Photovoltaic on-demand high voltage pulse generator as an on-board
power source for electrostatic actuator array
Jeong B. Lee a, Mark G. Allen b, and Ajeet Rohatgi b
a
Department of Electrical and Computer Engineering
Louisiana State University
Baton Rouge, Louisiana 70803-5901
b
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, Georgia 30332-0250
ABSTRACT
The use of amorphous silicon solar cell array high voltage power source as an on-demand wireless power source for
electrostatically actuated 32x32 micromirror array is presented. The amorphous silicon solar cell array has been reported
previously by authors of this paper1-4. In this work, the solar cell array has been used to drive distributed electrostatic
actuator array (micromirror array in this particular paper). A 32x32 micromirror array has been fabricated and the size of
single micromirror is 200 m x 200 m. Static deflection test of micromirrors has been carried out and pull-in voltage of 44
V and releasing voltage of 30V was found. The electrical output of the solar cell array has been directly connected to the
32x32 micromirror array to demonstrate a wireless powered distributed MEMS actuator array. A total solar cell array area of
0.3 cm2 (30 series-interconnected solar cells) were used to drive a part of 32x32 micromirror array (a total array area of 0.4
cm2). Motion of multiple numbers of micromirrors was reproducibly observed. The ultimate goal of this research is to
achieve power-integrated autonomous MEMS using solar cell array as a miniaturized wireless on-board power source and
distributed actuator array as a locomotive engine.
Keywords: Photovoltaic (PV), amorphous silicon, solar cell array, micromirror array, autonomous MEMS, wireless power
1. INTRODUCTION
Regardless of which transducer driving principles are employed, the power requirements of MEMS devices can be quite
different from those of general electrical circuitry, therefore requiring either an external power source or additional power
conversion circuitry. For autonomous MEMS systems, such as microrobots and space-based MEMS, self-contained onboard or remote (i.e., wireless) power sources are desirable. Though the importance of the problem, work focusing either on
wireless or on-board power sources for MEMS devices/systems or power-integrated MEMS systems are rare. One of the
previous works in this area is a series-interconnected array of 100 single solar cells (amorphous silicon solar cells) reported
by the authors of this paper1-4. In the previous work, we reported a series interconnected array of 100 single amorphous
silicon solar cells in an array area of 1 cm2 in an integrated fashion, and produces an array open circuit voltage of 150 V with
a short circuit current of 2.8 A. Another very promising work in wireless transmission of energy is from Sasaya et al5.
They reported an in-pipe wireless micro robot based on wireless energy supply by TE 11 mode of microwave.
In this paper, the use of solar cell array high voltage power source as an on-demand wireless power source for distributed
electrostatic MEMS actuator array (in particular, a 32x32 electrostatically-actuated micromirror array) is presented. This
paper consists of a brief reintroduction of solar cell array and discussion of ultimate goal of the research, design issues and
fabrication of 32x32 micromirror array, characterization and modeling of micromirrors, and demonstration of powerintegrated MEMS which combines photovoltaic (PV) wireless on-demand power source and the 32x32 micromirror array as
an example of a distributed actuator array.
Corresspondence: J. B. Lee; Email: jblee@ee.lsu.edu; Telephone: 225-388-5621; Fax: 225-388-5200; Homepage:
http://www.ee.lsu.edu/jblee.
2. PHOTOVOLTAIC TECHNOLOGY AS A WIRELESS POWER SOURCE FOR
ELECTROSTATIC/PIEZOELECTRIC AUTONOMOUS MEMS SYSTEMS
The power requirements of MEMS devices depend mainly on the driving principles involved. Several driving principles that
are suitable in the micro-domain are used to drive MEMS devices. The most common driving principles include electrostatic
drive, piezoelectric drive, electromagnetic drive, and electrothermal drive. Typical power requirements for each driving
principle are shown in Table 1 below. Regardless of which transducer driving principles are employed, the power
requirements of MEMS devices can be quite different from those of general electrical circuitry, therefore requiring either an
external power source or additional power conversion circuitry. Of the common driving principles, electrostatically- and
piezoelectrically-driven MEMS devices need relatively high voltage ranging from tens of volts to hundreds of volts with the
current in the range of nA~A. In many cases of laboratory-level experiments, external high voltage power source is
commonly used for powering electrostatically- and piezoelectrically-driven MEMS devices (see Figure 1).
Table 1. Typical power requirements of MEMS devices.
Driving principles
Electrostatic
Piezoelectric
Electromagnetic
Electrothermal
Power requirements
tens of volts ~ hundreds of volts / nA ~ A
tens of volts ~ hundreds of volts (AC) / A
Less than 1 V / hundreds of mAs
5 V ~ tens of volts / a few mA ~ tens of mAs
Power Supply
MEMS devices
dimensions in
mm ~ m
Figure 1. Schematic representation of common methods of powering MEMS.
Previous investigations1-4 from authors of this paper proposed a series-interconnected array of 100 single solar cells
(amorphous silicon solar cells) in a total array area of 1 cm 2 as a wireless power source for MEMS. The solar cell array was
fabricated in an integrated fashion to produce an array open circuit voltage (V oc) of 150 V, and an array short circuit current
(Isc) of 2.8 A under air mass (AM) 1.5 conditions. Such a high voltage output in miniaturized size has strong potential to be
used as wireless power sources for autonomous MEMS systems. The ultimate goal of the research is to realize a constant
high voltage PV power source (100 V or higher) with on-demand high voltage MOS (metal oxide semiconductor) switching
circuitry which is controllable by on-demand external electrical signals (3.3 V or 5 V level). Figure 2 shows a schematic
diagram of an on-demand high voltage switching circuitry with constant high voltage PV power source, which uses a
combination of high voltage PV power source and high voltage MOS switching circuitry. When high voltage MOS switch is
turned on output voltage would be low (near 0 V) and when high voltage MOS switch is turned off high voltage (~100 V)
would be delivered to individual MEMS devices.
PV array
SW cicruit
array
PV
array
power
source
High
voltage
MOS
Switch
ing
circuit
array
DeMUX
Distributed actuator array
(a)
(b)
Figure 2. (a) A schematic diagram of power-integrated autonomous MEMS; (b) a schematic block diagram of the power module.
As an initial step of the realization of such a power integrated autonomous MEMS, a simple optically modulated ondemand PV power source has been used to actuate multiple numbers of actuator array using electrostatically-driven
micromirror array that is described in the following section.
3. A 32x32 MICROMIRROR ARRAY
A 32 by 32 micromirror array built in this work is similar to Texas Instruments Digital Mirror Device (DMD)6, but has
several different approaches with the goal of enabling low cost manufacturing. The micromirror arrays have been built on
low cost substrates, such as glass, instead of relatively expensive CMOS-processed underlying circuitry. Such an approach
allows the realization of relatively low cost, passive micromirror array elements. Approaches taken in this work for the
fabrication of micromachined mirror arrays include a line addressing scheme 7, a seamless array design for high fill factor,
planarization techniques of polymeric interlayers8, a high yield methodology for the removal of sacrificial polymeric
interlayers, and low temperature and chemically safe fabrication techniques.
3.1. Design
Figure 3 shows a schematic drawing of a single micromirror. The square-shaped micromirror is suspended at its center by
thin and narrow hinges, which are supported at their ends by electroplated nickel posts. A higher fill factor results in higher
perceived resolution, yielding more natural images. The micromirror designed in this work has the size of 190 m on a side
and the width of the hinge is 4 m. The pixel pitch size is 200 m. The fill factor for this micromirror is 83.75 % (33,500
m2 / 40,000 m2). The thickness of the organic sacrificial layer (i.e., the air gap for micromirror actuation) ranges from 18
m to 24 m, resulting in deflection angle ranges from 10.7 to 14.2.
Figure 3. A schematic diagram of a micromachined mirror.
3.2. Finite element modeling for resonant frequencies
Finite element modeling (FEM) of the micromirror was performed using the finite element modeling package ANSYS 5.2 to
calculate resonant frequencies and mode shapes. The geometrical parameters used in the FEM are as shown in Table 2. The
element type used has eight nodes with six degrees of freedom (DOF) at each node: displacements in nodal x, y, and z
directions and rotations about nodal x, y, and z-axes. Since the hinge is the area of interest for torsional behavior of the
micromirror, hinges and adjacent areas were densely meshed while most of the plate was coarsely meshed.
Table 2. Parameters used in FEM for resonant frequencies of the micromirror.
Young’s modulus of Al
Poisson ratio of Al
Density of Al
70 GPa
0.33
2710 kg/m3
Figure 4 (a), (b), and (c) show the first three mode shapes. Resonant frequency data for the first six modes are shown in
Table 3. The fundamental mode resonant frequency is 6.5 kHz which is the determining factor for the switching speed of the
micromirror. Since this micromirror array uses a line addressing scheme, the minimum time field for one frame is 4.96 ms
(153 s * 32 = 4.9 ms). If the micromirror array works as a black & white display (no gray scale), then the maximum frame
rate would be as high as 204 Hz (1/4.9 ms).
(a)
(b)
(c)
Figure 4. Resonant mode shapes of the micromirror: (a) fundamental mode; (b) second mode; (s) third mode.
Table 3. Finite element modeling results for modal analysis of the micromirror.
Mode
1
2
3
4
5
6
Natural Frequency [Hz]
6531
15876
19529
41351
80003
83985
3.3. Fabrication of micromirror array
A brief fabrication procedure is shown in Figure 5. Fabrication of micromirror arrays started with 3 inch by 2 inch glass
substrates. Evaporated Ti/Au (thickness of 300 / 4,000 Å) row addressing lines were patterned using the liftoff process. A
BCB layer was spin-coated to planarize the patterned metallic lines. A silicon dioxide (SiO 2) passivation layer was deposited
using PECVD to protect the BCB layer during the very last step of dry etching for bonding pad opening. Evaporated Ti/Au
(300 / 4,000 Å) column addressing lines (also serving as an electroplating seed layer for posts) were patterned using the
liftoff process. Two different organic interlayers, both single and double coats of PI 2611, were spin coated as polymeric
sacrificial layers. In the case of a single coat of PI 2611, the coated layer was soft baked at 150 C for 30 minutes. The
thickness of the soft-baked single coat of PI 2611 layer was approximately 18 m. In the case of a double coat of PI 2611,
samples were soft baked after each spin at 120 C for 20 minutes and hard baked at 300 C for one hour in nitrogen ambient
after the second coat. The double-coated PI 2611 thickness was approximately 24 m.
A 1,000 Å aluminum hard mask was prepared for via cutting by the liftoff process. Reactive ion etching (incident power
of 300 W, pressure of 300 mTorr or less, oxygen gas flow rate of 50 sccm) was used to define 10 m by 10 m square via
holes. Etch rate was about 0.25 m/min. for hard cured PI 2611, and 0.6 m/min. for soft cured PI 2611. After via cut, the
aluminum hard mask was removed by diluted hydrofluoric acid (HF) which was followed by nickel (Ni) electroplating.
After the Ni electroplating, the surface of the polyimide electroplating mold and plated Ni had roughness of about less than 1
m. A 7,000 Å aluminum layer was then deposited using DC sputtering and patterned to form hinge and micromirror plate
structures. Finally, the organic sacrificial layer was etched away by an isotropic dry etch using a barrel plasma etcher. Figure
6 show SEM photomicrographs of a side view of the corner of the completely released 32 by 32 micromirror array and a
closeup view of the electroplated nickel post and the Ti/Au seed layer. The organic interlayer was safely and completely
removed and left overhanging micromirror array structures. The gap between micromirror plates and the planarization BCB
layer is 18 m, which allows 10.8° angular deflection. Figure 7 show SEM photomicrographs of top views of a part of
micromirror array and a single micromirror after the completion of organic interlayer etch.
(a) Surface planarization / Metallic row addressing
substrate
(b) BCB/SiO2 interlayer planarization
(c) Metallic column addressing
(d) Metal protection / Organic sacrificial layer / Via cut / Ni plating
(e) Plated surface polishing / Hinge and mirror plate formation
(f) Dry etch sacrificial organic layer
Figure 5. Fabrication procedures for micromachined mirror actuators on low cost substrates.
hinge
plated nickel post
Ti/Au seed layer
Figure 6. SEM photomicrographs of completely released 32 by 32 micromirror array.
hinge
plated nickel posts
Figure 7. SEM photomicrographs of top views of a part of the micromirror array after the completion of organic interlayer etch.
3.4. Micromirror actuation and static deflection modeling
The completely released micromirror array was placed on an optical microscope and the gap between the micromirror and
planarized BCB/SiO2 layer was measured to be 18 m. The deflection of the tip of the micromirror was measured by
focusing on the tip of the micromirror using a Nikon MM-11 Measurescope and measuring the deflection of the microscope
head necessary to keep the deflecting tip in focus. The displacement characteristic (deflection versus applied voltage) is
shown in Figure 8 (a). The measured pull-in voltage (Vp) is 44 V, and the releasing voltage (Vr) is approximately 30V.
10
20
30
40
0
50
2
0
0
Angluar deflection [°]
Angluar deflection [°]
0
2
-2
-4
-6
Attraction
-8
Release
10
20
30
40
50
-2
-4
-6
-8
-10
-10
-12
-12
Measurement
Theory
Applied Voltage [V]
Applied Voltage [V]
(a)
(b)
Figure 8. Displacement characteristic of the micromirror.
Theoretical modeling for the static deflection of the micromirror was performed with several assumptions and those
results are compared with the measurement results. Figure 9 shows the schematic drawing of a cross section of a micromirror
used for the theoretical modeling. When an external voltage is applied between the grounded micromirror and the address
electrode, a potential energy W is stored in the system. The electrostatic force which acts normal to the substrate is complex
since there is a fringing effect, and the direction of the electrostatic force changes as the micromirror rotates. Simple
theoretical models, however, may be established with following assumptions: (1) the hinge is straight, of uniform rectangular
cross section, and of homogeneous isotropic material; (2) the hinge is loaded only by equal and opposite twisting couples,
which are applied at its ends in planes normal to its axis; (3) the hinge is not stressed beyond the elastic limit; (4) the fringing
electric field is negligible. In reality, the fringing effect should not be neglected, but this assumption was made for this
simple theoretical model. Figure 9 and Table 4 shows the material properties and geometrical parameters used in the
theoretical modeling.
Table 4. Material properties and geometrical parameters used in theoretical modeling.
Material Properties
Young’s modulus of Al
70 GPa
Poisson ratio of Al
0.33
Shear modulus of Al
26.3 GPa
Density of Al
2710 kg/m3
Relative permittivity of BCB
Relative permittivity of SiO2
The mechanical torque Tm is defined as follows:
2.7
3.9
Geometrical Parameters
Z0
18 m
Z1
2.5 m
Z2
0.5 m
t
0.7 m
w
4 m
a
190 m
b
190 m
L
60 m
Tm  k 
GIp
,
L
(1)
where k is the torsional spring constant,  is the deflected angle in radians, G is the shear modulus of elasticity, Ip is the polar
moment of inertia, and L is the length of the hinge. The shear modulus of elasticity G is defined as follows:
G
where E is the Young’s modulus, and  is the Poisson ratio.
E
,
21   
(2)
a
L
t
b
w
(a)
Micromirror
b/2

x
O
dx
z
BCB
Z0
Z1
Z2
SiO2
Substrate
V
(b)
Figure 9. A schematic drawing of a single micromirror: (a) top view and a closeup of the hinge; (b) cross section of a micromirror.
When the aspect ratio (thickness/width) is lower than 1 (1 = square cross section), a theoretical expression for the polar
moment of inertia (Ip) is given9 as follows:
3
t4 
 w   t  16
 t 
I p        3.36   1 
 .
 2   2  3
 w   12 w 4  
(3)
At the maximum deflection (=10.8=0.1885 rad), the mechanical torque Tm turned out to be 3.3622*10-11 [N-m] based
on equation (3). The electrostatic torque Tel can be represented as the following expression:
Tel 
Wel V 2   b / 2 
 dC ,


2   0 
(4)
where Wel is the electrostatic energy stored in the system, V is the applied voltage, C is the capacitance of the system. Since
the rotation angle for this micromirror is small (between 0 and 10.8), the tangent of  could be assumed equal to . The
maximum error due to this assumption is 1.2 %. The analytical solution for the electrostatic torque Tel is calculated using
Mathematica. The Taylor expansion of the analytical solution about =0 is:
Tel 

ab 2  r21 r22  0V 2
16 r 1 r 2 z0   r 2 z1   r 1 z2 
3ab 4  r41 r42  0V 2
128 r 1 r 2 z0   r 2 z1   r 1 z 2 
2

4
24 r 1 r 2 z 0   r 2 z1   r 1 z 2 
 
2
ab 3 r31 r32  0V 2
3

(5)
ab 5 r51 r52  0V 2
80 r 1 r 2 z0   r 2 z1   r 1 z 2 
   ...
3
5
4
The first term is same as the parallel plate capacitor case. Higher order terms correct for the fact that the capacitance and
torque change nonlinearly as the micromirror rotates. Figure 8 (b) shows the theoretical model for the attraction cycle of the
micromirror compared with the measurement data. The discrepancy is within 39 %. The discrepancy between the
measurement data and the theoretical model for the attraction cycle of the static deflection characteristics of the micromirror
could be due to a combination of several causes. In our case, the aspect ratio of hinge is approximately 0.175 (0.7 m/4 m),
so the tensile residual stress of 0.79 GPa (which is approximately 1 % of the Young's modulus of aluminum) can increase the
required voltage for pull-in to the measured value of 44 V. The second important cause could be measurement errors in the
geometrical parameters of the hinge of the micromirror. If there is a 10 % measurement error in the thickness of the hinge,
then the polar moment of inertia changes 33.1 %, and subsequently the required voltage changes 15.4 %. A combination of
these two causes and other minor causes may make the 39 % discrepancy between the measurement data and the theoretical
model.
4. A PHOTOVOLTAIC POWER-INTEGRATED MICROSYSTEM
(A WIRELESS POWERED MICROMIRROR ARRAY)
The 32 by 32 micromirror array was connected to the output of the series interconnected solar cell array to demonstrate a
power integrated MEMS actuator array (see Figure 10). Since the micromirror requires 44 V for full deflection, only 30
series-connected cells (total array area of 0.3 cm2) under air mass (AM) 1.5 illumination were required to drive the
micromirror array. It should be noted that the size of the micromirror array (array area of 32x32 micromirrors is 0.4 cm2) is
about the same size of the wireless photovoltaic MEMS power source (0.3 cm2). Based on this size comparison, it can be
claimed that photovoltaic technology could be suitable wireless on-board power source technologies for certain (such as
electrostatic/piezoelectric) MEMS systems.
Light source
light
A 32x32 micromirror array
(array area of 0.4 cm2)
A 30 solar cells series-interconnected array
(array area of 0.3 cm2)
Figure 10. A schematic representation of a wireless powered micromirror array.
The fabricated 32 by 32 micromirror array was placed on a probe station (Signatone S-1160A-6N) and directly
connected to the output of a photovoltaic power (amorphous silicon solar cell array) through probes (Signatone S-725). The
device was observed using an optical microscope with video camera, connected to a display monitor and a video cassette
recorder (VCR). Motion of single micromirrors as well as a part of the micromirror array could be reproducibly observed
and video recorded. Light modulation at the light source has been successfully used to turn the multiple numbers of pixels
(micromirrors) on and off. Figure 11 shows optical micrographs of a part of the micromirror array, undeflected (a), and
several pixels at right of array energized and deflected (b), respectively.
(a)
(b)
Figure 11. Optical micrographs of a part of micromirror array: (a) undeflected; (b) several pixels at right of array energized and deflected.
ACKNOWLEDGEMENTS
Material donations from Dow Chemical are greatly appreciated. Microfabrication, except as noted below, was carried out at
the Georgia Tech Microelectronics Research Center. The support of the staff of the Pettit Microelectronics Research Center
at Georgia Tech is acknowledged. The amorphous silicon deposition was carried out at Solarex, Inc. The secretarial support
of the staff of the Department of Electrical and Computer Engineering at Louisiana State University is acknowledged.
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