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Berkeley ELENG C245 - A High Resolution Actuator Design For Laser Beam Steering Applications

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1A High Resolution Actuator Design For Laser Beam Steering Applications Baris Cagdaser and Vladimir Petkov Department of Electrical Engineering and Computer Science University of California, Berkeley, CA 94720-1772 E-mail: [email protected] [email protected] ABSTRACT An actuator design for beam steering micro-mirrors is reported. Coarse positioning is achieved with a 4-bit mechanical digital to analog converter [1]. The exact position is sensed by a set of lateral comb fingers and controlled through the least-significant bit of the DAC, which is embedded in a feedback loop. The actuator is designed for bilateral actuation of +/- 3µm with a resolution of 6nm providing a maximum force of 1mN. The voltage of operation is 30V. A single-mask SOI process with minimum feature size of 2µm is used. I.INTRODUCTION Micromirrors used for precision beam steering place specific force, displacement and resolution requirements on the actuators. A large force over a long displacement must be supplied for providing large angles of rotation. A single actuator working under those conditions would require an inconveniently high driving voltage. As an alternative several actuators operating on a system of levers can be used to obtain quantized displacements. Lower operation voltages are achieved through force multiplication. Such a system, called a mechanical digital-to-analog converter (DAC), has been reported in [1], [2] and [3]. Limitations due to various sources such as spring non-linearity, beam bending and processing tolerances restrict the accuracy to several hundred nanometers. In this work a feedback loop around the LSB of the MEMDAC is designed for canceling displacement errors. An overall block diagram is given in Fig.1. This approach uses the DAC actuators A1 to A3 for rough quantization of the displacement and the analog feedback loop for precise adjustment around each digital level. The force generated by the comb drive of the LSB (actuator A4) is amplified by the mechanical structure of the DAC, resulting in low operation voltage for the analog part. For this particular application, a maximum force of 1mN and a bi-directional motion of +/- 3µm are required. Steering accuracy of 1mrad sets a 6 nm resolution goal for the actuation. II. MECHANICAL DESIGN DAC Design A lever driven from either end can be used as a mechanical summing node. A previous design [1] uses cascaded lever arms for building a mechanical DAC whose operation is similar to an electrical R-2R digital-to-analog converter. As shown in Fig.2, the output displacement is equal to the average of the two displacements. Since the lever arm is a passive device, the forces must be amplified by two according to the principle of energy conservation. Consequently, in a network of lever arms, the force and displacement created at the output by the Nth bit are: )N(N)N(OUTF2F = N)N(IN)N(OUT2XX∆∆ = As described in [2], lever networks may have substantial nonlinearity and gain errors. One of the major contributors to the position error is the mismatch of gap spacing. The required accuracy of 6nm cannot be achieved through precise gap stop positioning due to general processing limitations. Another main error source is the finite stiffness of the coupling beams, the levers and the actuators. When one end of the lever is actuated, the lever pivots around the other end and applies2moment to the beams. Assuming small angular displacements, the amount of rotation is LxIN∆ . As the tips of the beams bend more, they become more compliant in the direction in which they provide coupling. Increasing the lever arm length was shown to decrease the conversion error until the lever arm itself starts bending [2]. Due to thicker device layers in the SOI process, longer lever arms can be used without significant bending. In the current design a displacement of 3 µm at the tip of a 1000 µm lever results in a 3 mrad (~0.172 deg) rotation. Support beams suspend the levers at the end which is coupled to the next stage. A 2 µm x 400 µm beam bends less than 1 nm under the gravitational force acting on the lever. Longer support beams are preferred for reducing the loading on latter stages. The ends of the coupling beams are thinned to allow the levers to pivot when the actuator is activated. Actuator Design The first three bits are digitally activated - they are either at +3 µm or –3 µm positions. A parallel plate gap-closing actuator is suitable for these stages. The final position of the rotor is determined by gap stops preventing the plates which are at different potentials from touching each other. Cascaded levers allow the higher force density of parallel plate actuators to be utilized without implementing a complicated electronic controller for stabilization beyond pull-in. However, as mentioned above, gap stops cannot be located with the desired accuracy. In other words, improving the mechanical design of the lever system is not sufficient for achieving the pointing accuracy of the mirror. In order to solve this problem, an analog actuator is employed for controlling the fine positioning. Since the analog actuation is in the LSB, the actuator must provide a displacement of +/- errorNx∆*2 in addition to the +/- 3 µm. Shuttles carrying the fingers of the gap closing actuators are supported by beams spanned parallel to the nominal lever orientation. This prevents the shuttle from rotating at the same angle as the lever. Even a small rotation of 3 mrad would bring the tips of the actuator fingers 3mrad*Lfinger closer to the stator fingers. For a 100 µm finger this corresponds to 0.3 µm (30 % of the final gap), which may cause pull-in instability. FEM simulation in ANSYS 5.7 was used to verify this approach. The MSB lever experiences the largest structural deflection, since it is directly subjected to the mirror loading and the largest actuation force. Bending of the lever and the beams makes the output displacement smaller than the ideal case shown in Fig. 2. The worst case for the MSB lever occurs when both ends are actuated in the same direction. The torque arm connecting the mirror to the actuator bends the center of the lever in a direction opposite to the motion at the ends. The lever width can be increased for increasing the lever stiffness in the direction of bending. FEM simulations were used to investigate the worst case (3 µm displacement at the


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Berkeley ELENG C245 - A High Resolution Actuator Design For Laser Beam Steering Applications

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