Optical MEMS Devices Based on Heactuators

Yafei Li, Minhao Zhou Department of Mechanical Engineering, UC Berkeley

Abstract: Optical MEMS has created a new fabrication paradigm for optical devices and systems. In this project, two MEMS optical devices: 5-axis auto focus (AF) and optical image stabilization (OIS) lens and scanning mirror are designed and analyzed. The practicability of both devices are discussed regarding to the deflection and force generated by the driving heactuators and parallel-plate capacitors. The fabrication process of 5-axis AF and OIS lens is discussed. I. Introduction Compared to traditional optical devices, MEMS optical devices are not only superior in size; they are generally safer and have much higher resolutions. Thus, they are currently widely used industrially, commercially, and bio-medically. Among all these applications, lens and mirrors are used the most extensively. Specifically, the small size 5-axis AF and OIS lens are usually used in cellphone cameras. It cancels out vibrations introduced during picture shooting for photos and videos of higher quality. For scanning mirror, it allows the mirror to move bi-axially to reflect the incoming lights in required directions in the space. However, for a complete legible scan, high frequency actuators are required. Based on the heactuator model given in literature [1], we establish heat transfer and deflection model to assess the capability of heactuators of 5-axis AF and OIS lens. In addition, a resonance model is established to estimate the performance of pico projector made up of multiple scanning mirrors. Also, the driving capability of parallel-plate capacitors is estimated. Therefore, we explore the possibility of designing both MEMS 5-axis AF and OIS lens and scanning mirror that can be driven by heactuators and parallel-plate capacitors. At the end, the fabrication process of the MEMS 5-axis AF and OIS lens is discussed. Three structural layers, total nine layers and nine masks are required. Moreover, an additional layer of silicon nitride is required for electrical insulation. II. Design 5-axis AF and OIS Lens: A 5-axis AF and OIS system is widely used in camera lens to achieve automatic focus on a manually selected point or area while reducing blurring associated with the camera motion during exposure. To properly achieve the function mentioned above, the lens must be able to be driven to translate tri-axially while rotating bi-axially. Therefore, we design our MEMS 5-axis AF and OIS lens as shown in Figure 2.1.

Figure 2.1. Overview of MEMS 5-axis AF and OIS lens

Specifically, heactuators that are actuated vertically with hot and cold arms structured in different poly silicon layers are arranged circumferentially around the lens. By partially or completely actuating them, the lens can rotate bi-axially or translate vertically to achieve AF and partial OIS. Besides, 4 parallel-plate capacitors are directly connected to the lens that is supported by the electrically insulated silicon nitride plate, to drive the lens to achieve plane motion for partial OIS. Under such schematics, the lens can translate and rotate in 5-axis and achieve AF and OIS theoretically. Scanning Mirror A pico projector is a handheld device that can be used as an image projector. In this system, the scanning mirror, which scans and projects the images onto the screen, is pivotal. To completely scan the screen both laterally and vertically, the mirror is required to rotate bi-axially. Therefore, we design our MEMS scanning mirror as shown in Figure 2.2.

Figure 2.2: Overview of MEMS scanning mirror

Different from the 5-axis AF and OIS lens, we simply rotate the lateral heactuators to achieve vertical movement range while arranging them circumferentially around the mirror that is supported by the electrically insulated silicon nitride plate so that the mirror can achieve bi-axial rotation. Specifically, for the scan, the maximum deflection of the heactuator determines the maximum number of pixel columns that can be scanned by one mirror while its maximum working frequency determines the maximum number of pixel rows that can be scanned within the minimum frame rate, which is 60 Hz for human beings. Since the scanning range of a single scanning mirror is usually too limited for a complete scan under a reasonable projection range, for the application of pico projector, a rectangular array of scanning mirrors will be used. Intentionally not using the same heactuators for driving purpose, we can compare the performance of these two optical devices that are driven differently. III. Analysis 5-Axis AF and OIS Lens According to previous literature [1], the heactuator’s tip can move laterally and drive the connected devices in the same direction. However, since the lens designed is driven by vertical heatuators, the given model is first calibrated regarding to the published deflection and force values. Specifically, we use the heactuator geometry given in the literature [1], as shown in the Table 3.1, to establish a heat transfer and deflection model of the heactuators used to theoretically predict the maximum deflection (movement range) and effective force (capability). For heat transfer, the schematic figure of the model is shown in the Figure 3.1.

Figure 3.1: Schematic figure of the heat transfer model

The yellow arrows represent the heat generated in the arms due to the input current, which is given by

𝑄! = 𝐼!𝑅! 𝑄! = 𝐼!𝑅! [1] where 𝑄! and 𝑄! are the heat generated in the hot and cold arm respectively, and 𝐼 is the current that flows through. 𝑅! and 𝑅! are the resistances of the hot and cold arm, which can be calculated by:

𝑅! = 𝜌𝐿!𝑊!𝑡

𝑅! = 𝜌𝐿!𝑊!𝑡

[2]

where 𝜌 is the resistivity of doped poly silicon. The blue arrows represent the thermal conduction within the device structure. 𝑇! and 𝑇! are the temperatures of the hot and cold arm respectively. 𝑇!"# is the temperature of the conduction pad while 𝑇! is the temperature at the via of these two arms. Since the areas related to thermal conduction for the hot and cold arm are different, we should separately evaluate the conduction from the hot to cold arm (i.e. from 𝑇! to 𝑇! and from 𝑇! to 𝑇!). The red arrows represent the thermal convection between the device and the ambient environment with 𝑇! being the ambient temperature. The purple arrows represent the thermal radiation, which is negligible according to subsequent calculations. Therefore, following equations of the model are generated with respect to energy conservation:

𝑄! = 𝑘𝑇! − 𝑇!"#𝐿!/2

𝑊!𝑡 + 𝑄!! + ℎ 𝑇! − 𝑇! 𝐴!

+ 𝜀𝜎𝑇!!𝐴! [3]

𝑄! + 𝑄!" = 𝑘𝑇! − 𝑇!"#𝐿!/2

𝑊!𝑡 + +ℎ 𝑇! − 𝑇! 𝐴!

+ 𝜀𝜎𝑇!!𝐴! [4]

𝑄!! = 𝑄!" = 𝑘𝑇! − 𝑇!𝐿!/2

𝑊!𝑡 = 𝑘𝑇! − 𝑇!𝐿!/2

𝑊!𝑡 [5]

Specifically,𝑄!! and 𝑄!" are respectively the thermal conduction from 𝑇! to 𝑇! and 𝑇! to 𝑇! ; 𝐴! and 𝐴! are the areas related to convection and radiation for the hot arm and the cold arm respectively, which can by given by

𝐴! = 2𝐿! 𝑊! + 𝑡 𝐴! = 2𝐿! 𝑊! + 𝑡 [6] All related parameters for the calibration of heat transfer are shown in the Table 3.1. By plugging in these values correspondingly, the steady state temperatures of both hot and cold arm can be calculated, with the results shown in Table 3.2. It is worth to mention that the calculated temperature difference is 540 𝐾.

Table 3.1. Parameters for the calibration of heat transfer [1]

Parameter Amount Thermal conductivity, 𝑘 125 𝑊/𝑚𝐾

Heat transfer coefficient, ℎ 10 𝑊/𝑚!𝐾

Stefan-Boltzmann constant, 𝜎 5.67×10!! 𝑊/𝑚!𝐾!

Emissivity, 𝜀 0.8 Resistivity, 𝜌 1×10!! Ω ∙𝑚

Ambient temperature, 𝑇! 300 𝐾 Pad temperature, 𝑇!"# 500 𝐾

Hot arm length, 𝐿! 240 𝜇𝑚 Hot arm width, 𝑊! 2.5 𝜇𝑚 Cold arm length, 𝐿! 200 𝜇𝑚 Cold arm width, 𝑊! 16 𝜇𝑚

Thickness, 𝑡 2 𝜇𝑚 Current, 𝐼 3.5 𝑚𝐴

Table 3.2 Results for the calibration of heat transfer

Result Amount Hot arm temperature, 𝑇! 1120 𝐾 Cold arm temperature, 𝑇! 580 𝐾

Temperature difference, Δ𝑇 540 𝐾 With the calculated temperature difference, the consequent deflection and force can be calculated using poly silicon’s thermal expansion coefficient. We consider the bending profile of the heactuator to be an arc, as shown in the Figure 3.2. Regarding to this geometry, we can calculate the maximum deflection 𝛿!"# . With the assumption that the heactuator can be considered as a cantilever beam structurally, as shown in the Figure 3.3, the force that locates at the tip would introduce a deflection given by

𝛿 =𝐹𝐿!!

3𝐸𝐼! [7]

where 𝐼! is the moment of inertia, which can be derived from the geometry of the arm cross-section, given by

𝐼! = 2𝑡 1.5𝑊!

!

12 [8]

Here, 2 indicates that there are two arms, and 1.5 is an effective modulation parameter of the width for the calibration.

Figure 3.2. Schematic figure of deflection model

Figure 3.3. Schematic figure of force model

Parameters for the calibration of deflection and force are shown in the Table 3.3. Results for the calibration are shown in the Table 3.4.

Table 3.3. Parameters for the calibration of deflection

and force Parameter Amount

Temperature difference, Δ𝑇 540 𝐾 Expansion coefficient, 𝛼 2.6×10!! 𝐾!!

Young’s modulus, 𝐸 150 𝐺𝑃𝑎

Table 3.4. Results for the calibration of deflection and force

Result Amount Maximum deflection, 𝛿!"# 13.46 𝜇𝑚 Force, 𝐹 (@𝛿 = 6.73 𝜇𝑚) 3.85 𝜇𝑁

The measured deflection and force are shown in the Table 3.5. According to Table 3.4 and Table 3.5, the theoretical and measured values are almost consistent, which confirms that the heat transfer and deflection model we establish is reliable. However, the theoretical temperature is higher than the measured value according to literature [2]. In the future, we should further improve the accuracy of the model to achieve the theoretical and calibrated temperature consistency.

Table 3.5. Measured deflection and force [1] Measured value Amount

Maximum deflection, 𝛿!"# 16 𝜇𝑚 Force, 𝐹 (@𝛿 = 8 𝜇𝑚) 4.4 𝜇𝑁

After model calibration, it is safe to use this model to calculate the maximum deflection and the generated force of the designed vertical heactuator. For our design, the geometrical parameters of the heactuator are listed in the Table 3.6. Other related parameters are the same as the values in the Table 3.1.

Table 3.6 Parameters for the calculation of the

designed vertical heactuator Parameter Amount

Hot arm length, 𝐿! 150 𝜇𝑚 Hot arm width, 𝑊! 2 𝜇𝑚 Cold arm length, 𝐿! 140 𝜇𝑚 Cold arm width, 𝑊! 16 𝜇𝑚

Thickness, 𝑡 2 𝜇𝑚

The model with detailed calculation procedures is the same with that of the calibration. By calculation, the maximum deflection is 𝛿!"# = 3.27 𝜇𝑚 and the effective force is 𝐹 = 2.61𝜇𝑁 (@ 𝛿 = 1.63 𝜇𝑚 ). Compared with the heactuator for calibration, both deflection and force decrease due to the decrease of the arm length. However, we can find that the order of magnitude of the maximum deflection and force are the same for both the lateral and vertical heactuators, which confirms that both the calibration and our calculated results are reliable. In current industrial applications (i.e. cameras in cell phones), the required lens moving range would require a deflection of approximately 0.1~1 𝑚𝑚with the required force 1~10 𝑚𝑁 for heactuators. However, the maximum deflection of heactuators used in our design is around 1~10 𝜇𝑚 while the maximum force 1~10 𝜇𝑁. Although heactuator array can be applied to increase the force generated, the consequent deflection would stay the same. As a result, this 5-axis AO and OIS lens cannot be commercialized currently. However, it can still be used in the cameras of micron-scale. In addition, the driving capability of the parallel-plate capacitor is assessed. The maximum deflection is calculated to be 10 𝜇𝑚 with the generated force to be around 0.1 𝜇𝑁, which are far from enough to drive the lens. Although capacitors array can be used to increase both generated force and deflection, a large number of capacitors would be required, which cannot be fit in a normal camera lens. Scanning Mirror Since both the working frequency and deflection of the heactuator have upper limits, multiple scanning mirrors would be required for a complete screen scan. For more straightforward analysis and easier manufacturing, if possible, the mirrors are arranged in a rectangular array. Specifically, the number of scanning mirrors required for a complete scan is calculated under the two cases below using the corresponding measured data [1]: Case I: Heactuators work under 8𝜇𝑚 maximum tip deflection and 300 𝐻𝑧 working frequency. Case II: Heactuators work under 1.75 𝜇𝑚 maximum tip deflection and 1000 𝐻𝑧 working frequency. For calculation sake, we assume that the screen to be projected is 15.4’’ with a 2880×1800 pixel resolution. To calculate the number of scanning mirrors required for a complete lateral scan, following resonance model whose schematics is shown in Figure 3.4 is established.

Figure 3.4. Schematic figure of resonance model

Related parameters are introduced in Table 3.7 and Table 3.8.

Table 3.7. Parameters for mirror motion calculations Parameter used Amount Mirror radius 𝑟 = 190 𝜇𝑚

Projection distance 𝑙 = 16 𝑐𝑚 Maximum deflection (Case I) 𝛿 = 8 𝜇𝑚 Maximum deflection (Case II) 𝛿 = 1.75 𝜇𝑚

Table 3.8. Results for mirror motion calculations Calculated parameter Amount

Maximum rotation (Case I) 𝜃 = 2.41 𝜇𝑚 Screen range (Case I) ∆𝑥 = 2.68 𝑐𝑚

Maximum rotation (Case II) 𝜃 = 0.528 𝜇𝑚 Screen range (Case II) ∆𝑥 = 0.590 𝑐𝑚

As shown by Figure 3.5, a rotation of the scanning mirror 𝜃 leads to a reflection and direction change of the input laser light, which generates a projection range ∆𝑥 on the screen given a projection distance 𝑙 . Thus, given the width of the screen, the numbers of scanning mirrors required for a complete lateral scan for Case I and Case II are calculated to be 13 and 56 respectively. To calculate the number of scanning mirrors for a complete vertical scan, we establish a governing equation [9] based on the fact that the pico projector scans the screen pixels rows by rows while 2 rows can be scanned within one heactuator resonance cycle:

2×𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦= 𝐹𝑟𝑎𝑚𝑒 𝑅𝑎𝑡𝑒×𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑖𝑥𝑒𝑙 𝑅𝑜𝑤𝑠

[9]

Since the optimal frame rate is 60 𝐻𝑧 for human beings, given the working frequencies of the 2 cases, the numbers of scanning mirrors required for vertical scan for Case I and Case II are calculated to be 180 and 55 respectively. Based on the calculation results, a 13 𝑐𝑚×1 𝑐𝑚 size pico projector made up of 2340 scanning mirrors would be made for Case I while a 4 𝑐𝑚×4 𝑐𝑚, 3080 for Case II. In real life applications, Case II would be more preferable due to its more reasonable shape.

It is important to point out that the scanning mirrors can function as expected since the force generated by one single heactuator would be more than enough to support and drive the central gold mirror. Other than pico projector, scanning mirrors can also be used in gesture recognition, eyewear display and other industrial scanning applications.

IV. Fabrication Process Since the 5-axis AF and OIS lens and the mirror of scanning mirror have similar structures while the former one has more complicated structures with an extra array of parallel-plate capacitors, its fabrication process will be discussed in details below. The structures of MEMS 5-axis AF and OIS lens are fabricated with a nine-mask process. The CAD layout of masks is shown in Figure 4.1. Three structural layers of poly silicon are used, two for arms of heactuators and one for capacitors. It is worth to mention that an additional layer of silicon nitride is required to hold the lens while providing electrical insulation between heactuators and capacitors. The process begins with a low stress silicon nitride deposition (Nitride-1) by LPCVD for insulation from the substrate. Then a layer of PSG (Oxide-1) is deposited on the wafer by LPCVD with the anchors (Anchor-1) being defined by wet etching. The next steps would involve deposition and definition of the first 2 𝜇𝑚-thick poly silicon layer (Poly-1) by LPCVD and wet etching respectively, which are used to form the structural layer of hot arm. Then a PSG layer (Oxide-2) is deposited on the wafer as a sacrificial layer, and another mask is used for wet etching to define the heactuator via (Anchor-2). The second 2 𝜇𝑚-thick poly silicon (Poly-2) structural layer is then deposited by LPCVD. Wet etching is used to define the cold arm. Then an additional silicon nitride layer (Nitride-2) is directly deposited and etched on the poly silicon, which forms the plate contacted with the cold arm. A sacrificial layer of PSG (Oxide-3) is then formed on the wafer by LPCVD; two masks are used in the subsequent wet etching step, one for the anchor of capacitors (Anchor-2) and another for the Poly-2 to Poly-3 via (Anchor-3) for electrical connection. The third 2 𝜇𝑚 -thick poly silicon (Poly-3) layer is deposited and etched to define the capacitors. And then, a metal layer (METAL) was deposited and etched to form the contact for pads. A stress-annealing step is optionally performed. After removing all the PSG layers, the fabrication process is completed. However, we should assemble lens on the silicon nitride holder manually. For scanning mirrors, since the lateral heactuators are rotated to achieve vertical movement while arms of the heactuator have different thicknesses, the technology that creates double thickness poly silicon layers might be used.

Figure 4.1. CAD layout of masks

V. Conclusion Two devices, scanning mirror and 5-axis AF and OIS lens are designed. For scanning mirror, a resonance model of the heactuator used is established to calculate the number of mirrors required for a complete scan. According to the analysis, a preferred design requires 3080 mirrors and is 4 𝑐𝑚×4 𝑐𝑚 in size, and it is proved to be able to function normally in real applications. For 5-axis AF and OIS lens, a heat transfer and deflection model of heactuator used is established and calibrated by a typical heactuator with measurement from previous literature [1]. Although the model overestimates the temperature of each arm, the theoretical values of deflection and force are consistent with the measured values. This model is also used to analyze our designed vertical heactuator. The orders of magnitude of deflection and force are the same as the lateral heactuator. Besides, according to the results shown by calculation, the vertical and lateral heactuators have comparable performance. However, in terms of maximum deflection and effective force, both the heactuator and the capacitor cannot meet the requirement of the real camera. At the end, the fabrication process of 5-axis AF and OIS lens is discussed. Nine layers with three structural layers of poly silicon and nine masks are needed. Besides, an additional silicon nitride layer is needed for electrical conduction and insulation. VI. References

1. Comtois, J., and Victor Bright. "Surface micromachined polysilicon thermal actuator arrays and applications." Proc. Solid-State Sensor and Actuator Workshop. 1996.

2. Phinney, Leslie M., et al. "Thermomechanical Measurements on Thermal Microactuators."