Design of planar comb-driven MEMS torsional mirror

The MEMS torsional mirror is an important MEMS optical device, and its related applications are very wide, including LiDAR, projection equipment, optical communication, and so on. At present, the electrostatically driven MEMS torsional mirror mainly adopts a vertical comb driver to achieve torsional motion, which has some disadvantages such as a complicated manufacturing process, low yield, and high driving voltage. In this paper, a novel MEMS torsional mirror structure is proposed, which provides flexible elastic constraint points for the torsional mirror with the bottom support rod structure as the center, and relies on the combination of planar comb and support rod to form a tie rod structure to achieve torsion, and achieves a torsion Angle of ±15.55° under the driving voltage of 65 V. The use of a planar comb instead of a vertical comb greatly reduces the difficulty of manufacturing. Finally, it is verified that the system stability is good, the correlation drift does not affect the results within the range, the fifth-order modes are within the reasonable range, and the maximum stress is 671 MPa, which is controlled within the range of fracture stress of silicon material.


Introduction
As an advanced MEMS optical device, MEMS torsional mirror has a wide range of applications, not only as a core component of LiDAR [1] and projection equipment but also as an optical switch, optical phase modulator, and other applications in the field of optical communication [2,3] .MEMS torsional mirror is mainly used to reflect light to achieve the purpose of changing the light path, and its advantages are that it has high integration, small size, low power consumption, and can be massmanufactured [4,5] .However, it also has certain disadvantages, due to the limitation of the MEMS process, it can not prepare a torsional structure such as bearings [6] , which leads to the limited torsion Angle of MEMS micromirror, which is very unfavorable for the application end.In addition, there are four driving methods of MEMS torsional mirrors, including electromagnetic drive [7] , electrostatic drive, electric heating drive [8] , and piezoelectric drive [9] .Although the electromagnetic drive has a large torque output, it is difficult to control and has poor stability due to the influence of travel and motion state.The advantage of electric heating drive is that the drive voltage is low, but the corresponding time is too long, and it is not suitable for application in the high-frequency field.Piezoelectric drive technology is not very mature, the relevant piezoelectric materials are often high cost, and the cost is difficult to reduce.Most of the MEMS torsional mirrors driven by static electricity are driven by vertical comb, and the vertical comb makes it difficult to achieve complete alignment in the process [10] , which causes the problem of low yield, and the driving voltage required by the vertical comb is often large, and the torsion Angle achieved is not ideal.
Given the difficulties of vertical comb driving MEMS torsional mirrors and the high driving voltage, a new structure of MEMS torsional mirrors driven by planar comb is proposed in this paper.
The structure adopts a planar comb combined with a central support rod structure, which can provide relatively flexible support points for the mirror and achieve torsion function with a planar comb.Because the planar comb process is simple, it can be formed by single lithography, which greatly reduces the difficulty of chip manufacturing and improves the yield.The structure achieved a torsion Angle of ±15.55° under 65 V driving voltage in ANSYS finite element simulation, which reduced the driving voltage and power consumption.The overall size of the structure is 1400 um×800 um, and the volume is relatively small, which is conducive to integration in the system.

Structure design of MEMS torsional mirror
The designed planar comb-driven MEMS micromirror structure is divided into two categories, namely, single support beam model and double support beam model.To facilitate display, part of the support structure is seen in the figure.As shown in Figure 1, the related micro-mirror system consists of four parts: mirror, planar comb, support rod, and outer frame.The support rod plays an overall supporting role for the mirror, in addition, the support rod provides a flexible fixed fulcrum for the micromirror, so that the mirror can do the twisting motion with the fixed fulcrum as the center under the horizontal driving force.In the above models, the mirror size is 800 um×400 um, and the surface is gold-plated by a metal evaporation sputtering process, which has good reflection characteristics.The mirror is in the same layer as the flat combs and the thickness is 20 um.The process is simple, the process steps are few, the yield is high, and the preparation cost is low.The outer frame is used as the overall support and the electrodes of the fixed comb are led out.The relevant electrical isolation is separated by way of cutting the electrodes on both sides, and SiO2 is used as the insulating medium between the upper and lower layers for isolation.

Theoretical analysis
There are three common ways of electrostatic drive, including flat plate drive, vertical comb drive, and planar comb drive.The principle of flat plate drive is shown in Figure 2. According to the principle of parallel plate capacitors, when the voltage between plates changes, a driving force will be generated to change the spacing between plates to maintain the balance between the electrostatic force and the spring force.The output electrostatic force can be expressed as Because the driving force provided by the flat plate driver is relatively small, and the pull effect and nonlinear driving force make it difficult to accurately control [11] , its application scenarios are very limited, and this driving method needs to be further optimized.
The vertical comb driver consists of a pair of comb teeth with a height difference in the vertical direction, as shown in Figure 3, with a fixed comb at the bottom and a movable comb at the top.Where Tf represents the thickness of the comb teeth, N represents the logarithm of the comb teeth, V represents the driving voltage, ε represents the air dielectric constant, g represents the comb tooth spacing, and L represents the overlap length of the comb teeth.The driving force in the vertical direction can be expressed as: According to the formula, it can be seen that the driving force of the vertical comb is inversely proportional to the gap of the comb teeth, proportional to the overlap length, and proportional to the square of the voltage.The performance of the vertical comb driver can be optimized by modifying these three parameters.
The vertical comb driver has good driving properties and can produce a driving force perpendicular to the plane where the mirror is located, which is more conducive to the use of torsional micromirrors.However, its structure is a double-layer overlapping structure, which is often difficult to achieve in the process, and the chip yield is not high.The planar comb driver is composed of a fixed comb and a movable comb distributed in the same plane, as shown in Figure 4.The manufacturing process is greatly simplified and can be formed only by single lithography, with simple process steps, low cost, and high yield.where L represents the length of comb teeth, g represents the spacing of comb teeth, and x represents the overlapping length of comb teeth.When a driving voltage is applied between the movable comb and the fixed comb, as shown in Figure 3, an unevenly distributed electric field will be generated between the comb [12] , and the movable comb will move towards the fixed comb under the attraction of electrostatic force.Then the electrostatic attraction in the plane can be expressed as: where t represents the thickness of the comb teeth, N represents the logarithm of the comb teeth, V represents the driving voltage, ε represents the dielectric constant of the air, and g represents the distance between the comb teeth.According to the formula, the electrostatic attraction is proportional to the logarithm of the comb teeth and the thickness of the comb teeth, inversely proportional to the distance between the comb teeth, and proportional to the square of the driving voltage.To increase the electrostatic attraction, the measures taken are generally to increase the logarithm of the comb teeth or to increase the thickness of the comb teeth and reduce the spacing of the comb teeth by optimizing the processing technology.

Simulation Analysis
Based on the above theoretical analysis and structural design, the MEMS torsional mirror is simulated and analyzed, and the finite element simulation software ANSYS is used for modeling.To reduce the computing time of the computer and reduce the difficulty of grid division, the equivalent method is adopted here, the comb part is equivalent to the mass block, and the pressure is applied to the corresponding effective area.The modeling is shown in Figure 5.According to Formula (3), different driving voltages are brought in to obtain the equivalent driving force, and then the pressure is obtained from the driving force ratio to the relevant area.The pressure was applied to the stress surface to obtain the simulation result, and the Z-displacement cloud image was selected in the result tree for observation, as shown in Figure 6.It can be seen that the mirror is in a torsion situation, and the maximum and minimum Z displacement of the mirror are located on both sides of the mirror, then the torsion Angle of the mirror can be expressed as: where θ is the torsion Angle, Zmax, and Zmin represent the maximum and minimum value of Zdisplacement respectively, and w represents the mirror width, which is 400 um.The corresponding displacement results are obtained by applying different driving voltages, and then the torsion Angle is calculated by Formula (4).The relationship curve between the driving voltage and the torsion Angle can be obtained by observing multiple sets of data, as shown in Figure 7.It can be seen from the figure that the torsion Angle is directly proportional to the driving voltage.Under the same driving voltage, Model 1 and Model 3 can obtain a large torsion Angle, but problems such as stress and drift should also be considered when obtaining a large torsion Angle, to ensure the feasibility and stability of the structure.

Stress and angle analysis
In addition, to ensure the feasibility of the structure, stress analysis was carried out for each model, and different driving voltages were applied to obtain the driving voltage-stress curves, as shown in Figure 8.It can be seen from the figure that the driving voltage and stress are in direct proportion.Under the same driving voltage, the stress of Model 1 is the largest, the stress of Model 3 is slightly less than that of Model 1, and the stress of Model 2 is the smallest and changes the slowest.To meet the reliability of the structure, it is necessary to ensure that the maximum stress of the structure is less than 700 MPa of the fracture stress of the silicon material, so it is necessary to carry out angular stress analysis for each model, and the results are shown in Figure 9.It can be seen from the figure that while the maximum stress is less than 700 MPa, the maximum driving voltages of each model are respectively 65 V for Model 1, 115 V for Model 2, 65 V for Model 3, and 85 V for Model 4.Moreover, under the driving voltage value, the torsion angles generated by each model are 12.68°, 7.82°, 15.55° and 10.91° respectively.It can be seen that Model 3 can produce a larger torsion Angle at a smaller driving voltage under the condition that the fracture stress of silicon material is not exceeded.

Drift analysis of mirror
Since the solid fulcrum provided by the support rod structure is not an absolute fixed point, although it is conducive to the torsion of the micromirror, it also causes a certain drift in other directions.The directional drift will have different impacts on the mirror, which is likely to have a certain impact in subsequent applications.In this simulation verification, the displacement of the center point of the mirror is the drift of the mirror.The three directions of X, Y, and Z are included, and the anisotropic drift curves of the four models are shown in Figure 10.The relative drift in Y and Z directions will affect the change of the center position of the micromirror, which may have a small impact on the calculation of light path difference, light alignment, and other issues.Secondary optimization can be carried out according to the subsequent use scenarios of the micromirror and the accuracy requirements of the application equipment.As can be seen from the figure, the drift in the Y and Z directions of Model 3 under 65 V driving voltage is only 18.42 um and 9.08 um, which is within a reasonable range.The X-direction drift not only affects the central position of the micromirror but also affects the gap of the comb teeth, resulting in changes.As can be seen from the graph, the X-direction drift value of all models is less than 0.0018 um, and Model 3 is only 0.0005 um, which changes the gap of the comb teeth at 2.7 um very little, and will not cause the problem of comb teeth sucking.

Modal analysis
Finally, the modal simulation analysis is carried out for this structure, ANSYS APDL is used for modal simulation, and the five-order modes are selected to obtain the modal table as shown in Table 1.Finally, according to the comprehensive comparison of various indicators, Model 3 is selected as the final design model.The torsion Angle of the model can reach ±15.55° under 65 V driving voltage, and the maximum stress of the structure is 671 MPa, which is far less than the maximum stress range of 700 MPa.The drift and modal data in all directions are within a reasonable range.It can be selectively optimized for different application scenarios.

Process
According to the finite element simulation results of ANSYS, we choose Model 3 to design the process flow, which includes three parts: pre-treatment, structure manufacturing, and post-treatment.a) Select a suitable wafer, as shown in Figure 11, with a device layer thickness of 20um, for wafer development.

Conclusions
The twisting action of MEMS torsional twisting driven by static electricity mainly relies on the vertical comb driver, and the vertical comb driver process is relatively difficult to manufacture.It not only requires multiple lithography, but is also difficult to align and easy to produce burrs in etching, which greatly affects the use of the structure, the chip yield is low, and it is difficult to achieve large Angle torsion.A new planar comb-driven MEMS micromirror structure is presented in this paper.The structure is composed of a mirror, planar comb, support beam, and external frame.The manufacturing process of the planar comb driver is very simple, using a single lithography molding.In this paper, two types of structures are proposed, including four models.After ANSYS APDL simulation verification, the third model of the two-beam structure is finally determined by comparing various performances.The section of the support beam is 1.6×1.6 um.The maximum stress is only 671 MPa, far less than the upper-stress limit of 700 MPa, and the drift and modal data are within a reasonable range, which does not affect the work of the micromirror structure.

Figure 1 .
Figure 1.Torsional mirror model driven by planar comb.By modifying the supporting beam parameters of the model, four models can be obtained, namely Model 1, single supporting beam, beam section of 2×2 um; Model 2, single support beam, beam section of 3×3 um; Model 3, double support beam, beam section of 1.6×1.6 um; Model 4, double support beam, beam section of 2×2 um.By simulating and comparing the four groups of models, the best model is obtained by considering all the indicators.In the above models, the mirror size is 800 um×400 um, and the surface is gold-plated by a metal evaporation sputtering process, which has good reflection characteristics.The mirror is in the same layer as the flat combs and the thickness is 20 um.The process is simple, the process steps are few, the yield is high, and the preparation cost is low.The outer frame is used as the overall support and the electrodes of the fixed comb are led out.The relevant electrical isolation is separated by way of cutting the electrodes on both sides, and SiO2 is used as the insulating medium between the upper and lower layers for isolation.

Figure 7 .
Figure 7. Relationship between torsion Angle and drive voltage.

Figure 13 .
Figure 13.Lithography and etching.d) Turning over the wafer, spinning photoresist, lithography and etching, as shown in Figure 14.

Figure 14 .
Figure 14.Turning over, Lithography and etching.e) Metal sputtering is performed on the front mirror structure and at the same time the metal electrode is sputtered, as shown in Figure 15.