Planar MEMS Van de Graaff Generator EE245 Project, Fall 2001 Angel V. Peterchev Department of Electrical Engineering and Computer Science University of California, Berkeley Abstract— This paper discusses a MEMS implementation of a planar Van de Graaff generator in a standard MUMPs process. The ability to generate high voltages in autonomous MEMS devices may be useful in various applications such as Smart Dust [1]. I. INTRODUCTION EMS power conversion has been the subject of recent Å interest. References [2], [3], and [4] address power con- version based on capacitively driven spring-mass structures. Reference [2] uses the resonance of such structures to achieve voltage conversion, while [3] and [4] develop vibration-to- electric power conversion. This paper discusses MEMS power conversion based on mechanical transport of charge analogous to the macro-scale Van de Graaff generator (Fig. 1). The me- chanical energy need to achieve the conversion can be supplied by various sources like electrical actuators, micro-combustion engines, vibrations, etc. In a Van de Graaff generator a belt consisting of insulated conductive tiles is positively charged by a voltage source and the charge is delivered to and deposited in a hollow metal sphere (a “dome”) [5]. There, the conductive tiles are charged by another voltage source with a negative charge of the same magnitude as the one they delivered up, and then travel back to ground. As a result positive charge accumulates on the dome yielding potentially very high voltages. II. DESIGN A. Topology and Analysis of Planar Van de Graaff Generator Fig. 2 shows a possible topology for a planar Van de Graaff Fig. 1. Diagram of a macro-scale Van de Graaff generator. C generator. A large capacitor × is used to implement the dome of the generator. Indeed, a parallel-plate capacitor is the 2-D returns to ground. The opeartion of the planar Van de Graaff equivalent of the 3-D spherical dome: for a charged conducting generator is thus exactly analogous to its 3-D counterpart. The E sphere all the electric field ( × ) is on the outside of the sphere, mechanical work done to move the shuttle back and forth over while for a parallel-plate capacitor the electric field is confined a cycle is ideally (ignoring friction, etc.) between the two plates [6]. Thus depositing a charge on the in- =¾Õ ´Î Î µ; side of the conducting sphere is analogous to depositing charge Ï × Ó c Ñech (1) on the top plate of a parallel-plate capacitor. C = C Î = Î Õ d c d × The belt of the Van de Graaff generator is implemented with where we assumed c and , and is the mag- a movable capacitor plate (shuttle). In the beginning of a charg- nitude of the charge of the shuttle. ing cycle the shuttle forms a capacitor with a grounded plate The planar Van de Graaff generator is governed by the dif- ference equation Î and is charged by voltage source c . The shuttle is then moved C C · C C C to connect with the top plate of × . There it forms a capacitor c Ô d Ô ¡Î [Ò]= Î · Î Î [Ò]; Ó d Ó c (2) C Î d d and is charged with negative charge from , which it then C C C × × × Cp TABLE I Vo high voltage mechanical MUMPS PROCESS SUMMARY terminal work Material Layer Thickness (m) Symbol Cs Cd Cc Substrate SUB Ø ¼:6 Nitride ÆÁÌ NIT Ø ¼:5 ¼ Es Vc Poly 0 È P0 Ø ¾:¼ ½ First Oxide ÇX OX1 Ø ¼:75 Dimple DÁ Å È DIMP Ø ¾:¼ ½ Poly 1 È P1 Ø ¼:75 ¾ Vd Second Oxide ÇX OX2 Ø ½:5 ¾ Poly 2 È P2 Ø ¼:5 Metal Å M discharging charging storage capacitor capacitor capacitor TABLE II PARAMETER SIZING Fig. 2. Principle of planar Van de Graaff generator. Constants where Ò is a discrete time index corresponding to the number ½¾ ¯ 8:9 ¢ ½¼ ¼ permittivity of air F/m C of charging cycles completed, and Ô is parasitic capacitance ¯ 4:4¯ ¼ ËiÇ permittivity of the oxides (*) ¾ ¯ 4:¾¯ Æ ¼ Ëi permittivity of the nitride (*) 4 between the shuttle and ground. Under the assumption that we ¿ want to operate the topology in Fig. 2 as a Van de Graaff (high Sizing Î = Î C = C Î Î Î ;Î ½5 c d c d Ó c c voltage) generator, we have , , , and d charging voltages V ¾ A ¾¼¼ ¢ ¾¼¼ ×h shuttle area m C C C c Ô × . Then (2) becomes C ;C ¼:5 c d shuttle capacitance pF C ¼:¼5 Ô parasitic shuttle capacitance pF C ¾C ¾ Ô c A 6¼¼ ¢ 6¼¼ C storage cap area m × Î Î [Ò]: ¡Î [Ò] c Ó Ó (3) 6¼ C × storage capacitor pF C C × × (*) From [9] C 6= ¼ It can be seen that Ô has a detrimental effect on the charge pumping, and the output voltage cannot be increased Î =¾Î C =C ;ÑaÜ c c Ô beyond ¼ . Therefore, in a practical design C it is desirable to keep Ô low. the topology on Fig. 2. Further, a metal layer is desirable for C = ¼ Another interesting case corresponds to d , which is the implementation of low-resistance contacts for the shuttle. C analogous to a Van de Graaff generator without a discharging C d Fig. 3 shows the layout of the shuttle, capacitor c and voltage source in its dome. Then we have bottom plates, and the contacts for the shuttle. The shuttle is made of a Poly 1 plate, reinforced with Poly 2. Its sizing and C C c Ô ¡Î [Ò] Î Î [Ò]; c Ó Ó (4) the resulting capacitances are shown in Table II. The size of the C C × × C C Ô shuttle was determined by requiring that c due to the C which is comparable to (4), and does not require a floating volt- discussion in Section II-A. The main contribution to Ô comes age source attached to the high voltage terminal. The problem, from the capacitance between the shuttle rails and ground. The however, is that in a planar implementation of such a scheme it rails were shrunk down to the design rule limit of the process, C C C c Ô will be very hard to keep Ô small. To keep small the mov- so that can be minimized which results in small charges C able top plate of c has to be kept away from ground when being transported and thus low currents in the mechanical con- C charging × , which is easy in a 3-D Van de Graaff generator tacts. Poly 2 and Metal (gold) implement the contacts needed Î Î Ó (the dome is high above ground), but difficult in the planar ver- to connect the shuttle sequentially to c and . The contacts sion. are modeled after [8]. The need of dynamically switched me- chanical contacts in this topology can be a major disadvantage B. MEMS implementation for practical applications. Nevertheless, other topologies that A planar Van de Graaff generator prototype was designed in use semiconductor switching may benefit from the principles the standard MUMPs process. The MUMPs process [7] is a discussed here. surface micromachining process with three structural polysili- In the present design the shuttle is not connected to any con layers, two sacrificial oxide layers, and a metal (gold) top source of mechanical energy, since this implementation is in- layer. The MUMPs layers are summarized in Table I. This tended as a proof-of-concept. In practice the shuttle may be process was chosen since it is accessible and the availablility connected to devices which generate substantial linear dis- of multiple poly layers allows for a direct implementation of placements such as inchworm motors [10]. One problem is TABLE III TEST STRUCTURE DESIGN PARAMETERS contacts (P2+M) Constants E ½55 È Young’s modulus for poly GPa Spring Ø ¾ b beam thickness m Ä 6¼ Cd (P0) ¼ single beam length m ½=½¾ « mult. for comb. of beams ¼:96 à spring constant N/m Comb Actuator ¾ g gap between fingers m ¾4 shuttle (P1+P2) ¬ mult. for comb. of fingers ¡Ü ½¼ displacement of comb < m Ú ¼:¾5 ¡ vernier resolution m rails capacitance. Continuous vias between the layers on the sides ensure that the capacitor is “sealed” and as a result the release etch will not affect the oxide between the plates which helps Cc (P0) achieve high capacitance. III. TEST STRUCTURES AND EXPECTED RESULTS The deflection of a simple spring-comb [11] structure can be contacts (P2+M) used to measure the output voltage of the Van de Graaff gen- erator. Layout of the test structure is shown in Fig. 5, and the design parameters are summarized in Table III. The structure C C further deploys a vernier scale to measure the displacement of c Fig. 3. Layout of shuttle, capacitor and d bottom plates, and contacts for the shuttle. the comb. The design was based on the following equations from basic beam and capacitor theory, M P2 ¿ Ø Ø OX2 E È ½ È b = « à (5) P1 ¿ Ä OX1 ¼ ½ Ø · Ø È ½ È ¾ P0 ¾ F = ¬ ¯ Î ¼ (6) ¼ g NIT ¾ Ü = F=à SUB ¡ (7) Fig. 4. Implementation of a large capacitor in MUMPs. aiming at a reasonable aspect ratio and small size. The expected output voltage as a function of the number of providing electrical insulation between the motor and the shut- charging cycles, and the deflection of the comb actuator as a tle (to prevent charge leakage) since the MUMPs structural lay- function of the output voltage are given in Fig. 6. The plots ers (poly) are conductive. Some hydrid process may have to be are based on equations (5–7) and the design values in Table II used to provide the shuttle insulation.