Introduction

MEMS scanner is reflecting mirror with rotational movement fabricated by Si-based semiconductor manufacturing process. MEMS scanners offer the advantages of compact size leading to rapid operation, and low power consumption. Consequently, they find practical applications in fields that demand miniaturization, such as AR display, LiDAR and medical imaging. While MEMS scanners come with various driving mechanisms, such as electrostatic, piezoelectric, electromagnetic, electrothemal etc., among them, the electrostatic comb-drive method stands out for its near absence of hysteresis and relative ease of fabrication [1,2,3,4,5].

The comb-drive actuator refers to a structure in which two sets of thin vertical electrodes are stacked in a lateral direction in the form of interdigitated electrodes, namely the stator and the rotor. When these parallel electrodes are arranged, they form capacitance. Upon applying a voltage between the two interdigitated electrodes, one electrode accumulates a positive charge (+ Q) while the opposite electrode accumulates a negative charge (−Q). According to Coulomb's law, these charges (accumulation) generates an attractive force in the direction where the capacitance is maximized, i.e., the direction with maximized overlapped area [6].

By inducing rotational degrees of freedom in the actuator's spring, it becomes possible to enable angular movement since rotation increases the overlapped area of combs. In this paper, our objective is to improve linearity and enlarge scanning angle of a micro mirror scanner that is driven by the electrostatic comb-drive actuator.

Theoretical analysis of comb actuators

The resonance (RS) type scanner is a method that utilizes the natural resonant frequency determined by the characteristics of the mirror and the spring featuring a large scanning angle [7]. The RS type scanner has the advantage of having a rigid spring and can be easily fabricated as it does not require a height difference between the fixed coms (stator) and movable combs (rotor). However, it has the limitation of being able to control the operating frequency only within a narrow range in a sinusoidal waveform.

On the other hand, the quasi-static (QS) type scanner has the advantage of being capable of driving the mirror with frequencies and waveforms desired by the user, when driving frequency is sufficiently smaller than resonant frequency. However, to achieve this, it requires an initial offset in height or angular displacement between the fixed and movable combs, unlike the resonance type, making its fabrication more complicated [8].

Figure 1 shows an example of a comb-drive actuator. When a voltage difference occurs between the fixed and movable comb electrodes, the rotor rotates by an angle dθ, causing the cross-sectional area A between the two electrodes to increase by dA. The torque T obtained by the actuator is proportional to V2 and δA/δθ, as indicated in Eqs. (1, 2).

$$E_C = - \frac{1}{2}CV^2 = - \frac{1}{2}\frac{\varepsilon A}{g}V^2$$
(1)
$$T = \frac{\delta E_c }{{\delta \theta }} = - \frac{1}{2}\frac{\varepsilon }{g}\frac{\delta A}{{\delta \theta }}V^2$$
(2)
Fig. 1
figure 1

Comb-driven rotation actuator: (a) top view, (b) side view, and (c) perspective view

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where, E C = energy stored in comb electrodes, C = capacitance, V = input voltage, T = torque, ε = permittivity, A = cross-section area and g = gap between combs.

Here, when δA/δθ maintains as a constant value, the torque T shows linear behavior, proportional to V2. In reality, δA/δθ is not a constant value and tends to slightly vary depending on the comb's shape and angular position. Moreover, the limit of rotational angle, where δA/δθ is kept close to a constant value, depends on the structure of the comb drive such as comb length, initial offset in height, and thickness of device layer, i.e. on the types of comb configuration.

Up to now, the conventional electrostatic actuators of the QS scanners have been configured in the form of SVC (staggered vertical combs) or AVC (angular vertical comb), as shown in Fig. 2a, b [9,10,11,12]. The fabrication of the SVC requires twice DRIE (Deep Reactive Ion Etching) of a silicon-on-insulator (SOI) wafer. Therefore, these structures increase the complexity in the device fabrication leading to high cost. Furthermore, SVC is accompanied by the problem that the driving angles of the rotor is comparatively small [13, 14].

Fig. 2
figure 2

Driving mechanism of (a) SVC (staggered vertical comb), (b) AVC (angular vertical comb) and (c) CVC (concentric vertical comb)

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Meanwhile, AVC (angular vertical comb) type can be manufactured with a simple semiconductor process. For instance, AVC type scanner only needs single DRIE process to form comb drive. However, its linearity is poor due to non-uniform increments of δA/δθ as shown in Fig. 3b and Table 1. In the calculation for three types of MEMS scanner, the thickness of device layer, the length of movable comb and overlapped length of movable comb and fixed comb are 70 µm, 180 µm, and 160 µm, respectively.

Fig. 3
figure 3

A (area) and δA/δθ varying with mechanical angle of (a) SVC (staggered vertical comb), (b) AVC (angular vertical comb), and (c) CVC (concentric vertical comb), Dotted line overlapped area (A), Solid line δA/δθ

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Table 1 Linearity comparison of quasi-static MEMS scanners
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To enhance a linearity of scanning angle with the square of input voltage (V2), we propose to use CVC type MEMS scanner. CVCs are different from AVC in that the movable combs are always angularly aligned with the stationary comb regardless of angular position of the movable electrodes. Thus, the increments of the overlapping area in the CVC type is almost constant, resulting in an improvement in linearity. Furthermore, CVC structure maximizes overlapped area of comb thereby increasing the maximum rotation angle.

MEMS design

The proposed CVC structure was incorporated into a Si-based quasi-static (QS) MEMS mirror scanner fabricated using silicon-on-insulator (SOI) wafers. There have been attempts to implement CVC (in other words, aligned AVC). CVC structure for a MEMS mirror using reflow was proposed, but was not actually fabricated [15]. Another approach aimed to achieve a CVC structure by inducing permanent deformation in silicon at high temperature, around 900 ℃ [16], but might damage the reflective surface in case of aluminum coating.

The CVC structure in this paper can take advantages of a simple three-layer microfabrication process similar to the conventional AVC fabrication, even though it requires an microassembly of tiling the part of comb electrodes [17].

Angle-amplifying linkages, as shown in Fig. 4, are also employed to magnify the scanning angle. In the design, these linkages provide a magnification ratio of α = 2. While the theoretical maximum rotation angle of the actuator under simulation conditions is 11.6 degrees (OSA), this linkage system enables the mirror to achieve even greater rotation.

Fig. 4
figure 4

Angle amplifying linkage mechanism

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The rotor of the comb driven MEMS scanner is designed to rotate in a torsional mode. The stator (stationary combs) is tilted and fixed at a certain angle, enabling the movable combs to rotate about the same axis of the rotor, as shown in Fig. 5. To lower the driving voltage, the comb electrodes is placed as many as possible by connecting the linkage between the mirror and actuator.

Fig. 5
figure 5

Design of process sequence for tilting the fixed comb electrodes

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The experimental driving characteristics of the CVC scanner will be compared with the theoretical one, and also with the formerly manufactured AVC scanners. Those two chips have identical chip size and the mirror size (ellipsoidal) as shown in Fig. 6 and the 1st mode (rotation mode) frequencies are similar each other. Note that scanners with AVC and CVC actuators were manufactured and their performances are compared, whereas those with SVC actuators were theoretically evaluated.

Fig. 6
figure 6

Top view schematics of the scanner chips with (a) AVC (angular vertical comb) and (b) CVC (concentric vertical comb)

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In the simulation, an input voltage of 130 V is applied to the scanner, resulting in an OSA of 15.47 degrees. This outcome is achieved by deliberately lowering the spring stiffness to increase the rotation angle, consequently yielding a slightly low resonance frequency of 371 Hz for the mirror's first mode.

Experiments

The proposed scanner chips were fabricated through a simple process using three masks, as depicted in Fig. 7.

Fig. 7
figure 7

Fabrication process of the packaged MEMS scanning mirror

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The overall structure and morphology of the produced chip are displayed in the photo image of Fig. 8, where the rotation axes of the stator and rotor coincide, along with a link structure to amplify the OSA of the mirror.

Fig. 8
figure 8

Photo image of the fabricated scanner chip

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The actuator section of the chip exhibits an initial angle in the SEM image of Fig. 9 through the tilting process, as depicted in Fig. 9. The extension lines of the lower comb (represented by a blue dashed line) and the upper comb (represented by a red solid line) are not parallel to each other, indicating upper combs are tilted to the lower ones.

Fig. 9
figure 9

SEM image of the concentric vertical combs (CVC) actuator

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The experimental setup is shown in Fig. 10. The packaged MEMS scanner is positioned and fixed on the pedestal while electrically interfaced to the connector. Upon receiving the driving signal, the Au-coated mirror at the central part of the chip rotates about the torsional springs. The reflected light reaches the position sensitive detector (PSD), generating electrical signals correlated with the OSA.

Fig. 10
figure 10

experimental setup

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Figure 11 shows the DC driving characteristic of the fabricated quasi-static MEMS scanner with CVC. The curves in blue and orange represent experimental and theoretical OSA, respectively. The theoretical value is very close to the experimental value, indicating high linearity with respect to the V2. This implies that the area change rate of the combs is consistently maintained constant, resolving the nonlinearity caused by drastic decreases in capacitance at the end of the rotation angle, so-called C-nonlinearity [18].

Fig. 11
figure 11

Static response curve (Vdc–OSA) of the quasi-static MEMS scanner with CVC electrodes

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The high linearity observed between V2 and the mirror rotation angle suggests greater convenience in generating scanning outputs in a triangular waveform. In the near future, we plan to introduce a new MEMS scanner driven with a high linearity between input voltage (V) and rotation angle of a mirror. The CVC actuator with this high linearity will be beneficial to generate arbitrary motion in the MEMS scanners.

In Table 2, the maximum OSA of the scanner is up to 15°, and average OSA (13.5 degrees) is increased by 39% compared to other types of MEMS scanners. The enlarged angular movement of the MEMS scanner is partially due to the linkage system, allowing it to surpass the theoretical maximum rotating angle estimated considering only comb configuration.

Table 2 Comparison of optical scanning angle (OSA) for quasi-static MEMS scanners
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The 1st mode frequency of rotational mirror motion is 343 Hz, and its deviation from the theoretical one is negligibly small. When it comes to the 1st mode frequency, they show similar characteristic regardless of the type of the MEMS scanner.

Input shaping

QS-type scanners are in high demand due to their capability to operate with triangular waveforms, which is desirable in the most of the scanner applications. Actually, there are various waveforms requested, including saw tooth, square waves, and even arbitrary waveforms.

Theoretically, an arbitrary waveform in angular scanning can be generated by using a certain input voltage whose shape corresponds to the targeted waveform of the output scanning, as shown in Fig. 12. This theory works well for sinusoidal waveform output, which has only one frequency component, whereas it does not work for complex waveforms such as triangular waves, resulting in the occurrence of ripples in the output waveform.

Fig. 12
figure 12

Theoretical input shaping process of the generation of input drive voltage for targeted scanning output waveform

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In case of complex input signals, such as triangular or rectangular waveform, they have high order terms in the frequency domain. When one of the high order frequencies are close to the resonant frequency of the system, this might be a main cause of the ripple in the motion of the MEMS mirror.

By applying an input shaping method based on the transfer function and static response of the MEMS mirror scanner, the shaped input waveform was theoretically calculated for the target output of triangular output waveform [18]. When the shaped input was applied to the scanner, the triangular output was obtainable as shown in Fig. 13. The ripples can be further suppressed by employing low pass filter at the cost of reducing the usable range in optical scan angle.

Fig. 13
figure 13

Waveform generated by applying input shaping method, shaped input drive voltage, output voltage of PSD correlated with optical scanning angle)

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Conclusions

It was confirmed that linearity and the scanning range were improved compared to the SVC and AVC MEMS scanners. Input voltage in certain waveforms such as triangular wave, can induces irregular angular output with a serious level of ripples caused by resonance mode of the scanner. To achieve desired output, it is recommended to apply the shaped input acquired from transfer function and static response curve of the scanner.

Increasing the stiffness of the torsional spring, which would increase the resonant frequency, can be an option to decrease ripple but it will reduce maximum rotation angle of mirror. In the near future, we will report on the improved QS MEMS scanner whose static response is linearly proportional to the input voltage by adopting multiple level of comb electrodes.