N based MOEMS influences the absolute and relative deflection and needs further investigations. for the larger deflection. In addition, the lower stiffness of the Al0.68Sc0.32N based MOEMS influences the absolute and relative deflection and needs further investigations.

For Design 1 the maximum deflection is 9.6° at 400 V with Al0.68Sc0.32N as piezoelectric transducer. AlN-based chips show deflections up to 4.1° at 200 V. By comparing the deflection of the MOEMS in relation of the electric field, the use of 2 µm Al0.68Sc0.32N and lower system stiffness increased the static deflection by a factor of approximately 4. It can be assumed that the high piezoelectric coefficient of the Al0.68Sc0.32N is one major reason

600 nm AlN 2000 nm Al0.68Sc0.32N 2000 nm Al0.68Sc0.32N

**Figure 8.** Performance of the presented micromirror designs at static high voltage actuation: (**a**) Mechanical tilt angle versus voltage; and (**b**) Mechanical tilt angle versus electrical field. **Figure 8.** Performance of the presented micromirror designs at static high voltage actuation: (**a**) Mechanical tilt angle versus voltage; and (**b**) Mechanical tilt angle versus electrical field.

**Figure 9.** Photography of an exemplary micromirror of Design 1 with electric breakthroughs at 220 V. The electric contact of the MOEMS is done with micro needles on a probe station.

Design 2 enabled deflections of up to 13.9◦ at 220 V, which is the limit of the measurement setup. The deflection per electric field of Design 2 is increased by a factor of 3 in relation to Al0.68Sc0.32N-MOEMS with Design 1. Design 2 with Al0.68Sc0.32N has more than ten times of the deflection per electric field compared to the previously reported AlN based MOEMS with Design 1. The scan angle can be defined by four times the mechanical tilt angle. Therefore, scan angles up to 55.6◦ for static displaced Al0.68Sc0.32N MOEMS are

shown. Figure 10 shows a photography of a static deflected MOEMS of Design 2 with Al0.68Sc0.32N at 200 V.

**Figure 10.** Photography of an exemplary micromirror of Design 2 in static operation (12.5◦ , 200 V). Captured by a single lens reflex (SLR) camera (Canon EOS 600D) and macro lens.

In Figure 8 the linearity for deflections < 15◦ can be seen. Relevant non-linear effects are not observed for the static deflections. Therefore, stress-stiffening effects have minor relevance for both MOEMS designs and static deflections < 15◦ .

For high electric fields the AlN and Al0.68Sc0.32N shows electric breakthroughs. In Figure 9 a chip is shown after a breakthrough. Optically, lightning discharges were observed spontaneously. If a lightning appears at one position of the chip, an avalanche effect starts immediately and multiple areas of the chip show electric breakthroughs. The positions of the breakthroughs are random. Therefore, imperfections of the AlN and Al0.68Sc0.32N growth could be the reason for the breakthrough. Nevertheless, a very electric field of up to 200 MV/m is applied to the piezoelectric layer, which indicates a high quality of the crystal growth and structure.

Future measurement setups need power supplies with voltages higher 400 V DC and a larger optical bank for the documentation of lager scan angles.

Figure <sup>11</sup> shows a photography of the Design 1 MOEMS with 2 <sup>×</sup> 3 mm<sup>2</sup> footprint and the Design 2 MOEMS with 6 <sup>×</sup> 8 mm<sup>2</sup> chip size in comparison.

**Figure 11.** Photography of the Design 1 and Design 2 MOEMS with piezoelectric Al0.68Sc0.32N actuators on a copper sulfate crystal as a backdrop.
